LMFDB - Embedded newform 273.2.by.c.97.2

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			97.2
Character	$\chi$	$=$	273.97
Dual form			273.2.by.c.76.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500642 - 1.86842i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-1.50830 + 0.870817i) q^{4} +(-2.44068 - 2.44068i) q^{5} +(0.500642 - 1.86842i) q^{6} +(-2.60515 + 0.461729i) q^{7} +(-0.353388 - 0.353388i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500642 - 1.86842i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-1.50830 + 0.870817i) q^{4} +(-2.44068 - 2.44068i) q^{5} +(0.500642 - 1.86842i) q^{6} +(-2.60515 + 0.461729i) q^{7} +(-0.353388 - 0.353388i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-3.33831 + 5.78213i) q^{10} +(2.85290 - 0.764433i) q^{11} -1.74163 q^{12} +(-3.60488 + 0.0697642i) q^{13} +(2.16695 + 4.63635i) q^{14} +(-0.893352 - 3.33403i) q^{15} +(-2.22499 + 3.85380i) q^{16} +(0.667729 + 1.15654i) q^{17} +(1.36778 - 1.36778i) q^{18} +(1.32547 - 4.94673i) q^{19} +(5.80667 + 1.55589i) q^{20} +(-2.48699 - 0.902706i) q^{21} +(-2.85656 - 4.94771i) q^{22} +(-7.61450 - 4.39623i) q^{23} +(-0.129349 - 0.482736i) q^{24} +6.91386i q^{25} +(1.93510 + 6.70049i) q^{26} +1.00000i q^{27} +(3.52726 - 2.96503i) q^{28} +(3.97913 - 6.89205i) q^{29} +(-5.78213 + 3.33831i) q^{30} +(2.04259 + 2.04259i) q^{31} +(7.34896 + 1.96915i) q^{32} +(2.85290 + 0.764433i) q^{33} +(1.82661 - 1.82661i) q^{34} +(7.48528 + 5.23141i) q^{35} +(-1.50830 - 0.870817i) q^{36} +(4.73577 - 1.26895i) q^{37} -9.90616 q^{38} +(-3.15680 - 1.74202i) q^{39} +1.72501i q^{40} +(1.45657 - 0.390287i) q^{41} +(-0.441543 + 5.09867i) q^{42} +(-0.212417 + 0.122639i) q^{43} +(-3.63735 + 3.63735i) q^{44} +(0.893352 - 3.33403i) q^{45} +(-4.40187 + 16.4280i) q^{46} +(1.13049 - 1.13049i) q^{47} +(-3.85380 + 2.22499i) q^{48} +(6.57361 - 2.40574i) q^{49} +(12.9180 - 3.46137i) q^{50} +1.33546i q^{51} +(5.37648 - 3.24441i) q^{52} +2.62146 q^{53} +(1.86842 - 0.500642i) q^{54} +(-8.82877 - 5.09729i) q^{55} +(1.08380 + 0.757458i) q^{56} +(3.62126 - 3.62126i) q^{57} +(-14.8694 - 3.98423i) q^{58} +(-3.96915 - 1.06353i) q^{59} +(4.25078 + 4.25078i) q^{60} +(7.82911 - 4.52014i) q^{61} +(2.79382 - 4.83903i) q^{62} +(-1.70244 - 2.02526i) q^{63} -5.81681i q^{64} +(8.96863 + 8.62809i) q^{65} -5.71313i q^{66} +(-2.97553 - 11.1048i) q^{67} +(-2.01427 - 1.16294i) q^{68} +(-4.39623 - 7.61450i) q^{69} +(6.02703 - 16.6047i) q^{70} +(-11.0479 - 2.96028i) q^{71} +(0.129349 - 0.482736i) q^{72} +(-1.06136 + 1.06136i) q^{73} +(-4.74184 - 8.21311i) q^{74} +(-3.45693 + 5.98758i) q^{75} +(2.30849 + 8.61540i) q^{76} +(-7.07928 + 3.30873i) q^{77} +(-1.67440 + 6.77035i) q^{78} +7.65266 q^{79} +(14.8364 - 3.97540i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.45844 - 2.52609i) q^{82} +(10.1314 + 10.1314i) q^{83} +(4.53722 - 0.804162i) q^{84} +(1.19303 - 4.45246i) q^{85} +(0.335486 + 0.335486i) q^{86} +(6.89205 - 3.97913i) q^{87} +(-1.27832 - 0.738039i) q^{88} +(-4.11486 - 15.3569i) q^{89} -6.67662 q^{90} +(9.35903 - 1.84622i) q^{91} +15.3133 q^{92} +(0.747641 + 2.79024i) q^{93} +(-2.67819 - 1.54626i) q^{94} +(-15.3085 + 8.83835i) q^{95} +(5.37981 + 5.37981i) q^{96} +(-3.28484 + 12.2592i) q^{97} +(-7.78596 - 11.0779i) q^{98} +(2.08847 + 2.08847i) 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 $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{5}{12}\right)$	$-1$

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 $

$2$	−0.500642	−	1.86842i	−0.354007	−	1.32117i	−0.881729	−	0.471755i	$-0.843621\pi$
$2$	−0.500642	−	1.86842i	−0.354007	−	1.32117i	0.527722	−	0.849417i	$-0.323046\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−1.50830	+	0.870817i	−0.754150	+	0.435408i
$5$	−2.44068	−	2.44068i	−1.09151	−	1.09151i	−0.995368	−	0.0961385i	$-0.969351\pi$
$5$	−2.44068	−	2.44068i	−1.09151	−	1.09151i	−0.0961385	−	0.995368i	$-0.530649\pi$
$6$	0.500642	−	1.86842i	0.204386	−	0.762779i
$7$	−2.60515	+	0.461729i	−0.984654	+	0.174517i
$7$	−2.60515	+	0.461729i	−0.984654	+	0.174517i
$8$	−0.353388	−	0.353388i	−0.124941	−	0.124941i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−3.33831	+	5.78213i	−1.05567	+	1.82847i
$11$	2.85290	−	0.764433i	0.860183	−	0.230485i	0.198345	−	0.980132i	$-0.436443\pi$
$11$	2.85290	−	0.764433i	0.860183	−	0.230485i	0.661838	+	0.749647i	$0.269777\pi$
$12$	−1.74163			−0.502766
$13$	−3.60488	+	0.0697642i	−0.999813	+	0.0193491i
$13$	−3.60488	+	0.0697642i	−0.999813	+	0.0193491i
$14$	2.16695	+	4.63635i	0.579142	+	1.23912i
$15$	−0.893352	−	3.33403i	−0.230662	−	0.860844i
$16$	−2.22499	+	3.85380i	−0.556247	+	0.963449i
$17$	0.667729	+	1.15654i	0.161948	+	0.280502i	0.935567	−	0.353149i	$-0.114889\pi$
$17$	0.667729	+	1.15654i	0.161948	+	0.280502i	−0.773619	+	0.633651i	$0.781556\pi$
$18$	1.36778	−	1.36778i	0.322388	−	0.322388i
$19$	1.32547	−	4.94673i	0.304084	−	1.13486i	−0.629646	−	0.776882i	$-0.716800\pi$
$19$	1.32547	−	4.94673i	0.304084	−	1.13486i	0.933731	−	0.357977i	$-0.116533\pi$
$20$	5.80667	+	1.55589i	1.29841	+	0.347908i
$21$	−2.48699	−	0.902706i	−0.542706	−	0.196987i
$22$	−2.85656	−	4.94771i	−0.609022	−	1.05486i
$23$	−7.61450	−	4.39623i	−1.58773	−	0.916678i	−0.993680	−	0.112253i	$-0.964193\pi$
$23$	−7.61450	−	4.39623i	−1.58773	−	0.916678i	−0.594053	−	0.804426i	$-0.702473\pi$
$24$	−0.129349	−	0.482736i	−0.0264032	−	0.0985381i
$25$			6.91386i			1.38277i
$26$	1.93510	+	6.70049i	0.379504	+	1.31408i
$27$			1.00000i			0.192450i
$28$	3.52726	−	2.96503i	0.666590	−	0.560339i
$29$	3.97913	−	6.89205i	0.738905	−	1.27982i	−0.214084	−	0.976815i	$-0.568677\pi$
$29$	3.97913	−	6.89205i	0.738905	−	1.27982i	0.952989	−	0.303006i	$-0.0979901\pi$
$30$	−5.78213	+	3.33831i	−1.05567	+	0.609490i
$31$	2.04259	+	2.04259i	0.366861	+	0.366861i	0.866331	−	0.499470i	$-0.166472\pi$
$31$	2.04259	+	2.04259i	0.366861	+	0.366861i	−0.499470	+	0.866331i	$0.666472\pi$
$32$	7.34896	+	1.96915i	1.29912	+	0.348099i
$33$	2.85290	+	0.764433i	0.496627	+	0.133071i
$34$	1.82661	−	1.82661i	0.313261	−	0.313261i
$35$	7.48528	+	5.23141i	1.26524	+	0.884270i
$36$	−1.50830	−	0.870817i	−0.251383	−	0.145136i
$37$	4.73577	−	1.26895i	0.778555	−	0.208613i	0.152408	−	0.988318i	$-0.451297\pi$
$37$	4.73577	−	1.26895i	0.778555	−	0.208613i	0.626148	+	0.779704i	$0.284631\pi$
$38$	−9.90616			−1.60699
$39$	−3.15680	−	1.74202i	−0.505492	−	0.278947i
$40$			1.72501i			0.272749i
$41$	1.45657	−	0.390287i	0.227478	−	0.0609527i	−0.143279	−	0.989682i	$-0.545765\pi$
$41$	1.45657	−	0.390287i	0.227478	−	0.0609527i	0.370758	+	0.928730i	$0.379098\pi$
$42$	−0.441543	+	5.09867i	−0.0681316	+	0.786742i
$43$	−0.212417	+	0.122639i	−0.0323933	+	0.0187023i	−0.516109	−	0.856523i	$-0.672620\pi$
$43$	−0.212417	+	0.122639i	−0.0323933	+	0.0187023i	0.483716	+	0.875225i	$0.339287\pi$
$44$	−3.63735	+	3.63735i	−0.548351	+	0.548351i
$45$	0.893352	−	3.33403i	0.133173	−	0.497009i
$46$	−4.40187	+	16.4280i	−0.649021	+	2.42218i
$47$	1.13049	−	1.13049i	0.164899	−	0.164899i	−0.619834	−	0.784733i	$-0.712800\pi$
$47$	1.13049	−	1.13049i	0.164899	−	0.164899i	0.784733	+	0.619834i	$0.212800\pi$
$48$	−3.85380	+	2.22499i	−0.556247	+	0.321150i
$49$	6.57361	−	2.40574i	0.939088	−	0.343678i
$50$	12.9180	−	3.46137i	1.82688	−	0.489511i
$51$			1.33546i			0.187001i
$52$	5.37648	−	3.24441i	0.745584	−	0.449919i
$53$	2.62146			0.360085			0.180043	−	0.983659i	$-0.442376\pi$
$53$	2.62146			0.360085			0.180043	+	0.983659i	$0.442376\pi$
$54$	1.86842	−	0.500642i	0.254260	−	0.0681287i
$55$	−8.82877	−	5.09729i	−1.19047	−	0.687319i
$56$	1.08380	+	0.757458i	0.144828	+	0.101220i
$57$	3.62126	−	3.62126i	0.479648	−	0.479648i
$58$	−14.8694	−	3.98423i	−1.95244	−	0.523155i
$59$	−3.96915	−	1.06353i	−0.516739	−	0.138460i	−0.00898130	−	0.999960i	$-0.502859\pi$
$59$	−3.96915	−	1.06353i	−0.516739	−	0.138460i	−0.507758	+	0.861500i	$0.669526\pi$
$60$	4.25078	+	4.25078i	0.548773	+	0.548773i
$61$	7.82911	−	4.52014i	1.00241	−	0.578744i	0.0934527	−	0.995624i	$-0.470210\pi$
$61$	7.82911	−	4.52014i	1.00241	−	0.578744i	0.908962	+	0.416879i	$0.136876\pi$
$62$	2.79382	−	4.83903i	0.354815	−	0.614558i
$63$	−1.70244	−	2.02526i	−0.214488	−	0.255159i
$64$		−	5.81681i		−	0.727101i
$65$	8.96863	+	8.62809i	1.11242	+	1.07018i
$66$		−	5.71313i		−	0.703238i
$67$	−2.97553	−	11.1048i	−0.363519	−	1.35667i	−0.869417	−	0.494079i	$-0.835505\pi$
$67$	−2.97553	−	11.1048i	−0.363519	−	1.35667i	0.505898	−	0.862593i	$-0.331161\pi$
$68$	−2.01427	−	1.16294i	−0.244266	−	0.141027i
$69$	−4.39623	−	7.61450i	−0.529244	−	0.916678i
$70$	6.02703	−	16.6047i	0.720368	−	1.98464i
$71$	−11.0479	−	2.96028i	−1.31115	−	0.351320i	−0.465492	−	0.885052i	$-0.654123\pi$
$71$	−11.0479	−	2.96028i	−1.31115	−	0.351320i	−0.845654	+	0.533732i	$0.820789\pi$
$72$	0.129349	−	0.482736i	0.0152439	−	0.0568910i
$73$	−1.06136	+	1.06136i	−0.124222	+	0.124222i	−0.766485	−	0.642262i	$-0.777996\pi$
$73$	−1.06136	+	1.06136i	−0.124222	+	0.124222i	0.642262	+	0.766485i	$0.277996\pi$
$74$	−4.74184	−	8.21311i	−0.551228	−	0.954755i
$75$	−3.45693	+	5.98758i	−0.399172	+	0.691386i
$76$	2.30849	+	8.61540i	0.264802	+	0.988254i
$77$	−7.07928	+	3.30873i	−0.806759	+	0.377065i
$78$	−1.67440	+	6.77035i	−0.189589	+	0.766591i
$79$	7.65266			0.860992			0.430496	−	0.902593i	$-0.358339\pi$
$79$	7.65266			0.860992			0.430496	+	0.902593i	$0.358339\pi$
$80$	14.8364	−	3.97540i	1.65876	−	0.444463i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.45844	−	2.52609i	−0.161058	−	0.278960i
$83$	10.1314	+	10.1314i	1.11207	+	1.11207i	0.992871	+	0.119194i	$0.0380311\pi$
$83$	10.1314	+	10.1314i	1.11207	+	1.11207i	0.119194	+	0.992871i	$0.461969\pi$
$84$	4.53722	−	0.804162i	0.495051	−	0.0877413i
$85$	1.19303	−	4.45246i	0.129403	−	0.482937i
$86$	0.335486	+	0.335486i	0.0361763	+	0.0361763i
$87$	6.89205	−	3.97913i	0.738905	−	0.426607i
$88$	−1.27832	−	0.738039i	−0.136270	−	0.0786753i
$89$	−4.11486	−	15.3569i	−0.436174	−	1.62782i	−0.738241	−	0.674537i	$-0.764343\pi$
$89$	−4.11486	−	15.3569i	−0.436174	−	1.62782i	0.302067	−	0.953287i	$-0.402323\pi$
$90$	−6.67662			−0.703778
$91$	9.35903	−	1.84622i	0.981093	−	0.193537i
$92$	15.3133			1.59652
$93$	0.747641	+	2.79024i	0.0775268	+	0.289334i
$94$	−2.67819	−	1.54626i	−0.276235	−	0.159484i
$95$	−15.3085	+	8.83835i	−1.57062	+	0.906795i
$96$	5.37981	+	5.37981i	0.549074	+	0.549074i
$97$	−3.28484	+	12.2592i	−0.333525	+	1.24473i	0.571934	+	0.820300i	$0.306193\pi$
$97$	−3.28484	+	12.2592i	−0.333525	+	1.24473i	−0.905459	+	0.424433i	$0.860473\pi$
$98$	−7.78596	−	11.0779i	−0.786501	−	1.11903i
$99$	2.08847	+	2.08847i	0.209899	+	0.209899i
$100$	−6.02071	−	10.4282i	−0.602071	−	1.04282i
$101$	4.49790	−	7.79059i	0.447558	−	0.775192i	−0.550669	−	0.834724i	$-0.685627\pi$
$101$	4.49790	−	7.79059i	0.447558	−	0.775192i	0.998226	+	0.0595314i	$0.0189606\pi$
$102$	2.49519	−	0.668585i	0.247061	−	0.0661998i
$103$	6.31734			0.622466			0.311233	−	0.950334i	$-0.399258\pi$
$103$	6.31734			0.622466			0.311233	+	0.950334i	$0.399258\pi$
$104$	1.29857	+	1.24926i	0.127335	+	0.122500i
$105$	3.86673	+	8.27317i	0.377355	+	0.807379i
$106$	−1.31241	−	4.89799i	−0.127473	−	0.475735i
$107$	−9.52494	+	16.4977i	−0.920810	+	1.59489i	−0.122646	+	0.992450i	$0.539138\pi$
$107$	−9.52494	+	16.4977i	−0.920810	+	1.59489i	−0.798164	+	0.602440i	$0.794195\pi$
$108$	−0.870817	−	1.50830i	−0.0837944	−	0.145136i
$109$	−9.27465	+	9.27465i	−0.888351	+	0.888351i	−0.994365	−	0.106014i	$-0.966191\pi$
$109$	−9.27465	+	9.27465i	−0.888351	+	0.888351i	0.106014	+	0.994365i	$0.466191\pi$
$110$	−5.10383	+	19.0478i	−0.486631	+	1.81613i
$111$	4.73577	+	1.26895i	0.449499	+	0.120443i
$112$	4.01702	−	11.0671i	0.379573	−	1.04574i
$113$	−3.53376	−	6.12066i	−0.332429	−	0.575783i	0.650559	−	0.759456i	$-0.274535\pi$
$113$	−3.53376	−	6.12066i	−0.332429	−	0.575783i	−0.982987	+	0.183673i	$0.941201\pi$
$114$	−8.57899	−	4.95308i	−0.803496	−	0.463899i
$115$	7.85477	+	29.3144i	0.732461	+	2.73358i
$116$			13.8604i			1.28690i
$117$	−1.86286	−	3.08703i	−0.172221	−	0.285396i
$118$			7.94848i			0.731717i
$119$	−2.27354	−	2.70465i	−0.208415	−	0.247935i
$120$	−0.862507	+	1.49391i	−0.0787357	+	0.136374i
$121$	−1.97158	+	1.13829i	−0.179234	+	0.103481i
$122$	−12.3651	−	12.3651i	−1.11948	−	1.11948i
$123$	1.45657	+	0.390287i	0.131335	+	0.0351910i
$124$	−4.85957	−	1.30212i	−0.436402	−	0.116934i
$125$	4.67113	−	4.67113i	0.417799	−	0.417799i
$126$	−2.93172	+	4.19481i	−0.261179	+	0.373703i
$127$	12.2515	+	7.07343i	1.08715	+	0.627665i	0.932816	−	0.360354i	$-0.117344\pi$
$127$	12.2515	+	7.07343i	1.08715	+	0.627665i	0.154332	+	0.988019i	$0.450677\pi$
$128$	3.82967	−	1.02616i	0.338498	−	0.0907002i
$129$	−0.245278			−0.0215955
$130$	11.6308	−	21.0767i	1.02009	−	1.84855i
$131$			9.97987i			0.871945i	0.899960	+	0.435973i	$0.143596\pi$
$131$			9.97987i			0.871945i	−0.899960	+	0.435973i	$0.856404\pi$
$132$	−4.96871	+	1.33136i	−0.432471	+	0.115880i
$133$	−1.16901	+	13.4990i	−0.101366	+	1.17051i
$134$	−19.2588	+	11.1191i	−1.66371	+	0.960543i
$135$	2.44068	−	2.44068i	0.210061	−	0.210061i
$136$	0.172740	−	0.644674i	0.0148123	−	0.0552803i
$137$	−0.141310	+	0.527376i	−0.0120729	+	0.0450567i	−0.971700	−	0.236220i	$-0.924091\pi$
$137$	−0.141310	+	0.527376i	−0.0120729	+	0.0450567i	0.959627	+	0.281277i	$0.0907580\pi$
$138$	−12.0261	+	12.0261i	−1.02373	+	1.02373i
$139$	2.89550	−	1.67172i	0.245593	−	0.141793i	−0.372152	−	0.928172i	$-0.621380\pi$
$139$	2.89550	−	1.67172i	0.245593	−	0.141793i	0.617745	+	0.786379i	$0.288047\pi$
$140$	−15.8456	−	1.37223i	−1.33920	−	0.115974i
$141$	1.54427	−	0.413787i	0.130051	−	0.0348472i
$142$			22.1242i			1.85662i
$143$	−10.2310	+	2.95472i	−0.855562	+	0.247086i
$144$	−4.44998			−0.370832
$145$	−26.5331	+	7.10952i	−2.20345	+	0.590413i
$146$	2.51442	+	1.45170i	0.208095	+	0.120144i
$147$	6.89579	+	1.20337i	0.568755	+	0.0992523i
$148$	−6.03794	+	6.03794i	−0.496315	+	0.496315i
$149$	−8.56339	−	2.29455i	−0.701540	−	0.187977i	−0.109620	−	0.993974i	$-0.534963\pi$
$149$	−8.56339	−	2.29455i	−0.701540	−	0.187977i	−0.591920	+	0.805996i	$0.701630\pi$
$150$	12.9180	+	3.46137i	1.05475	+	0.282619i
$151$	−10.4345	−	10.4345i	−0.849144	−	0.849144i	0.140882	−	0.990026i	$-0.455006\pi$
$151$	−10.4345	−	10.4345i	−0.849144	−	0.849144i	−0.990026	+	0.140882i	$0.955006\pi$
$152$	−2.21652	+	1.27971i	−0.179784	+	0.103798i
$153$	−0.667729	+	1.15654i	−0.0539827	+	0.0935007i
$154$	9.72628	+	11.5706i	0.783766	+	0.932384i
$155$		−	9.97065i		−	0.800862i
$156$	6.27837	−	0.121504i	0.502672	−	0.00972808i
$157$		−	1.05925i		−	0.0845376i	−0.999106	−	0.0422688i	$-0.986541\pi$
$157$		−	1.05925i		−	0.0845376i	0.999106	−	0.0422688i	$-0.0134586\pi$
$158$	−3.83124	−	14.2984i	−0.304797	−	1.13752i
$159$	2.27025	+	1.31073i	0.180043	+	0.103948i
$160$	−13.1304	−	22.7425i	−1.03805	−	1.79795i
$161$	21.8668	+	7.93702i	1.72334	+	0.625525i
$162$	1.86842	+	0.500642i	0.146797	+	0.0393341i
$163$	2.76615	−	10.3234i	0.216661	−	0.808591i	−0.768914	−	0.639353i	$-0.779202\pi$
$163$	2.76615	−	10.3234i	0.216661	−	0.808591i	0.985575	−	0.169239i	$-0.0541309\pi$
$164$	−1.85708	+	1.85708i	−0.145013	+	0.145013i
$165$	−5.09729	−	8.82877i	−0.396824	−	0.687319i
$166$	13.8575	−	24.0019i	1.07555	−	1.86291i
$167$	0.203527	+	0.759573i	0.0157494	+	0.0587775i	0.973353	−	0.229310i	$-0.0736471\pi$
$167$	0.203527	+	0.759573i	0.0157494	+	0.0587775i	−0.957604	+	0.288088i	$0.906980\pi$
$168$	0.559866	+	1.19788i	0.0431946	+	0.0924182i
$169$	12.9903	−	0.502983i	0.999251	−	0.0386910i
$170$	−8.91635			−0.683853
$171$	4.94673	−	1.32547i	0.378286	−	0.101361i
$172$	0.213592	−	0.369952i	0.0162862	−	0.0282086i
$173$	−2.78559	−	4.82478i	−0.211784	−	0.366821i	0.740489	−	0.672069i	$-0.234594\pi$
$173$	−2.78559	−	4.82478i	−0.211784	−	0.366821i	−0.952273	+	0.305248i	$0.901261\pi$
$174$	−10.8851	−	10.8851i	−0.825199	−	0.825199i
$175$	−3.19233	−	18.0117i	−0.241317	−	1.36155i
$176$	−3.40171	+	12.6954i	−0.256414	+	0.956949i
$177$	−2.90562	−	2.90562i	−0.218400	−	0.218400i
$178$	−26.6330	+	15.3766i	−1.99623	+	1.15252i
$179$	−3.04329	−	1.75705i	−0.227466	−	0.131328i	0.381936	−	0.924189i	$-0.375257\pi$
$179$	−3.04329	−	1.75705i	−0.227466	−	0.131328i	−0.609403	+	0.792861i	$0.708591\pi$
$180$	1.55589	+	5.80667i	0.115969	+	0.432803i
$181$	23.3185			1.73325			0.866624	−	0.498961i	$-0.166285\pi$
$181$	23.3185			1.73325			0.866624	+	0.498961i	$0.166285\pi$
$182$	−8.13503	−	16.5623i	−0.603009	−	1.22768i
$183$	9.04027			0.668276
$184$	1.13730	+	4.24444i	0.0838425	+	0.312905i
$185$	−14.6556	−	8.46141i	−1.07750	−	0.622096i
$186$	4.83903	−	2.79382i	0.354815	−	0.204853i
$187$	2.78906	+	2.78906i	0.203956	+	0.203956i
$188$	−0.720666	+	2.68956i	−0.0525599	+	0.196156i
$189$	−0.461729	−	2.60515i	−0.0335858	−	0.189497i
$190$	24.1778	+	24.1778i	1.75404	+	1.75404i
$191$	6.95240	+	12.0419i	0.503058	+	0.871322i	0.999994	+	0.00353445i	$0.00112505\pi$
$191$	6.95240	+	12.0419i	0.503058	+	0.871322i	−0.496936	+	0.867787i	$0.665542\pi$
$192$	2.90841	−	5.03751i	0.209896	−	0.363551i
$193$	2.80644	−	0.751984i	0.202012	−	0.0541290i	−0.156394	−	0.987695i	$-0.549987\pi$
$193$	2.80644	−	0.751984i	0.202012	−	0.0541290i	0.358406	+	0.933566i	$0.383320\pi$
$194$	24.5499			1.76258
$195$	3.45302	+	11.9565i	0.247276	+	0.856220i
$196$	−7.82001	+	9.35300i	−0.558572	+	0.668071i
$197$	0.210804	+	0.786731i	0.0150192	+	0.0560523i	0.973029	−	0.230684i	$-0.0740963\pi$
$197$	0.210804	+	0.786731i	0.0150192	+	0.0560523i	−0.958010	+	0.286736i	$0.907430\pi$
$198$	2.85656	−	4.94771i	0.203007	−	0.351619i
$199$	−0.861092	−	1.49145i	−0.0610412	−	0.105726i	0.833890	−	0.551931i	$-0.186109\pi$
$199$	−0.861092	−	1.49145i	−0.0610412	−	0.105726i	−0.894931	+	0.446204i	$0.852775\pi$
$200$	2.44327	−	2.44327i	0.172766	−	0.172766i
$201$	2.97553	−	11.1048i	0.209878	−	0.783275i
$202$	−16.8079	−	4.50367i	−1.18260	−	0.316877i
$203$	−7.18396	+	19.7921i	−0.504215	+	1.38913i
$204$	−1.16294	−	2.01427i	−0.0814220	−	0.141027i
$205$	−4.50760	−	2.60246i	−0.314824	−	0.181764i
$206$	−3.16272	−	11.8034i	−0.220357	−	0.822385i
$207$		−	8.79247i		−	0.611119i
$208$	7.75196	−	14.0477i	0.537501	−	0.974031i
$209$		−	15.1258i		−	1.04627i
$210$	13.5219	−	11.3666i	0.933101	−	0.784368i
$211$	−1.84269	+	3.19163i	−0.126856	+	0.219721i	−0.922457	−	0.386100i	$-0.873822\pi$
$211$	−1.84269	+	3.19163i	−0.126856	+	0.219721i	0.795601	+	0.605821i	$0.207155\pi$
$212$	−3.95395	+	2.28281i	−0.271558	+	0.156784i
$213$	−8.08763	−	8.08763i	−0.554155	−	0.554155i
$214$	35.5932	+	9.53716i	2.43310	+	0.651947i
$215$	0.817765	+	0.219119i	0.0557711	+	0.0149438i
$216$	0.353388	−	0.353388i	0.0240450	−	0.0240450i
$217$	−6.26439	−	4.37814i	−0.425254	−	0.297208i
$218$	21.9722	+	12.6857i	1.48815	+	0.859182i
$219$	−1.44984	+	0.388484i	−0.0979711	+	0.0262513i
$220$	17.7552			1.19706
$221$	−2.48776	−	4.12260i	−0.167345	−	0.277316i
$222$		−	9.48369i		−	0.636503i
$223$	−18.0743	+	4.84300i	−1.21035	+	0.324311i	−0.806898	−	0.590691i	$-0.798855\pi$
$223$	−18.0743	+	4.84300i	−1.21035	+	0.324311i	−0.403449	+	0.915002i	$0.632189\pi$
$224$	−20.0543	−	1.73670i	−1.33994	−	0.116038i
$225$	−5.98758	+	3.45693i	−0.399172	+	0.230462i
$226$	−9.66681	+	9.66681i	−0.643027	+	0.643027i
$227$	0.339915	−	1.26858i	0.0225609	−	0.0841985i	−0.953727	−	0.300672i	$-0.902789\pi$
$227$	0.339915	−	1.26858i	0.0225609	−	0.0841985i	0.976288	+	0.216474i	$0.0694556\pi$
$228$	−2.30849	+	8.61540i	−0.152883	+	0.570569i
$229$	−6.99659	+	6.99659i	−0.462348	+	0.462348i	−0.899424	−	0.437077i	$-0.856014\pi$
$229$	−6.99659	+	6.99659i	−0.462348	+	0.462348i	0.437077	+	0.899424i	$0.356014\pi$
$230$	50.8392	−	29.3520i	3.35224	−	1.93541i
$231$	−7.78520	−	0.674196i	−0.512229	−	0.0443588i
$232$	−3.84174	+	1.02939i	−0.252222	+	0.0675828i
$233$		−	24.7335i		−	1.62035i	−0.586189	−	0.810174i	$-0.699373\pi$
$233$		−	24.7335i		−	1.62035i	0.586189	−	0.810174i	$-0.300627\pi$
$234$	−4.83525	+	5.02609i	−0.316090	+	0.328566i
$235$	−5.51832			−0.359976
$236$	6.91280	−	1.85228i	0.449985	−	0.120573i
$237$	6.62740	+	3.82633i	0.430496	+	0.248547i
$238$	−3.91519	+	5.60199i	−0.253784	+	0.363123i
$239$	−7.30351	+	7.30351i	−0.472425	+	0.472425i	−0.902698	−	0.430274i	$-0.858417\pi$
$239$	−7.30351	+	7.30351i	−0.472425	+	0.472425i	0.430274	+	0.902698i	$0.358417\pi$
$240$	14.8364	+	3.97540i	0.957684	+	0.256611i
$241$	8.63024	+	2.31247i	0.555923	+	0.148959i	0.525833	−	0.850588i	$-0.323754\pi$
$241$	8.63024	+	2.31247i	0.555923	+	0.148959i	0.0300903	+	0.999547i	$0.490421\pi$
$242$	3.11386	+	3.11386i	0.200166	+	0.200166i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−7.87242	+	13.6354i	−0.503980	+	0.872920i
$245$	−21.9158	−	10.1724i	−1.40015	−	0.649894i
$246$		−	2.91688i		−	0.185974i
$247$	−4.43306	+	17.9248i	−0.282069	+	1.14053i
$248$		−	1.44365i		−	0.0916722i
$249$	3.70835	+	13.8397i	0.235007	+	0.877058i
$250$	−11.0662	−	6.38907i	−0.699888	−	0.404081i
$251$	−6.13739	−	10.6303i	−0.387389	−	0.670977i	0.604709	−	0.796447i	$-0.293290\pi$
$251$	−6.13739	−	10.6303i	−0.387389	−	0.670977i	−0.992097	+	0.125470i	$0.959956\pi$
$252$	4.33143	+	1.57218i	0.272854	+	0.0990383i
$253$	−25.0841	−	6.72126i	−1.57702	−	0.422562i
$254$	7.08250	−	26.4323i	0.444396	−	1.65851i
$255$	3.25943	−	3.25943i	0.204113	−	0.204113i
$256$	−9.65139	−	16.7167i	−0.603212	−	1.04479i
$257$	2.78870	−	4.83017i	0.173954	−	0.301298i	−0.765845	−	0.643026i	$-0.777679\pi$
$257$	2.78870	−	4.83017i	0.173954	−	0.301298i	0.939799	+	0.341728i	$0.111012\pi$
$258$	0.122796	+	0.458282i	0.00764496	+	0.0285314i
$259$	−11.7515	+	5.49243i	−0.730201	+	0.341283i
$260$	−21.0409	−	5.20370i	−1.30490	−	0.322720i
$261$	7.95825			0.492603
$262$	18.6466	−	4.99634i	1.15199	−	0.308675i
$263$	−0.243621	+	0.421964i	−0.0150223	+	0.0260194i	−0.873439	−	0.486934i	$-0.838115\pi$
$263$	−0.243621	+	0.421964i	−0.0150223	+	0.0260194i	0.858417	+	0.512953i	$0.171449\pi$
$264$	−0.738039	−	1.27832i	−0.0454232	−	0.0786753i
$265$	−6.39815	−	6.39815i	−0.393035	−	0.393035i
$266$	25.8070	−	4.57396i	1.58233	−	0.280447i
$267$	4.11486	−	15.3569i	0.251825	−	0.939824i
$268$	14.1583	+	14.1583i	0.864854	+	0.864854i
$269$	−14.2503	+	8.22741i	−0.868855	+	0.501634i	−0.866968	−	0.498364i	$-0.833934\pi$
$269$	−14.2503	+	8.22741i	−0.868855	+	0.501634i	−0.00188759	+	0.999998i	$0.500601\pi$
$270$	−5.78213	−	3.33831i	−0.351889	−	0.203163i
$271$	5.62502	+	20.9928i	0.341695	+	1.27522i	0.896426	+	0.443194i	$0.146155\pi$
$271$	5.62502	+	20.9928i	0.341695	+	1.27522i	−0.554730	+	0.832030i	$0.687178\pi$
$272$	−5.94276			−0.360333
$273$	9.02827	+	3.08064i	0.546416	+	0.186449i
$274$	1.05610			0.0638016
$275$	5.28519	+	19.7246i	0.318709	+	1.18944i
$276$	13.2617	+	7.65663i	0.798259	+	0.460875i
$277$	23.9312	−	13.8167i	1.43789	−	0.830165i	0.440186	−	0.897907i	$-0.354913\pi$
$277$	23.9312	−	13.8167i	1.43789	−	0.830165i	0.997703	+	0.0677412i	$0.0215792\pi$
$278$	−4.57307	−	4.57307i	−0.274275	−	0.274275i
$279$	−0.747641	+	2.79024i	−0.0447601	+	0.167047i
$280$	−0.796488	−	4.49392i	−0.0475993	−	0.268563i
$281$	15.4703	+	15.4703i	0.922880	+	0.922880i	0.997232	−	0.0743517i	$-0.0236887\pi$
$281$	15.4703	+	15.4703i	0.922880	+	0.922880i	−0.0743517	+	0.997232i	$0.523689\pi$
$282$	−1.54626	−	2.67819i	−0.0920782	−	0.159484i
$283$	−2.67677	+	4.63631i	−0.159118	+	0.275600i	−0.934551	−	0.355830i	$-0.884198\pi$
$283$	−2.67677	+	4.63631i	−0.159118	+	0.275600i	0.775433	+	0.631430i	$0.217532\pi$
$284$	19.2414	−	5.15572i	1.14177	−	0.305936i
$285$	−17.6767			−1.04708
$286$	10.6427	+	17.6366i	0.629318	+	1.04287i
$287$	−3.61438	+	1.68930i	−0.213350	+	0.0997161i
$288$	1.96915	+	7.34896i	0.116033	+	0.433041i
$289$	7.60828	−	13.1779i	0.447546	−	0.775172i
$290$	26.5671	+	46.0156i	1.56008	+	2.70213i
$291$	−8.97436	+	8.97436i	−0.526086	+	0.526086i
$292$	0.676596	−	2.52509i	0.0395948	−	0.147770i
$293$	11.8844	+	3.18441i	0.694294	+	0.186035i	0.588673	−	0.808371i	$-0.299650\pi$
$293$	11.8844	+	3.18441i	0.694294	+	0.186035i	0.105620	+	0.994407i	$0.466317\pi$
$294$	−1.20392	−	13.4867i	−0.0702138	−	0.786559i
$295$	7.09169	+	12.2832i	0.412894	+	0.715154i
$296$	−2.12199	−	1.22513i	−0.123338	−	0.0712093i
$297$	0.764433	+	2.85290i	0.0443569	+	0.165542i
$298$			17.1488i			0.993401i
$299$	27.7560	+	15.3167i	1.60517	+	0.885785i
$300$		−	12.0414i		−	0.695212i
$301$	0.496752	−	0.417572i	0.0286323	−	0.0240684i
$302$	−14.2720	+	24.7199i	−0.821263	+	1.42247i
$303$	7.79059	−	4.49790i	0.447558	−	0.258397i
$304$	16.1145	+	16.1145i	0.924232	+	0.924232i
$305$	−30.1406	−	8.07615i	−1.72585	−	0.462439i
$306$	2.49519	+	0.668585i	0.142641	+	0.0382205i
$307$	8.36730	−	8.36730i	0.477547	−	0.477547i	−0.426799	−	0.904346i	$-0.640359\pi$
$307$	8.36730	−	8.36730i	0.477547	−	0.477547i	0.904346	+	0.426799i	$0.140359\pi$
$308$	7.79638	−	11.1553i	0.444240	−	0.635633i
$309$	5.47098	+	3.15867i	0.311233	+	0.179690i
$310$	−18.6294	+	4.99172i	−1.05808	+	0.283511i
$311$	−2.28494			−0.129567			−0.0647836	−	0.997899i	$-0.520636\pi$
$311$	−2.28494			−0.129567			−0.0647836	+	0.997899i	$0.520636\pi$
$312$	0.499964	+	1.73118i	0.0283049	+	0.0980088i
$313$		−	24.6656i		−	1.39418i	−0.716982	−	0.697091i	$-0.754477\pi$
$313$		−	24.6656i		−	1.39418i	0.716982	−	0.697091i	$-0.245523\pi$
$314$	−1.97913	+	0.530306i	−0.111689	+	0.0299269i
$315$	−0.787896	+	9.09815i	−0.0443929	+	0.512622i
$316$	−11.5425	+	6.66407i	−0.649317	+	0.374883i
$317$	3.55562	−	3.55562i	0.199704	−	0.199704i	−0.600169	−	0.799873i	$-0.704900\pi$
$317$	3.55562	−	3.55562i	0.199704	−	0.199704i	0.799873	+	0.600169i	$0.204900\pi$
$318$	1.31241	−	4.89799i	0.0735964	−	0.274666i
$319$	6.08355	−	22.7041i	0.340613	−	1.27119i
$320$	−14.1970	+	14.1970i	−0.793636	+	0.793636i
$321$	−16.4977	+	9.52494i	−0.920810	+	0.531630i
$322$	3.88226	−	44.8299i	0.216350	−	2.49827i
$323$	6.60615	−	1.77011i	0.367576	−	0.0984917i
$324$		−	1.74163i		−	0.0967574i
$325$	−0.482340	−	24.9236i	−0.0267554	−	1.38251i
$326$	−20.6733			−1.14499
$327$	−12.6694	+	3.39476i	−0.700620	+	0.187731i
$328$	−0.652657	−	0.376812i	−0.0360370	−	0.0208060i
$329$	−2.42311	+	3.46707i	−0.133590	+	0.191146i
$330$	−13.9439	+	13.9439i	−0.767588	+	0.767588i
$331$	17.6446	+	4.72784i	0.969832	+	0.259866i	0.708757	−	0.705453i	$-0.249256\pi$
$331$	17.6446	+	4.72784i	0.969832	+	0.259866i	0.261075	+	0.965318i	$0.415923\pi$
$332$	−24.1038	−	6.45858i	−1.32287	−	0.354461i
$333$	3.46682	+	3.46682i	0.189981	+	0.189981i
$334$	1.31731	−	0.760548i	0.0720798	−	0.0416153i
$335$	−19.8411	+	34.3657i	−1.08403	+	1.87760i
$336$	9.01237	−	7.57584i	0.491665	−	0.413296i
$337$		−	22.3954i		−	1.21996i	−0.792418	−	0.609978i	$-0.791178\pi$
$337$		−	22.3954i		−	1.21996i	0.792418	−	0.609978i	$-0.208822\pi$
$338$	−7.44325	−	24.0195i	−0.404859	−	1.30649i
$339$		−	7.06753i		−	0.383856i
$340$	2.07783	+	7.75456i	0.112686	+	0.420550i
$341$	7.38875	+	4.26590i	0.400123	+	0.231011i
$342$	−4.95308	−	8.57899i	−0.267832	−	0.463899i
$343$	−16.0144	+	9.30255i	−0.864699	+	0.502291i
$344$	0.118405	+	0.0317264i	0.00638394	+	0.00171057i
$345$	−7.85477	+	29.3144i	−0.422886	+	1.57823i
$346$	−7.62013	+	7.62013i	−0.409661	+	0.409661i
$347$	7.01258	+	12.1461i	0.376455	+	0.652039i	0.990544	−	0.137198i	$-0.0438096\pi$
$347$	7.01258	+	12.1461i	0.376455	+	0.652039i	−0.614089	+	0.789237i	$0.710476\pi$
$348$	−6.93018	+	12.0034i	−0.371497	+	0.643451i
$349$	−2.12038	−	7.91338i	−0.113502	−	0.423594i	0.885669	−	0.464317i	$-0.153700\pi$
$349$	−2.12038	−	7.91338i	−0.113502	−	0.423594i	−0.999170	+	0.0407238i	$0.987034\pi$
$350$	−32.0551	+	14.9820i	−1.71342	+	0.800821i
$351$	−0.0697642	−	3.60488i	−0.00372374	−	0.192414i
$352$	22.4711			1.19772
$353$	25.1216	−	6.73131i	1.33709	−	0.358271i	0.481734	−	0.876318i	$-0.340007\pi$
$353$	25.1216	−	6.73131i	1.33709	−	0.358271i	0.855353	+	0.518046i	$0.173341\pi$
$354$	−3.97424	+	6.88359i	−0.211229	+	0.365859i
$355$	19.7393	+	34.1895i	1.04766	+	1.81459i
$356$	19.5794	+	19.5794i	1.03771	+	1.03771i
$357$	−0.616619	−	3.47907i	−0.0326349	−	0.184132i
$358$	−1.75930	+	6.56579i	−0.0929819	+	0.347013i
$359$	3.71625	+	3.71625i	0.196136	+	0.196136i	0.798341	−	0.602205i	$-0.205711\pi$
$359$	3.71625	+	3.71625i	0.196136	+	0.196136i	−0.602205	+	0.798341i	$0.705711\pi$
$360$	−1.49391	+	0.862507i	−0.0787357	+	0.0454581i
$361$	−6.25881	−	3.61353i	−0.329411	−	0.190186i
$362$	−11.6742	−	43.5687i	−0.613582	−	2.28992i
$363$	−2.27658			−0.119490
$364$	−12.5085	+	10.9347i	−0.655623	+	0.573132i
$365$	5.18087			0.271179
$366$	−4.52594	−	16.8910i	−0.236575	−	0.882908i
$367$	−26.8907	−	15.5253i	−1.40368	−	0.810416i	−0.408913	−	0.912573i	$-0.634092\pi$
$367$	−26.8907	−	15.5253i	−1.40368	−	0.810416i	−0.994768	+	0.102157i	$0.967426\pi$
$368$	33.8844	−	19.5632i	1.76634	−	1.01980i
$369$	1.06629	+	1.06629i	0.0555086	+	0.0555086i
$370$	−8.47227	+	31.6189i	−0.440452	+	1.64379i
$371$	−6.82930	+	1.21040i	−0.354559	+	0.0628410i
$372$	−3.55745	−	3.55745i	−0.184445	−	0.184445i
$373$	−6.35916	−	11.0144i	−0.329265	−	0.570304i	0.653101	−	0.757271i	$-0.273468\pi$
$373$	−6.35916	−	11.0144i	−0.329265	−	0.570304i	−0.982366	+	0.186967i	$0.940134\pi$
$374$	3.81482	−	6.60746i	0.197260	−	0.341664i
$375$	6.38089	−	1.70975i	0.329508	−	0.0882913i
$376$	−0.799000			−0.0412053
$377$	−13.8634	+	25.1226i	−0.714003	+	1.29388i
$378$	−4.63635	+	2.16695i	−0.238468	+	0.111456i
$379$	−5.03747	−	18.8001i	−0.258757	−	0.965696i	−0.965961	−	0.258686i	$-0.916710\pi$
$379$	−5.03747	−	18.8001i	−0.258757	−	0.965696i	0.707204	−	0.707010i	$-0.249956\pi$
$380$	15.3932	−	26.6617i	0.789653	−	1.36772i
$381$	7.07343	+	12.2515i	0.362383	+	0.627665i
$382$	19.0187	−	19.0187i	0.973080	−	0.973080i
$383$	1.38240	−	5.15917i	0.0706372	−	0.263621i	−0.921572	−	0.388209i	$-0.873094\pi$
$383$	1.38240	−	5.15917i	0.0706372	−	0.263621i	0.992209	+	0.124587i	$0.0397607\pi$
$384$	3.82967	+	1.02616i	0.195432	+	0.0523658i
$385$	25.3538	+	9.20272i	1.29215	+	0.469014i
$386$	−2.81004	−	4.86714i	−0.143028	−	0.247731i
$387$	−0.212417	−	0.122639i	−0.0107978	−	0.00623409i
$388$	−5.72099	−	21.3510i	−0.290439	−	1.08393i
$389$			3.01128i			0.152678i	0.997082	+	0.0763390i	$0.0243231\pi$
$389$			3.01128i			0.152678i	−0.997082	+	0.0763390i	$0.975677\pi$
$390$	20.6110	−	12.4376i	1.04368	−	0.629802i
$391$		−	11.7420i		−	0.593817i
$392$	−3.17319	−	1.47287i	−0.160270	−	0.0743913i
$393$	−4.98993	+	8.64282i	−0.251709	+	0.435973i
$394$	1.36441	−	0.787740i	0.0687378	−	0.0396858i
$395$	−18.6777	−	18.6777i	−0.939778	−	0.939778i
$396$	−4.96871	−	1.33136i	−0.249687	−	0.0669035i
$397$	13.7845	+	3.69353i	0.691822	+	0.185373i	0.587565	−	0.809177i	$-0.300087\pi$
$397$	13.7845	+	3.69353i	0.691822	+	0.185373i	0.104257	+	0.994550i	$0.466753\pi$
$398$	−2.35556	+	2.35556i	−0.118074	+	0.118074i
$399$	−7.76189	+	11.1060i	−0.388580	+	0.555994i
$400$	−26.6446	−	15.3833i	−1.33223	−	0.769164i
$401$	29.6397	−	7.94193i	1.48014	−	0.396601i	0.573742	−	0.819036i	$-0.305491\pi$
$401$	29.6397	−	7.94193i	1.48014	−	0.396601i	0.906393	+	0.422435i	$0.138824\pi$
$402$	−22.2382			−1.10914
$403$	−7.50580	−	7.22080i	−0.373891	−	0.359694i
$404$			15.6674i			0.779481i
$405$	3.33403	−	0.893352i	0.165670	−	0.0443910i
$406$	40.5765	+	3.51391i	2.01378	+	0.174393i
$407$	12.5407	−	7.24036i	0.621618	−	0.358891i
$408$	0.471934	−	0.471934i	0.0233642	−	0.0233642i
$409$	2.88987	−	10.7851i	0.142895	−	0.533291i	−0.856945	−	0.515408i	$-0.827641\pi$
$409$	2.88987	−	10.7851i	0.142895	−	0.533291i	0.999840	−	0.0178834i	$-0.00569276\pi$
$410$	−2.60580	+	9.72499i	−0.128691	+	0.480283i
$411$	−0.386066	+	0.386066i	−0.0190432	+	0.0190432i
$412$	−9.52844	+	5.50125i	−0.469433	+	0.271027i
$413$	10.8313	+	0.937986i	0.532973	+	0.0461553i
$414$	−16.4280	+	4.40187i	−0.807393	+	0.216340i
$415$		−	49.4550i		−	2.42765i
$416$	−26.6295	−	6.58584i	−1.30562	−	0.322897i
$417$	3.34343			0.163728
$418$	−28.2613	+	7.57260i	−1.38231	+	0.370388i
$419$	−9.49737	−	5.48331i	−0.463977	−	0.267877i	0.249738	−	0.968313i	$-0.419655\pi$
$419$	−9.49737	−	5.48331i	−0.463977	−	0.267877i	−0.713715	+	0.700436i	$0.752989\pi$
$420$	−13.0366	−	9.11120i	−0.636122	−	0.444581i
$421$	6.63694	−	6.63694i	0.323465	−	0.323465i	−0.526630	−	0.850095i	$-0.676545\pi$
$421$	6.63694	−	6.63694i	0.323465	−	0.323465i	0.850095	+	0.526630i	$0.176545\pi$
$422$	6.88584	+	1.84505i	0.335197	+	0.0898159i
$423$	1.54427	+	0.413787i	0.0750852	+	0.0201190i
$424$	−0.926392	−	0.926392i	−0.0449895	−	0.0449895i
$425$	−7.99616	+	4.61658i	−0.387871	+	0.223937i
$426$	−11.0621	+	19.1601i	−0.535960	+	0.928309i
$427$	−18.3089	+	15.3906i	−0.886031	+	0.744801i
$428$		−	33.1779i		−	1.60371i
$429$	−10.3377	−	2.55666i	−0.499109	−	0.123437i
$430$		−	1.63763i		−	0.0789734i
$431$	8.92021	+	33.2907i	0.429671	+	1.60355i	0.753506	+	0.657441i	$0.228361\pi$
$431$	8.92021	+	33.2907i	0.429671	+	1.60355i	−0.323835	+	0.946114i	$0.604972\pi$
$432$	−3.85380	−	2.22499i	−0.185416	−	0.107050i
$433$	−19.6718	−	34.0725i	−0.945365	−	1.63742i	−0.755019	−	0.655703i	$-0.772372\pi$
$433$	−19.6718	−	34.0725i	−0.945365	−	1.63742i	−0.190346	−	0.981717i	$-0.560961\pi$
$434$	−5.04399	+	13.8964i	−0.242119	+	0.667048i
$435$	−26.5331	−	7.10952i	−1.27216	−	0.340875i
$436$	5.91243	−	22.0655i	0.283154	−	1.05674i
$437$	−31.8398	+	31.8398i	−1.52311	+	1.52311i
$438$	1.45170	+	2.51442i	0.0693649	+	0.120144i
$439$	0.862363	−	1.49366i	0.0411583	−	0.0712883i	−0.844712	−	0.535220i	$-0.820229\pi$
$439$	0.862363	−	1.49366i	0.0411583	−	0.0712883i	0.885871	+	0.463932i	$0.153562\pi$
$440$	1.31866	+	4.92130i	0.0628645	+	0.234614i
$441$	5.37024	+	4.49004i	0.255726	+	0.213812i
$442$	−6.45727	+	6.71213i	−0.307141	+	0.319264i
$443$	−3.62484			−0.172221			−0.0861107	−	0.996286i	$-0.527444\pi$
$443$	−3.62484			−0.172221			−0.0861107	+	0.996286i	$0.527444\pi$
$444$	−8.24797	+	2.21004i	−0.391431	+	0.104884i
$445$	−27.4382	+	47.5243i	−1.30069	+	2.25287i
$446$	18.0975	+	31.3458i	0.856943	+	1.48427i
$447$	−6.26884	−	6.26884i	−0.296506	−	0.296506i
$448$	2.68579	+	15.1537i	0.126892	+	0.715943i
$449$	3.15356	−	11.7692i	0.148826	−	0.555425i	−0.850730	−	0.525604i	$-0.823840\pi$
$449$	3.15356	−	11.7692i	0.148826	−	0.555425i	0.999555	−	0.0298212i	$-0.00949379\pi$
$450$	9.45663	+	9.45663i	0.445790	+	0.445790i
$451$	3.85711	−	2.22690i	0.181624	−	0.104861i
$452$	10.6599	+	6.15452i	0.501402	+	0.289484i
$453$	−3.81928	−	14.2537i	−0.179445	−	0.669699i
$454$	−2.54041			−0.119227
$455$	−27.3485	−	18.3364i	−1.28212	−	0.859623i
$456$	−2.55942			−0.119856
$457$	−4.20527	−	15.6943i	−0.196714	−	0.734147i	−0.991816	−	0.127672i	$-0.959250\pi$
$457$	−4.20527	−	15.6943i	−0.196714	−	0.734147i	0.795102	−	0.606475i	$-0.207417\pi$
$458$	16.5754	+	9.56978i	0.774515	+	0.447167i
$459$	−1.15654	+	0.667729i	−0.0539827	+	0.0311669i
$460$	−37.3748	−	37.3748i	−1.74261	−	1.74261i
$461$	0.972700	−	3.63017i	0.0453031	−	0.169074i	−0.939568	−	0.342363i	$-0.888773\pi$
$461$	0.972700	−	3.63017i	0.0453031	−	0.169074i	0.984871	+	0.173289i	$0.0554395\pi$
$462$	2.63792	+	14.8836i	0.122727	+	0.692446i
$463$	−8.26689	−	8.26689i	−0.384195	−	0.384195i	0.488416	−	0.872611i	$-0.337575\pi$
$463$	−8.26689	−	8.26689i	−0.384195	−	0.384195i	−0.872611	+	0.488416i	$0.837575\pi$
$464$	17.7070	+	30.6695i	0.822028	+	1.42379i
$465$	4.98533	−	8.63484i	0.231189	−	0.400431i
$466$	−46.2126	+	12.3826i	−2.14076	+	0.573615i
$467$	32.1951			1.48981			0.744905	−	0.667170i	$-0.232495\pi$
$467$	32.1951			1.48981			0.744905	+	0.667170i	$0.232495\pi$
$468$	5.49798	+	3.03396i	0.254144	+	0.140245i
$469$	12.8791	+	27.5559i	0.594703	+	1.27241i
$470$	2.76270	+	10.3105i	0.127434	+	0.475590i
$471$	0.529626	−	0.917340i	0.0244039	−	0.0422688i
$472$	1.02681	+	1.77849i	0.0472627	+	0.0818615i
$473$	−0.512255	+	0.512255i	−0.0235535	+	0.0235535i
$474$	3.83124	−	14.2984i	0.175975	−	0.656747i
$475$	34.2010	+	9.16414i	1.56925	+	0.420480i
$476$	5.78444	+	2.09958i	0.265129	+	0.0962343i
$477$	1.31073	+	2.27025i	0.0600142	+	0.103948i
$478$	17.3025	+	9.98958i	0.791396	+	0.456913i
$479$	−0.610243	−	2.27746i	−0.0278827	−	0.104060i	0.950582	−	0.310473i	$-0.100487\pi$
$479$	−0.610243	−	2.27746i	−0.0278827	−	0.104060i	−0.978465	+	0.206413i	$0.933821\pi$
$480$		−	26.2608i		−	1.19864i
$481$	−16.9833	+	4.90478i	−0.774373	+	0.223639i
$482$		−	17.2826i		−	0.787202i
$483$	14.9687	+	17.8070i	0.681099	+	0.810249i
$484$	1.98249	−	3.43377i	0.0901130	−	0.156080i
$485$	37.9381	−	21.9036i	1.72268	−	0.994589i
$486$	1.36778	+	1.36778i	0.0620437	+	0.0620437i
$487$	−13.0172	−	3.48794i	−0.589864	−	0.158054i	−0.0484729	−	0.998824i	$-0.515435\pi$
$487$	−13.0172	−	3.48794i	−0.589864	−	0.158054i	−0.541391	+	0.840771i	$0.682102\pi$
$488$	−4.36407	−	1.16935i	−0.197552	−	0.0529339i
$489$	7.55726	−	7.55726i	0.341751	−	0.341751i
$490$	−8.03445	+	46.0406i	−0.362960	+	2.07990i
$491$	−24.0166	−	13.8660i	−1.08386	−	0.625764i	−0.151921	−	0.988393i	$-0.548546\pi$
$491$	−24.0166	−	13.8660i	−1.08386	−	0.625764i	−0.931934	+	0.362628i	$0.881879\pi$
$492$	−2.53682	+	0.679738i	−0.114368	+	0.0306449i
$493$	10.6279			0.478657
$494$	35.7105	−	0.691095i	1.60669	−	0.0310938i
$495$		−	10.1946i		−	0.458213i
$496$	−12.4165	+	3.32699i	−0.557517	+	0.149386i
$497$	30.1483	+	2.61083i	1.35234	+	0.117112i
$498$	24.0019	−	13.8575i	1.07555	−	0.620969i
$499$	−12.5883	+	12.5883i	−0.563529	+	0.563529i	−0.930308	−	0.366779i	$-0.880460\pi$
$499$	−12.5883	+	12.5883i	−0.563529	+	0.563529i	0.366779	+	0.930308i	$0.380460\pi$
$500$	−2.97776	+	11.1132i	−0.133170	+	0.496996i
$501$	−0.203527	+	0.759573i	−0.00909292	+	0.0339352i
$502$	−16.7892	+	16.7892i	−0.749338	+	0.749338i
$503$	35.8460	−	20.6957i	1.59829	−	0.922776i	0.606479	−	0.795100i	$-0.292582\pi$
$503$	35.8460	−	20.6957i	1.59829	−	0.922776i	0.991816	−	0.127676i	$-0.0407518\pi$
$504$	−0.114080	+	1.31732i	−0.00508152	+	0.0586783i
$505$	−29.9923	+	8.03641i	−1.33464	+	0.357616i
$506$			50.2325i			2.23311i
$507$	11.5014	+	6.05954i	0.510795	+	0.269114i
$508$	−24.6386			−1.09316
$509$	3.60857	−	0.966913i	0.159947	−	0.0428577i	−0.177957	−	0.984038i	$-0.556949\pi$
$509$	3.60857	−	0.966913i	0.159947	−	0.0428577i	0.337904	+	0.941181i	$0.390282\pi$
$510$	−7.72178	−	4.45817i	−0.341926	−	0.197411i
$511$	2.27494	−	3.25505i	0.100637	−	0.143995i
$512$	−20.7949	+	20.7949i	−0.919014	+	0.919014i
$513$	4.94673	+	1.32547i	0.218404	+	0.0585211i
$514$	−10.4209	−	2.79228i	−0.459647	−	0.123162i
$515$	−15.4186	−	15.4186i	−0.679426	−	0.679426i
$516$	0.369952	−	0.213592i	0.0162862	−	0.00940287i
$517$	2.36099	−	4.08935i	0.103836	−	0.179850i
$518$	16.1454	+	19.2070i	0.709390	+	0.843905i
$519$		−	5.57117i		−	0.244547i
$520$	−0.120344	−	6.21846i	−0.00527744	−	0.272698i
$521$			38.7341i			1.69697i	0.529219	+	0.848486i	$0.322485\pi$
$521$			38.7341i			1.69697i	−0.529219	+	0.848486i	$0.677515\pi$
$522$	−3.98423	−	14.8694i	−0.174385	−	0.650814i
$523$	30.8201	+	17.7940i	1.34767	+	0.778077i	0.987919	−	0.154972i	$-0.0495289\pi$
$523$	30.8201	+	17.7940i	1.34767	+	0.778077i	0.359749	+	0.933049i	$0.382862\pi$
$524$	−8.69064	−	15.0526i	−0.379652	−	0.657577i
$525$	6.24119	−	17.1947i	0.272388	−	0.750439i
$526$	0.910373	+	0.243934i	0.0396942	+	0.0106360i
$527$	−0.998443	+	3.72624i	−0.0434929	+	0.162318i
$528$	−9.29365	+	9.29365i	−0.404454	+	0.404454i
$529$	27.1537	+	47.0317i	1.18060	+	2.04486i
$530$	−8.75125	+	15.1576i	−0.380130	+	0.658405i
$531$	−1.06353	−	3.96915i	−0.0461533	−	0.172246i
$532$	−9.99194	−	21.3785i	−0.433205	−	0.926876i
$533$	−5.22354	+	1.50855i	−0.226256	+	0.0653427i
$534$	−30.7531			−1.33082
$535$	63.5129	−	17.0182i	2.74590	−	0.735763i
$536$	−2.87280	+	4.97583i	−0.124086	+	0.214923i
$537$	−1.75705	−	3.04329i	−0.0758221	−	0.131328i
$538$	22.5065	+	22.5065i	0.970326	+	0.970326i
$539$	16.9149	−	11.8884i	0.728574	−	0.512072i
$540$	−1.55589	+	5.80667i	−0.0669549	+	0.249879i
$541$	12.2027	+	12.2027i	0.524634	+	0.524634i	0.918967	−	0.394333i	$-0.129025\pi$
$541$	12.2027	+	12.2027i	0.524634	+	0.524634i	−0.394333	+	0.918967i	$0.629025\pi$
$542$	36.4073	−	21.0198i	1.56383	−	0.902877i
$543$	20.1944	+	11.6592i	0.866624	+	0.500346i
$544$	2.62971	+	9.81422i	0.112748	+	0.420781i
$545$	45.2730			1.93928
$546$	1.23600	−	18.4109i	0.0528961	−	0.787913i
$547$	−12.9228			−0.552538			−0.276269	−	0.961080i	$-0.589098\pi$
$547$	−12.9228			−0.552538			−0.276269	+	0.961080i	$0.589098\pi$
$548$	−0.246110	−	0.918495i	−0.0105133	−	0.0392362i
$549$	7.82911	+	4.52014i	0.334138	+	0.192915i
$550$	34.2078	−	19.7499i	1.45863	−	0.842138i
$551$	−28.8189	−	28.8189i	−1.22773	−	1.22773i
$552$	−1.13730	+	4.24444i	−0.0484065	+	0.180656i
$553$	−19.9363	+	3.53345i	−0.847779	+	0.150258i
$554$	−37.7964	−	37.7964i	−1.60581	−	1.60581i
$555$	−8.46141	−	14.6556i	−0.359167	−	0.622096i
$556$	−2.91152	+	5.04289i	−0.123476	+	0.213866i
$557$	5.77693	−	1.54792i	0.244777	−	0.0655877i	−0.134345	−	0.990935i	$-0.542893\pi$
$557$	5.77693	−	1.54792i	0.244777	−	0.0655877i	0.379121	+	0.925347i	$0.376226\pi$
$558$	5.58763			0.236543
$559$	0.757180	−	0.456917i	0.0320253	−	0.0193255i
$560$	−36.8155	+	17.2069i	−1.55574	+	0.727124i
$561$	1.02087	+	3.80993i	0.0431011	+	0.160855i
$562$	21.1599	−	36.6501i	0.892578	−	1.54599i
$563$	3.80484	+	6.59017i	0.160355	+	0.277743i	0.934996	−	0.354658i	$-0.115403\pi$
$563$	3.80484	+	6.59017i	0.160355	+	0.277743i	−0.774641	+	0.632401i	$0.782070\pi$
$564$	−1.96890	+	1.96890i	−0.0829054	+	0.0829054i
$565$	−6.31379	+	23.5634i	−0.265623	+	0.991319i
$566$	10.0027	+	2.68021i	0.420443	+	0.112657i
$567$	0.902706	−	2.48699i	0.0379101	−	0.104444i
$568$	2.85807	+	4.95032i	0.119922	+	0.207711i
$569$	−23.3969	−	13.5082i	−0.980848	−	0.566293i	−0.0783217	−	0.996928i	$-0.524956\pi$
$569$	−23.3969	−	13.5082i	−0.980848	−	0.566293i	−0.902526	+	0.430635i	$0.858289\pi$
$570$	8.84969	+	33.0275i	0.370673	+	1.38337i
$571$			17.2946i			0.723757i	0.932225	+	0.361878i	$0.117864\pi$
$571$			17.2946i			0.723757i	−0.932225	+	0.361878i	$0.882136\pi$
$572$	12.8584	−	13.3660i	0.537639	−	0.558859i
$573$			13.9048i			0.580881i
$574$	4.96583	+	5.90745i	0.207270	+	0.246572i
$575$	30.3950	−	52.6456i	1.26756	−	2.19547i
$576$	5.03751	−	2.90841i	0.209896	−	0.121184i
$577$	1.06958	+	1.06958i	0.0445272	+	0.0445272i	0.729020	−	0.684493i	$-0.239976\pi$
$577$	1.06958	+	1.06958i	0.0445272	+	0.0445272i	−0.684493	+	0.729020i	$0.739976\pi$
$578$	−28.4309	−	7.61804i	−1.18257	−	0.316869i
$579$	2.80644	+	0.751984i	0.116632	+	0.0312514i
$580$	33.8287	−	33.8287i	1.40466	−	1.40466i
$581$	−31.0718	−	21.7158i	−1.28907	−	0.900925i
$582$	21.2608	+	12.2749i	0.881288	+	0.508812i
$583$	7.47878	−	2.00393i	0.309739	−	0.0829944i
$584$	0.750141			0.0310410
$585$	−2.98783	+	12.0811i	−0.123531	+	0.499492i
$586$		−	23.7993i		−	0.983139i
$587$	−42.5402	+	11.3986i	−1.75582	+	0.470471i	−0.985853	−	0.167613i	$-0.946394\pi$
$587$	−42.5402	+	11.3986i	−1.75582	+	0.470471i	−0.769967	+	0.638083i	$0.779728\pi$
$588$	−11.4488	+	4.18993i	−0.472142	+	0.172790i
$589$	12.8116	−	7.39677i	0.527892	−	0.304778i
$590$	19.3997	−	19.3997i	0.798674	−	0.798674i
$591$	−0.210804	+	0.786731i	−0.00867131	+	0.0323618i
$592$	−5.64678	+	21.0741i	−0.232081	+	0.866139i
$593$	14.9496	−	14.9496i	0.613907	−	0.613907i	−0.330055	−	0.943962i	$-0.607067\pi$
$593$	14.9496	−	14.9496i	0.613907	−	0.613907i	0.943962	+	0.330055i	$0.107067\pi$
$594$	4.94771	−	2.85656i	0.203007	−	0.117206i
$595$	−1.05220	+	12.1502i	−0.0431361	+	0.498109i
$596$	14.9143	−	3.99627i	0.610913	−	0.163694i
$597$		−	1.72218i		−	0.0704843i
$598$	14.7221	−	59.5281i	0.602033	−	2.43428i
$599$	22.8397			0.933203			0.466601	−	0.884468i	$-0.345478\pi$
$599$	22.8397			0.933203			0.466601	+	0.884468i	$0.345478\pi$
$600$	3.33757	−	0.894300i	0.136256	−	0.0365096i
$601$	−24.7100	−	14.2663i	−1.00794	−	0.581936i	−0.0973547	−	0.995250i	$-0.531038\pi$
$601$	−24.7100	−	14.2663i	−1.00794	−	0.581936i	−0.910589	+	0.413313i	$0.864371\pi$
$602$	−1.02889	−	0.719087i	−0.0419346	−	0.0293078i
$603$	8.12931	−	8.12931i	0.331051	−	0.331051i
$604$	24.8248	+	6.65178i	1.01011	+	0.270657i
$605$	7.59020	+	2.03379i	0.308586	+	0.0826852i
$606$	−12.3043	−	12.3043i	−0.499826	−	0.499826i
$607$	−22.6642	+	13.0852i	−0.919913	+	0.531112i	−0.883607	−	0.468229i	$-0.844892\pi$
$607$	−22.6642	+	13.0852i	−0.919913	+	0.531112i	−0.0363055	+	0.999341i	$0.511559\pi$
$608$	19.4817	−	33.7433i	0.790087	−	1.36847i
$609$	−16.1175	+	13.5485i	−0.653116	+	0.549012i
$610$			60.3585i			2.44385i
$611$	−3.99640	+	4.15413i	−0.161677	+	0.168058i
$612$		−	2.32588i		−	0.0940180i
$613$	7.15174	+	26.6907i	0.288856	+	1.07803i	0.945975	+	0.324239i	$0.105108\pi$
$613$	7.15174	+	26.6907i	0.288856	+	1.07803i	−0.657119	+	0.753787i	$0.728225\pi$
$614$	−19.8226	−	11.4446i	−0.799977	−	0.461867i
$615$	−2.60246	−	4.50760i	−0.104941	−	0.181764i
$616$	3.67099	+	1.33247i	0.147909	+	0.0536866i
$617$	18.4697	+	4.94894i	0.743562	+	0.199237i	0.610660	−	0.791893i	$-0.290904\pi$
$617$	18.4697	+	4.94894i	0.743562	+	0.199237i	0.132901	+	0.991129i	$0.457571\pi$
$618$	3.16272	−	11.8034i	0.127223	−	0.474804i
$619$	−5.80624	+	5.80624i	−0.233373	+	0.233373i	−0.814099	−	0.580726i	$-0.802769\pi$
$619$	−5.80624	+	5.80624i	−0.233373	+	0.233373i	0.580726	+	0.814099i	$0.302769\pi$
$620$	8.68261	+	15.0387i	0.348702	+	0.603970i
$621$	4.39623	−	7.61450i	0.176415	−	0.305559i
$622$	1.14394	+	4.26923i	0.0458677	+	0.171180i
$623$	17.8105	+	38.1070i	0.713563	+	1.52672i
$624$	13.7372	−	8.28967i	0.549929	−	0.331852i
$625$	11.7678			0.470712
$626$	−46.0857	+	12.3486i	−1.84196	+	0.493550i
$627$	7.56290	−	13.0993i	0.302033	−	0.523136i
$628$	0.922415	+	1.59767i	0.0368084	+	0.0637540i
$629$	4.62979	+	4.62979i	0.184602	+	0.184602i
$630$	17.3936	−	3.08279i	0.692978	−	0.122821i
$631$	1.64802	−	6.15049i	0.0656065	−	0.244847i	−0.925333	−	0.379155i	$-0.876215\pi$
$631$	1.64802	−	6.15049i	0.0656065	−	0.244847i	0.990940	+	0.134308i	$0.0428813\pi$
$632$	−2.70436	−	2.70436i	−0.107573	−	0.107573i
$633$	−3.19163	+	1.84269i	−0.126856	+	0.0732404i
$634$	−8.42348	−	4.86330i	−0.334539	−	0.193146i
$635$	−12.6381	−	47.1661i	−0.501529	−	1.87173i
$636$	−4.56562			−0.181039
$637$	−23.5292	+	9.13101i	−0.932262	+	0.361784i
$638$	−45.4665			−1.80004
$639$	−2.96028	−	11.0479i	−0.117107	−	0.437049i
$640$	−11.8515	−	6.84248i	−0.468473	−	0.270473i
$641$	−12.5318	+	7.23523i	−0.494976	+	0.285774i	−0.726636	−	0.687022i	$-0.758917\pi$
$641$	−12.5318	+	7.23523i	−0.494976	+	0.285774i	0.231660	+	0.972797i	$0.425584\pi$
$642$	26.0560	+	26.0560i	1.02835	+	1.02835i
$643$	7.35905	−	27.4644i	0.290213	−	1.08309i	−0.654733	−	0.755861i	$-0.727219\pi$
$643$	7.35905	−	27.4644i	0.290213	−	1.08309i	0.944945	−	0.327228i	$-0.106115\pi$
$644$	−39.8933	+	7.07057i	−1.57202	+	0.278620i
$645$	0.598645	+	0.598645i	0.0235716	+	0.0235716i
$646$	−6.61463	−	11.4569i	−0.260249	−	0.450765i
$647$	4.83456	−	8.37370i	0.190066	−	0.329204i	−0.755206	−	0.655488i	$-0.772463\pi$
$647$	4.83456	−	8.37370i	0.190066	−	0.329204i	0.945272	+	0.326284i	$0.105796\pi$
$648$	0.482736	−	0.129349i	0.0189637	−	0.00508130i
$649$	−12.1366			−0.476403
$650$	−46.3263	+	13.3790i	−1.81707	+	0.524768i
$651$	−3.23605	−	6.92378i	−0.126831	−	0.271364i
$652$	4.81762	+	17.9796i	0.188672	+	0.704135i
$653$	−16.6586	+	28.8535i	−0.651900	+	1.12912i	0.330762	+	0.943714i	$0.392694\pi$
$653$	−16.6586	+	28.8535i	−0.651900	+	1.12912i	−0.982661	+	0.185409i	$0.940639\pi$
$654$	12.6857	+	21.9722i	0.496049	+	0.859182i
$655$	24.3577	−	24.3577i	0.951734	−	0.951734i
$656$	−1.73677	+	6.48172i	−0.0678095	+	0.253069i
$657$	−1.44984	−	0.388484i	−0.0565637	−	0.0151562i
$658$	7.69105	+	2.79163i	0.299828	+	0.108829i
$659$	13.4367	+	23.2730i	0.523418	+	0.906586i	0.999629	+	0.0272549i	$0.00867657\pi$
$659$	13.4367	+	23.2730i	0.523418	+	0.906586i	−0.476211	+	0.879331i	$0.657990\pi$
$660$	15.3765	+	8.87762i	0.598529	+	0.345561i
$661$	−4.30948	−	16.0832i	−0.167619	−	0.625564i	−0.997692	−	0.0679081i	$-0.978368\pi$
$661$	−4.30948	−	16.0832i	−0.167619	−	0.625564i	0.830072	−	0.557656i	$-0.188299\pi$
$662$		−	35.3344i		−	1.37331i
$663$	−0.0931671	−	4.81416i	−0.00361831	−	0.186966i
$664$		−	7.16062i		−	0.277886i
$665$	35.7999	−	30.0936i	1.38826	−	1.16698i
$666$	4.74184	−	8.21311i	0.183743	−	0.318252i
$667$	−60.5981	+	34.9863i	−2.34637	+	1.35468i
$668$	−0.968429	−	0.968429i	−0.0374696	−	0.0374696i
$669$	−18.0743	−	4.84300i	−0.698794	−	0.187241i
$670$	74.1428	+	19.8665i	2.86439	+	0.767510i
$671$	18.8803	−	18.8803i	0.728868	−	0.728868i
$672$	−16.4992	−	11.5312i	−0.636471	−	0.444826i
$673$	22.1779	+	12.8044i	0.854896	+	0.493574i	0.862300	−	0.506398i	$-0.169023\pi$
$673$	22.1779	+	12.8044i	0.854896	+	0.493574i	−0.00740398	+	0.999973i	$0.502357\pi$
$674$	−41.8440	+	11.2121i	−1.61177	+	0.431873i
$675$	−6.91386			−0.266115
$676$	−19.1552	+	12.0708i	−0.736739	+	0.464261i
$677$			11.4036i			0.438275i	0.975694	+	0.219138i	$0.0703244\pi$
$677$			11.4036i			0.438275i	−0.975694	+	0.219138i	$0.929676\pi$
$678$	−13.2051	+	3.53830i	−0.507139	+	0.135888i
$679$	2.89708	−	33.4538i	0.111180	−	1.28384i
$680$	−1.99505	+	1.15184i	−0.0765066	+	0.0441711i
$681$	0.928664	−	0.928664i	0.0355865	−	0.0355865i
$682$	4.27137	−	15.9410i	0.163559	−	0.610412i
$683$	9.10656	−	33.9861i	0.348453	−	1.30044i	−0.540073	−	0.841618i	$-0.681604\pi$
$683$	9.10656	−	33.9861i	0.348453	−	1.30044i	0.888526	−	0.458826i	$-0.151730\pi$
$684$	−6.30691	+	6.30691i	−0.241151	+	0.241151i
$685$	1.63205	−	0.942264i	0.0623574	−	0.0360021i
$686$	25.3986	+	25.2645i	0.969722	+	0.964602i
$687$	−9.55752	+	2.56093i	−0.364642	+	0.0977056i
$688$		−	1.09148i		−	0.0416123i
$689$	−9.45004	+	0.182884i	−0.360018	+	0.00696733i
$690$	58.7040			2.23482
$691$	−40.2685	+	10.7899i	−1.53189	+	0.410468i	−0.923634	−	0.383276i	$-0.874796\pi$
$691$	−40.2685	+	10.7899i	−1.53189	+	0.410468i	−0.608252	+	0.793744i	$0.708129\pi$
$692$	8.40300	+	4.85147i	0.319434	+	0.184425i
$693$	−6.40509	−	4.47647i	−0.243309	−	0.170047i
$694$	19.1833	−	19.1833i	0.728188	−	0.728188i
$695$	−11.1471	−	2.98686i	−0.422834	−	0.113298i
$696$	−3.84174	−	1.02939i	−0.145621	−	0.0390189i
$697$	1.42398	+	1.42398i	0.0539370	+	0.0539370i
$698$	−13.7240	+	7.92353i	−0.519460	+	0.299910i
$699$	12.3668	−	21.4199i	0.467754	−	0.810174i
$700$	20.4998	+	24.3870i	0.774821	+	0.921743i
$701$			8.53135i			0.322225i	0.986936	+	0.161112i	$0.0515081\pi$
$701$			8.53135i			0.322225i	−0.986936	+	0.161112i	$0.948492\pi$
$702$	−6.70049	+	1.93510i	−0.252894	+	0.0730356i
$703$		−	25.1085i		−	0.946986i
$704$	−4.44656	−	16.5948i	−0.167586	−	0.625440i
$705$	−4.77901	−	2.75916i	−0.179988	−	0.103916i
$706$	−25.1538	−	43.5677i	−0.946676	−	1.63969i
$707$	−8.12056	+	22.3725i	−0.305405	+	0.841403i
$708$	6.91280	+	1.85228i	0.259799	+	0.0696130i
$709$	−0.424499	+	1.58425i	−0.0159424	+	0.0594978i	−0.973439	−	0.228947i	$-0.926472\pi$
$709$	−0.424499	+	1.58425i	−0.0159424	+	0.0594978i	0.957496	+	0.288445i	$0.0931383\pi$
$710$	53.9981	−	53.9981i	2.02651	−	2.02651i
$711$	3.82633	+	6.62740i	0.143499	+	0.248547i
$712$	−3.97278	+	6.88106i	−0.148886	+	0.257879i
$713$	−6.57361	−	24.5331i	−0.246184	−	0.918770i
$714$	−6.19165	+	2.89387i	−0.231717	+	0.108300i
$715$	32.1822	+	17.7592i	1.20355	+	0.664156i
$716$	6.12026			0.228725
$717$	−9.97678	+	2.67327i	−0.372590	+	0.0998351i
$718$	5.08300	−	8.80401i	0.189696	−	0.328563i
$719$	−7.35184	−	12.7338i	−0.274177	−	0.474889i	0.695750	−	0.718284i	$-0.255072\pi$
$719$	−7.35184	−	12.7338i	−0.274177	−	0.474889i	−0.969927	+	0.243395i	$0.921739\pi$
$720$	10.8610	+	10.8610i	0.404765	+	0.404765i
$721$	−16.4576	+	2.91690i	−0.612914	+	0.108631i
$722$	−3.61816	+	13.5032i	−0.134654	+	0.502536i
$723$	6.31778	+	6.31778i	0.234961	+	0.234961i
$724$	−35.1712	+	20.3061i	−1.30713	+	0.754671i
$725$	47.6507	+	27.5111i	1.76970	+	1.02174i
$726$	1.13975	+	4.25361i	0.0423001	+	0.157866i
$727$	−26.9644			−1.00005			−0.500026	−	0.866010i	$-0.666676\pi$
$727$	−26.9644			−1.00005			−0.500026	+	0.866010i	$0.666676\pi$
$728$	−3.95980	−	2.65493i	−0.146760	−	0.0983984i
$729$	−1.00000			−0.0370370
$730$	−2.59376	−	9.68004i	−0.0959993	−	0.358274i
$731$	−0.283674	−	0.163779i	−0.0104920	−	0.00605759i
$732$	−13.6354	+	7.87242i	−0.503980	+	0.290973i
$733$	27.0088	+	27.0088i	0.997593	+	0.997593i	0.999997	−	0.00240406i	$-0.000765238\pi$
$733$	27.0088	+	27.0088i	0.997593	+	0.997593i	−0.00240406	+	0.999997i	$0.500765\pi$
$734$	−15.5453	+	58.0157i	−0.573786	+	2.14140i
$735$	−13.8934	−	19.7675i	−0.512465	−	0.729134i
$736$	−47.3018	−	47.3018i	−1.74357	−	1.74357i
$737$	−16.9778	−	29.4064i	−0.625386	−	1.08320i
$738$	1.45844	−	2.52609i	0.0536860	−	0.0929868i
$739$	45.4039	−	12.1659i	1.67021	−	0.447532i	0.705043	−	0.709165i	$-0.250928\pi$
$739$	45.4039	−	12.1659i	1.67021	−	0.447532i	0.965167	+	0.261633i	$0.0842610\pi$
$740$	29.4734			1.08346
$741$	−12.8016	+	13.3068i	−0.470277	+	0.488839i
$742$	5.68057	+	12.1540i	0.208540	+	0.446188i
$743$	7.20187	+	26.8777i	0.264211	+	0.986049i	0.962732	+	0.270459i	$0.0871754\pi$
$743$	7.20187	+	26.8777i	0.264211	+	0.986049i	−0.698521	+	0.715590i	$0.746158\pi$
$744$	0.721827	−	1.25024i	0.0264635	−	0.0458361i
$745$	15.3002	+	26.5008i	0.560557	+	0.970914i
$746$	−17.3958	+	17.3958i	−0.636907	+	0.636907i
$747$	−3.70835	+	13.8397i	−0.135681	+	0.506370i
$748$	−6.63550	−	1.77798i	−0.242618	−	0.0650093i
$749$	17.1964	−	47.3769i	0.628344	−	1.73111i
$750$	−6.38907	−	11.0662i	−0.233296	−	0.404081i
$751$	35.2503	+	20.3518i	1.28630	+	0.742647i	0.977993	−	0.208639i	$-0.0669034\pi$
$751$	35.2503	+	20.3518i	1.28630	+	0.742647i	0.308310	+	0.951286i	$0.400237\pi$
$752$	1.84134	+	6.87199i	0.0671469	+	0.250596i
$753$		−	12.2748i		−	0.447318i
$754$	53.8801	+	13.3253i	1.96220	+	0.485279i
$755$			50.9344i			1.85369i
$756$	2.96503	+	3.52726i	0.107837	+	0.128285i
$757$	6.21461	−	10.7640i	0.225874	−	0.391225i	−0.730707	−	0.682691i	$-0.760810\pi$
$757$	6.21461	−	10.7640i	0.225874	−	0.391225i	0.956581	+	0.291466i	$0.0941430\pi$
$758$	−32.6045	+	18.8242i	−1.18425	+	0.683726i
$759$	−18.3628	−	18.3628i	−0.666528	−	0.666528i
$760$	8.53318	+	2.28646i	0.309531	+	0.0829386i
$761$	9.99508	+	2.67817i	0.362322	+	0.0970838i	0.435387	−	0.900243i	$-0.356612\pi$
$761$	9.99508	+	2.67817i	0.362322	+	0.0970838i	−0.0730655	+	0.997327i	$0.523278\pi$
$762$	19.3498	−	19.3498i	0.700968	−	0.700968i
$763$	19.8795	−	28.4442i	0.719686	−	1.02975i
$764$	−20.9726	−	12.1085i	−0.758762	−	0.438071i
$765$	4.45246	−	1.19303i	0.160979	−	0.0431342i
$766$	−10.3316			−0.373295
$767$	14.3825	+	3.55699i	0.519322	+	0.128435i
$768$		−	19.3028i		−	0.696529i
$769$	−12.9631	+	3.47345i	−0.467461	+	0.125256i	−0.484858	−	0.874593i	$-0.661129\pi$
$769$	−12.9631	+	3.47345i	−0.467461	+	0.125256i	0.0173970	+	0.999849i	$0.494462\pi$
$770$	4.50135	−	51.9789i	0.162218	−	1.87319i
$771$	4.83017	−	2.78870i	0.173954	−	0.100433i
$772$	−3.57812	+	3.57812i	−0.128779	+	0.128779i
$773$	−8.80996	+	32.8792i	−0.316872	+	1.18258i	0.605362	+	0.795950i	$0.293028\pi$
$773$	−8.80996	+	32.8792i	−0.316872	+	1.18258i	−0.922234	+	0.386632i	$0.873638\pi$
$774$	−0.122796	+	0.458282i	−0.00441382	+	0.0164726i
$775$	−14.1222	+	14.1222i	−0.507285	+	0.507285i
$776$	5.49307	−	3.17143i	0.197190	−	0.113848i
$777$	−12.9233	−	1.11915i	−0.463621	−	0.0401494i
$778$	5.62633	−	1.50757i	0.201714	−	0.0540491i
$779$		−	7.72259i		−	0.276691i
$780$	−15.6201	−	15.0270i	−0.559288	−	0.538052i
$781$	−33.7816			−1.20880
$782$	−21.9389	+	5.87852i	−0.784534	+	0.210215i
$783$	6.89205	+	3.97913i	0.246302	+	0.142202i
$784$	−5.35497	+	30.6861i	−0.191249	+	1.09593i
$785$	−2.58530	+	2.58530i	−0.0922733	+	0.0922733i
$786$	18.6466	+	4.99634i	0.665102	+	0.178213i
$787$	−44.0881	−	11.8134i	−1.57157	−	0.421101i	−0.635267	−	0.772293i	$-0.719110\pi$
$787$	−44.0881	−	11.8134i	−1.57157	−	0.421101i	−0.936303	+	0.351192i	$0.885776\pi$
$788$	−1.00305	−	1.00305i	−0.0357323	−	0.0357323i
$789$	−0.421964	+	0.243621i	−0.0150223	+	0.00867315i
$790$	−25.5470	+	44.2487i	−0.908921	+	1.57430i
$791$	12.0321	+	14.3136i	0.427811	+	0.508933i
$792$		−	1.47608i		−	0.0524502i
$793$	−27.9076	+	16.8407i	−0.991029	+	0.598032i
$794$		−	27.6043i		−	0.979639i
$795$	−2.34189	−	8.74004i	−0.0830582	−	0.309977i
$796$	2.59757	+	1.49971i	0.0920683	+	0.0531557i
$797$	2.38876	+	4.13745i	0.0846141	+	0.146556i	0.905227	−	0.424929i	$-0.139701\pi$
$797$	2.38876	+	4.13745i	0.0846141	+	0.146556i	−0.820613	+	0.571485i	$0.806368\pi$
$798$	24.6365	+	8.94235i	0.872124	+	0.316556i
$799$	2.06231	+	0.552595i	0.0729594	+	0.0195494i
$800$	−13.6144	+	50.8097i	−0.481342	+	1.79639i
$801$	11.2420	−	11.2420i	0.397217	−	0.397217i
$802$	−29.6777	−	51.4033i	−1.04796	−	1.81511i
$803$	−2.21661	+	3.83929i	−0.0782226	+	0.135485i
$804$	5.18229	+	19.3406i	0.182765	+	0.682089i
$805$	−33.9981	−	72.7416i	−1.19828	−	2.56381i
$806$	−9.73377	+	17.6390i	−0.342857	+	0.621308i
$807$	−16.4548			−0.579237
$808$	−4.34260	+	1.16360i	−0.152772	+	0.0409351i
$809$	15.3742	−	26.6289i	0.540529	−	0.936224i	−0.458345	−	0.888775i	$-0.651557\pi$
$809$	15.3742	−	26.6289i	0.540529	−	0.936224i	0.998874	−	0.0474491i	$-0.0151092\pi$
$810$	−3.33831	−	5.78213i	−0.117296	−	0.203163i
$811$	27.1910	+	27.1910i	0.954806	+	0.954806i	0.999022	−	0.0442157i	$-0.0140789\pi$
$811$	27.1910	+	27.1910i	0.954806	+	0.954806i	−0.0442157	+	0.999022i	$0.514079\pi$
$812$	−6.39972	−	36.1083i	−0.224586	−	1.26715i
$813$	−5.62502	+	20.9928i	−0.197278	+	0.736251i
$814$	−19.8064	−	19.8064i	−0.694214	−	0.694214i
$815$	−31.9474	+	18.4449i	−1.11907	+	0.646095i
$816$	−5.14658	−	2.97138i	−0.180166	−	0.104019i
$817$	0.325109	+	1.21332i	0.0113741	+	0.0424488i
$818$	−21.5980			−0.755155
$819$	6.27839	+	7.18205i	0.219385	+	0.250961i
$820$	9.06508			0.316566
$821$	0.190347	+	0.710386i	0.00664317	+	0.0247926i	0.969168	−	0.246401i	$-0.0792482\pi$
$821$	0.190347	+	0.710386i	0.00664317	+	0.0247926i	−0.962525	+	0.271194i	$0.912581\pi$
$822$	0.914613	+	0.528052i	0.0319008	+	0.0184179i
$823$	−29.7715	+	17.1886i	−1.03777	+	0.599157i	−0.919201	−	0.393789i	$-0.871164\pi$
$823$	−29.7715	+	17.1886i	−1.03777	+	0.599157i	−0.118570	+	0.992946i	$0.537831\pi$
$824$	−2.23247	−	2.23247i	−0.0777718	−	0.0777718i
$825$	−5.28519	+	19.7246i	−0.184007	+	0.686722i
$826$	−3.67004	−	20.7070i	−0.127697	−	0.720488i
$827$	17.5703	+	17.5703i	0.610979	+	0.610979i	0.943201	−	0.332222i	$-0.107798\pi$
$827$	17.5703	+	17.5703i	0.610979	+	0.610979i	−0.332222	+	0.943201i	$0.607798\pi$
$828$	7.65663	+	13.2617i	0.266086	+	0.460875i
$829$	0.225668	−	0.390869i	0.00783778	−	0.0135754i	−0.862080	−	0.506772i	$-0.830838\pi$
$829$	0.225668	−	0.390869i	0.00783778	−	0.0135754i	0.869918	+	0.493197i	$0.164172\pi$
$830$	−92.4028	+	24.7592i	−3.20735	+	0.859406i
$831$	27.6334			0.958593
$832$	0.405805	+	20.9689i	0.0140688	+	0.726965i
$833$	7.17173	+	5.99626i	0.248486	+	0.207758i
$834$	−1.67386	−	6.24693i	−0.0579610	−	0.216314i
$835$	1.35713	−	2.35062i	0.0469655	−	0.0813466i
$836$	13.1718	+	22.8142i	0.455556	+	0.789046i
$837$	−2.04259	+	2.04259i	−0.0706024	+	0.0706024i
$838$	−5.49034	+	20.4902i	−0.189661	+	0.707824i
$839$	−42.5808	−	11.4095i	−1.47005	−	0.393899i	−0.567102	−	0.823647i	$-0.691936\pi$
$839$	−42.5808	−	11.4095i	−1.47005	−	0.393899i	−0.902949	+	0.429748i	$0.858602\pi$
$840$	1.55718	−	4.29009i	0.0537278	−	0.148022i
$841$	−17.1669	−	29.7339i	−0.591961	−	1.02531i
$842$	−15.7233	−	9.07786i	−0.541861	−	0.312844i
$843$	5.66252	+	21.1328i	0.195028	+	0.727853i
$844$		−	6.41858i		−	0.220937i
$845$	−32.9327	−	30.4775i	−1.13292	−	1.04846i
$846$		−	3.09251i		−	0.106323i
$847$	4.61067	−	3.87575i	0.158425	−	0.133172i
$848$	−5.83272	+	10.1026i	−0.200297	+	0.346924i
$849$	−4.63631	+	2.67677i	−0.159118	+	0.0918666i
$850$	12.6289	+	12.6289i	0.433169	+	0.433169i
$851$	−41.6391	−	11.1572i	−1.42737	−	0.382463i
$852$	19.2414	+	5.15572i	0.659200	+	0.176632i
$853$	−3.63181	+	3.63181i	−0.124351	+	0.124351i	−0.766543	−	0.642193i	$-0.778025\pi$
$853$	−3.63181	+	3.63181i	−0.124351	+	0.124351i	0.642193	+	0.766543i	$0.278025\pi$
$854$	37.9222	+	26.5036i	1.29767	+	0.906934i
$855$	−15.3085	−	8.83835i	−0.523539	−	0.302265i
$856$	9.19607	−	2.46408i	0.314315	−	0.0842205i
$857$	12.7961			0.437106			0.218553	−	0.975825i	$-0.429866\pi$
$857$	12.7961			0.437106			0.218553	+	0.975825i	$0.429866\pi$
$858$	0.398572	+	20.5951i	0.0136070	+	0.703106i
$859$		−	8.61431i		−	0.293917i	−0.989143	−	0.146958i	$-0.953052\pi$
$859$		−	8.61431i		−	0.293917i	0.989143	−	0.146958i	$-0.0469483\pi$
$860$	−1.42425	+	0.381626i	−0.0485664	+	0.0130133i
$861$	−3.97480	−	0.344216i	−0.135461	−	0.0117309i
$862$	57.7351	−	33.3334i	1.96647	−	1.13534i
$863$	36.6611	−	36.6611i	1.24796	−	1.24796i	0.291338	−	0.956620i	$-0.405899\pi$
$863$	36.6611	−	36.6611i	1.24796	−	1.24796i	0.956620	−	0.291338i	$-0.0941006\pi$
$864$	−1.96915	+	7.34896i	−0.0669917	+	0.250017i
$865$	−4.97702	+	18.5745i	−0.169224	+	0.631552i
$866$	−53.8132	+	53.8132i	−1.82865	+	1.82865i
$867$	13.1779	−	7.60828i	0.447546	−	0.258391i
$868$	13.2611	+	1.14841i	0.450112	+	0.0389796i
$869$	21.8323	−	5.84995i	0.740610	−	0.198446i
$870$			53.1342i			1.80142i
$871$	11.5011	+	39.8240i	0.389701	+	1.34938i
$872$	6.55509			0.221983
$873$	−12.2592	+	3.28484i	−0.414911	+	0.111175i
$874$	75.4305	+	43.5498i	2.55147	+	1.47309i
$875$	−10.0122	+	14.3258i	−0.338474	+	0.484300i
$876$	1.84850	−	1.84850i	0.0624549	−	0.0624549i
$877$	−8.12066	−	2.17593i	−0.274215	−	0.0734758i	0.119091	−	0.992883i	$-0.462002\pi$
$877$	−8.12066	−	2.17593i	−0.274215	−	0.0734758i	−0.393306	+	0.919408i	$0.628669\pi$
$878$	−3.22251	−	0.863470i	−0.108755	−	0.0291407i
$879$	8.69998	+	8.69998i	0.293443	+	0.293443i
$880$	39.2879	−	22.6829i	1.32439	−	0.764639i
$881$	−24.2720	+	42.0404i	−0.817745	+	1.41638i	0.0895951	+	0.995978i	$0.471443\pi$
$881$	−24.2720	+	42.0404i	−0.817745	+	1.41638i	−0.907340	+	0.420397i	$0.861891\pi$
$882$	5.70072	−	12.2818i	0.191953	−	0.413549i
$883$			41.4666i			1.39546i	0.716359	+	0.697731i	$0.245807\pi$
$883$			41.4666i			1.39546i	−0.716359	+	0.697731i	$0.754193\pi$
$884$	7.34232	+	4.05173i	0.246949	+	0.136274i
$885$			14.1834i			0.476769i
$886$	1.81475	+	6.77273i	0.0609676	+	0.227534i
$887$	−35.6698	−	20.5940i	−1.19768	−	0.691479i	−0.237640	−	0.971353i	$-0.576374\pi$
$887$	−35.6698	−	20.5940i	−1.19768	−	0.691479i	−0.960037	+	0.279875i	$0.909707\pi$
$888$	−1.22513	−	2.12199i	−0.0411127	−	0.0712093i
$889$	−35.1831	−	12.7705i	−1.18000	−	0.428307i
$890$	102.532	+	27.4734i	3.43688	+	0.920909i
$891$	−0.764433	+	2.85290i	−0.0256095	+	0.0955759i
$892$	23.0441	−	23.0441i	0.771575	−	0.771575i
$893$	−4.09379	−	7.09065i	−0.136993	−	0.237280i
$894$	−8.57438	+	14.8513i	−0.286770	+	0.496700i
$895$	3.13932	+	11.7161i	0.104936	+	0.391626i
$896$	−9.50305	+	4.44156i	−0.317475	+	0.148382i
$897$	16.3791	+	27.1426i	0.546882	+	0.906266i
$898$	−23.5687			−0.786497
$899$	22.2054	−	5.94992i	0.740591	−	0.198441i
$900$	6.02071	−	10.4282i	0.200690	−	0.347606i
$901$	1.75042	+	3.03182i	0.0583151	+	0.101005i
$902$	−6.09182	−	6.09182i	−0.202836	−	0.202836i
$903$	0.638985	−	0.113252i	0.0212641	−	0.00376878i
$904$	−0.914177	+	3.41175i	−0.0304051	+	0.113473i
$905$	−56.9130	−	56.9130i	−1.89185	−	1.89185i
$906$	−24.7199	+	14.2720i	−0.821263	+	0.474156i
$907$	−11.7828	−	6.80280i	−0.391241	−	0.225883i	0.291456	−	0.956584i	$-0.405860\pi$
$907$	−11.7828	−	6.80280i	−0.391241	−	0.225883i	−0.682698	+	0.730701i	$0.739193\pi$
$908$	0.592007	+	2.20940i	0.0196464	+	0.0733215i
$909$	8.99579			0.298372
$910$	−20.5683	+	60.2784i	−0.681832	+	1.99821i
$911$	−4.82402			−0.159827			−0.0799135	−	0.996802i	$-0.525464\pi$
$911$	−4.82402			−0.159827			−0.0799135	+	0.996802i	$0.525464\pi$
$912$	5.89833	+	22.0129i	0.195313	+	0.728919i
$913$	36.6487	+	21.1591i	1.21289	+	0.700265i
$914$	−27.2181	+	15.7144i	−0.900296	+	0.519786i
$915$	−22.0644	−	22.0644i	−0.729428	−	0.729428i
$916$	4.46020	−	16.6457i	0.147369	−	0.549989i
$917$	−4.60799	−	25.9991i	−0.152169	−	0.858564i
$918$	1.82661	+	1.82661i	0.0602871	+	0.0602871i
$919$	26.8960	+	46.5852i	0.887216	+	1.53670i	0.843153	+	0.537674i	$0.180697\pi$
$919$	26.8960	+	46.5852i	0.887216	+	1.53670i	0.0440628	+	0.999029i	$0.485970\pi$
$920$	7.58356	−	13.1351i	0.250023	−	0.433052i
$921$	11.4299	−	3.06265i	0.376630	−	0.100918i
$922$	−7.26965			−0.239413
$923$	40.0329	+	9.90069i	1.31770	+	0.325885i
$924$	12.3295	−	5.76260i	0.405611	−	0.189576i
$925$	8.77331	+	32.7425i	0.288465	+	1.07657i
$926$	−11.3073	+	19.5848i	−0.371580	+	0.643596i
$927$	3.15867	+	5.47098i	0.103744	+	0.179690i
$928$	42.8139	−	42.8139i	1.40543	−	1.40543i
$929$	−1.83189	+	6.83673i	−0.0601025	+	0.224306i	−0.989444	−	0.144916i	$-0.953709\pi$
$929$	−1.83189	+	6.83673i	−0.0601025	+	0.224306i	0.929341	+	0.369221i	$0.120376\pi$
$930$	−18.6294	−	4.99172i	−0.610881	−	0.163685i
$931$	−3.18743	−	35.7067i	−0.104464	−	1.17024i
$932$	21.5384	+	37.3056i	0.705513	+	1.22198i
$933$	−1.97882	−	1.14247i	−0.0647836	−	0.0374028i
$934$	−16.1182	−	60.1539i	−0.527403	−	1.96830i
$935$		−	13.6144i		−	0.445240i
$936$	−0.432609	+	1.74923i	−0.0141403	+	0.0571753i
$937$		−	17.4831i		−	0.571147i	−0.958357	−	0.285574i	$-0.907816\pi$
$937$		−	17.4831i		−	0.571147i	0.958357	−	0.285574i	$-0.0921841\pi$
$938$	45.0381	−	37.8592i	1.47055	−	1.23615i
$939$	12.3328	−	21.3610i	0.402466	−	0.697091i
$940$	8.32328	−	4.80545i	0.271475	−	0.156736i
$941$	−11.1218	−	11.1218i	−0.362560	−	0.362560i	0.502195	−	0.864754i	$-0.332526\pi$
$941$	−11.1218	−	11.1218i	−0.362560	−	0.362560i	−0.864754	+	0.502195i	$0.832526\pi$
$942$	−1.97913	−	0.530306i	−0.0644835	−	0.0172783i
$943$	−12.8069	−	3.43159i	−0.417049	−	0.111748i
$944$	12.9299	−	12.9299i	0.420834	−	0.420834i
$945$	−5.23141	+	7.48528i	−0.170178	+	0.243496i
$946$	1.21356	+	0.700652i	0.0394564	+	0.0227802i
$947$	−42.7851	+	11.4642i	−1.39033	+	0.372537i	−0.874862	−	0.484373i	$-0.839048\pi$
$947$	−42.7851	+	11.4642i	−1.39033	+	0.372537i	−0.515466	+	0.856910i	$0.672381\pi$
$948$	−13.3281			−0.432878
$949$	3.75202	−	3.90011i	0.121796	−	0.126603i
$950$		−	68.4899i		−	2.22210i
$951$	4.85707	−	1.30145i	0.157501	−	0.0422023i
$952$	−0.152349	+	1.75923i	−0.00493765	+	0.0570170i
$953$	−46.1967	+	26.6717i	−1.49646	+	0.863980i	−0.999992	−	0.00407700i	$-0.998702\pi$
$953$	−46.1967	+	26.6717i	−1.49646	+	0.863980i	−0.496465	+	0.868057i	$0.665369\pi$
$954$	3.58558	−	3.58558i	0.116087	−	0.116087i
$955$	12.4219	−	46.3591i	0.401962	−	1.50014i
$956$	4.65586	−	17.3759i	0.150581	−	0.561976i
$957$	16.6206	−	16.6206i	0.537267	−	0.537267i
$958$	−3.94974	+	2.28038i	−0.127610	+	0.0736758i
$959$	0.124629	−	1.43914i	0.00402448	−	0.0464722i
$960$	−19.3935	+	5.19646i	−0.625921	+	0.167715i
$961$		−	22.6556i		−	0.730826i
$962$	17.6667	+	29.2765i	0.569599	+	0.943911i
$963$	−19.0499			−0.613874
$964$	−15.0307	+	4.02747i	−0.484107	+	0.129716i
$965$	−8.68499	−	5.01428i	−0.279580	−	0.161415i
$966$	25.7771	−	36.8827i	0.829365	−	1.18668i
$967$	8.45160	−	8.45160i	0.271785	−	0.271785i	−0.558033	−	0.829819i	$-0.688444\pi$
$967$	8.45160	−	8.45160i	0.271785	−	0.271785i	0.829819	+	0.558033i	$0.188444\pi$
$968$	1.09899	+	0.294473i	0.0353228	+	0.00946472i
$969$	6.60615	+	1.77011i	0.212220	+	0.0568642i
$970$	−59.9184	−	59.9184i	−1.92386	−	1.92386i
$971$	14.8642	−	8.58184i	0.477014	−	0.275404i	−0.242157	−	0.970237i	$-0.577855\pi$
$971$	14.8642	−	8.58184i	0.477014	−	0.275404i	0.719171	+	0.694833i	$0.244522\pi$
$972$	0.870817	−	1.50830i	0.0279315	−	0.0483787i
$973$	−6.77132	+	5.69200i	−0.217079	+	0.182477i
$974$			26.0677i			0.835264i
$975$	12.0441	−	21.8257i	0.385720	−	0.698981i
$976$			40.2290i			1.28770i
$977$	−0.601718	−	2.24564i	−0.0192507	−	0.0718444i	0.955632	−	0.294562i	$-0.0951738\pi$
$977$	−0.601718	−	2.24564i	−0.0192507	−	0.0718444i	−0.974883	+	0.222718i	$0.928507\pi$
$978$	−17.9036	−	10.3367i	−0.572494	−	0.330530i
$979$	−23.4786	−	40.6661i	−0.750379	−	1.29969i
$980$	41.9139	−	3.74153i	1.33889	−	0.119519i
$981$	−12.6694	−	3.39476i	−0.404503	−	0.108386i
$982$	−13.8838	+	51.8150i	−0.443050	+	1.65348i
$983$	−28.2865	+	28.2865i	−0.902198	+	0.902198i	−0.995626	−	0.0934279i	$-0.970218\pi$
$983$	−28.2865	+	28.2865i	−0.902198	+	0.902198i	0.0934279	+	0.995626i	$0.470218\pi$
$984$	−0.376812	−	0.652657i	−0.0120123	−	0.0208060i
$985$	1.40566	−	2.43467i	0.0447879	−	0.0775749i
$986$	−5.32077	−	19.8574i	−0.169448	−	0.632388i
$987$	−3.83201	+	1.79101i	−0.121974	+	0.0570086i
$988$	−8.92286	−	30.8964i	−0.283874	−	0.982945i
$989$	2.15660			0.0685758
$990$	−19.0478	+	5.10383i	−0.605378	+	0.162210i
$991$	19.2831	−	33.3993i	0.612549	−	1.06097i	−0.378261	−	0.925699i	$-0.623478\pi$
$991$	19.2831	−	33.3993i	0.612549	−	1.06097i	0.990809	−	0.135266i	$-0.0431889\pi$
$992$	10.9888	+	19.0331i	0.348894	+	0.604302i
$993$	12.9167	+	12.9167i	0.409899	+	0.409899i
$994$	−10.2154	−	57.6368i	−0.324012	−	1.82813i
$995$	−1.53852	+	5.74182i	−0.0487742	+	0.182028i
$996$	−17.6452	−	17.6452i	−0.559109	−	0.559109i
$997$	27.3485	−	15.7897i	0.866136	−	0.500064i	7.37730e−5	−	1.00000i	$-0.499977\pi$
$997$	27.3485	−	15.7897i	0.866136	−	0.500064i	0.866062	+	0.499936i	$0.166643\pi$
$998$	29.8224	+	17.2180i	0.944012	+	0.545026i
$999$	1.26895	+	4.73577i	0.0401476	+	0.149833i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.by.c.97.2	yes	32
3.2	odd	2		819.2.fm.f.370.7		32
7.6	odd	2		273.2.by.d.97.2	yes	32
13.11	odd	12		273.2.by.d.76.2	yes	32
21.20	even	2		819.2.fm.e.370.7		32
39.11	even	12		819.2.fm.e.622.7		32
91.76	even	12	inner	273.2.by.c.76.2	✓	32
273.167	odd	12		819.2.fm.f.622.7		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.c.76.2	✓	32	91.76	even	12	inner
273.2.by.c.97.2	yes	32	1.1	even	1	trivial
273.2.by.d.76.2	yes	32	13.11	odd	12
273.2.by.d.97.2	yes	32	7.6	odd	2
819.2.fm.e.370.7		32	21.20	even	2
819.2.fm.e.622.7		32	39.11	even	12
819.2.fm.f.370.7		32	3.2	odd	2
819.2.fm.f.622.7		32	273.167	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)

\(f(q)\)	\(=\)	\(q+(-0.500642 - 1.86842i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-1.50830 + 0.870817i) q^{4} +(-2.44068 - 2.44068i) q^{5} +(0.500642 - 1.86842i) q^{6} +(-2.60515 + 0.461729i) q^{7} +(-0.353388 - 0.353388i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500642 - 1.86842i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-1.50830 + 0.870817i) q^{4} +(-2.44068 - 2.44068i) q^{5} +(0.500642 - 1.86842i) q^{6} +(-2.60515 + 0.461729i) q^{7} +(-0.353388 - 0.353388i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-3.33831 + 5.78213i) q^{10} +(2.85290 - 0.764433i) q^{11} -1.74163 q^{12} +(-3.60488 + 0.0697642i) q^{13} +(2.16695 + 4.63635i) q^{14} +(-0.893352 - 3.33403i) q^{15} +(-2.22499 + 3.85380i) q^{16} +(0.667729 + 1.15654i) q^{17} +(1.36778 - 1.36778i) q^{18} +(1.32547 - 4.94673i) q^{19} +(5.80667 + 1.55589i) q^{20} +(-2.48699 - 0.902706i) q^{21} +(-2.85656 - 4.94771i) q^{22} +(-7.61450 - 4.39623i) q^{23} +(-0.129349 - 0.482736i) q^{24} +6.91386i q^{25} +(1.93510 + 6.70049i) q^{26} +1.00000i q^{27} +(3.52726 - 2.96503i) q^{28} +(3.97913 - 6.89205i) q^{29} +(-5.78213 + 3.33831i) q^{30} +(2.04259 + 2.04259i) q^{31} +(7.34896 + 1.96915i) q^{32} +(2.85290 + 0.764433i) q^{33} +(1.82661 - 1.82661i) q^{34} +(7.48528 + 5.23141i) q^{35} +(-1.50830 - 0.870817i) q^{36} +(4.73577 - 1.26895i) q^{37} -9.90616 q^{38} +(-3.15680 - 1.74202i) q^{39} +1.72501i q^{40} +(1.45657 - 0.390287i) q^{41} +(-0.441543 + 5.09867i) q^{42} +(-0.212417 + 0.122639i) q^{43} +(-3.63735 + 3.63735i) q^{44} +(0.893352 - 3.33403i) q^{45} +(-4.40187 + 16.4280i) q^{46} +(1.13049 - 1.13049i) q^{47} +(-3.85380 + 2.22499i) q^{48} +(6.57361 - 2.40574i) q^{49} +(12.9180 - 3.46137i) q^{50} +1.33546i q^{51} +(5.37648 - 3.24441i) q^{52} +2.62146 q^{53} +(1.86842 - 0.500642i) q^{54} +(-8.82877 - 5.09729i) q^{55} +(1.08380 + 0.757458i) q^{56} +(3.62126 - 3.62126i) q^{57} +(-14.8694 - 3.98423i) q^{58} +(-3.96915 - 1.06353i) q^{59} +(4.25078 + 4.25078i) q^{60} +(7.82911 - 4.52014i) q^{61} +(2.79382 - 4.83903i) q^{62} +(-1.70244 - 2.02526i) q^{63} -5.81681i q^{64} +(8.96863 + 8.62809i) q^{65} -5.71313i q^{66} +(-2.97553 - 11.1048i) q^{67} +(-2.01427 - 1.16294i) q^{68} +(-4.39623 - 7.61450i) q^{69} +(6.02703 - 16.6047i) q^{70} +(-11.0479 - 2.96028i) q^{71} +(0.129349 - 0.482736i) q^{72} +(-1.06136 + 1.06136i) q^{73} +(-4.74184 - 8.21311i) q^{74} +(-3.45693 + 5.98758i) q^{75} +(2.30849 + 8.61540i) q^{76} +(-7.07928 + 3.30873i) q^{77} +(-1.67440 + 6.77035i) q^{78} +7.65266 q^{79} +(14.8364 - 3.97540i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.45844 - 2.52609i) q^{82} +(10.1314 + 10.1314i) q^{83} +(4.53722 - 0.804162i) q^{84} +(1.19303 - 4.45246i) q^{85} +(0.335486 + 0.335486i) q^{86} +(6.89205 - 3.97913i) q^{87} +(-1.27832 - 0.738039i) q^{88} +(-4.11486 - 15.3569i) q^{89} -6.67662 q^{90} +(9.35903 - 1.84622i) q^{91} +15.3133 q^{92} +(0.747641 + 2.79024i) q^{93} +(-2.67819 - 1.54626i) q^{94} +(-15.3085 + 8.83835i) q^{95} +(5.37981 + 5.37981i) q^{96} +(-3.28484 + 12.2592i) q^{97} +(-7.78596 - 11.0779i) q^{98} +(2.08847 + 2.08847i) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more