LMFDB - Embedded newform 637.2.bl.b.534.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$29$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			534.4
Character	$\chi$	$=$	637.534
Dual form			637.2.bl.b.235.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.50899 + 0.378169i) q^{2} +(2.68579 + 1.83114i) q^{3} +(4.24086 - 1.30813i) q^{4} +(-0.0815020 + 1.08757i) q^{5} +(-7.43110 - 3.57863i) q^{6} +(-1.85680 + 1.88475i) q^{7} +(-5.57346 + 2.68404i) q^{8} +(2.76437 + 7.04351i) q^{9} +O(q^{10})$	\(q+(-2.50899 + 0.378169i) q^{2} +(2.68579 + 1.83114i) q^{3} +(4.24086 - 1.30813i) q^{4} +(-0.0815020 + 1.08757i) q^{5} +(-7.43110 - 3.57863i) q^{6} +(-1.85680 + 1.88475i) q^{7} +(-5.57346 + 2.68404i) q^{8} +(2.76437 + 7.04351i) q^{9} +(-0.206797 - 2.75952i) q^{10} +(1.58390 - 4.03571i) q^{11} +(13.7854 + 4.25224i) q^{12} +(0.623490 + 0.781831i) q^{13} +(3.94595 - 5.43099i) q^{14} +(-2.21039 + 2.77174i) q^{15} +(5.63497 - 3.84186i) q^{16} +(-2.71297 + 2.51727i) q^{17} +(-9.59942 - 16.6267i) q^{18} +(-3.05975 + 5.29964i) q^{19} +(1.07704 + 4.71884i) q^{20} +(-8.43823 + 1.66197i) q^{21} +(-2.44781 + 10.7245i) q^{22} +(-3.25900 - 3.02391i) q^{23} +(-19.8840 - 2.99703i) q^{24} +(3.76799 + 0.567933i) q^{25} +(-1.85999 - 1.72582i) q^{26} +(-3.30314 + 14.4720i) q^{27} +(-5.40895 + 10.4219i) q^{28} +(-0.314786 - 1.37917i) q^{29} +(4.49765 - 7.79016i) q^{30} +(1.21741 + 2.10861i) q^{31} +(-3.61578 + 3.35495i) q^{32} +(11.6440 - 7.93874i) q^{33} +(5.85485 - 7.34175i) q^{34} +(-1.89846 - 2.17301i) q^{35} +(20.9372 + 26.2544i) q^{36} +(-3.25439 - 1.00385i) q^{37} +(5.67271 - 14.4538i) q^{38} +(0.242919 + 3.24153i) q^{39} +(-2.46482 - 6.28027i) q^{40} +(-6.85890 + 3.30307i) q^{41} +(20.5429 - 7.36093i) q^{42} +(7.77025 + 3.74196i) q^{43} +(1.43786 - 19.1868i) q^{44} +(-7.88560 + 2.43239i) q^{45} +(9.32034 + 6.35450i) q^{46} +(10.8241 - 1.63147i) q^{47} +22.1693 q^{48} +(-0.104552 - 6.99922i) q^{49} -9.66862 q^{50} +(-11.8959 + 1.79302i) q^{51} +(3.66687 + 2.50003i) q^{52} +(1.93326 - 0.596331i) q^{53} +(2.81467 - 37.5592i) q^{54} +(4.26002 + 2.05152i) q^{55} +(5.29009 - 15.4883i) q^{56} +(-17.9223 + 8.63090i) q^{57} +(1.31135 + 3.34128i) q^{58} +(-0.0449346 - 0.599610i) q^{59} +(-5.74814 + 14.6460i) q^{60} +(-6.71464 - 2.07119i) q^{61} +(-3.85187 - 4.83009i) q^{62} +(-18.4081 - 7.86827i) q^{63} +(-0.701239 + 0.879326i) q^{64} +(-0.901111 + 0.614367i) q^{65} +(-26.2124 + 24.3216i) q^{66} +(2.94936 + 5.10845i) q^{67} +(-8.21240 + 14.2243i) q^{68} +(-3.21579 - 14.0893i) q^{69} +(5.58497 + 4.73412i) q^{70} +(2.82382 - 12.3720i) q^{71} +(-34.3122 - 31.8370i) q^{72} +(12.5062 + 1.88501i) q^{73} +(8.54484 + 1.28793i) q^{74} +(9.08008 + 8.42508i) q^{75} +(-6.04334 + 26.4776i) q^{76} +(4.66531 + 10.4788i) q^{77} +(-1.83533 - 8.04110i) q^{78} +(-0.0838893 + 0.145301i) q^{79} +(3.71902 + 6.44153i) q^{80} +(-18.7318 + 17.3805i) q^{81} +(15.9598 - 10.8812i) q^{82} +(-9.64234 + 12.0911i) q^{83} +(-33.6113 + 18.0865i) q^{84} +(-2.51659 - 3.15570i) q^{85} +(-20.9106 - 6.45005i) q^{86} +(1.68000 - 4.28058i) q^{87} +(2.00420 + 26.7441i) q^{88} +(-2.38330 - 6.07254i) q^{89} +(18.8650 - 9.08491i) q^{90} +(-2.63125 - 0.276587i) q^{91} +(-17.7766 - 8.56078i) q^{92} +(-0.591463 + 7.89253i) q^{93} +(-26.5405 + 8.18666i) q^{94} +(-5.51435 - 3.75962i) q^{95} +(-15.8546 + 2.38970i) q^{96} -2.99453 q^{97} +(2.90921 + 17.5214i) q^{98} +32.8041 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) $ 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{4}{21}\right)$

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 $

$2$	−2.50899	+	0.378169i	−1.77412	+	0.267406i	−0.952918	−	0.303229i	$-0.901935\pi$
$2$	−2.50899	+	0.378169i	−1.77412	+	0.267406i	−0.821204	+	0.570635i	$0.806697\pi$
$3$	2.68579	+	1.83114i	1.55064	+	1.05721i	0.970016	+	0.243040i	$0.0781447\pi$
$3$	2.68579	+	1.83114i	1.55064	+	1.05721i	0.580626	+	0.814170i	$0.302808\pi$
$4$	4.24086	−	1.30813i	2.12043	−	0.654066i
$5$	−0.0815020	+	1.08757i	−0.0364488	+	0.486375i	0.948872	+	0.315661i	$0.102226\pi$
$5$	−0.0815020	+	1.08757i	−0.0364488	+	0.486375i	−0.985321	+	0.170714i	$0.945393\pi$
$6$	−7.43110	−	3.57863i	−3.03373	−	1.46097i
$7$	−1.85680	+	1.88475i	−0.701806	+	0.712368i
$7$	−1.85680	+	1.88475i	−0.701806	+	0.712368i
$8$	−5.57346	+	2.68404i	−1.97051	+	0.948950i
$9$	2.76437	+	7.04351i	0.921458	+	2.34784i
$10$	−0.206797	−	2.75952i	−0.0653950	−	0.872635i
$11$	1.58390	−	4.03571i	0.477564	−	1.21681i	−0.465751	−	0.884916i	$-0.654216\pi$
$11$	1.58390	−	4.03571i	0.477564	−	1.21681i	0.943315	−	0.331898i	$-0.107689\pi$
$12$	13.7854	+	4.25224i	3.97951	+	1.22752i
$13$	0.623490	+	0.781831i	0.172925	+	0.216841i
$13$	0.623490	+	0.781831i	0.172925	+	0.216841i
$14$	3.94595	−	5.43099i	1.05460	−	1.45149i
$15$	−2.21039	+	2.77174i	−0.570720	+	0.715660i
$16$	5.63497	−	3.84186i	1.40874	−	0.960464i
$17$	−2.71297	+	2.51727i	−0.657991	+	0.610527i	−0.936819	−	0.349814i	$-0.886245\pi$
$17$	−2.71297	+	2.51727i	−0.657991	+	0.610527i	0.278828	+	0.960341i	$0.410054\pi$
$18$	−9.59942	−	16.6267i	−2.26260	−	3.91895i
$19$	−3.05975	+	5.29964i	−0.701955	+	1.21582i	0.265824	+	0.964022i	$0.414356\pi$
$19$	−3.05975	+	5.29964i	−0.701955	+	1.21582i	−0.967779	+	0.251800i	$0.918977\pi$
$20$	1.07704	+	4.71884i	0.240834	+	1.05516i
$21$	−8.43823	+	1.66197i	−1.84137	+	0.362671i
$22$	−2.44781	+	10.7245i	−0.521874	+	2.28648i
$23$	−3.25900	−	3.02391i	−0.679549	−	0.630529i	0.262922	−	0.964817i	$-0.415314\pi$
$23$	−3.25900	−	3.02391i	−0.679549	−	0.630529i	−0.942471	+	0.334288i	$0.891504\pi$
$24$	−19.8840	−	2.99703i	−4.05880	−	0.611766i
$25$	3.76799	+	0.567933i	0.753599	+	0.113587i
$26$	−1.85999	−	1.72582i	−0.364774	−	0.338461i
$27$	−3.30314	+	14.4720i	−0.635689	+	2.78514i
$28$	−5.40895	+	10.4219i	−1.02219	+	1.96955i
$29$	−0.314786	−	1.37917i	−0.0584544	−	0.256105i	0.937255	−	0.348646i	$-0.113358\pi$
$29$	−0.314786	−	1.37917i	−0.0584544	−	0.256105i	−0.995709	+	0.0925405i	$0.970501\pi$
$30$	4.49765	−	7.79016i	0.821155	−	1.42228i
$31$	1.21741	+	2.10861i	0.218653	+	0.378717i	0.954396	−	0.298543i	$-0.0965005\pi$
$31$	1.21741	+	2.10861i	0.218653	+	0.378717i	−0.735744	+	0.677260i	$0.763167\pi$
$32$	−3.61578	+	3.35495i	−0.639185	+	0.593077i
$33$	11.6440	−	7.93874i	2.02696	−	1.38196i
$34$	5.85485	−	7.34175i	1.00410	−	1.25910i
$35$	−1.89846	−	2.17301i	−0.320898	−	0.367306i
$36$	20.9372	+	26.2544i	3.48953	+	4.37573i
$37$	−3.25439	−	1.00385i	−0.535018	−	0.165031i	0.0154604	−	0.999880i	$-0.495079\pi$
$37$	−3.25439	−	1.00385i	−0.535018	−	0.165031i	−0.550479	+	0.834849i	$0.685555\pi$
$38$	5.67271	−	14.4538i	0.920236	−	2.34472i
$39$	0.242919	+	3.24153i	0.0388982	+	0.519061i
$40$	−2.46482	−	6.28027i	−0.389723	−	0.992997i
$41$	−6.85890	+	3.30307i	−1.07118	+	0.515853i	−0.884487	−	0.466565i	$-0.845491\pi$
$41$	−6.85890	+	3.30307i	−1.07118	+	0.515853i	−0.186693	+	0.982418i	$0.559777\pi$
$42$	20.5429	−	7.36093i	3.16984	−	1.13582i
$43$	7.77025	+	3.74196i	1.18495	+	0.570643i	0.919350	−	0.393440i	$-0.128715\pi$
$43$	7.77025	+	3.74196i	1.18495	+	0.570643i	0.265602	+	0.964083i	$0.414429\pi$
$44$	1.43786	−	19.1868i	0.216765	−	2.89253i
$45$	−7.88560	+	2.43239i	−1.17552	+	0.362599i
$46$	9.32034	+	6.35450i	1.37421	+	0.936920i
$47$	10.8241	−	1.63147i	1.57885	−	0.237974i	0.699674	−	0.714462i	$-0.253329\pi$
$47$	10.8241	−	1.63147i	1.57885	−	0.237974i	0.879181	+	0.476488i	$0.158091\pi$
$48$	22.1693			3.19987
$49$	−0.104552	−	6.99922i	−0.0149360	−	0.999888i
$50$	−9.66862			−1.36735
$51$	−11.8959	+	1.79302i	−1.66576	+	0.251074i
$52$	3.66687	+	2.50003i	0.508503	+	0.346692i
$53$	1.93326	−	0.596331i	0.265553	−	0.0819123i	−0.159119	−	0.987259i	$-0.550865\pi$
$53$	1.93326	−	0.596331i	0.265553	−	0.0819123i	0.424673	+	0.905347i	$0.360389\pi$
$54$	2.81467	−	37.5592i	0.383028	−	5.11116i
$55$	4.26002	+	2.05152i	0.574421	+	0.276627i
$56$	5.29009	−	15.4883i	0.706918	−	2.06971i
$57$	−17.9223	+	8.63090i	−2.37386	+	1.14319i
$58$	1.31135	+	3.34128i	0.172189	+	0.438731i
$59$	−0.0449346	−	0.599610i	−0.00584998	−	0.0780626i	0.993515	−	0.113704i	$-0.0362716\pi$
$59$	−0.0449346	−	0.599610i	−0.00584998	−	0.0780626i	−0.999365	+	0.0356415i	$0.988653\pi$
$60$	−5.74814	+	14.6460i	−0.742082	+	1.89079i
$61$	−6.71464	−	2.07119i	−0.859722	−	0.265189i	−0.166613	−	0.986022i	$-0.553283\pi$
$61$	−6.71464	−	2.07119i	−0.859722	−	0.265189i	−0.693108	+	0.720833i	$0.743759\pi$
$62$	−3.85187	−	4.83009i	−0.489188	−	0.613422i
$63$	−18.4081	−	7.86827i	−2.31921	−	0.991309i
$64$	−0.701239	+	0.879326i	−0.0876549	+	0.109916i
$65$	−0.901111	+	0.614367i	−0.111769	+	0.0762028i
$66$	−26.2124	+	24.3216i	−3.22653	+	2.99378i
$67$	2.94936	+	5.10845i	0.360322	+	0.624096i	0.988014	−	0.154366i	$-0.0493334\pi$
$67$	2.94936	+	5.10845i	0.360322	+	0.624096i	−0.627692	+	0.778462i	$0.716000\pi$
$68$	−8.21240	+	14.2243i	−0.995899	+	1.72495i
$69$	−3.21579	−	14.0893i	−0.387136	−	1.69615i
$70$	5.58497	+	4.73412i	0.667532	+	0.565836i
$71$	2.82382	−	12.3720i	0.335125	−	1.46828i	−0.473937	−	0.880559i	$-0.657168\pi$
$71$	2.82382	−	12.3720i	0.335125	−	1.46828i	0.809063	−	0.587722i	$-0.199975\pi$
$72$	−34.3122	−	31.8370i	−4.04373	−	3.75203i
$73$	12.5062	+	1.88501i	1.46374	+	0.220624i	0.832096	−	0.554632i	$-0.187141\pi$
$73$	12.5062	+	1.88501i	1.46374	+	0.220624i	0.631647	+	0.775256i	$0.282379\pi$
$74$	8.54484	+	1.28793i	0.993318	+	0.149719i
$75$	9.08008	+	8.42508i	1.04848	+	0.972844i
$76$	−6.04334	+	26.4776i	−0.693218	+	3.03719i
$77$	4.66531	+	10.4788i	0.531662	+	1.19417i
$78$	−1.83533	−	8.04110i	−0.207810	−	0.910476i
$79$	−0.0838893	+	0.145301i	−0.00943828	+	0.0163476i	−0.870706	−	0.491804i	$-0.836338\pi$
$79$	−0.0838893	+	0.145301i	−0.00943828	+	0.0163476i	0.861268	+	0.508152i	$0.169671\pi$
$80$	3.71902	+	6.44153i	0.415799	+	0.720185i
$81$	−18.7318	+	17.3805i	−2.08131	+	1.93117i
$82$	15.9598	−	10.8812i	1.76246	−	1.20163i
$83$	−9.64234	+	12.0911i	−1.05838	+	1.32717i	−0.115775	+	0.993276i	$0.536935\pi$
$83$	−9.64234	+	12.0911i	−1.05838	+	1.32717i	−0.942610	+	0.333896i	$0.891636\pi$
$84$	−33.6113	+	18.0865i	−3.66729	+	1.97340i
$85$	−2.51659	−	3.15570i	−0.272962	−	0.342284i
$86$	−20.9106	−	6.45005i	−2.25484	−	0.695527i
$87$	1.68000	−	4.28058i	0.180115	−	0.458927i
$88$	2.00420	+	26.7441i	0.213648	+	2.85093i
$89$	−2.38330	−	6.07254i	−0.252629	−	0.643688i	0.747151	−	0.664654i	$-0.231421\pi$
$89$	−2.38330	−	6.07254i	−0.252629	−	0.643688i	−0.999780	+	0.0209659i	$0.993326\pi$
$90$	18.8650	−	9.08491i	1.98855	−	0.957634i
$91$	−2.63125	−	0.276587i	−0.275830	−	0.0289942i
$92$	−17.7766	−	8.56078i	−1.85334	−	0.892523i
$93$	−0.591463	+	7.89253i	−0.0613319	+	0.818417i
$94$	−26.5405	+	8.18666i	−2.73744	+	0.844390i
$95$	−5.51435	−	3.75962i	−0.565760	−	0.385729i
$96$	−15.8546	+	2.38970i	−1.61815	+	0.243897i
$97$	−2.99453			−0.304048			−0.152024	−	0.988377i	$-0.548579\pi$
$97$	−2.99453			−0.304048			−0.152024	+	0.988377i	$0.548579\pi$
$98$	2.90921	+	17.5214i	0.293874	+	1.76993i
$99$	32.8041			3.29694
$100$	16.7225	−	2.52050i	1.67225	−	0.252050i
$101$	−4.59897	−	3.13553i	−0.457615	−	0.311996i	0.312482	−	0.949924i	$-0.398840\pi$
$101$	−4.59897	−	3.13553i	−0.457615	−	0.311996i	−0.770097	+	0.637927i	$0.779792\pi$
$102$	29.1687	−	8.99735i	2.88813	−	0.890870i
$103$	−0.605793	+	8.08374i	−0.0596905	+	0.796514i	0.884379	+	0.466769i	$0.154582\pi$
$103$	−0.605793	+	8.08374i	−0.0596905	+	0.796514i	−0.944070	+	0.329746i	$0.893037\pi$
$104$	−5.57346	−	2.68404i	−0.546522	−	0.263191i
$105$	−1.11977	−	9.31261i	−0.109279	−	0.908817i
$106$	−4.62500	+	2.22728i	−0.449220	+	0.216333i
$107$	−1.30334	−	3.32086i	−0.125999	−	0.321040i	0.853930	−	0.520388i	$-0.174213\pi$
$107$	−1.30334	−	3.32086i	−0.125999	−	0.321040i	−0.979929	+	0.199348i	$0.936117\pi$
$108$	4.92313	+	65.6946i	0.473728	+	6.32147i
$109$	4.86853	−	12.4048i	0.466321	−	1.18817i	−0.483492	−	0.875349i	$-0.660632\pi$
$109$	4.86853	−	12.4048i	0.466321	−	1.18817i	0.949813	−	0.312818i	$-0.101273\pi$
$110$	−11.4642	−	3.53623i	−1.09307	−	0.337166i
$111$	−6.90243	−	8.65537i	−0.655150	−	0.821532i
$112$	−3.22210	+	17.7541i	−0.304460	+	1.67760i
$113$	6.63873	−	8.32470i	0.624519	−	0.783122i	−0.364453	−	0.931222i	$-0.618744\pi$
$113$	6.63873	−	8.32470i	0.624519	−	0.783122i	0.988972	+	0.148100i	$0.0473156\pi$
$114$	41.7028	−	28.4325i	3.90582	−	2.66294i
$115$	3.55433	−	3.29793i	0.331443	−	0.307534i
$116$	−3.13910	−	5.43708i	−0.291458	−	0.504820i
$117$	−3.78328	+	6.55283i	−0.349764	+	0.605810i
$118$	0.339494	+	1.48742i	0.0312530	+	0.136928i
$119$	0.293038	−	9.78733i	0.0268628	−	0.897203i
$120$	4.88006	−	21.3809i	0.445486	−	1.95180i
$121$	−5.71468	−	5.30245i	−0.519516	−	0.482041i
$122$	17.6302	+	2.65733i	1.59616	+	0.240583i
$123$	−24.4700	−	3.68825i	−2.20638	−	0.332559i
$124$	7.92119	+	7.34979i	0.711343	+	0.660030i
$125$	−2.13819	+	9.36803i	−0.191246	+	0.837902i
$126$	49.1613	+	12.7800i	4.37964	+	1.13853i
$127$	0.326341	+	1.42979i	0.0289581	+	0.126874i	0.987341	−	0.158613i	$-0.0507021\pi$
$127$	0.326341	+	1.42979i	0.0289581	+	0.126874i	−0.958383	+	0.285486i	$0.907845\pi$
$128$	6.35936	−	11.0147i	0.562094	−	0.973575i
$129$	14.0172	+	24.2786i	1.23415	+	2.13761i
$130$	2.02854	−	1.88221i	0.177915	−	0.165081i
$131$	−13.5791	+	9.25807i	−1.18641	+	0.808881i	−0.985324	−	0.170692i	$-0.945400\pi$
$131$	−13.5791	+	9.25807i	−1.18641	+	0.808881i	−0.201086	+	0.979574i	$0.564447\pi$
$132$	38.9956	−	48.8989i	3.39413	−	4.25611i
$133$	−4.30714	−	15.6073i	−0.373476	−	1.35332i
$134$	−9.33177	−	11.7017i	−0.806142	−	1.01087i
$135$	−15.4701	−	4.77188i	−1.33145	−	0.410698i
$136$	8.36418	−	21.3116i	0.717222	−	1.82745i
$137$	1.24389	+	16.5986i	0.106273	+	1.41811i	0.754317	+	0.656510i	$0.227968\pi$
$137$	1.24389	+	16.5986i	0.106273	+	1.41811i	−0.648045	+	0.761602i	$0.724413\pi$
$138$	13.3965	+	34.1337i	1.14039	+	2.90566i
$139$	7.54731	−	3.63459i	0.640154	−	0.308282i	−0.0855035	−	0.996338i	$-0.527250\pi$
$139$	7.54731	−	3.63459i	0.640154	−	0.308282i	0.725658	+	0.688056i	$0.241536\pi$
$140$	−10.8937	−	6.73200i	−0.920684	−	0.568958i
$141$	32.0587	+	15.4386i	2.69983	+	1.30017i
$142$	−2.40623	+	32.1089i	−0.201927	+	2.69452i
$143$	4.14280	−	1.27788i	0.346438	−	0.106862i
$144$	42.6373	+	29.0696i	3.55311	+	2.42247i
$145$	1.52560	−	0.229947i	0.126694	−	0.0190960i
$146$	−32.0908			−2.65585
$147$	12.5358	−	18.9899i	1.03393	−	1.56626i
$148$	−15.1146			−1.24241
$149$	21.2586	−	3.20422i	1.74157	−	0.262500i	0.800168	−	0.599775i	$-0.204743\pi$
$149$	21.2586	−	3.20422i	1.74157	−	0.262500i	0.941406	+	0.337275i	$0.109505\pi$
$150$	−25.9679	−	17.7046i	−2.12027	−	1.44558i
$151$	9.80394	−	3.02411i	0.797833	−	0.246099i	0.131074	−	0.991373i	$-0.458157\pi$
$151$	9.80394	−	3.02411i	0.797833	−	0.246099i	0.666759	+	0.745274i	$0.267681\pi$
$152$	2.82896	−	37.7498i	0.229459	−	3.06191i
$153$	−25.2301	−	12.1502i	−2.03973	−	0.982282i
$154$	−15.6680	−	24.5269i	−1.26256	−	1.97643i
$155$	−2.39248	+	1.15216i	−0.192168	+	0.0925434i
$156$	5.27054	+	13.4291i	0.421981	+	1.07519i
$157$	−0.512100	−	6.83350i	−0.0408701	−	0.545373i	−0.979631	−	0.200805i	$-0.935644\pi$
$157$	−0.512100	−	6.83350i	−0.0408701	−	0.545373i	0.938761	−	0.344568i	$-0.111975\pi$
$158$	0.155529	−	0.396281i	0.0123732	−	0.0315265i
$159$	6.28429	+	1.93845i	0.498377	+	0.153729i
$160$	−3.35404	−	4.20584i	−0.265160	−	0.332501i
$161$	11.7506	−	0.527584i	0.926080	−	0.0415795i
$162$	40.4250	−	50.6913i	3.17609	−	3.98269i
$163$	1.80767	−	1.23245i	0.141588	−	0.0965328i	−0.490455	−	0.871467i	$-0.663169\pi$
$163$	1.80767	−	1.23245i	0.141588	−	0.0965328i	0.632042	+	0.774934i	$0.282217\pi$
$164$	−24.7668	+	22.9802i	−1.93396	+	1.79445i
$165$	7.68491	+	13.3107i	0.598270	+	1.03623i
$166$	19.6200	−	33.9829i	1.52281	−	2.63758i
$167$	1.59544	+	6.99009i	0.123459	+	0.540909i	0.998393	+	0.0566672i	$0.0180474\pi$
$167$	1.59544	+	6.99009i	0.123459	+	0.540909i	−0.874934	+	0.484242i	$0.839095\pi$
$168$	42.5693	−	31.9114i	3.28430	−	2.46202i
$169$	−0.222521	+	0.974928i	−0.0171170	+	0.0749945i
$170$	7.50747	+	6.96591i	0.575797	+	0.534261i
$171$	−45.7864	−	6.90119i	−3.50137	−	0.527747i
$172$	37.8475	+	5.70459i	2.88585	+	0.434971i
$173$	5.96962	+	5.53900i	0.453862	+	0.421122i	0.873691	−	0.486481i	$-0.161720\pi$
$173$	5.96962	+	5.53900i	0.453862	+	0.421122i	−0.419829	+	0.907603i	$0.637910\pi$
$174$	−2.59633	+	11.3752i	−0.196827	+	0.862355i
$175$	−8.06684	+	6.04718i	−0.609796	+	0.457124i
$176$	−6.57940	−	28.8263i	−0.495941	−	2.17286i
$177$	0.977286	−	1.69271i	0.0734573	−	0.127232i
$178$	8.27611	+	14.3346i	0.620320	+	1.07443i
$179$	0.394261	−	0.365821i	0.0294685	−	0.0273427i	−0.665301	−	0.746575i	$-0.731697\pi$
$179$	0.394261	−	0.365821i	0.0294685	−	0.0273427i	0.694770	+	0.719232i	$0.255506\pi$
$180$	−30.2598	+	20.6308i	−2.25543	+	1.53773i
$181$	−3.62675	+	4.54779i	−0.269574	+	0.338035i	−0.898131	−	0.439729i	$-0.855075\pi$
$181$	−3.62675	+	4.54779i	−0.269574	+	0.338035i	0.628557	+	0.777764i	$0.283646\pi$
$182$	6.70638	−	0.301105i	0.497110	−	0.0223194i
$183$	−14.2415	−	17.8582i	−1.05276	−	1.32012i
$184$	26.2802	+	8.10637i	1.93740	+	0.597609i
$185$	1.35699	−	3.45755i	0.0997679	−	0.254204i
$186$	−1.50074	−	20.0259i	−0.110039	−	1.46837i
$187$	5.86190	+	14.9359i	0.428664	+	1.09222i
$188$	43.7692	−	21.0781i	3.19220	−	1.53728i
$189$	−21.1428	−	33.0973i	−1.53791	−	2.40747i
$190$	15.2572	+	7.34748i	1.10687	+	0.533042i
$191$	0.167158	−	2.23057i	0.0120952	−	0.161399i	−0.987886	−	0.155184i	$-0.950403\pi$
$191$	0.167158	−	2.23057i	0.0120952	−	0.161399i	0.999981	−	0.00621436i	$-0.00197811\pi$
$192$	−3.49355	+	1.07762i	−0.252126	+	0.0777704i
$193$	14.6677	+	10.0002i	1.05580	+	0.719833i	0.961248	−	0.275687i	$-0.0889052\pi$
$193$	14.6677	+	10.0002i	1.05580	+	0.719833i	0.0945537	+	0.995520i	$0.469858\pi$
$194$	7.51323	−	1.13244i	0.539418	−	0.0813042i
$195$	−3.54519			−0.253876
$196$	−9.59929	−	29.5459i	−0.685663	−	2.11042i
$197$	22.1971			1.58148			0.790740	−	0.612152i	$-0.209696\pi$
$197$	22.1971			1.58148			0.790740	+	0.612152i	$0.209696\pi$
$198$	−82.3051	+	12.4055i	−5.84917	+	0.881620i
$199$	−15.2278	−	10.3822i	−1.07947	−	0.735972i	−0.113220	−	0.993570i	$-0.536117\pi$
$199$	−15.2278	−	10.3822i	−1.07947	−	0.735972i	−0.966252	+	0.257598i	$0.917069\pi$
$200$	−22.5251	+	6.94807i	−1.59276	+	0.491303i
$201$	−1.43292	+	19.1209i	−0.101070	+	1.34869i
$202$	12.7245	+	6.12781i	0.895294	+	0.431151i
$203$	3.18388	+	1.96756i	0.223465	+	0.138095i
$204$	−48.1035	+	23.1654i	−3.36792	+	1.62190i
$205$	−3.03330	−	7.72872i	−0.211855	−	0.539797i
$206$	−1.53709	−	20.5111i	−0.107094	−	1.42908i
$207$	12.2899	−	31.3140i	0.854204	−	2.17648i
$208$	6.51703	+	2.01024i	0.451875	+	0.139385i
$209$	16.5415	+	20.7424i	1.14420	+	1.43478i
$210$	6.33123	+	22.9417i	0.436896	+	1.58313i
$211$	13.9079	−	17.4400i	0.957461	−	1.20062i	−0.0221582	−	0.999754i	$-0.507054\pi$
$211$	13.9079	−	17.4400i	0.957461	−	1.20062i	0.979619	−	0.200864i	$-0.0643748\pi$
$212$	7.41859	−	5.05791i	0.509511	−	0.347379i
$213$	30.2390	−	28.0577i	2.07194	−	1.92248i
$214$	4.52591	+	7.83911i	0.309385	+	0.535871i
$215$	−4.70292	+	8.14570i	−0.320737	+	0.555532i
$216$	−20.4334	−	89.5248i	−1.39032	−	6.09139i
$217$	−6.23468	−	1.62077i	−0.423238	−	0.110025i
$218$	−7.52397	+	32.9647i	−0.509588	+	2.23265i
$219$	30.1374	+	27.9634i	2.03650	+	1.88959i
$220$	20.7498	+	3.12753i	1.39895	+	0.210858i
$221$	−3.65959	−	0.551594i	−0.246170	−	0.0371042i
$222$	20.5913	+	19.1059i	1.38200	+	1.28231i
$223$	−5.96163	+	26.1196i	−0.399220	+	1.74910i	0.231259	+	0.972892i	$0.425715\pi$
$223$	−5.96163	+	26.1196i	−0.399220	+	1.74910i	−0.630479	+	0.776206i	$0.717142\pi$
$224$	0.390554	−	13.0443i	0.0260950	−	0.871560i
$225$	6.41590	+	28.1099i	0.427726	+	1.87399i
$226$	−13.5083	+	23.3971i	−0.898561	+	1.55635i
$227$	−1.83811	−	3.18370i	−0.122000	−	0.211310i	0.798556	−	0.601920i	$-0.205597\pi$
$227$	−1.83811	−	3.18370i	−0.122000	−	0.211310i	−0.920556	+	0.390610i	$0.872264\pi$
$228$	−64.7154	+	60.0471i	−4.28588	+	3.97672i
$229$	17.0595	−	11.6310i	1.12733	−	0.768597i	0.151784	−	0.988414i	$-0.451498\pi$
$229$	17.0595	−	11.6310i	1.12733	−	0.768597i	0.975541	+	0.219817i	$0.0705459\pi$
$230$	−7.67058	+	9.61860i	−0.505783	+	0.634232i
$231$	−6.65810	+	36.6867i	−0.438071	+	2.41381i
$232$	5.45619	+	6.84184i	0.358216	+	0.449189i
$233$	19.5967	+	6.04477i	1.28382	+	0.396006i	0.860257	−	0.509860i	$-0.170303\pi$
$233$	19.5967	+	6.04477i	1.28382	+	0.396006i	0.423564	+	0.905866i	$0.360779\pi$
$234$	7.01412	−	17.8717i	0.458527	−	1.16831i
$235$	0.892149	+	11.9049i	0.0581974	+	0.776590i
$236$	−0.974930	−	2.48408i	−0.0634625	−	0.161700i
$237$	−0.491375	+	0.236634i	−0.0319182	+	0.0153710i
$238$	2.96604	+	24.6671i	0.192260	+	1.59893i
$239$	−4.98804	−	2.40211i	−0.322649	−	0.155380i	0.265547	−	0.964098i	$-0.414447\pi$
$239$	−4.98804	−	2.40211i	−0.322649	−	0.155380i	−0.588196	+	0.808718i	$0.700162\pi$
$240$	−1.80684	+	24.1107i	−0.116631	+	1.55634i
$241$	4.44134	−	1.36997i	0.286092	−	0.0882476i	−0.148388	−	0.988929i	$-0.547408\pi$
$241$	4.44134	−	1.36997i	0.286092	−	0.0882476i	0.434480	+	0.900682i	$0.356932\pi$
$242$	16.3433	+	11.1427i	1.05059	+	0.716277i
$243$	−38.1008	+	5.74277i	−2.44417	+	0.368399i
$244$	−31.1852			−1.99643
$245$	7.62065	+	0.456742i	0.486865	+	0.0291802i
$246$	62.7896			4.00332
$247$	−6.05115	+	0.912065i	−0.385026	+	0.0580333i
$248$	−12.4447	−	8.48468i	−0.790242	−	0.538778i
$249$	−48.0379	+	14.8177i	−3.04428	+	0.939035i
$250$	1.82200	−	24.3129i	0.115233	−	1.53768i
$251$	25.3129	+	12.1900i	1.59773	+	0.769428i	0.999491	−	0.0318869i	$-0.0101516\pi$
$251$	25.3129	+	12.1900i	1.59773	+	0.769428i	0.598243	+	0.801315i	$0.295866\pi$
$252$	−88.3591	−	9.28796i	−5.56610	−	0.585086i
$253$	−17.3656	+	8.36283i	−1.09176	+	0.525766i
$254$	−1.35949	−	3.46392i	−0.0853020	−	0.217346i
$255$	−0.980494	−	13.0838i	−0.0614009	−	0.819338i
$256$	−10.9683	+	27.9468i	−0.685520	+	1.74668i
$257$	0.935287	+	0.288498i	0.0583416	+	0.0179960i	0.323789	−	0.946129i	$-0.395043\pi$
$257$	0.935287	+	0.288498i	0.0583416	+	0.0179960i	−0.265447	+	0.964125i	$0.585520\pi$
$258$	−44.3504	−	55.6137i	−2.76114	−	3.46236i
$259$	7.93476	−	4.26976i	0.493042	−	0.265310i
$260$	−3.01781	+	3.78421i	−0.187157	+	0.234687i
$261$	8.84401	−	6.02974i	0.547430	−	0.373232i
$262$	30.5686	−	28.3636i	1.88854	−	1.75231i
$263$	−3.62158	−	6.27275i	−0.223316	−	0.386795i	0.732497	−	0.680770i	$-0.238355\pi$
$263$	−3.62158	−	6.27275i	−0.223316	−	0.386795i	−0.955813	+	0.293976i	$0.905021\pi$
$264$	−43.5894	+	75.4991i	−2.68274	+	4.64665i
$265$	0.490986	+	2.15115i	0.0301610	+	0.132144i
$266$	16.7087	+	37.5296i	1.02448	+	2.30109i
$267$	4.71865	−	20.6737i	0.288776	−	1.26521i
$268$	19.1904	+	17.8060i	1.17224	+	1.08768i
$269$	4.92602	+	0.742479i	0.300345	+	0.0452697i	0.297486	−	0.954726i	$-0.403852\pi$
$269$	4.92602	+	0.742479i	0.300345	+	0.0452697i	0.00285904	+	0.999996i	$0.499090\pi$
$270$	40.6188	+	6.12229i	2.47198	+	0.372591i
$271$	−19.3927	−	17.9938i	−1.17802	−	1.09305i	−0.993916	−	0.110141i	$-0.964870\pi$
$271$	−19.3927	−	17.9938i	−1.17802	−	1.09305i	−0.184108	−	0.982906i	$-0.558940\pi$
$272$	−5.61651	+	24.6076i	−0.340551	+	1.49205i
$273$	−6.56053	−	5.56106i	−0.397061	−	0.336570i
$274$	−9.39797	−	41.1752i	−0.567752	−	2.48749i
$275$	8.26015	−	14.3070i	0.498106	−	0.862744i
$276$	−32.0684	−	55.5440i	−1.93029	−	3.34336i
$277$	11.0643	−	10.2661i	0.664787	−	0.616832i	−0.273836	−	0.961776i	$-0.588293\pi$
$277$	11.0643	−	10.2661i	0.664787	−	0.616832i	0.938623	+	0.344944i	$0.112102\pi$
$278$	−17.5616	+	11.9733i	−1.05328	+	0.718111i
$279$	−11.4866	+	14.4038i	−0.687688	+	0.862333i
$280$	16.4134	+	7.01566i	0.980889	+	0.419266i
$281$	−9.11755	−	11.4330i	−0.543907	−	0.682038i	0.431585	−	0.902072i	$-0.357955\pi$
$281$	−9.11755	−	11.4330i	−0.543907	−	0.682038i	−0.975492	+	0.220034i	$0.929383\pi$
$282$	−86.2732	−	26.6118i	−5.13750	−	1.58471i
$283$	3.10860	−	7.92059i	0.184787	−	0.470830i	−0.808220	−	0.588880i	$-0.799569\pi$
$283$	3.10860	−	7.92059i	0.184787	−	0.470830i	0.993008	+	0.118050i	$0.0376643\pi$
$284$	−4.20873	−	56.1616i	−0.249742	−	3.33258i
$285$	−7.92600	−	20.1951i	−0.469496	−	1.19626i
$286$	−9.91096	+	4.77287i	−0.586048	+	0.282226i
$287$	6.51018	−	19.0605i	0.384284	−	1.12510i
$288$	−33.6260	−	16.1934i	−1.98143	−	0.954206i
$289$	−0.246847	+	3.29394i	−0.0145204	+	0.193761i
$290$	−3.74074	+	1.15387i	−0.219664	+	0.0677574i
$291$	−8.04267	−	5.48340i	−0.471470	−	0.321443i
$292$	55.5030	−	8.36573i	3.24807	−	0.489567i
$293$	−9.81870			−0.573614			−0.286807	−	0.957988i	$-0.592594\pi$
$293$	−9.81870			−0.573614			−0.286807	+	0.957988i	$0.592594\pi$
$294$	−24.2707	+	52.3860i	−1.41549	+	3.05522i
$295$	0.655779			0.0381809
$296$	20.8326	−	3.14000i	1.21087	−	0.182509i
$297$	53.1730	+	36.2527i	3.08541	+	2.10360i
$298$	−52.1259	+	16.0787i	−3.01957	+	0.931414i
$299$	0.332235	−	4.43337i	0.0192137	−	0.256388i
$300$	49.5284	+	23.8516i	2.85952	+	1.37707i
$301$	−21.4805	+	7.69689i	−1.23811	+	0.443641i
$302$	−23.4543	+	11.2950i	−1.34964	+	0.649955i
$303$	−6.61029	−	16.8427i	−0.379751	−	0.967590i
$304$	3.11887	+	41.6185i	0.178880	+	2.38698i
$305$	2.79982	−	7.13382i	0.160317	−	0.408481i
$306$	67.8967	+	20.9434i	3.88139	+	1.19725i
$307$	−13.6740	−	17.1467i	−0.780419	−	0.978614i	−0.999995	−	0.00301884i	$-0.999039\pi$
$307$	−13.6740	−	17.1467i	−0.780419	−	0.978614i	0.219577	−	0.975595i	$-0.429532\pi$
$308$	33.4926	+	38.3362i	1.90842	+	2.18441i
$309$	−16.4295	+	20.6019i	−0.934642	+	1.17200i
$310$	5.56698	−	3.79551i	0.316183	−	0.215570i
$311$	−6.43480	+	5.97062i	−0.364884	+	0.338563i	−0.841213	−	0.540705i	$-0.818158\pi$
$311$	−6.43480	+	5.97062i	−0.364884	+	0.338563i	0.476329	+	0.879267i	$0.341967\pi$
$312$	−10.0543	−	17.4145i	−0.569212	−	0.985905i
$313$	6.02896	−	10.4425i	0.340777	−	0.590243i	−0.643800	−	0.765193i	$-0.722643\pi$
$313$	6.02896	−	10.4425i	0.340777	−	0.590243i	0.984577	+	0.174951i	$0.0559766\pi$
$314$	3.86907	+	16.9515i	0.218344	+	0.956629i
$315$	10.0576	−	19.3788i	0.566681	−	1.09187i
$316$	−0.165690	+	0.725937i	−0.00932081	+	0.0408372i
$317$	−8.26423	−	7.66809i	−0.464165	−	0.430683i	0.413102	−	0.910685i	$-0.364445\pi$
$317$	−8.26423	−	7.66809i	−0.464165	−	0.430683i	−0.877267	+	0.480002i	$0.840636\pi$
$318$	−16.5003	−	2.48702i	−0.925289	−	0.139465i
$319$	−6.06453	−	0.914080i	−0.339548	−	0.0511787i
$320$	−0.899175	−	0.834312i	−0.0502654	−	0.0466395i
$321$	2.58046	−	11.3057i	0.144027	−	0.631025i
$322$	−29.2827	+	5.76743i	−1.63186	+	0.321406i
$323$	−5.03961	−	22.0800i	−0.280411	−	1.22856i
$324$	−56.7028	+	98.2120i	−3.15015	+	5.45622i
$325$	1.90528	+	3.30004i	0.105686	+	0.183053i
$326$	−4.06935	+	3.77580i	−0.225380	+	0.209122i
$327$	35.7909	−	24.4018i	1.97924	−	1.34942i
$328$	29.3622	−	36.8190i	1.62126	−	2.03299i
$329$	−17.0233	+	23.4300i	−0.938525	+	1.29174i
$330$	−24.3150	−	30.4901i	−1.33850	−	1.67842i
$331$	27.3117	+	8.42456i	1.50119	+	0.463055i	0.933010	−	0.359850i	$-0.117172\pi$
$331$	27.3117	+	8.42456i	1.50119	+	0.463055i	0.568179	+	0.822905i	$0.307648\pi$
$332$	−25.0750	+	63.8901i	−1.37617	+	3.50643i
$333$	−1.92575	−	25.6973i	−0.105530	−	1.40821i
$334$	−6.64638	−	16.9347i	−0.363674	−	0.926625i
$335$	−5.79616	+	2.79129i	−0.316678	+	0.152504i
$336$	−41.1641	+	41.7836i	−2.24569	+	2.27948i
$337$	−1.44397	−	0.695379i	−0.0786580	−	0.0378797i	0.394141	−	0.919050i	$-0.371042\pi$
$337$	−1.44397	−	0.695379i	−0.0786580	−	0.0378797i	−0.472799	+	0.881170i	$0.656756\pi$
$338$	0.189615	−	2.53023i	0.0103137	−	0.137626i
$339$	33.0740	−	10.2020i	1.79633	−	0.554095i
$340$	−14.8006	−	10.0908i	−0.802673	−	0.547253i
$341$	10.4380	−	1.57328i	0.565249	−	0.0851976i
$342$	117.487			6.35299
$343$	13.3859	+	12.7991i	0.722771	+	0.691088i
$344$	−53.3507			−2.87648
$345$	15.5852	−	2.34908i	0.839077	−	0.126470i
$346$	−17.0724	−	11.6397i	−0.917817	−	0.625757i
$347$	11.6572	−	3.59576i	0.625790	−	0.193031i	0.0343895	−	0.999409i	$-0.489051\pi$
$347$	11.6572	−	3.59576i	0.625790	−	0.193031i	0.591401	+	0.806378i	$0.298575\pi$
$348$	1.52510	−	20.3510i	0.0817538	−	1.09093i
$349$	2.83828	+	1.36684i	0.151929	+	0.0731654i	0.508303	−	0.861178i	$-0.330273\pi$
$349$	2.83828	+	1.36684i	0.151929	+	0.0731654i	−0.356374	+	0.934343i	$0.615987\pi$
$350$	17.9527	−	18.2229i	0.959614	−	0.974056i
$351$	−13.3741	+	6.44064i	−0.713858	+	0.343776i
$352$	7.81259	+	19.9061i	0.416412	+	1.06100i
$353$	1.92675	+	25.7106i	0.102550	+	1.36844i	0.776712	+	0.629856i	$0.216886\pi$
$353$	1.92675	+	25.7106i	0.102550	+	1.36844i	−0.674162	+	0.738584i	$0.735495\pi$
$354$	−1.81187	+	4.61656i	−0.0962997	+	0.245368i
$355$	13.2252	+	4.07943i	0.701920	+	0.216514i
$356$	−18.0509	−	22.6351i	−0.956696	−	1.19966i
$357$	18.7090	−	25.7501i	0.990187	−	1.36284i
$358$	−0.850854	+	1.06694i	−0.0449690	+	0.0563894i
$359$	5.63201	−	3.83984i	0.297246	−	0.202659i	−0.405509	−	0.914091i	$-0.632906\pi$
$359$	5.63201	−	3.83984i	0.297246	−	0.202659i	0.702755	+	0.711432i	$0.251953\pi$
$360$	37.4214	−	34.7220i	1.97228	−	1.83001i
$361$	−9.22416	−	15.9767i	−0.485482	−	0.840879i
$362$	7.37962	−	12.7819i	0.387864	−	0.671801i
$363$	−5.63891	−	24.7057i	−0.295966	−	1.29671i
$364$	−11.5206	+	2.26906i	−0.603843	+	0.118931i
$365$	−3.06936	+	13.4477i	−0.160658	+	0.703887i
$366$	42.4851	+	39.4204i	2.22073	+	2.06054i
$367$	−22.5755	−	3.40272i	−1.17843	−	0.177620i	−0.469524	−	0.882920i	$-0.655574\pi$
$367$	−22.5755	−	3.40272i	−1.17843	−	0.177620i	−0.708910	+	0.705299i	$0.750813\pi$
$368$	−29.9818	−	4.51903i	−1.56291	−	0.235571i
$369$	−42.2258	−	39.1798i	−2.19819	−	2.03962i
$370$	−2.09713	+	9.18813i	−0.109025	+	0.477668i
$371$	−2.46575	+	4.75097i	−0.128015	+	0.246658i
$372$	7.81615	+	34.2448i	0.405249	+	1.77551i
$373$	7.99078	−	13.8404i	0.413747	−	0.716630i	−0.581549	−	0.813511i	$-0.697553\pi$
$373$	7.99078	−	13.8404i	0.413747	−	0.716630i	0.995296	+	0.0968808i	$0.0308865\pi$
$374$	−20.3557	−	35.2571i	−1.05257	−	1.82310i
$375$	−22.8969	+	21.2452i	−1.18239	+	1.09710i
$376$	−55.9486	+	38.1451i	−2.88533	+	1.96719i
$377$	0.882012	−	1.10601i	0.0454259	−	0.0569623i
$378$	65.5633	+	75.0450i	3.37221	+	3.85990i
$379$	−6.26257	−	7.85302i	−0.321687	−	0.403382i	0.594525	−	0.804077i	$-0.297340\pi$
$379$	−6.26257	−	7.85302i	−0.321687	−	0.403382i	−0.916212	+	0.400695i	$0.868769\pi$
$380$	−28.3036	−	8.73052i	−1.45195	−	0.447866i
$381$	−1.74167	+	4.43771i	−0.0892285	+	0.227351i
$382$	0.424136	+	5.65970i	0.0217007	+	0.289575i
$383$	9.38272	+	23.9068i	0.479435	+	1.22158i	0.942186	+	0.335091i	$0.108767\pi$
$383$	9.38272	+	23.9068i	0.479435	+	1.22158i	−0.462751	+	0.886488i	$0.653138\pi$
$384$	37.2495	−	17.9384i	1.90088	−	0.915415i
$385$	−11.7766	+	4.21980i	−0.600193	+	0.215061i
$386$	−40.5827	−	19.5436i	−2.06561	−	0.994744i
$387$	−4.87662	+	65.0740i	−0.247893	+	3.30790i
$388$	−12.6994	+	3.91723i	−0.644712	+	0.198867i
$389$	15.9688	+	10.8873i	0.809650	+	0.552010i	0.895896	−	0.444264i	$-0.146535\pi$
$389$	15.9688	+	10.8873i	0.809650	+	0.552010i	−0.0862457	+	0.996274i	$0.527487\pi$
$390$	8.89483	−	1.34068i	0.450407	−	0.0678880i
$391$	16.4536			0.832092
$392$	19.3689	+	38.7292i	0.978276	+	1.95612i
$393$	−53.4235			−2.69486
$394$	−55.6923	+	8.39426i	−2.80574	+	0.422897i
$395$	−0.151187	−	0.103078i	−0.00760705	−	0.00518640i
$396$	139.118	−	42.9121i	6.99092	−	2.15641i
$397$	−0.403725	+	5.38733i	−0.0202624	+	0.270382i	0.977866	+	0.209231i	$0.0670962\pi$
$397$	−0.403725	+	5.38733i	−0.0202624	+	0.270382i	−0.998129	+	0.0611510i	$0.980523\pi$
$398$	42.1326	+	20.2900i	2.11192	+	1.01705i
$399$	17.0111	−	49.8048i	0.851618	−	2.49336i
$400$	23.4144	−	11.2758i	1.17072	−	0.563790i
$401$	−4.48114	−	11.4178i	−0.223778	−	0.570176i	0.774255	−	0.632874i	$-0.218125\pi$
$401$	−4.48114	−	11.4178i	−0.223778	−	0.570176i	−0.998033	+	0.0626978i	$0.980030\pi$
$402$	−3.63578	−	48.5161i	−0.181336	−	2.41976i
$403$	−0.889537	+	2.26650i	−0.0443110	+	0.112903i
$404$	−23.6053	−	7.28126i	−1.17441	−	0.362256i
$405$	−17.3759	−	21.7886i	−0.863413	−	1.08269i
$406$	−8.73239	−	3.73252i	−0.433381	−	0.185242i
$407$	−9.20587	+	11.5438i	−0.456318	+	0.572205i
$408$	61.4890	−	41.9225i	3.04416	−	2.07547i
$409$	3.24327	−	3.00932i	0.160369	−	0.148801i	−0.595907	−	0.803054i	$-0.703207\pi$
$409$	3.24327	−	3.00932i	0.160369	−	0.148801i	0.756276	+	0.654253i	$0.227017\pi$
$410$	10.5333	+	18.2442i	0.520201	+	0.901015i
$411$	−27.0535	+	46.8581i	−1.33445	+	2.31134i
$412$	8.00551	+	35.0744i	0.394403	+	1.72799i
$413$	1.21355	+	1.02867i	0.0597148	+	0.0506175i
$414$	−18.9931	+	83.2142i	−0.933459	+	4.08975i
$415$	−12.3640	−	11.4722i	−0.606927	−	0.563146i
$416$	−4.87740	−	0.735150i	−0.239134	−	0.0360437i
$417$	26.9259	+	4.05843i	1.31857	+	0.198742i
$418$	−49.3466	−	45.7869i	−2.41362	−	2.23951i
$419$	−1.98639	+	8.70293i	−0.0970414	+	0.425166i	−0.999989	−	0.00458355i	$-0.998541\pi$
$419$	−1.98639	+	8.70293i	−0.0970414	+	0.425166i	0.902948	+	0.429750i	$0.141398\pi$
$420$	−16.9309	−	38.0286i	−0.826143	−	1.85561i
$421$	4.00139	+	17.5312i	0.195016	+	0.854420i	0.973850	+	0.227191i	$0.0729540\pi$
$421$	4.00139	+	17.5312i	0.195016	+	0.854420i	−0.778835	+	0.627229i	$0.784189\pi$
$422$	−28.2995	+	49.0162i	−1.37760	+	2.38607i
$423$	41.4131	+	71.7296i	2.01357	+	3.48761i
$424$	−9.17435	+	8.51255i	−0.445546	+	0.413406i
$425$	−11.6521	+	7.94426i	−0.565209	+	0.385353i
$426$	−65.2587	+	81.8318i	−3.16179	+	3.96476i
$427$	16.3715	−	8.80961i	0.792270	−	0.426327i
$428$	−9.87141	−	12.3784i	−0.477153	−	0.598330i
$429$	13.4667	+	4.15392i	0.650177	+	0.200553i
$430$	8.71912	−	22.2160i	0.420473	−	1.07135i
$431$	−0.147751	−	1.97160i	−0.00711690	−	0.0949684i	0.992514	−	0.122130i	$-0.0389723\pi$
$431$	−0.147751	−	1.97160i	−0.00711690	−	0.0949684i	−0.999631	+	0.0271611i	$0.991353\pi$
$432$	36.9863	+	94.2394i	1.77950	+	4.53410i
$433$	11.5885	−	5.58072i	0.556907	−	0.268192i	−0.134188	−	0.990956i	$-0.542843\pi$
$433$	11.5885	−	5.58072i	0.556907	−	0.268192i	0.691096	+	0.722763i	$0.257128\pi$
$434$	16.2557	+	1.70873i	0.780297	+	0.0820217i
$435$	4.51850	+	2.17599i	0.216645	+	0.104331i
$436$	4.41962	−	58.9758i	0.211662	−	2.82443i
$437$	25.9974	−	8.01914i	1.24362	−	0.383607i
$438$	−86.1892	−	58.7628i	−4.11828	−	2.80780i
$439$	0.284644	−	0.0429032i	0.0135853	−	0.00204766i	−0.142246	−	0.989831i	$-0.545432\pi$
$439$	0.284644	−	0.0429032i	0.0135853	−	0.00204766i	0.155831	+	0.987784i	$0.450194\pi$
$440$	−29.2494			−1.39441
$441$	49.0101	−	20.0849i	2.33381	−	0.956423i
$442$	9.39045			0.446658
$443$	−32.8304	+	4.94839i	−1.55982	+	0.235105i	−0.871534	−	0.490335i	$-0.836875\pi$
$443$	−32.8304	+	4.94839i	−1.55982	+	0.235105i	−0.688286	+	0.725440i	$0.741636\pi$
$444$	−40.5946	−	27.6769i	−1.92653	−	1.31349i
$445$	6.79855	−	2.09707i	0.322282	−	0.0994108i
$446$	5.08003	−	67.7883i	0.240546	−	3.20987i
$447$	62.9636	+	30.3217i	2.97808	+	1.43417i
$448$	−0.355244	−	2.95440i	−0.0167837	−	0.139582i
$449$	26.4234	−	12.7248i	1.24700	−	0.600522i	0.310291	−	0.950642i	$-0.399573\pi$
$449$	26.4234	−	12.7248i	1.24700	−	0.600522i	0.936705	+	0.350120i	$0.113859\pi$
$450$	−26.7277	−	68.1010i	−1.25995	−	3.21031i
$451$	2.46644	+	32.9123i	0.116140	+	1.54978i
$452$	17.2641	−	43.9882i	0.812035	−	2.06903i
$453$	31.8689	+	9.83026i	1.49733	+	0.461866i
$454$	5.81577	+	7.29275i	0.272948	+	0.342266i
$455$	0.515260	−	2.83913i	0.0241557	−	0.133100i
$456$	76.7233	−	96.2079i	3.59290	−	4.50535i
$457$	−18.9559	+	12.9239i	−0.886721	+	0.604556i	−0.918710	−	0.394932i	$-0.870768\pi$
$457$	−18.9559	+	12.9239i	−0.886721	+	0.604556i	0.0319896	+	0.999488i	$0.489816\pi$
$458$	−38.4036	+	35.6334i	−1.79448	+	1.66504i
$459$	−27.4686	−	47.5769i	−1.28212	−	2.22070i
$460$	10.7593	−	18.6356i	0.501653	−	0.868889i
$461$	−4.46418	−	19.5589i	−0.207918	−	0.910947i	−0.965950	−	0.258730i	$-0.916696\pi$
$461$	−4.46418	−	19.5589i	−0.207918	−	0.910947i	0.758032	−	0.652217i	$-0.226161\pi$
$462$	2.83131	−	94.5643i	0.131724	−	4.39953i
$463$	−2.59767	+	11.3811i	−0.120724	+	0.528927i	0.878011	+	0.478641i	$0.158870\pi$
$463$	−2.59767	+	11.3811i	−0.120724	+	0.528927i	−0.998735	+	0.0502859i	$0.983987\pi$
$464$	−7.07239	−	6.56222i	−0.328327	−	0.304643i
$465$	−8.53546	−	1.28651i	−0.395822	−	0.0596606i
$466$	−51.4538	−	7.75541i	−2.38355	−	0.359262i
$467$	−9.35248	−	8.67783i	−0.432781	−	0.401562i	0.433472	−	0.901167i	$-0.357288\pi$
$467$	−9.35248	−	8.67783i	−0.432781	−	0.401562i	−0.866254	+	0.499605i	$0.833479\pi$
$468$	−7.47238	+	32.7387i	−0.345411	+	1.51334i
$469$	−15.1045	−	3.92658i	−0.697463	−	0.181313i
$470$	−6.74045	−	29.5318i	−0.310914	−	1.36220i
$471$	11.1377	−	19.2911i	0.513199	−	0.888887i
$472$	1.85981	+	3.22129i	0.0856049	+	0.148272i
$473$	27.4088	−	25.4316i	1.26026	−	1.16935i
$474$	1.14337	−	0.779534i	0.0525165	−	0.0358052i
$475$	−14.5390	+	18.2313i	−0.667094	+	0.836509i
$476$	−11.5604	−	41.8900i	−0.529869	−	1.92003i
$477$	9.54451	+	11.9684i	0.437013	+	0.547997i
$478$	13.4233	+	4.14055i	0.613969	+	0.189384i
$479$	1.35702	−	3.45762i	0.0620036	−	0.157983i	−0.896514	−	0.443015i	$-0.853909\pi$
$479$	1.35702	−	3.45762i	0.0620036	−	0.157983i	0.958518	+	0.285032i	$0.0920042\pi$
$480$	−1.30678	−	17.4377i	−0.0596459	−	0.795920i
$481$	−1.24424	−	3.17027i	−0.0567325	−	0.144552i
$482$	−10.6252	+	5.11682i	−0.483964	+	0.233065i
$483$	32.5259	+	20.1001i	1.47998	+	0.914587i
$484$	−31.1714	−	15.0114i	−1.41688	−	0.682335i
$485$	0.244060	−	3.25675i	0.0110822	−	0.147881i
$486$	93.4226	−	28.8171i	4.23774	−	1.30717i
$487$	−16.5943	−	11.3138i	−0.751957	−	0.512676i	0.125639	−	0.992076i	$-0.459902\pi$
$487$	−16.5943	−	11.3138i	−0.751957	−	0.512676i	−0.877596	+	0.479400i	$0.840854\pi$
$488$	42.9829	−	6.47863i	1.94574	−	0.293274i
$489$	7.11181			0.321607
$490$	−19.2928	+	1.73593i	−0.871561	+	0.0784214i
$491$	0.664092			0.0299701			0.0149850	−	0.999888i	$-0.495230\pi$
$491$	0.664092			0.0299701			0.0149850	+	0.999888i	$0.495230\pi$
$492$	−108.598	+	16.3686i	−4.89599	+	0.737952i
$493$	4.32574	+	2.94924i	0.194822	+	0.132827i
$494$	14.8373	−	4.57672i	0.667564	−	0.205916i
$495$	−2.67360	+	35.6767i	−0.120169	+	1.60355i
$496$	14.9610	+	7.20485i	0.671770	+	0.323507i
$497$	18.0747	+	28.2945i	0.810763	+	1.26918i
$498$	114.923	−	55.3439i	5.14981	−	2.48002i
$499$	14.3134	+	36.4699i	0.640756	+	1.63262i	0.767776	+	0.640718i	$0.221363\pi$
$499$	14.3134	+	36.4699i	0.640756	+	1.63262i	−0.127020	+	0.991900i	$0.540541\pi$
$500$	3.18685	+	42.5255i	0.142520	+	1.90180i
$501$	−8.51482	+	21.6954i	−0.380414	+	0.969279i
$502$	−68.1195	−	21.0121i	−3.04032	−	0.937816i
$503$	−11.7241	−	14.7016i	−0.522752	−	0.655510i	0.448439	−	0.893813i	$-0.351980\pi$
$503$	−11.7241	−	14.7016i	−0.522752	−	0.655510i	−0.971191	+	0.238304i	$0.923409\pi$
$504$	123.716	−	5.55463i	5.51074	−	0.247423i
$505$	3.78492	−	4.74614i	0.168427	−	0.211201i
$506$	40.4075	−	27.5493i	1.79633	−	1.22472i
$507$	−2.38288	+	2.21099i	−0.105827	+	0.0981933i
$508$	3.25433	+	5.63666i	0.144387	+	0.250086i
$509$	3.68251	−	6.37830i	0.163224	−	0.282713i	−0.772799	−	0.634651i	$-0.781144\pi$
$509$	3.68251	−	6.37830i	0.163224	−	0.282713i	0.936023	+	0.351938i	$0.114477\pi$
$510$	7.40792	+	32.4562i	0.328028	+	1.43719i
$511$	−26.7744	+	20.0710i	−1.18443	+	0.887889i
$512$	11.2904	−	49.4664i	0.498970	−	2.18613i
$513$	−66.5896	−	61.7862i	−2.94000	−	2.72793i
$514$	−2.45572	−	0.370141i	−0.108317	−	0.0163262i
$515$	−8.74224	−	1.31768i	−0.385229	−	0.0580640i
$516$	91.2046	+	84.6255i	4.01506	+	3.72543i
$517$	10.5601	−	46.2670i	0.464434	−	2.03482i
$518$	−18.2935	+	13.7135i	−0.803772	+	0.602534i
$519$	5.89047	+	25.8078i	0.258563	+	1.13284i
$520$	3.37332	−	5.84276i	0.147930	−	0.256222i
$521$	−2.98370	−	5.16793i	−0.130718	−	0.226411i	0.793235	−	0.608915i	$-0.208395\pi$
$521$	−2.98370	−	5.16793i	−0.130718	−	0.226411i	−0.923954	+	0.382504i	$0.875062\pi$
$522$	−19.9092	+	18.4731i	−0.871404	+	0.808545i
$523$	25.4679	−	17.3637i	1.11363	−	0.759262i	0.140632	−	0.990062i	$-0.455087\pi$
$523$	25.4679	−	17.3637i	1.11363	−	0.759262i	0.973001	+	0.230800i	$0.0741342\pi$
$524$	−45.4762	+	57.0254i	−1.98664	+	2.49117i
$525$	−32.7391	+	1.46993i	−1.42885	+	0.0641530i
$526$	11.4586	+	14.3687i	0.499621	+	0.626505i
$527$	−8.61072	−	2.65605i	−0.375089	−	0.115700i
$528$	35.1141	−	89.4692i	1.52814	−	3.89365i
$529$	−0.241741	−	3.22581i	−0.0105105	−	0.140253i
$530$	−2.04538	−	5.21153i	−0.0888455	−	0.226375i
$531$	4.09914	−	1.97404i	0.177888	−	0.0856662i
$532$	−38.6823	−	60.5539i	−1.67709	−	2.62534i
$533$	−6.85890	−	3.30307i	−0.297092	−	0.143072i
$534$	−4.02086	+	53.6546i	−0.173999	+	2.32186i
$535$	3.71789	−	1.14682i	0.160738	−	0.0495812i
$536$	−30.1494	−	20.5555i	−1.30226	−	0.887863i
$537$	1.72877	−	0.260571i	0.0746021	−	0.0112445i
$538$	−12.6401			−0.544954
$539$	−28.4125	−	10.6641i	−1.22381	−	0.459337i
$540$	−71.8486			−3.09187
$541$	−19.3843	+	2.92171i	−0.833396	+	0.125614i	−0.551860	−	0.833937i	$-0.686082\pi$
$541$	−19.3843	+	2.92171i	−0.833396	+	0.125614i	−0.281536	+	0.959551i	$0.590844\pi$
$542$	55.4608	+	37.8125i	2.38225	+	1.62419i
$543$	−18.0683	+	5.57335i	−0.775387	+	0.239175i
$544$	1.36418	−	18.2037i	0.0584888	−	0.780479i
$545$	13.0943	+	6.30588i	0.560898	+	0.270114i
$546$	18.5633	+	11.4716i	0.794436	+	0.490940i
$547$	−16.9181	+	8.14733i	−0.723366	+	0.348355i	−0.759071	−	0.651008i	$-0.774347\pi$
$547$	−16.9181	+	8.14733i	−0.723366	+	0.348355i	0.0357053	+	0.999362i	$0.488632\pi$
$548$	26.9883	+	68.7650i	1.15288	+	2.93750i
$549$	−3.97331	−	53.0202i	−0.169577	−	2.26285i
$550$	−15.3141	+	39.0198i	−0.652997	+	1.66381i
$551$	8.27228	+	2.55166i	0.352411	+	0.108704i
$552$	55.7392	+	69.8948i	2.37242	+	2.97492i
$553$	−0.118089	−	0.427905i	−0.00502165	−	0.0181964i
$554$	−23.8777	+	29.9417i	−1.01447	+	1.27210i
$555$	9.97587	−	6.80143i	0.423452	−	0.288705i
$556$	27.2525	−	25.2867i	1.15576	−	1.07239i
$557$	−15.1886	−	26.3074i	−0.643560	−	1.11468i	−0.984632	−	0.174642i	$-0.944123\pi$
$557$	−15.1886	−	26.3074i	−0.643560	−	1.11468i	0.341072	−	0.940037i	$-0.389210\pi$
$558$	23.3728	−	40.4828i	0.989449	−	1.71378i
$559$	1.91909	+	8.40810i	0.0811690	+	0.355625i
$560$	−19.0462	−	4.95125i	−0.804847	−	0.209229i
$561$	−11.6059	+	50.8486i	−0.490000	+	2.14683i
$562$	27.1994	+	25.2374i	1.14734	+	1.06457i
$563$	6.36372	+	0.959176i	0.268199	+	0.0404245i	0.281765	−	0.959484i	$-0.409080\pi$
$563$	6.36372	+	0.959176i	0.268199	+	0.0404245i	−0.0135660	+	0.999908i	$0.504318\pi$
$564$	156.152	+	23.5361i	6.57519	+	0.991050i
$565$	8.51261	+	7.89855i	0.358128	+	0.332294i
$566$	−4.80412	+	21.0482i	−0.201932	+	0.884723i
$567$	2.02329	−	67.5770i	0.0849703	−	2.83797i
$568$	17.4683	+	76.5338i	0.732955	+	3.21129i
$569$	−12.2512	+	21.2197i	−0.513597	+	0.889576i	0.486279	+	0.873804i	$0.338354\pi$
$569$	−12.2512	+	21.2197i	−0.513597	+	0.889576i	−0.999876	+	0.0157720i	$0.994979\pi$
$570$	27.5234	+	47.6719i	1.15283	+	1.99676i
$571$	−15.5992	+	14.4740i	−0.652807	+	0.605717i	−0.935429	−	0.353515i	$-0.884986\pi$
$571$	−15.5992	+	14.4740i	−0.652807	+	0.605717i	0.282622	+	0.959231i	$0.408796\pi$
$572$	15.8974	−	10.8386i	0.664702	−	0.453186i
$573$	4.53345	−	5.68477i	0.189388	−	0.237485i
$574$	−9.12587	+	50.2844i	−0.380907	+	2.09883i
$575$	−10.5625	−	13.2450i	−0.440487	−	0.552354i
$576$	−8.13203	−	2.50840i	−0.338835	−	0.104517i
$577$	5.86081	−	14.9331i	0.243989	−	0.621673i	−0.755449	−	0.655208i	$-0.772581\pi$
$577$	5.86081	−	14.9331i	0.243989	−	0.621673i	0.999438	+	0.0335345i	$0.0106764\pi$
$578$	−0.626330	−	8.35780i	−0.0260519	−	0.347639i
$579$	21.0824	+	53.7171i	0.876156	+	2.23241i
$580$	6.16904	−	2.97085i	0.256155	−	0.123358i
$581$	−4.88476	−	40.6242i	−0.202654	−	1.68538i
$582$	22.2526	+	10.7163i	0.922401	+	0.444205i
$583$	0.655467	−	8.74660i	0.0271467	−	0.362247i
$584$	−74.7623	+	23.0611i	−3.09369	+	0.954276i
$585$	−6.81831	−	4.64864i	−0.281902	−	0.192198i
$586$	24.6350	−	3.71313i	1.01766	−	0.153388i
$587$	−43.1116			−1.77941			−0.889704	−	0.456538i	$-0.849089\pi$
$587$	−43.1116			−1.77941			−0.889704	+	0.456538i	$0.849089\pi$
$588$	28.3211	−	96.9319i	1.16794	−	3.99740i
$589$	−14.8998			−0.613937
$590$	−1.64534	+	0.247995i	−0.0677376	+	0.0102098i
$591$	59.6169	+	40.6461i	2.45231	+	1.67196i
$592$	−22.1950	+	6.84626i	−0.912210	+	0.281379i
$593$	0.204216	−	2.72508i	0.00838616	−	0.111906i	−0.991440	−	0.130565i	$-0.958321\pi$
$593$	0.204216	−	2.72508i	0.00838616	−	0.111906i	0.999826	+	0.0186596i	$0.00593987\pi$
$594$	−147.120	−	70.8493i	−6.03641	−	2.90698i
$595$	10.6205	+	1.11639i	0.435398	+	0.0457674i
$596$	85.9633	−	41.3977i	3.52119	−	1.69572i
$597$	−21.8876	−	55.7686i	−0.895799	−	2.28246i
$598$	0.842989	+	11.2489i	0.0344724	+	0.460002i
$599$	−11.4927	+	29.2829i	−0.469579	+	1.19647i	0.478403	+	0.878141i	$0.341216\pi$
$599$	−11.4927	+	29.2829i	−0.469579	+	1.19647i	−0.947981	+	0.318326i	$0.896879\pi$
$600$	−73.2206	−	22.5856i	−2.98922	−	0.922052i
$601$	−23.2368	−	29.1380i	−0.947848	−	1.18856i	−0.981949	−	0.189145i	$-0.939428\pi$
$601$	−23.2368	−	29.1380i	−0.947848	−	1.18856i	0.0341012	−	0.999418i	$-0.489143\pi$
$602$	50.9835	−	27.4346i	2.07793	−	1.11815i
$603$	−27.8283	+	34.8955i	−1.13325	+	1.42106i
$604$	37.6212	−	25.6497i	1.53078	−	1.04367i
$605$	6.23253	−	5.78294i	0.253388	−	0.235110i
$606$	22.9545	+	39.7584i	0.932464	+	1.61507i
$607$	−2.66221	+	4.61109i	−0.108056	+	0.187158i	−0.914983	−	0.403493i	$-0.867796\pi$
$607$	−2.66221	+	4.61109i	−0.108056	+	0.187158i	0.806927	+	0.590652i	$0.201129\pi$
$608$	−6.71667	−	29.4276i	−0.272397	−	1.19345i
$609$	4.94838	+	11.1146i	0.200518	+	0.450386i
$610$	−4.32692	+	18.9575i	−0.175192	+	0.767565i
$611$	8.02424	+	7.44541i	0.324626	+	0.301209i
$612$	−122.891	−	18.5228i	−4.96758	−	0.748742i
$613$	10.7046	+	1.61346i	0.432354	+	0.0651669i	0.361614	−	0.932328i	$-0.382226\pi$
$613$	10.7046	+	1.61346i	0.432354	+	0.0651669i	0.0707399	+	0.997495i	$0.477464\pi$
$614$	40.7923	+	37.8498i	1.64624	+	1.52749i
$615$	6.00558	−	26.3121i	0.242168	−	1.06101i
$616$	−54.1273	−	45.8812i	−2.18085	−	1.84861i
$617$	−4.76328	−	20.8693i	−0.191762	−	0.840166i	−0.975662	−	0.219279i	$-0.929630\pi$
$617$	−4.76328	−	20.8693i	−0.191762	−	0.840166i	0.783900	−	0.620887i	$-0.213228\pi$
$618$	33.4304	−	57.9031i	1.34477	−	2.32921i
$619$	0.860017	+	1.48959i	0.0345670	+	0.0598718i	0.882791	−	0.469765i	$-0.155661\pi$
$619$	0.860017	+	1.48959i	0.0345670	+	0.0598718i	−0.848224	+	0.529637i	$0.822328\pi$
$620$	−8.63898	+	8.01581i	−0.346950	+	0.321923i
$621$	54.5270	−	37.1759i	2.18809	−	1.49182i
$622$	13.8869	−	17.4136i	0.556815	−	0.698224i
$623$	15.8705	+	6.78361i	0.635839	+	0.271780i
$624$	13.8224	+	17.3327i	0.553337	+	0.693863i
$625$	8.19220	+	2.52696i	0.327688	+	0.101078i
$626$	−11.1776	+	28.4800i	−0.446745	+	1.13829i
$627$	6.44478	+	85.9996i	0.257380	+	3.43449i
$628$	−11.1109	−	28.3100i	−0.443372	−	1.12969i
$629$	11.3560	−	5.46876i	0.452794	−	0.218054i
$630$	−17.9059	+	52.4247i	−0.713387	+	2.08865i
$631$	−34.8470	−	16.7814i	−1.38724	−	0.668058i	−0.416707	−	0.909041i	$-0.636816\pi$
$631$	−34.8470	−	16.7814i	−1.38724	−	0.668058i	−0.970529	+	0.240983i	$0.922530\pi$
$632$	0.0775616	−	1.03499i	0.00308524	−	0.0411696i
$633$	69.2889	−	21.3728i	2.75399	−	0.849492i
$634$	23.6347	+	16.1139i	0.938653	+	0.639963i
$635$	−1.58160	+	0.238387i	−0.0627637	+	0.00946011i
$636$	29.1865			1.15732
$637$	5.40702	−	4.44568i	0.214234	−	0.176144i
$638$	15.5615			0.616085
$639$	94.9481	−	14.3111i	3.75609	−	0.566139i
$640$	11.4610	+	7.81396i	0.453035	+	0.308874i
$641$	5.84262	−	1.80221i	0.230770	−	0.0711831i	−0.177214	−	0.984172i	$-0.556708\pi$
$641$	5.84262	−	1.80221i	0.230770	−	0.0711831i	0.407983	+	0.912989i	$0.366232\pi$
$642$	−2.19887	+	29.3418i	−0.0867823	+	1.15803i
$643$	−45.1476	−	21.7419i	−1.78045	−	0.857418i	−0.957034	−	0.289975i	$-0.906353\pi$
$643$	−45.1476	−	21.7419i	−1.78045	−	0.857418i	−0.823413	−	0.567443i	$-0.807933\pi$
$644$	49.1427	−	17.6088i	1.93649	−	0.693884i
$645$	−27.5470	+	13.2659i	−1.08466	+	0.522346i
$646$	20.9943	+	53.4925i	0.826009	+	2.10464i
$647$	−2.42622	−	32.3756i	−0.0953845	−	1.27282i	−0.815416	−	0.578876i	$-0.803492\pi$
$647$	−2.42622	−	32.3756i	−0.0953845	−	1.27282i	0.720031	−	0.693942i	$-0.244128\pi$
$648$	57.7507	−	147.146i	2.26866	−	5.78046i
$649$	−2.49103	−	0.768380i	−0.0977814	−	0.0301616i
$650$	−6.02828	−	7.55923i	−0.236449	−	0.296497i
$651$	−13.7772	−	15.7696i	−0.539971	−	0.618061i
$652$	6.05387	−	7.59131i	0.237088	−	0.297299i
$653$	−34.3555	+	23.4232i	−1.34443	+	0.916620i	−0.999756	−	0.0221010i	$-0.992964\pi$
$653$	−34.3555	+	23.4232i	−1.34443	+	0.916620i	−0.344679	+	0.938721i	$0.612012\pi$
$654$	−80.5708	+	74.7588i	−3.15057	+	2.92330i
$655$	−8.96206	−	15.5227i	−0.350177	−	0.606524i
$656$	−25.9598	+	44.9636i	−1.01356	+	1.75553i
$657$	21.2948	+	93.2986i	0.830789	+	3.63993i
$658$	33.8507	−	65.2232i	1.31964	−	2.54267i
$659$	−7.41240	+	32.4758i	−0.288746	+	1.26508i	0.597502	+	0.801867i	$0.296160\pi$
$659$	−7.41240	+	32.4758i	−0.288746	+	1.26508i	−0.886248	+	0.463211i	$0.846697\pi$
$660$	50.0027	+	46.3957i	1.94635	+	1.80595i
$661$	11.9685	+	1.80396i	0.465520	+	0.0701659i	0.377614	−	0.925963i	$-0.376745\pi$
$661$	11.9685	+	1.80396i	0.465520	+	0.0701659i	0.0879056	+	0.996129i	$0.471983\pi$
$662$	−71.7107	−	10.8086i	−2.78712	−	0.420090i
$663$	−8.81884	−	8.18269i	−0.342495	−	0.317789i
$664$	21.2882	−	93.2697i	0.826142	−	3.61956i
$665$	17.3250	−	3.41228i	0.671835	−	0.132323i
$666$	14.5496	+	63.7460i	0.563786	+	2.47011i
$667$	−3.14460	+	5.44660i	−0.121759	+	0.210893i
$668$	15.9100	+	27.5569i	0.615576	+	1.06621i
$669$	−63.8404	+	59.2352i	−2.46821	+	2.29017i
$670$	13.4869	−	9.19523i	0.521045	−	0.355243i
$671$	−18.9941	+	23.8178i	−0.733258	+	0.919476i
$672$	24.9349	−	34.3191i	0.961886	−	1.32389i
$673$	−17.1941	−	21.5608i	−0.662785	−	0.831107i	0.330858	−	0.943681i	$-0.392662\pi$
$673$	−17.1941	−	21.5608i	−0.662785	−	0.831107i	−0.993643	+	0.112574i	$0.964090\pi$
$674$	3.88587	+	1.19863i	0.149678	+	0.0461696i
$675$	−20.6653	+	52.6544i	−0.795409	+	2.02667i
$676$	0.331654	+	4.42562i	0.0127559	+	0.170216i
$677$	−5.24606	−	13.3668i	−0.201623	−	0.513726i	0.793922	−	0.608020i	$-0.208036\pi$
$677$	−5.24606	−	13.3668i	−0.201623	−	0.513726i	−0.995544	+	0.0942938i	$0.969941\pi$
$678$	−79.1240	+	38.1041i	−3.03874	+	1.46338i
$679$	5.56025	−	5.64393i	0.213383	−	0.216594i
$680$	22.4961	+	10.8335i	0.862686	+	0.415448i
$681$	0.893026	−	11.9166i	0.0342208	−	0.456645i
$682$	−25.5938	+	7.89465i	−0.980039	+	0.302302i
$683$	−26.2274	−	17.8816i	−1.00357	−	0.684219i	−0.0542443	−	0.998528i	$-0.517275\pi$
$683$	−26.2274	−	17.8816i	−1.00357	−	0.684219i	−0.949321	+	0.314309i	$0.898227\pi$
$684$	−203.201	+	30.6277i	−7.76960	+	1.17108i
$685$	−18.1535			−0.693608
$686$	−38.4253	−	27.0507i	−1.46708	−	1.03280i
$687$	67.1163			2.56065
$688$	58.1612	−	8.76639i	2.21738	−	0.334216i
$689$	1.67160	+	1.13968i	0.0636827	+	0.0434182i
$690$	−38.2146	+	11.7876i	−1.45481	+	0.448748i
$691$	1.39483	−	18.6127i	0.0530617	−	0.708059i	−0.905713	−	0.423892i	$-0.860664\pi$
$691$	1.39483	−	18.6127i	0.0530617	−	0.708059i	0.958775	−	0.284168i	$-0.0917172\pi$
$692$	32.5620	+	15.6811i	1.23782	+	0.596104i
$693$	−60.9108	+	61.8275i	−2.31381	+	2.34863i
$694$	−27.8879	+	13.4301i	−1.05861	+	0.509800i
$695$	3.33775	+	8.50444i	0.126608	+	0.322592i
$696$	2.12580	+	28.3668i	0.0805782	+	1.07524i
$697$	10.2933	−	26.2268i	0.389885	−	0.993411i
$698$	−7.63809	−	2.35604i	−0.289106	−	0.0891774i
$699$	41.5638	+	52.1193i	1.57209	+	1.97133i
$700$	−26.2998	+	36.1977i	−0.994039	+	1.36814i
$701$	−14.2745	+	17.8996i	−0.539140	+	0.676060i	−0.974549	−	0.224172i	$-0.928032\pi$
$701$	−14.2745	+	17.8996i	−0.539140	+	0.676060i	0.435410	+	0.900232i	$0.356604\pi$
$702$	31.1199	−	21.2172i	1.17454	−	0.800790i
$703$	15.2777	−	14.1756i	0.576208	−	0.534643i
$704$	2.43802	+	4.22277i	0.0918862	+	0.159152i
$705$	−19.4034	+	33.6077i	−0.730775	+	1.26574i
$706$	−14.5571	−	63.7790i	−0.547866	−	2.40036i
$707$	14.4491	−	2.84585i	0.543413	−	0.107029i
$708$	1.93025	−	8.45696i	0.0725431	−	0.317832i
$709$	−3.52535	−	3.27105i	−0.132397	−	0.122847i	0.611195	−	0.791480i	$-0.290689\pi$
$709$	−3.52535	−	3.27105i	−0.132397	−	0.122847i	−0.743592	+	0.668633i	$0.766880\pi$
$710$	−34.7245	−	5.23388i	−1.30319	−	0.196424i
$711$	−1.25533	−	0.189210i	−0.0470785	−	0.00709594i
$712$	29.5821	+	27.4482i	1.10864	+	1.02866i
$713$	2.40872	−	10.5533i	0.0902073	−	0.395224i
$714$	−37.2028	+	71.6820i	−1.39228	+	2.68263i
$715$	1.05214	+	4.60972i	0.0393478	+	0.172394i
$716$	1.19346	−	2.06714i	0.0446018	−	0.0772527i
$717$	−8.99822	−	15.5854i	−0.336045	−	0.582047i
$718$	−12.6785	+	11.7640i	−0.473159	+	0.439027i
$719$	−19.8139	+	13.5089i	−0.738935	+	0.503797i	−0.873329	−	0.487130i	$-0.838044\pi$
$719$	−19.8139	+	13.5089i	−0.738935	+	0.503797i	0.134394	+	0.990928i	$0.457091\pi$
$720$	−35.0902	+	44.0018i	−1.30774	+	1.63985i
$721$	−14.1110	−	16.1517i	−0.525520	−	0.601520i
$722$	29.1852	+	36.5971i	1.08616	+	1.36200i
$723$	14.4371	+	4.45326i	0.536922	+	0.165619i
$724$	−9.43140	+	24.0308i	−0.350515	+	0.893098i
$725$	−0.402836	−	5.37548i	−0.0149610	−	0.199640i
$726$	23.4909	+	59.8537i	0.871827	+	2.22138i
$727$	4.67037	−	2.24913i	0.173214	−	0.0834156i	−0.345267	−	0.938504i	$-0.612212\pi$
$727$	4.67037	−	2.24913i	0.173214	−	0.0834156i	0.518482	+	0.855089i	$0.326497\pi$
$728$	15.4076	−	5.52083i	0.571042	−	0.204616i
$729$	−43.7789	−	21.0828i	−1.62144	−	0.780844i
$730$	2.61546	−	34.9009i	0.0968027	−	1.29174i
$731$	−30.4999	+	9.40799i	−1.12808	+	0.347967i
$732$	−83.7570	−	57.1046i	−3.09575	−	2.11065i
$733$	−4.72458	+	0.712116i	−0.174506	+	0.0263026i	−0.235714	−	0.971822i	$-0.575743\pi$
$733$	−4.72458	+	0.712116i	−0.174506	+	0.0263026i	0.0612077	+	0.998125i	$0.480505\pi$
$734$	57.9285			2.13818
$735$	19.6311	+	15.1812i	0.724105	+	0.559967i
$736$	21.9289			0.808310
$737$	25.2877	−	3.81151i	0.931486	−	0.140399i
$738$	120.760	+	82.3331i	4.44526	+	3.03072i
$739$	33.3435	−	10.2851i	1.22656	−	0.378344i	0.387239	−	0.921979i	$-0.373429\pi$
$739$	33.3435	−	10.2851i	1.22656	−	0.378344i	0.839321	+	0.543636i	$0.182953\pi$
$740$	1.23187	−	16.4381i	0.0452843	−	0.604277i
$741$	−17.9223	−	8.63090i	−0.658391	−	0.317064i
$742$	4.38986	−	12.8526i	0.161157	−	0.471834i
$743$	1.45199	−	0.699243i	0.0532684	−	0.0256527i	−0.407060	−	0.913401i	$-0.633446\pi$
$743$	1.45199	−	0.699243i	0.0532684	−	0.0256527i	0.460328	+	0.887749i	$0.347732\pi$
$744$	−17.8873	−	45.5762i	−0.655781	−	1.67090i
$745$	1.75219	+	23.3814i	0.0641953	+	0.856626i
$746$	−14.8147	+	37.7473i	−0.542406	+	1.38203i
$747$	−111.819	−	34.4916i	−4.09124	−	1.26198i
$748$	44.3975	+	55.6728i	1.62333	+	2.03560i
$749$	8.67904	+	3.70972i	0.317125	+	0.135550i
$750$	49.4138	−	61.9629i	1.80434	−	2.26257i
$751$	−18.4717	+	12.5938i	−0.674042	+	0.459554i	−0.851348	−	0.524602i	$-0.824214\pi$
$751$	−18.4717	+	12.5938i	−0.674042	+	0.459554i	0.177306	+	0.984156i	$0.443262\pi$
$752$	54.7255	−	50.7779i	1.99563	−	1.85168i
$753$	45.6634	+	79.0914i	1.66407	+	2.88225i
$754$	−1.79470	+	3.10851i	−0.0653591	+	0.113205i
$755$	2.48989	+	10.9089i	0.0906164	+	0.397016i
$756$	−132.959	−	112.703i	−4.83567	−	4.09898i
$757$	−6.74990	+	29.5733i	−0.245329	+	1.07486i	0.690757	+	0.723087i	$0.257278\pi$
$757$	−6.74990	+	29.5733i	−0.245329	+	1.07486i	−0.936086	+	0.351771i	$0.885580\pi$
$758$	18.6825	+	17.3348i	0.678578	+	0.629629i
$759$	−61.9539	−	9.33804i	−2.24878	−	0.338949i
$760$	40.8249	+	6.15337i	1.48088	+	0.223206i
$761$	−18.1483	−	16.8392i	−0.657875	−	0.610419i	0.278913	−	0.960316i	$-0.410026\pi$
$761$	−18.1483	−	16.8392i	−0.657875	−	0.610419i	−0.936788	+	0.349897i	$0.886216\pi$
$762$	2.69163	−	11.7928i	0.0975074	−	0.427208i
$763$	14.3401	+	32.2093i	0.519145	+	1.16605i
$764$	−2.20899	−	9.67821i	−0.0799184	−	0.350145i
$765$	15.2704	−	26.4491i	0.552103	−	0.956271i
$766$	−32.5819	−	56.4336i	−1.17723	−	2.03903i
$767$	0.440778	−	0.408982i	0.0159156	−	0.0147675i
$768$	−80.6333	+	54.9748i	−2.90960	+	1.98373i
$769$	16.2409	−	20.3654i	0.585662	−	0.734397i	−0.397405	−	0.917643i	$-0.630089\pi$
$769$	16.2409	−	20.3654i	0.585662	−	0.734397i	0.983067	+	0.183246i	$0.0586606\pi$
$770$	27.9516	−	15.0410i	1.00731	−	0.542039i
$771$	1.98371	+	2.48749i	0.0714414	+	0.0895847i
$772$	75.2851	+	23.2224i	2.70957	+	0.835791i
$773$	8.32846	−	21.2206i	0.299554	−	0.763251i	−0.699274	−	0.714853i	$-0.746493\pi$
$773$	8.32846	−	21.2206i	0.299554	−	0.763251i	0.998828	−	0.0483973i	$-0.0154114\pi$
$774$	−12.3736	−	165.114i	−0.444760	−	5.93490i
$775$	3.38963	+	8.63663i	0.121759	+	0.310237i
$776$	16.6899	−	8.03741i	0.599131	−	0.288526i
$777$	29.1297	+	3.06199i	1.04502	+	0.109848i
$778$	−44.1828	−	21.2773i	−1.58403	−	0.762828i
$779$	3.48142	−	46.4563i	0.124735	−	1.66447i
$780$	−15.0346	+	4.63757i	−0.538326	+	0.166052i
$781$	−45.4570	−	30.9921i	−1.62658	−	1.10898i
$782$	−41.2818	+	6.22223i	−1.47623	+	0.222506i
$783$	20.9991			0.750447
$784$	−27.4792	−	39.0387i	−0.981398	−	1.39424i
$785$	7.47364			0.266746
$786$	134.039	−	20.2031i	4.78100	−	0.720620i
$787$	−29.5616	−	20.1548i	−1.05376	−	0.718440i	−0.0929549	−	0.995670i	$-0.529631\pi$
$787$	−29.5616	−	20.1548i	−1.05376	−	0.718440i	−0.960804	+	0.277230i	$0.910584\pi$
$788$	94.1349	−	29.0368i	3.35342	−	1.03439i
$789$	1.75950	−	23.4789i	0.0626399	−	0.835872i
$790$	0.418307	+	0.201446i	0.0148827	+	0.00716713i
$791$	3.36315	+	27.9697i	0.119580	+	0.994487i
$792$	−182.832	+	88.0473i	−6.49666	+	3.12863i
$793$	−2.56719	−	6.54108i	−0.0911635	−	0.232281i
$794$	−1.02438	−	13.6694i	−0.0363539	−	0.485109i
$795$	−2.62038	+	6.67661i	−0.0929352	+	0.236795i
$796$	−78.1603	−	24.1093i	−2.77032	−	0.854530i
$797$	−13.0631	−	16.3806i	−0.462717	−	0.580229i	0.494654	−	0.869090i	$-0.335295\pi$
$797$	−13.0631	−	16.3806i	−0.462717	−	0.580229i	−0.957371	+	0.288861i	$0.906723\pi$
$798$	−23.8459	+	131.393i	−0.844134	+	4.65125i
$799$	−25.2586	+	31.6732i	−0.893583	+	1.12052i
$800$	−15.5296	+	10.5879i	−0.549054	+	0.374339i
$801$	36.1837	−	33.5736i	1.27849	−	1.18626i
$802$	15.5610	+	26.9524i	0.549477	+	0.951722i
$803$	27.4160	−	47.4859i	0.967489	−	1.67574i
$804$	18.9359	+	82.9636i	0.667818	+	2.92590i
$805$	−0.383917	+	12.8226i	−0.0135313	+	0.451938i
$806$	1.37472	−	6.02302i	0.0484223	−	0.212152i
$807$	11.8707	+	11.0144i	0.417868	+	0.387725i
$808$	34.0480	+	5.13191i	1.19781	+	0.180540i
$809$	7.65317	+	1.15353i	0.269071	+	0.0405560i	0.282192	−	0.959358i	$-0.408938\pi$
$809$	7.65317	+	1.15353i	0.269071	+	0.0405560i	−0.0131207	+	0.999914i	$0.504177\pi$
$810$	51.8356	+	48.0964i	1.82132	+	1.68993i
$811$	−7.49099	+	32.8202i	−0.263044	+	1.15247i	0.654885	+	0.755728i	$0.272717\pi$
$811$	−7.49099	+	32.8202i	−0.263044	+	1.15247i	−0.917929	+	0.396744i	$0.870140\pi$
$812$	16.0762	+	4.17918i	0.564165	+	0.146661i
$813$	−19.1356	−	83.8385i	−0.671114	−	2.94034i
$814$	18.7319	−	32.4446i	0.656553	−	1.13718i
$815$	1.19304	+	2.06641i	0.0417905	+	0.0723832i
$816$	−60.1447	+	55.8061i	−2.10549	+	1.95361i
$817$	−43.6061	+	29.7301i	−1.52558	+	1.04013i
$818$	−6.99930	+	8.77684i	−0.244725	+	0.306875i
$819$	−5.32563	−	19.2979i	−0.186093	−	0.674322i
$820$	−22.9740	−	28.8085i	−0.802286	−	1.00604i
$821$	−42.8043	−	13.2034i	−1.49388	−	0.460801i	−0.563102	−	0.826387i	$-0.690392\pi$
$821$	−42.8043	−	13.2034i	−1.49388	−	0.460801i	−0.930777	+	0.365586i	$0.880869\pi$
$822$	50.1567	−	127.797i	1.74941	−	4.45744i
$823$	2.31246	+	30.8577i	0.0806074	+	1.07563i	0.880048	+	0.474885i	$0.157510\pi$
$823$	2.31246	+	30.8577i	0.0806074	+	1.07563i	−0.799440	+	0.600745i	$0.794871\pi$
$824$	−18.3207	−	46.6803i	−0.638231	−	1.62619i
$825$	48.3832	−	23.3001i	1.68449	−	0.811206i
$826$	−3.43379	−	2.12199i	−0.119477	−	0.0738334i
$827$	−4.72514	−	2.27551i	−0.164309	−	0.0791271i	0.349922	−	0.936779i	$-0.386208\pi$
$827$	−4.72514	−	2.27551i	−0.164309	−	0.0791271i	−0.514231	+	0.857652i	$0.671922\pi$
$828$	11.1566	−	148.875i	0.387720	−	5.17377i
$829$	47.6783	−	14.7068i	1.65594	−	0.510788i	0.680813	−	0.732457i	$-0.261627\pi$
$829$	47.6783	−	14.7068i	1.65594	−	0.510788i	0.975122	+	0.221669i	$0.0711503\pi$
$830$	35.3596	+	24.1078i	1.22735	+	0.836793i
$831$	48.5150	−	7.31246i	1.68297	−	0.253667i
$832$	−1.12470			−0.0389920
$833$	17.9025	+	18.7255i	0.620286	+	0.648799i
$834$	−69.0916			−2.39245
$835$	−7.73223	+	1.16545i	−0.267585	+	0.0403319i
$836$	97.2840	+	66.3271i	3.36464	+	2.29397i
$837$	−34.5370	+	10.6533i	−1.19378	+	0.368231i
$838$	1.69264	−	22.5867i	0.0584713	−	0.780246i
$839$	10.7423	+	5.17323i	0.370866	+	0.178600i	0.610028	−	0.792380i	$-0.291158\pi$
$839$	10.7423	+	5.17323i	0.370866	+	0.178600i	−0.239162	+	0.970980i	$0.576873\pi$
$840$	31.2364	+	48.8979i	1.07776	+	1.68714i
$841$	24.3251	−	11.7143i	0.838796	−	0.403943i
$842$	−16.6692	−	42.4724i	−0.574459	−	1.46370i
$843$	−3.55231	−	47.4023i	−0.122348	−	1.63262i
$844$	36.1677	−	92.1539i	1.24494	−	3.17207i
$845$	−1.04216	−	0.321465i	−0.0358515	−	0.0110587i
$846$	−131.031	−	164.307i	−4.50493	−	5.64900i
$847$	20.6048	−	0.925123i	0.707990	−	0.0317876i
$848$	8.60283	−	10.7876i	0.295422	−	0.370448i
$849$	22.8528	−	15.5808i	0.784305	−	0.534730i
$850$	26.2307	−	24.3385i	0.899704	−	0.834803i
$851$	7.57052	+	13.1125i	0.259514	+	0.449492i
$852$	91.5361	−	158.545i	3.13598	−	5.43167i
$853$	−1.87253	−	8.20409i	−0.0641142	−	0.280903i	0.932701	−	0.360651i	$-0.117445\pi$
$853$	−1.87253	−	8.20409i	−0.0641142	−	0.280903i	−0.996815	+	0.0797484i	$0.974588\pi$
$854$	−37.7442	+	28.2944i	−1.29158	+	0.968213i
$855$	11.2372	−	49.2334i	0.384304	−	1.68375i
$856$	16.1774	+	15.0105i	0.552933	+	0.513047i
$857$	−7.70699	−	1.16164i	−0.263266	−	0.0396809i	0.0160829	−	0.999871i	$-0.494880\pi$
$857$	−7.70699	−	1.16164i	−0.263266	−	0.0396809i	−0.279349	+	0.960190i	$0.590119\pi$
$858$	−35.3586	−	5.32945i	−1.20712	−	0.181944i
$859$	4.53173	+	4.20483i	0.154621	+	0.143467i	0.753690	−	0.657230i	$-0.228272\pi$
$859$	4.53173	+	4.20483i	0.154621	+	0.143467i	−0.599069	+	0.800697i	$0.704463\pi$
$860$	−9.28878	+	40.6968i	−0.316745	+	1.38775i
$861$	52.3874	−	39.2714i	1.78536	−	1.33836i
$862$	1.11630	+	4.89083i	0.0380214	+	0.166582i
$863$	23.5889	−	40.8572i	0.802977	−	1.39080i	−0.114671	−	0.993403i	$-0.536582\pi$
$863$	23.5889	−	40.8572i	0.802977	−	1.39080i	0.917648	−	0.397393i	$-0.130085\pi$
$864$	−36.6094	−	63.4093i	−1.24548	−	2.15723i
$865$	−6.51057	+	6.04093i	−0.221366	+	0.205398i
$866$	−26.9649	+	18.3844i	−0.916305	+	0.624726i
$867$	−6.69465	+	8.39482i	−0.227362	+	0.285103i
$868$	−28.5606	+	1.28232i	−0.969410	+	0.0435249i
$869$	0.453519	+	0.568695i	0.0153846	+	0.0192917i
$870$	−12.1598	−	3.75079i	−0.412254	−	0.127164i
$871$	−2.15505	+	5.49097i	−0.0730210	+	0.186054i
$872$	6.16042	+	82.2051i	0.208618	+	2.78381i
$873$	−8.27799	−	21.0920i	−0.280168	−	0.713855i
$874$	−62.1945	+	29.9513i	−2.10376	+	1.01312i
$875$	−13.6862	−	21.4246i	−0.462677	−	0.724282i
$876$	164.388	+	79.1652i	5.55416	+	2.67474i
$877$	−0.467592	+	6.23958i	−0.0157895	+	0.210696i	0.983729	+	0.179660i	$0.0574997\pi$
$877$	−0.467592	+	6.23958i	−0.0157895	+	0.210696i	−0.999518	+	0.0310360i	$0.990119\pi$
$878$	−0.697944	+	0.215287i	−0.0235545	+	0.00726559i
$879$	−26.3710	−	17.9794i	−0.889471	−	0.606431i
$880$	31.8867	−	4.80615i	1.07490	−	0.162015i
$881$	44.1778			1.48839			0.744193	−	0.667964i	$-0.232834\pi$
$881$	44.1778			1.48839			0.744193	+	0.667964i	$0.232834\pi$
$882$	−115.370	+	68.9268i	−3.88471	+	2.32089i
$883$	46.7319			1.57266			0.786328	−	0.617810i	$-0.211980\pi$
$883$	46.7319			1.57266			0.786328	+	0.617810i	$0.211980\pi$
$884$	−16.2413	+	2.44799i	−0.546255	+	0.0823347i
$885$	1.76129	+	1.20082i	0.0592050	+	0.0403653i
$886$	80.4997	−	24.8309i	2.70444	−	0.834210i
$887$	2.14205	−	28.5837i	0.0719231	−	0.959747i	−0.838188	−	0.545382i	$-0.816385\pi$
$887$	2.14205	−	28.5837i	0.0719231	−	0.959747i	0.910111	−	0.414365i	$-0.135996\pi$
$888$	61.7017	+	29.7140i	2.07057	+	0.997136i
$889$	−3.30075	−	2.03978i	−0.110704	−	0.0684120i
$890$	−16.2644	+	7.83253i	−0.545184	+	0.262547i
$891$	40.4736	+	103.125i	1.35592	+	3.45482i
$892$	8.88545	+	118.568i	0.297507	+	3.96995i
$893$	−24.4728	+	62.3557i	−0.818951	+	2.08665i
$894$	−169.442	−	52.2658i	−5.66698	−	1.74803i
$895$	0.365722	+	0.458601i	0.0122247	+	0.0153293i
$896$	8.95192	+	32.4380i	0.299063	+	1.08368i
$897$	9.01044	−	11.2987i	0.300850	−	0.377254i
$898$	−61.4838	+	41.9189i	−2.05174	+	1.39885i
$899$	2.52491	−	2.34277i	0.0842104	−	0.0781358i
$900$	63.9803	+	110.817i	2.13268	+	3.69391i
$901$	−3.74374	+	6.48435i	−0.124722	+	0.216025i
$902$	−18.6347	−	81.6438i	−0.620466	−	2.71844i
$903$	−71.7862	−	18.6616i	−2.38890	−	0.621019i
$904$	−14.6569	+	64.2159i	−0.487480	+	2.13579i
$905$	−4.65045	−	4.31499i	−0.154586	−	0.143435i
$906$	−83.6762	−	12.6122i	−2.77996	−	0.419011i
$907$	−30.4003	−	4.58210i	−1.00942	−	0.152146i	−0.376546	−	0.926398i	$-0.622888\pi$
$907$	−30.4003	−	4.58210i	−1.00942	−	0.152146i	−0.632878	+	0.774252i	$0.718126\pi$
$908$	−11.9599	−	11.0971i	−0.396902	−	0.368271i
$909$	9.37183	−	41.0607i	0.310844	−	1.36190i
$910$	−0.219111	+	7.31818i	−0.00726344	+	0.242595i
$911$	10.1879	+	44.6362i	0.337541	+	1.47886i	0.804165	+	0.594406i	$0.202613\pi$
$911$	10.1879	+	44.6362i	0.337541	+	1.47886i	−0.466624	+	0.884456i	$0.654530\pi$
$912$	−67.8327	+	117.490i	−2.24616	+	3.89047i
$913$	33.5238	+	58.0649i	1.10947	+	1.92167i
$914$	42.6727	−	39.5945i	1.41149	−	1.30967i
$915$	20.5828	−	14.0331i	0.680445	−	0.463920i
$916$	57.1322	−	71.6415i	1.88770	−	2.36710i
$917$	7.76459	−	42.7836i	0.256409	−	1.41284i
$918$	86.9104	+	108.982i	2.86847	+	3.59695i
$919$	−2.79761	−	0.862949i	−0.0922847	−	0.0284661i	0.248269	−	0.968691i	$-0.420138\pi$
$919$	−2.79761	−	0.862949i	−0.0922847	−	0.0284661i	−0.340554	+	0.940225i	$0.610615\pi$
$920$	−10.9581	+	27.9208i	−0.361278	+	0.920522i
$921$	−5.32758	−	71.0916i	−0.175550	−	2.34255i
$922$	18.5971	+	47.3847i	0.612464	+	1.56053i
$923$	11.4334	−	5.50604i	0.376335	−	0.181233i
$924$	19.7550	+	164.293i	0.649891	+	5.40483i
$925$	−11.6924	−	5.63076i	−0.384444	−	0.185138i
$926$	2.21353	−	29.5375i	0.0727411	−	0.970663i
$927$	−58.6125	+	18.0796i	−1.92509	+	0.593811i
$928$	5.76524	+	3.93067i	0.189253	+	0.129031i
$929$	0.897846	−	0.135328i	0.0294574	−	0.00443998i	−0.134297	−	0.990941i	$-0.542878\pi$
$929$	0.897846	−	0.135328i	0.0294574	−	0.00443998i	0.163754	+	0.986501i	$0.447640\pi$
$930$	21.9019			0.718191
$931$	37.4133	+	20.8618i	1.22617	+	0.683717i
$932$	91.0141			2.98127
$933$	−28.2156	+	4.25281i	−0.923737	+	0.139231i
$934$	26.7469	+	18.2357i	0.875186	+	0.596692i
$935$	−16.7215	+	5.15791i	−0.546852	+	0.168682i
$936$	3.49791	−	46.6764i	0.114333	−	1.52567i
$937$	36.1905	+	17.4284i	1.18229	+	0.569362i	0.918579	−	0.395239i	$-0.129338\pi$
$937$	36.1905	+	17.4284i	1.18229	+	0.569362i	0.263714	+	0.964601i	$0.415052\pi$
$938$	39.3820	+	4.13968i	1.28587	+	0.135165i
$939$	35.3141	−	17.0064i	1.15243	−	0.554983i
$940$	19.3566	+	49.3199i	0.631344	+	1.60864i
$941$	−0.249829	−	3.33374i	−0.00814419	−	0.108677i	0.991650	−	0.128957i	$-0.0411631\pi$
$941$	−0.249829	−	3.33374i	−0.00814419	−	0.108677i	−0.999794	+	0.0202807i	$0.993544\pi$
$942$	−20.6491	+	52.6131i	−0.672784	+	1.71423i
$943$	32.3414	+	9.97599i	1.05318	+	0.324863i
$944$	−2.55682	−	3.20615i	−0.0832174	−	0.104351i
$945$	37.7187	−	20.2967i	1.22699	−	0.660252i
$946$	−59.1508	+	74.1728i	−1.92316	+	2.41157i
$947$	−29.5479	+	20.1454i	−0.960179	+	0.654639i	−0.938556	−	0.345127i	$-0.887836\pi$
$947$	−29.5479	+	20.1454i	−0.960179	+	0.654639i	−0.0216231	+	0.999766i	$0.506883\pi$
$948$	−1.77430	+	1.64631i	−0.0576267	+	0.0534698i
$949$	6.32374	+	10.9530i	0.205277	+	0.355551i
$950$	29.5836	−	51.2402i	0.959818	−	1.66245i
$951$	−8.15465	−	35.7279i	−0.264433	−	1.15856i
$952$	24.6363	+	55.3358i	0.798467	+	1.79344i
$953$	−8.26222	+	36.1992i	−0.267640	+	1.17261i	0.645111	+	0.764089i	$0.276811\pi$
$953$	−8.26222	+	36.1992i	−0.267640	+	1.17261i	−0.912751	+	0.408517i	$0.866046\pi$
$954$	−28.4731	−	26.4192i	−0.921852	−	0.855354i
$955$	2.41228	+	0.363592i	0.0780595	+	0.0117656i
$956$	−24.2958	−	3.66201i	−0.785783	−	0.118438i
$957$	−14.6142	−	13.5600i	−0.472411	−	0.438334i
$958$	−2.09717	+	9.18830i	−0.0677565	+	0.296860i
$959$	−33.5938	−	28.4759i	−1.08480	−	0.919535i
$960$	−0.887252	−	3.88731i	−0.0286359	−	0.125462i
$961$	12.5358	−	21.7127i	0.404382	−	0.700410i
$962$	4.32068	+	7.48364i	0.139304	+	0.241282i
$963$	19.7876	−	18.3602i	0.637646	−	0.591649i
$964$	17.0430	−	11.6197i	0.548917	−	0.374246i
$965$	−12.0714	+	15.1370i	−0.388592	+	0.487279i
$966$	−89.2082	−	38.1307i	−2.87023	−	1.22683i
$967$	−32.3035	−	40.5073i	−1.03881	−	1.30263i	−0.951900	−	0.306410i	$-0.900872\pi$
$967$	−32.3035	−	40.5073i	−1.03881	−	1.30263i	−0.0869096	−	0.996216i	$-0.527699\pi$
$968$	46.0825	+	14.2146i	1.48115	+	0.456873i
$969$	26.8962	−	68.5305i	0.864031	−	2.20152i
$970$	0.619259	+	8.26344i	0.0198832	+	0.265323i
$971$	11.2174	+	28.5816i	0.359985	+	0.917226i	0.990054	+	0.140687i	$0.0449313\pi$
$971$	11.2174	+	28.5816i	0.359985	+	0.917226i	−0.630069	+	0.776539i	$0.716974\pi$
$972$	−154.068	+	74.1951i	−4.94172	+	2.37981i
$973$	−7.16359	+	20.9735i	−0.229654	+	0.672380i
$974$	45.9133	+	22.1107i	1.47116	+	0.708472i
$975$	−0.925658	+	12.3520i	−0.0296448	+	0.395582i
$976$	−45.7940	+	14.1256i	−1.46583	+	0.452149i
$977$	−1.83089	−	1.24828i	−0.0585753	−	0.0399359i	0.533678	−	0.845688i	$-0.320809\pi$
$977$	−1.83089	−	1.24828i	−0.0585753	−	0.0399359i	−0.592254	+	0.805752i	$0.701762\pi$
$978$	−17.8434	+	2.68947i	−0.570571	+	0.0859997i
$979$	−28.2820			−0.903895
$980$	32.9156	−	8.03183i	1.05145	−	0.256567i
$981$	100.832			3.21932
$982$	−1.66620	+	0.251139i	−0.0531705	+	0.00801417i
$983$	−19.1556	−	13.0601i	−0.610970	−	0.416552i	0.217918	−	0.975967i	$-0.430074\pi$
$983$	−19.1556	−	13.0601i	−0.610970	−	0.416552i	−0.828888	+	0.559415i	$0.811026\pi$
$984$	146.282	−	45.1219i	4.66329	−	1.43843i
$985$	−1.80911	+	24.1409i	−0.0576430	+	0.769193i
$986$	−11.9685	−	5.76375i	−0.381156	−	0.183555i
$987$	−88.6247	+	31.7560i	−2.82095	+	1.01080i
$988$	−24.4690	+	11.7836i	−0.778462	+	0.374887i
$989$	−14.0079	−	35.6916i	−0.445426	−	1.13493i
$990$	−6.78379	−	90.5234i	−0.215603	−	2.87702i
$991$	16.4230	−	41.8451i	0.521694	−	1.32925i	−0.390918	−	0.920426i	$-0.627842\pi$
$991$	16.4230	−	41.8451i	0.521694	−	1.32925i	0.912611	−	0.408828i	$-0.134062\pi$
$992$	−11.4761	−	3.53992i	−0.364368	−	0.112393i
$993$	57.9271	+	72.6383i	1.83826	+	2.30511i
$994$	−56.0494	−	64.1552i	−1.77778	−	2.03488i
$995$	12.5324	−	15.7151i	0.397304	−	0.498203i
$996$	−184.338	+	125.680i	−5.84098	+	3.98231i
$997$	6.77010	−	6.28173i	0.214411	−	0.198944i	−0.565654	−	0.824643i	$-0.691376\pi$
$997$	6.77010	−	6.28173i	0.214411	−	0.198944i	0.780065	+	0.625698i	$0.215186\pi$
$998$	−49.7039	−	86.0897i	−1.57335	−	2.72512i
$999$	25.2774	−	43.7817i	0.799740	−	1.38519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.b.534.4	yes	348
49.39	even	21	inner	637.2.bl.b.235.4	✓	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.b.235.4	✓	348	49.39	even	21	inner
637.2.bl.b.534.4	yes	348	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.50899 + 0.378169i) q^{2} +(2.68579 + 1.83114i) q^{3} +(4.24086 - 1.30813i) q^{4} +(-0.0815020 + 1.08757i) q^{5} +(-7.43110 - 3.57863i) q^{6} +(-1.85680 + 1.88475i) q^{7} +(-5.57346 + 2.68404i) q^{8} +(2.76437 + 7.04351i) q^{9} +O(q^{10})\)	\(q+(-2.50899 + 0.378169i) q^{2} +(2.68579 + 1.83114i) q^{3} +(4.24086 - 1.30813i) q^{4} +(-0.0815020 + 1.08757i) q^{5} +(-7.43110 - 3.57863i) q^{6} +(-1.85680 + 1.88475i) q^{7} +(-5.57346 + 2.68404i) q^{8} +(2.76437 + 7.04351i) q^{9} +(-0.206797 - 2.75952i) q^{10} +(1.58390 - 4.03571i) q^{11} +(13.7854 + 4.25224i) q^{12} +(0.623490 + 0.781831i) q^{13} +(3.94595 - 5.43099i) q^{14} +(-2.21039 + 2.77174i) q^{15} +(5.63497 - 3.84186i) q^{16} +(-2.71297 + 2.51727i) q^{17} +(-9.59942 - 16.6267i) q^{18} +(-3.05975 + 5.29964i) q^{19} +(1.07704 + 4.71884i) q^{20} +(-8.43823 + 1.66197i) q^{21} +(-2.44781 + 10.7245i) q^{22} +(-3.25900 - 3.02391i) q^{23} +(-19.8840 - 2.99703i) q^{24} +(3.76799 + 0.567933i) q^{25} +(-1.85999 - 1.72582i) q^{26} +(-3.30314 + 14.4720i) q^{27} +(-5.40895 + 10.4219i) q^{28} +(-0.314786 - 1.37917i) q^{29} +(4.49765 - 7.79016i) q^{30} +(1.21741 + 2.10861i) q^{31} +(-3.61578 + 3.35495i) q^{32} +(11.6440 - 7.93874i) q^{33} +(5.85485 - 7.34175i) q^{34} +(-1.89846 - 2.17301i) q^{35} +(20.9372 + 26.2544i) q^{36} +(-3.25439 - 1.00385i) q^{37} +(5.67271 - 14.4538i) q^{38} +(0.242919 + 3.24153i) q^{39} +(-2.46482 - 6.28027i) q^{40} +(-6.85890 + 3.30307i) q^{41} +(20.5429 - 7.36093i) q^{42} +(7.77025 + 3.74196i) q^{43} +(1.43786 - 19.1868i) q^{44} +(-7.88560 + 2.43239i) q^{45} +(9.32034 + 6.35450i) q^{46} +(10.8241 - 1.63147i) q^{47} +22.1693 q^{48} +(-0.104552 - 6.99922i) q^{49} -9.66862 q^{50} +(-11.8959 + 1.79302i) q^{51} +(3.66687 + 2.50003i) q^{52} +(1.93326 - 0.596331i) q^{53} +(2.81467 - 37.5592i) q^{54} +(4.26002 + 2.05152i) q^{55} +(5.29009 - 15.4883i) q^{56} +(-17.9223 + 8.63090i) q^{57} +(1.31135 + 3.34128i) q^{58} +(-0.0449346 - 0.599610i) q^{59} +(-5.74814 + 14.6460i) q^{60} +(-6.71464 - 2.07119i) q^{61} +(-3.85187 - 4.83009i) q^{62} +(-18.4081 - 7.86827i) q^{63} +(-0.701239 + 0.879326i) q^{64} +(-0.901111 + 0.614367i) q^{65} +(-26.2124 + 24.3216i) q^{66} +(2.94936 + 5.10845i) q^{67} +(-8.21240 + 14.2243i) q^{68} +(-3.21579 - 14.0893i) q^{69} +(5.58497 + 4.73412i) q^{70} +(2.82382 - 12.3720i) q^{71} +(-34.3122 - 31.8370i) q^{72} +(12.5062 + 1.88501i) q^{73} +(8.54484 + 1.28793i) q^{74} +(9.08008 + 8.42508i) q^{75} +(-6.04334 + 26.4776i) q^{76} +(4.66531 + 10.4788i) q^{77} +(-1.83533 - 8.04110i) q^{78} +(-0.0838893 + 0.145301i) q^{79} +(3.71902 + 6.44153i) q^{80} +(-18.7318 + 17.3805i) q^{81} +(15.9598 - 10.8812i) q^{82} +(-9.64234 + 12.0911i) q^{83} +(-33.6113 + 18.0865i) q^{84} +(-2.51659 - 3.15570i) q^{85} +(-20.9106 - 6.45005i) q^{86} +(1.68000 - 4.28058i) q^{87} +(2.00420 + 26.7441i) q^{88} +(-2.38330 - 6.07254i) q^{89} +(18.8650 - 9.08491i) q^{90} +(-2.63125 - 0.276587i) q^{91} +(-17.7766 - 8.56078i) q^{92} +(-0.591463 + 7.89253i) q^{93} +(-26.5405 + 8.18666i) q^{94} +(-5.51435 - 3.75962i) q^{95} +(-15.8546 + 2.38970i) q^{96} -2.99453 q^{97} +(2.90921 + 17.5214i) q^{98} +32.8041 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Introduction

L-functions

Modular forms

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