LMFDB - Embedded newform 637.2.bl.b.534.10

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			534.10
Character	$\chi$	$=$	637.534
Dual form			637.2.bl.b.235.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.985016 + 0.148467i) q^{2} +(1.55762 + 1.06197i) q^{3} +(-0.962931 + 0.297025i) q^{4} +(-0.0612958 + 0.817935i) q^{5} +(-1.69195 - 0.814798i) q^{6} +(-1.98261 - 1.75193i) q^{7} +(2.69939 - 1.29996i) q^{8} +(0.202377 + 0.515649i) q^{9} +O(q^{10})$	\(q+(-0.985016 + 0.148467i) q^{2} +(1.55762 + 1.06197i) q^{3} +(-0.962931 + 0.297025i) q^{4} +(-0.0612958 + 0.817935i) q^{5} +(-1.69195 - 0.814798i) q^{6} +(-1.98261 - 1.75193i) q^{7} +(2.69939 - 1.29996i) q^{8} +(0.202377 + 0.515649i) q^{9} +(-0.0610593 - 0.814780i) q^{10} +(2.19864 - 5.60206i) q^{11} +(-1.81531 - 0.559948i) q^{12} +(0.623490 + 0.781831i) q^{13} +(2.21301 + 1.43133i) q^{14} +(-0.964094 + 1.20894i) q^{15} +(-0.800742 + 0.545936i) q^{16} +(-1.16502 + 1.08098i) q^{17} +(-0.275902 - 0.477876i) q^{18} +(3.07896 - 5.33291i) q^{19} +(-0.183923 - 0.805821i) q^{20} +(-1.22766 - 4.83430i) q^{21} +(-1.33398 + 5.84454i) q^{22} +(-3.21205 - 2.98035i) q^{23} +(5.58513 + 0.841823i) q^{24} +(4.27889 + 0.644939i) q^{25} +(-0.730224 - 0.677549i) q^{26} +(1.02611 - 4.49567i) q^{27} +(2.42948 + 1.09810i) q^{28} +(0.715759 + 3.13595i) q^{29} +(0.770161 - 1.33396i) q^{30} +(4.54590 + 7.87372i) q^{31} +(-3.68490 + 3.41909i) q^{32} +(9.37384 - 6.39097i) q^{33} +(0.987070 - 1.23775i) q^{34} +(1.55449 - 1.51426i) q^{35} +(-0.348036 - 0.436423i) q^{36} +(-0.0339874 - 0.0104837i) q^{37} +(-2.24106 + 5.71013i) q^{38} +(0.140880 + 1.87992i) q^{39} +(0.897820 + 2.28761i) q^{40} +(8.05908 - 3.88105i) q^{41} +(1.92700 + 4.57960i) q^{42} +(-9.72337 - 4.68253i) q^{43} +(-0.453193 + 6.04744i) q^{44} +(-0.434172 + 0.133924i) q^{45} +(3.60640 + 2.45881i) q^{46} +(-4.38718 + 0.661262i) q^{47} -1.82701 q^{48} +(0.861493 + 6.94679i) q^{49} -4.31053 q^{50} +(-2.96261 + 0.446541i) q^{51} +(-0.832601 - 0.567658i) q^{52} +(8.48568 - 2.61748i) q^{53} +(-0.343273 + 4.58065i) q^{54} +(4.44735 + 2.14173i) q^{55} +(-7.62928 - 2.15183i) q^{56} +(10.4592 - 5.03689i) q^{57} +(-1.17062 - 2.98269i) q^{58} +(0.356798 + 4.76113i) q^{59} +(0.569272 - 1.45048i) q^{60} +(-8.43583 - 2.60211i) q^{61} +(-5.64677 - 7.08083i) q^{62} +(0.502145 - 1.37688i) q^{63} +(4.33056 - 5.43035i) q^{64} +(-0.677705 + 0.462051i) q^{65} +(-8.28453 + 7.68692i) q^{66} +(-5.69146 - 9.85789i) q^{67} +(0.800753 - 1.38694i) q^{68} +(-1.83812 - 8.05332i) q^{69} +(-1.30638 + 1.72236i) q^{70} +(-0.207022 + 0.907025i) q^{71} +(1.21662 + 1.12886i) q^{72} +(9.52154 + 1.43514i) q^{73} +(0.0350347 + 0.00528063i) q^{74} +(5.97997 + 5.54861i) q^{75} +(-1.38082 + 6.04975i) q^{76} +(-14.1735 + 7.25483i) q^{77} +(-0.417876 - 1.83083i) q^{78} +(2.86210 - 4.95730i) q^{79} +(-0.397458 - 0.688418i) q^{80} +(7.59073 - 7.04317i) q^{81} +(-7.36212 + 5.01941i) q^{82} +(7.32215 - 9.18168i) q^{83} +(2.61806 + 4.29045i) q^{84} +(-0.812758 - 1.01917i) q^{85} +(10.2729 + 3.16876i) q^{86} +(-2.21539 + 5.64471i) q^{87} +(-1.34744 - 17.9803i) q^{88} +(1.44145 + 3.67276i) q^{89} +(0.407783 - 0.196378i) q^{90} +(0.133575 - 2.64238i) q^{91} +(3.97822 + 1.91581i) q^{92} +(-1.28086 + 17.0918i) q^{93} +(4.22327 - 1.30271i) q^{94} +(4.17325 + 2.84527i) q^{95} +(-9.37062 + 1.41239i) q^{96} -8.45417 q^{97} +(-1.87996 - 6.71479i) q^{98} +3.33365 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 $

$2$	−0.985016	+	0.148467i	−0.696512	+	0.104982i	−0.487749	−	0.872984i	$-0.662182\pi$
$2$	−0.985016	+	0.148467i	−0.696512	+	0.104982i	−0.208763	+	0.977966i	$0.566944\pi$
$3$	1.55762	+	1.06197i	0.899291	+	0.613126i	0.922243	−	0.386611i	$-0.126354\pi$
$3$	1.55762	+	1.06197i	0.899291	+	0.613126i	−0.0229525	+	0.999737i	$0.507307\pi$
$4$	−0.962931	+	0.297025i	−0.481465	+	0.148512i
$5$	−0.0612958	+	0.817935i	−0.0274123	+	0.365792i	0.966582	+	0.256358i	$0.0825227\pi$
$5$	−0.0612958	+	0.817935i	−0.0274123	+	0.365792i	−0.993994	+	0.109433i	$0.965096\pi$
$6$	−1.69195	−	0.814798i	−0.690734	−	0.332640i
$7$	−1.98261	−	1.75193i	−0.749357	−	0.662167i
$7$	−1.98261	−	1.75193i	−0.749357	−	0.662167i
$8$	2.69939	−	1.29996i	0.954379	−	0.459605i
$9$	0.202377	+	0.515649i	0.0674591	+	0.171883i
$10$	−0.0610593	−	0.814780i	−0.0193086	−	0.257656i
$11$	2.19864	−	5.60206i	0.662916	−	1.68908i	−0.0600456	−	0.998196i	$-0.519125\pi$
$11$	2.19864	−	5.60206i	0.662916	−	1.68908i	0.722962	−	0.690888i	$-0.242780\pi$
$12$	−1.81531	−	0.559948i	−0.524034	−	0.161643i
$13$	0.623490	+	0.781831i	0.172925	+	0.216841i
$13$	0.623490	+	0.781831i	0.172925	+	0.216841i
$14$	2.21301	+	1.43133i	0.591451	+	0.382538i
$15$	−0.964094	+	1.20894i	−0.248928	+	0.312146i
$16$	−0.800742	+	0.545936i	−0.200185	+	0.136484i
$17$	−1.16502	+	1.08098i	−0.282558	+	0.262175i	−0.808700	−	0.588221i	$-0.799828\pi$
$17$	−1.16502	+	1.08098i	−0.282558	+	0.262175i	0.526142	+	0.850397i	$0.323638\pi$
$18$	−0.275902	−	0.477876i	−0.0650307	−	0.112637i
$19$	3.07896	−	5.33291i	0.706361	−	1.22345i	−0.259837	−	0.965653i	$-0.583669\pi$
$19$	3.07896	−	5.33291i	0.706361	−	1.22345i	0.966198	−	0.257801i	$-0.0829980\pi$
$20$	−0.183923	−	0.805821i	−0.0411265	−	0.180187i
$21$	−1.22766	−	4.83430i	−0.267898	−	1.05493i
$22$	−1.33398	+	5.84454i	−0.284405	+	1.24606i
$23$	−3.21205	−	2.98035i	−0.669758	−	0.621445i	0.270172	−	0.962812i	$-0.412920\pi$
$23$	−3.21205	−	2.98035i	−0.669758	−	0.621445i	−0.939930	+	0.341367i	$0.889110\pi$
$24$	5.58513	+	0.841823i	1.14006	+	0.171836i
$25$	4.27889	+	0.644939i	0.855779	+	0.128988i
$26$	−0.730224	−	0.677549i	−0.143209	−	0.132878i
$27$	1.02611	−	4.49567i	0.197475	−	0.865192i
$28$	2.42948	+	1.09810i	0.459129	+	0.207522i
$29$	0.715759	+	3.13595i	0.132913	+	0.582330i	0.996890	+	0.0787998i	$0.0251088\pi$
$29$	0.715759	+	3.13595i	0.132913	+	0.582330i	−0.863977	+	0.503531i	$0.832034\pi$
$30$	0.770161	−	1.33396i	0.140612	−	0.243546i
$31$	4.54590	+	7.87372i	0.816467	+	1.41416i	0.908270	+	0.418385i	$0.137404\pi$
$31$	4.54590	+	7.87372i	0.816467	+	1.41416i	−0.0918024	+	0.995777i	$0.529263\pi$
$32$	−3.68490	+	3.41909i	−0.651405	+	0.604415i
$33$	9.37384	−	6.39097i	1.63178	−	1.11253i
$34$	0.987070	−	1.23775i	0.169281	−	0.212272i
$35$	1.55449	−	1.51426i	0.262757	−	0.255957i
$36$	−0.348036	−	0.436423i	−0.0580060	−	0.0727372i
$37$	−0.0339874	−	0.0104837i	−0.00558750	−	0.00172352i	0.291960	−	0.956430i	$-0.405693\pi$
$37$	−0.0339874	−	0.0104837i	−0.00558750	−	0.00172352i	−0.297548	+	0.954707i	$0.596169\pi$
$38$	−2.24106	+	5.71013i	−0.363548	+	0.926305i
$39$	0.140880	+	1.87992i	0.0225589	+	0.301028i
$40$	0.897820	+	2.28761i	0.141958	+	0.361703i
$41$	8.05908	−	3.88105i	1.25862	−	0.606118i	0.318808	−	0.947819i	$-0.396717\pi$
$41$	8.05908	−	3.88105i	1.25862	−	0.606118i	0.939809	+	0.341701i	$0.111003\pi$
$42$	1.92700	+	4.57960i	0.297343	+	0.706647i
$43$	−9.72337	−	4.68253i	−1.48280	−	0.714079i	−0.494868	−	0.868968i	$-0.664783\pi$
$43$	−9.72337	−	4.68253i	−1.48280	−	0.714079i	−0.987932	+	0.154890i	$0.950498\pi$
$44$	−0.453193	+	6.04744i	−0.0683215	+	0.911686i
$45$	−0.434172	+	0.133924i	−0.0647226	+	0.0199643i
$46$	3.60640	+	2.45881i	0.531735	+	0.362531i
$47$	−4.38718	+	0.661262i	−0.639937	+	0.0964549i	−0.460992	−	0.887404i	$-0.652506\pi$
$47$	−4.38718	+	0.661262i	−0.639937	+	0.0964549i	−0.178945	+	0.983859i	$0.557268\pi$
$48$	−1.82701			−0.263707
$49$	0.861493	+	6.94679i	0.123070	+	0.992398i
$50$	−4.31053			−0.609601
$51$	−2.96261	+	0.446541i	−0.414848	+	0.0625283i
$52$	−0.832601	−	0.567658i	−0.115461	−	0.0787199i
$53$	8.48568	−	2.61748i	1.16560	−	0.359539i	0.349210	−	0.937044i	$-0.386450\pi$
$53$	8.48568	−	2.61748i	1.16560	−	0.359539i	0.816387	+	0.577505i	$0.195974\pi$
$54$	−0.343273	+	4.58065i	−0.0467135	+	0.623348i
$55$	4.44735	+	2.14173i	0.599681	+	0.288791i
$56$	−7.62928	−	2.15183i	−1.01950	−	0.287550i
$57$	10.4592	−	5.03689i	1.38536	−	0.667152i
$58$	−1.17062	−	2.98269i	−0.153710	−	0.391647i
$59$	0.356798	+	4.76113i	0.0464511	+	0.619847i	0.971046	+	0.238894i	$0.0767849\pi$
$59$	0.356798	+	4.76113i	0.0464511	+	0.619847i	−0.924595	+	0.380953i	$0.875596\pi$
$60$	0.569272	−	1.45048i	0.0734927	−	0.187256i
$61$	−8.43583	−	2.60211i	−1.08010	−	0.333166i	−0.296881	−	0.954915i	$-0.595946\pi$
$61$	−8.43583	−	2.60211i	−1.08010	−	0.333166i	−0.783217	+	0.621749i	$0.786423\pi$
$62$	−5.64677	−	7.08083i	−0.717141	−	0.899266i
$63$	0.502145	−	1.37688i	0.0632643	−	0.173471i
$64$	4.33056	−	5.43035i	0.541320	−	0.678794i
$65$	−0.677705	+	0.462051i	−0.0840589	+	0.0573104i
$66$	−8.28453	+	7.68692i	−1.01976	+	0.946195i
$67$	−5.69146	−	9.85789i	−0.695322	−	1.20433i	−0.970072	−	0.242817i	$-0.921928\pi$
$67$	−5.69146	−	9.85789i	−0.695322	−	1.20433i	0.274750	−	0.961516i	$-0.411405\pi$
$68$	0.800753	−	1.38694i	0.0971055	−	0.168192i
$69$	−1.83812	−	8.05332i	−0.221283	−	0.969506i
$70$	−1.30638	+	1.72236i	−0.156142	+	0.205862i
$71$	−0.207022	+	0.907025i	−0.0245691	+	0.107644i	−0.985726	−	0.168360i	$-0.946153\pi$
$71$	−0.207022	+	0.907025i	−0.0245691	+	0.107644i	0.961157	+	0.276004i	$0.0890102\pi$
$72$	1.21662	+	1.12886i	0.143380	+	0.133037i
$73$	9.52154	+	1.43514i	1.11441	+	0.167971i	0.680332	−	0.732904i	$-0.261835\pi$
$73$	9.52154	+	1.43514i	1.11441	+	0.167971i	0.434080	+	0.900874i	$0.357074\pi$
$74$	0.0350347	+	0.00528063i	0.00407270	+	0.000613860i
$75$	5.97997	+	5.54861i	0.690508	+	0.640698i
$76$	−1.38082	+	6.04975i	−0.158390	+	0.693954i
$77$	−14.1735	+	7.25483i	−1.61522	+	0.826765i
$78$	−0.417876	−	1.83083i	−0.0473151	−	0.207301i
$79$	2.86210	−	4.95730i	0.322011	−	0.557740i	−0.658892	−	0.752238i	$-0.728974\pi$
$79$	2.86210	−	4.95730i	0.322011	−	0.557740i	0.980903	+	0.194498i	$0.0623078\pi$
$80$	−0.397458	−	0.688418i	−0.0444372	−	0.0769675i
$81$	7.59073	−	7.04317i	0.843415	−	0.782574i
$82$	−7.36212	+	5.01941i	−0.813010	+	0.554301i
$83$	7.32215	−	9.18168i	0.803710	−	1.00782i	−0.195920	−	0.980620i	$-0.562769\pi$
$83$	7.32215	−	9.18168i	0.803710	−	1.00782i	0.999630	−	0.0272009i	$-0.00865937\pi$
$84$	2.61806	+	4.29045i	0.285654	+	0.468126i
$85$	−0.812758	−	1.01917i	−0.0881560	−	0.110544i
$86$	10.2729	+	3.16876i	1.10775	+	0.341697i
$87$	−2.21539	+	5.64471i	−0.237514	+	0.605177i
$88$	−1.34744	−	17.9803i	−0.143637	−	1.91670i
$89$	1.44145	+	3.67276i	0.152794	+	0.389312i	0.986691	−	0.162608i	$-0.0519906\pi$
$89$	1.44145	+	3.67276i	0.152794	+	0.389312i	−0.833897	+	0.551920i	$0.813895\pi$
$90$	0.407783	−	0.196378i	0.0429841	−	0.0207001i
$91$	0.133575	−	2.64238i	0.0140025	−	0.276996i
$92$	3.97822	+	1.91581i	0.414758	+	0.199737i
$93$	−1.28086	+	17.0918i	−0.132819	+	1.77234i
$94$	4.22327	−	1.30271i	0.435597	−	0.134364i
$95$	4.17325	+	2.84527i	0.428166	+	0.291919i
$96$	−9.37062	+	1.41239i	−0.956385	+	0.144152i
$97$	−8.45417			−0.858391			−0.429196	−	0.903212i	$-0.641203\pi$
$97$	−8.45417			−0.858391			−0.429196	+	0.903212i	$0.641203\pi$
$98$	−1.87996	−	6.71479i	−0.189904	−	0.678297i
$99$	3.33365			0.335045
$100$	−4.31184	+	0.649905i	−0.431184	+	0.0649905i
$101$	5.47770	+	3.73463i	0.545052	+	0.371610i	0.804321	−	0.594195i	$-0.202529\pi$
$101$	5.47770	+	3.73463i	0.545052	+	0.371610i	−0.259269	+	0.965805i	$0.583482\pi$
$102$	2.85192	−	0.879701i	0.282382	−	0.0871034i
$103$	0.953685	−	12.7260i	0.0939693	−	1.25393i	−0.728469	−	0.685079i	$-0.759768\pi$
$103$	0.953685	−	12.7260i	0.0939693	−	1.25393i	0.822438	−	0.568855i	$-0.192613\pi$
$104$	2.69939	+	1.29996i	0.264697	+	0.127471i
$105$	4.02939	−	0.707825i	0.393228	−	0.0690767i
$106$	−7.96992	+	3.83811i	−0.774107	+	0.372790i
$107$	1.97088	+	5.02172i	0.190532	+	0.485468i	0.993935	−	0.109968i	$-0.0350747\pi$
$107$	1.97088	+	5.02172i	0.190532	+	0.485468i	−0.803403	+	0.595436i	$0.796980\pi$
$108$	0.347255	+	4.63380i	0.0334147	+	0.445888i
$109$	3.28532	−	8.37087i	0.314677	−	0.801784i	−0.682788	−	0.730617i	$-0.739233\pi$
$109$	3.28532	−	8.37087i	0.314677	−	0.801784i	0.997464	−	0.0711667i	$-0.0226722\pi$
$110$	−4.69869	−	1.44935i	−0.448003	−	0.138190i
$111$	−0.0418060	−	0.0524231i	−0.00396805	−	0.00497578i
$112$	2.54400	+	0.320463i	0.240385	+	0.0302809i
$113$	2.22396	−	2.78876i	0.209212	−	0.262344i	−0.666143	−	0.745824i	$-0.732056\pi$
$113$	2.22396	−	2.78876i	0.209212	−	0.262344i	0.875355	+	0.483480i	$0.160627\pi$
$114$	−9.55467	+	6.51427i	−0.894877	+	0.610117i
$115$	2.63461	−	2.44456i	0.245679	−	0.227957i
$116$	−1.62068	−	2.80710i	−0.150476	−	0.260633i
$117$	−0.276970	+	0.479727i	−0.0256059	+	0.0443508i
$118$	−1.05832	−	4.63682i	−0.0974266	−	0.426854i
$119$	4.20357	−	0.102132i	0.385340	−	0.00936242i
$120$	−1.03090	+	4.51667i	−0.0941079	+	0.412314i
$121$	−18.4854	−	17.1520i	−1.68049	−	1.55927i
$122$	8.69576	+	1.31068i	0.787277	+	0.118663i
$123$	16.6745	+	2.51328i	1.50349	+	0.226614i
$124$	−6.71608	−	6.23161i	−0.603121	−	0.559615i
$125$	−1.70239	+	7.45864i	−0.152266	+	0.667121i
$126$	−0.290199	+	1.43080i	−0.0258530	+	0.127466i
$127$	−2.77178	−	12.1439i	−0.245955	−	1.07760i	−0.935491	−	0.353350i	$-0.885043\pi$
$127$	−2.77178	−	12.1439i	−0.245955	−	1.07760i	0.689536	−	0.724251i	$-0.257814\pi$
$128$	1.56735	−	2.71473i	0.138535	−	0.239950i
$129$	−10.1726	−	17.6195i	−0.895647	−	1.55131i
$130$	0.598951	−	0.555745i	0.0525315	−	0.0487421i
$131$	−0.592655	+	0.404065i	−0.0517805	+	0.0353034i	−0.588934	−	0.808181i	$-0.700452\pi$
$131$	−0.592655	+	0.404065i	−0.0517805	+	0.0353034i	0.537153	+	0.843485i	$0.319500\pi$
$132$	−7.12808	+	8.93833i	−0.620419	+	0.777981i
$133$	−15.4473	+	5.17897i	−1.33945	+	0.449074i
$134$	7.06975	+	8.86519i	0.610734	+	0.765836i
$135$	3.61427	+	1.11485i	0.311067	+	0.0959514i
$136$	−1.73961	+	4.43245i	−0.149170	+	0.380080i
$137$	1.27639	+	17.0323i	0.109050	+	1.45517i	0.736462	+	0.676478i	$0.236495\pi$
$137$	1.27639	+	17.0323i	0.109050	+	1.45517i	−0.627413	+	0.778687i	$0.715886\pi$
$138$	3.00623	+	7.65975i	0.255907	+	0.652041i
$139$	−7.95840	+	3.83256i	−0.675023	+	0.325074i	−0.739801	−	0.672826i	$-0.765080\pi$
$139$	−7.95840	+	3.83256i	−0.675023	+	0.325074i	0.0647782	+	0.997900i	$0.479366\pi$
$140$	−1.04709	+	1.91985i	−0.0884955	+	0.162257i
$141$	−7.53579	−	3.62905i	−0.634628	−	0.305621i
$142$	0.0692570	−	0.924170i	0.00581192	−	0.0775547i
$143$	5.75070	−	1.77385i	0.480897	−	0.148337i
$144$	−0.443564	−	0.302416i	−0.0369636	−	0.0252014i
$145$	−2.60887	+	0.393224i	−0.216655	+	0.0326555i
$146$	−9.59195			−0.793835
$147$	−6.03537	+	11.7353i	−0.497789	+	0.967912i
$148$	0.0358415			0.00294615
$149$	−1.35908	+	0.204848i	−0.111340	+	0.0167818i	−0.204476	−	0.978872i	$-0.565549\pi$
$149$	−1.35908	+	0.204848i	−0.111340	+	0.0167818i	0.0931359	+	0.995653i	$0.470311\pi$
$150$	−6.71416	−	4.57764i	−0.548209	−	0.373762i
$151$	−14.7688	+	4.55559i	−1.20187	+	0.370728i	−0.830110	−	0.557600i	$-0.811722\pi$
$151$	−14.7688	+	4.55559i	−1.20187	+	0.370728i	−0.371762	+	0.928328i	$0.621246\pi$
$152$	1.37875	−	18.3981i	0.111831	−	1.49229i
$153$	−0.793178	−	0.381974i	−0.0641246	−	0.0308808i
$154$	12.8840	−	9.25042i	1.03822	−	0.745420i
$155$	−6.71884	+	3.23562i	−0.539670	+	0.259891i
$156$	−0.694040	−	1.76839i	−0.0555677	−	0.141584i
$157$	0.600700	+	8.01579i	0.0479411	+	0.639730i	0.968482	+	0.249084i	$0.0801294\pi$
$157$	0.600700	+	8.01579i	0.0479411	+	0.639730i	−0.920541	+	0.390646i	$0.872252\pi$
$158$	−2.08322	+	5.30795i	−0.165732	+	0.422278i
$159$	15.9971	+	4.93446i	1.26865	+	0.391328i
$160$	−2.57072	−	3.22358i	−0.203234	−	0.254847i
$161$	1.14689	+	11.5361i	0.0903876	+	0.909176i
$162$	−6.43132	+	8.06461i	−0.505292	+	0.633616i
$163$	0.341270	−	0.232674i	0.0267303	−	0.0182244i	−0.549881	−	0.835243i	$-0.685327\pi$
$163$	0.341270	−	0.232674i	0.0267303	−	0.0182244i	0.576612	+	0.817018i	$0.304375\pi$
$164$	−6.60757	+	6.13093i	−0.515964	+	0.478745i
$165$	4.65282	+	8.05893i	0.362222	+	0.627387i
$166$	−5.84926	+	10.1312i	−0.453990	+	0.786334i
$167$	3.85196	+	16.8765i	0.298073	+	1.30594i	0.872992	+	0.487734i	$0.162176\pi$
$167$	3.85196	+	16.8765i	0.298073	+	1.30594i	−0.574919	+	0.818210i	$0.694966\pi$
$168$	−9.59832	−	11.4538i	−0.740527	−	0.883676i
$169$	−0.222521	+	0.974928i	−0.0171170	+	0.0749945i
$170$	0.951893	+	0.883228i	0.0730069	+	0.0677405i
$171$	3.37302	+	0.508401i	0.257941	+	0.0388784i
$172$	10.7538	+	1.62087i	0.819966	+	0.123590i
$173$	5.54294	+	5.14310i	0.421422	+	0.391022i	0.862179	−	0.506604i	$-0.169099\pi$
$173$	5.54294	+	5.14310i	0.421422	+	0.391022i	−0.440757	+	0.897627i	$0.645290\pi$
$174$	1.34414	−	5.88905i	0.101899	−	0.446448i
$175$	−7.35349	−	8.77498i	−0.555872	−	0.663326i
$176$	1.29782	+	5.68612i	0.0978268	+	0.428607i
$177$	−4.50040	+	7.79493i	−0.338271	+	0.585903i
$178$	−1.96514	−	3.40372i	−0.147294	−	0.255120i
$179$	−13.4887	+	12.5157i	−1.00819	+	0.935467i	−0.997919	−	0.0644804i	$-0.979461\pi$
$179$	−13.4887	+	12.5157i	−1.00819	+	0.935467i	−0.0102745	+	0.999947i	$0.503271\pi$
$180$	0.378299	−	0.257920i	0.0281967	−	0.0192242i
$181$	−14.3310	+	17.9705i	−1.06521	+	1.33573i	−0.126141	+	0.992012i	$0.540259\pi$
$181$	−14.3310	+	17.9705i	−1.06521	+	1.33573i	−0.939072	+	0.343722i	$0.888312\pi$
$182$	0.260733	+	2.62262i	0.0193268	+	0.194401i
$183$	−10.3764	−	13.0117i	−0.767049	−	0.961849i
$184$	−12.5449	−	3.86959i	−0.924822	−	0.285270i
$185$	0.0106583	−	0.0271569i	0.000783614	−	0.00199661i
$186$	−1.27591	−	17.0259i	−0.0935546	−	1.24840i
$187$	3.49424	+	8.90317i	0.255524	+	0.651064i
$188$	4.02814	−	1.93985i	0.293783	−	0.141478i
$189$	−9.91047	+	7.11550i	−0.720880	+	0.517576i
$190$	−4.53315	−	2.18305i	−0.328869	−	0.158375i
$191$	−0.335613	+	4.47844i	−0.0242841	+	0.324049i	0.971811	+	0.235761i	$0.0757584\pi$
$191$	−0.335613	+	4.47844i	−0.0242841	+	0.324049i	−0.996095	+	0.0882873i	$0.971861\pi$
$192$	12.5122	−	3.85950i	0.902991	−	0.278536i
$193$	3.53785	+	2.41206i	0.254660	+	0.173624i	0.683921	−	0.729556i	$-0.260273\pi$
$193$	3.53785	+	2.41206i	0.254660	+	0.173624i	−0.429261	+	0.903181i	$0.641226\pi$
$194$	8.32750	−	1.25517i	0.597880	−	0.0901158i
$195$	−1.54629			−0.110732
$196$	−2.89293	−	6.43339i	−0.206638	−	0.459528i
$197$	−2.71429			−0.193385			−0.0966926	−	0.995314i	$-0.530826\pi$
$197$	−2.71429			−0.193385			−0.0966926	+	0.995314i	$0.530826\pi$
$198$	−3.28370	+	0.494938i	−0.233362	+	0.0351737i
$199$	13.5390	+	9.23075i	0.959756	+	0.654350i	0.938447	−	0.345423i	$-0.112264\pi$
$199$	13.5390	+	9.23075i	0.959756	+	0.654350i	0.0213084	+	0.999773i	$0.493217\pi$
$200$	12.3888	−	3.82144i	0.876021	−	0.270217i
$201$	1.60363	−	21.3989i	0.113111	−	1.50937i
$202$	−5.95010	−	2.86542i	−0.418647	−	0.201610i
$203$	4.07488	−	7.47132i	0.286001	−	0.524384i
$204$	2.72015	−	1.30996i	0.190449	−	0.0917153i
$205$	2.68046	+	6.82969i	0.187211	+	0.477007i
$206$	0.950006	+	12.6769i	0.0661900	+	0.883245i
$207$	0.886766	−	2.25944i	0.0616345	−	0.157042i
$208$	−0.926084	−	0.285659i	−0.0642124	−	0.0198069i
$209$	−23.1057	−	28.9737i	−1.59826	−	2.00415i
$210$	−3.86393	+	1.29545i	−0.266636	+	0.0893947i
$211$	−8.90116	+	11.1617i	−0.612781	+	0.768403i	−0.987309	−	0.158813i	$-0.949233\pi$
$211$	−8.90116	+	11.1617i	−0.612781	+	0.768403i	0.374528	+	0.927216i	$0.377805\pi$
$212$	−7.39366	+	5.04091i	−0.507799	+	0.346211i
$213$	−1.28569	+	1.19295i	−0.0880941	+	0.0817394i
$214$	−2.68691	−	4.65386i	−0.183673	−	0.318132i
$215$	4.42600	−	7.66606i	0.301851	−	0.522821i
$216$	−3.07432	−	13.4695i	−0.209181	−	0.916481i
$217$	4.78146	−	23.5746i	0.324586	−	1.60035i
$218$	−1.99330	+	8.73321i	−0.135003	+	0.591487i
$219$	13.3068	+	12.3469i	0.899193	+	0.834329i
$220$	−4.91864	−	0.741365i	−0.331614	−	0.0499828i
$221$	−1.57152	−	0.236868i	−0.105712	−	0.0159335i
$222$	0.0489628	+	0.0454308i	0.00328616	+	0.00304912i
$223$	0.628870	−	2.75526i	0.0421122	−	0.184506i	−0.949497	−	0.313775i	$-0.898406\pi$
$223$	0.628870	−	2.75526i	0.0421122	−	0.184506i	0.991609	+	0.129270i	$0.0412633\pi$
$224$	13.2957	−	0.323039i	0.888358	−	0.0215840i
$225$	0.533389	+	2.33693i	0.0355592	+	0.155795i
$226$	−1.77660	+	3.07716i	−0.118177	+	0.204689i
$227$	−7.59744	−	13.1592i	−0.504260	−	0.873404i	−0.999988	−	0.00492591i	$-0.998432\pi$
$227$	−7.59744	−	13.1592i	−0.504260	−	0.873404i	0.495728	−	0.868478i	$-0.334901\pi$
$228$	−8.57541	+	7.95682i	−0.567920	+	0.526953i
$229$	13.5947	−	9.26870i	0.898362	−	0.612493i	−0.0236216	−	0.999721i	$-0.507520\pi$
$229$	13.5947	−	9.26870i	0.898362	−	0.612493i	0.921984	+	0.387228i	$0.126567\pi$
$230$	−2.23220	+	2.79909i	−0.147187	+	0.184567i
$231$	−29.7812	−	3.75148i	−1.95946	−	0.246829i
$232$	6.00871	+	7.53469i	0.394491	+	0.494676i
$233$	−24.6598	−	7.60654i	−1.61552	−	0.498321i	−0.650280	−	0.759695i	$-0.725348\pi$
$233$	−24.6598	−	7.60654i	−1.61552	−	0.498321i	−0.965238	+	0.261374i	$0.915824\pi$
$234$	0.201597	−	0.513660i	0.0131788	−	0.0335790i
$235$	−0.271953	−	3.62896i	−0.0177403	−	0.236728i
$236$	−1.75775	−	4.47866i	−0.114420	−	0.291536i
$237$	9.72253	−	4.68212i	0.631546	−	0.304137i
$238$	−4.12542	+	0.724694i	−0.267411	+	0.0469749i
$239$	19.3982	+	9.34167i	1.25476	+	0.604263i	0.938785	−	0.344504i	$-0.111953\pi$
$239$	19.3982	+	9.34167i	1.25476	+	0.604263i	0.315979	+	0.948766i	$0.397667\pi$
$240$	0.111988	−	1.49438i	0.00722881	−	0.0964617i
$241$	23.0449	−	7.10839i	1.48445	−	0.457892i	0.556579	−	0.830795i	$-0.312114\pi$
$241$	23.0449	−	7.10839i	1.48445	−	0.457892i	0.927870	+	0.372903i	$0.121638\pi$
$242$	20.7550	+	14.1505i	1.33418	+	0.909628i
$243$	5.62371	−	0.847638i	0.360761	−	0.0543760i
$244$	8.89601			0.569509
$245$	−5.73482	+	0.278837i	−0.366385	+	0.0178142i
$246$	−16.7978			−1.07099
$247$	6.08914	−	0.917790i	0.387442	−	0.0583976i
$248$	22.5067	+	15.3448i	1.42917	+	0.974395i
$249$	21.1557	−	6.52568i	1.34069	−	0.413548i
$250$	0.569514	−	7.59964i	0.0360192	−	0.480643i
$251$	20.1690	+	9.71287i	1.27305	+	0.613071i	0.943596	−	0.331099i	$-0.107419\pi$
$251$	20.1690	+	9.71287i	1.27305	+	0.613071i	0.329459	+	0.944170i	$0.393134\pi$
$252$	−0.0745625	+	1.47499i	−0.00469699	+	0.0929157i
$253$	−23.7582	+	11.4414i	−1.49367	+	0.719312i
$254$	4.53322	+	11.5505i	0.284440	+	0.724741i
$255$	−0.183647	−	2.45059i	−0.0115004	−	0.153462i
$256$	−6.21590	+	15.8379i	−0.388494	+	0.989866i
$257$	−25.0168	−	7.71666i	−1.56051	−	0.481352i	−0.610089	−	0.792333i	$-0.708866\pi$
$257$	−25.0168	−	7.71666i	−1.56051	−	0.481352i	−0.950416	+	0.310981i	$0.899343\pi$
$258$	12.6361	+	15.8452i	0.786689	+	0.986477i
$259$	0.0490171	+	0.0803287i	0.00304577	+	0.00499138i
$260$	0.515342	−	0.646218i	0.0319602	−	0.0400768i
$261$	−1.47219	+	1.00372i	−0.0911265	+	0.0621290i
$262$	0.523784	−	0.486001i	0.0323595	−	0.0300252i
$263$	13.6088	+	23.5711i	0.839155	+	1.45346i	0.890602	+	0.454783i	$0.150283\pi$
$263$	13.6088	+	23.5711i	0.839155	+	1.45346i	−0.0514475	+	0.998676i	$0.516383\pi$
$264$	16.9957	−	29.4373i	1.04601	−	1.81174i
$265$	1.62080	+	7.10117i	0.0995647	+	0.436222i
$266$	14.4469	−	7.39479i	0.885796	−	0.453404i
$267$	−1.65512	+	7.25153i	−0.101291	+	0.443787i
$268$	8.40852	+	7.80196i	0.513632	+	0.476581i
$269$	4.11225	+	0.619822i	0.250728	+	0.0377912i	0.273204	−	0.961956i	$-0.411917\pi$
$269$	4.11225	+	0.619822i	0.250728	+	0.0377912i	−0.0224755	+	0.999747i	$0.507155\pi$
$270$	−3.72564	−	0.561549i	−0.226735	−	0.0341748i
$271$	−8.97103	−	8.32390i	−0.544952	−	0.505641i	0.358964	−	0.933351i	$-0.383130\pi$
$271$	−8.97103	−	8.32390i	−0.544952	−	0.505641i	−0.903916	+	0.427710i	$0.859320\pi$
$272$	0.342732	−	1.50161i	0.0207812	−	0.0910483i
$273$	3.01417	−	3.97396i	0.182426	−	0.240515i
$274$	−3.78600	−	16.5876i	−0.228721	−	1.00209i
$275$	13.0208	−	22.5526i	0.785181	−	1.35997i
$276$	4.16202	+	7.20882i	0.250524	+	0.433920i
$277$	−2.75548	+	2.55672i	−0.165561	+	0.153618i	−0.758602	−	0.651554i	$-0.774117\pi$
$277$	−2.75548	+	2.55672i	−0.165561	+	0.153618i	0.593041	+	0.805172i	$0.297927\pi$
$278$	7.27014	−	4.95670i	0.436034	−	0.297283i
$279$	−3.14009	+	3.93755i	−0.187992	+	0.235735i
$280$	2.22770	−	6.10835i	0.133130	−	0.365044i
$281$	13.0112	+	16.3155i	0.776182	+	0.973302i	0.999999	−	0.00132960i	$-0.000423226\pi$
$281$	13.0112	+	16.3155i	0.776182	+	0.973302i	−0.223817	+	0.974631i	$0.571852\pi$
$282$	7.96167	+	2.45585i	0.474111	+	0.146244i
$283$	4.99799	−	12.7347i	0.297100	−	0.756998i	−0.701900	−	0.712276i	$-0.747665\pi$
$283$	4.99799	−	12.7347i	0.297100	−	0.756998i	0.998999	−	0.0447221i	$-0.0142402\pi$
$284$	−0.0700605	−	0.934893i	−0.00415733	−	0.0554757i
$285$	3.47874	+	8.86369i	0.206063	+	0.525040i
$286$	−5.40117	+	2.60107i	−0.319378	+	0.153804i
$287$	−22.7773	−	6.42432i	−1.34450	−	0.379216i
$288$	−2.50879	−	1.20817i	−0.147832	−	0.0711921i
$289$	−1.08166	+	14.4338i	−0.0636271	+	0.849044i
$290$	2.51140	−	0.774665i	0.147475	−	0.0454899i
$291$	−13.1684	−	8.97804i	−0.771943	−	0.526302i
$292$	−9.59486	+	1.44619i	−0.561497	+	0.0846320i
$293$	11.2430			0.656824			0.328412	−	0.944535i	$-0.393487\pi$
$293$	11.2430			0.656824			0.328412	+	0.944535i	$0.393487\pi$
$294$	4.20263	−	12.4555i	0.245102	−	0.726421i
$295$	−3.91617			−0.228008
$296$	−0.105374	+	0.0158825i	−0.00612473	+	0.000923154i
$297$	−22.9290	−	15.6327i	−1.33047	−	0.907101i
$298$	1.30830	−	0.403557i	0.0757878	−	0.0233774i
$299$	0.327448	−	4.36950i	0.0189368	−	0.252694i
$300$	−7.40637	−	3.56672i	−0.427607	−	0.205925i
$301$	11.0742	+	26.3183i	0.638306	+	1.51696i
$302$	13.8712	−	6.68002i	0.798198	−	0.384392i
$303$	4.56611	+	11.6343i	0.262316	+	0.668371i
$304$	0.445981	+	5.95120i	0.0255787	+	0.341325i
$305$	2.64544	−	6.74046i	0.151477	−	0.385958i
$306$	0.838004	+	0.258490i	0.0479055	+	0.0147769i
$307$	−10.2709	−	12.8793i	−0.586191	−	0.735060i	0.396964	−	0.917834i	$-0.370064\pi$
$307$	−10.2709	−	12.8793i	−0.586191	−	0.735060i	−0.983155	+	0.182774i	$0.941492\pi$
$308$	11.4932	−	11.1958i	0.654886	−	0.637938i
$309$	15.0001	−	18.8095i	0.853325	−	1.07004i
$310$	6.13778	−	4.18467i	0.348603	−	0.237673i
$311$	0.577864	−	0.536179i	0.0327677	−	0.0304039i	−0.663619	−	0.748071i	$-0.730980\pi$
$311$	0.577864	−	0.536179i	0.0327677	−	0.0304039i	0.696387	+	0.717667i	$0.254790\pi$
$312$	2.82411	+	4.89150i	0.159884	+	0.276926i
$313$	−9.64330	+	16.7027i	−0.545072	+	0.944092i	0.453531	+	0.891241i	$0.350164\pi$
$313$	−9.64330	+	16.7027i	−0.545072	+	0.944092i	−0.998602	+	0.0528511i	$0.983169\pi$
$314$	−1.78178	−	7.80650i	−0.100552	−	0.440546i
$315$	1.09542	+	0.495119i	0.0617200	+	0.0278968i
$316$	−1.28356	+	5.62365i	−0.0722060	+	0.316355i
$317$	−10.6074	−	9.84219i	−0.595768	−	0.552792i	0.323598	−	0.946195i	$-0.395107\pi$
$317$	−10.6074	−	9.84219i	−0.595768	−	0.552792i	−0.919366	+	0.393402i	$0.871298\pi$
$318$	−16.4900	−	2.48547i	−0.924715	−	0.139378i
$319$	19.1414	+	2.88511i	1.07172	+	0.161535i
$320$	4.17623	+	3.87498i	0.233458	+	0.216618i
$321$	−2.26302	+	9.91492i	−0.126309	+	0.553397i
$322$	−2.84245	−	11.1930i	−0.158403	−	0.623762i
$323$	2.17772	+	9.54121i	0.121172	+	0.530887i
$324$	−5.21735	+	9.03672i	−0.289853	+	0.502040i
$325$	2.16361	+	3.74749i	0.120016	+	0.207873i
$326$	−0.301612	+	0.279855i	−0.0167047	+	0.0154997i
$327$	14.0068	−	9.54971i	0.774580	−	0.528100i
$328$	16.7094	−	20.9529i	0.922623	−	1.15693i
$329$	9.85656	+	6.37501i	0.543410	+	0.351466i
$330$	−5.77960	−	7.24738i	−0.318156	−	0.398955i
$331$	33.8327	+	10.4360i	1.85961	+	0.573614i	0.997793	+	0.0663976i	$0.0211506\pi$
$331$	33.8327	+	10.4360i	1.85961	+	0.573614i	0.861819	+	0.507217i	$0.169326\pi$
$332$	−4.32353	+	11.0162i	−0.237285	+	0.604592i
$333$	−0.00147236	−	0.0196473i	−8.06847e−5	−	0.00107666i
$334$	−6.29985	−	16.0518i	−0.344713	−	0.878313i
$335$	8.41198	−	4.05099i	0.459595	−	0.221329i
$336$	3.62226	+	3.20080i	0.197610	+	0.174618i
$337$	−1.25325	−	0.603534i	−0.0682690	−	0.0328766i	0.399438	−	0.916760i	$-0.369205\pi$
$337$	−1.25325	−	0.603534i	−0.0682690	−	0.0328766i	−0.467707	+	0.883884i	$0.654920\pi$
$338$	0.0744418	−	0.993357i	0.00404910	−	0.0540315i
$339$	6.42564	−	1.98205i	0.348993	−	0.107650i
$340$	1.08535	+	0.739978i	0.0588612	+	0.0401309i
$341$	54.1039	−	8.15484i	2.92989	−	0.441610i
$342$	−3.39796			−0.183741
$343$	10.4623	−	15.2820i	0.564909	−	0.825153i
$344$	−32.3343			−1.74335
$345$	6.69976	−	1.00983i	0.360703	−	0.0543672i
$346$	−6.22347	−	4.24309i	−0.334576	−	0.228110i
$347$	18.6855	−	5.76370i	1.00309	−	0.309412i	0.250652	−	0.968077i	$-0.419355\pi$
$347$	18.6855	−	5.76370i	1.00309	−	0.309412i	0.752436	+	0.658666i	$0.228879\pi$
$348$	0.456644	−	6.09349i	0.0244787	−	0.326646i
$349$	−8.38883	−	4.03985i	−0.449044	−	0.216248i	0.195674	−	0.980669i	$-0.437311\pi$
$349$	−8.38883	−	4.03985i	−0.449044	−	0.216248i	−0.644717	+	0.764421i	$0.723025\pi$
$350$	8.54611	+	7.55175i	0.456809	+	0.403658i
$351$	4.15463	−	2.00076i	0.221757	−	0.106793i
$352$	11.0521	+	28.1604i	0.589081	+	1.50095i
$353$	−1.01733	−	13.5753i	−0.0541469	−	0.722540i	−0.956535	−	0.291616i	$-0.905807\pi$
$353$	−1.01733	−	13.5753i	−0.0541469	−	0.722540i	0.902388	−	0.430923i	$-0.141812\pi$
$354$	3.27568	−	8.34630i	0.174100	−	0.443601i
$355$	−0.729198	−	0.224928i	−0.0387018	−	0.0119379i
$356$	−2.47892	−	3.10847i	−0.131383	−	0.164749i
$357$	6.65601	+	4.30496i	0.352273	+	0.227843i
$358$	11.4284	−	14.3308i	0.604011	−	0.757406i
$359$	15.3577	−	10.4707i	0.810547	−	0.552622i	−0.0856253	−	0.996327i	$-0.527289\pi$
$359$	15.3577	−	10.4707i	0.810547	−	0.552622i	0.896173	+	0.443706i	$0.146336\pi$
$360$	−0.997905	+	0.925920i	−0.0525942	+	0.0488003i
$361$	−9.45996	−	16.3851i	−0.497893	−	0.862376i
$362$	11.4482	−	19.8289i	0.601705	−	1.04218i
$363$	−10.5784	−	46.3471i	−0.555223	−	2.43259i
$364$	0.656228	+	2.58410i	0.0343957	+	0.135444i
$365$	−1.75748	+	7.70003i	−0.0919908	+	0.403038i
$366$	12.1528	+	11.2761i	0.635236	+	0.589413i
$367$	−9.08043	−	1.36865i	−0.473994	−	0.0714432i	−0.0922990	−	0.995731i	$-0.529422\pi$
$367$	−9.08043	−	1.36865i	−0.473994	−	0.0714432i	−0.381695	+	0.924288i	$0.624660\pi$
$368$	4.19910	+	0.632912i	0.218893	+	0.0329928i
$369$	3.63223	+	3.37022i	0.189087	+	0.175447i
$370$	−0.00646669	+	0.0283324i	−0.000336187	+	0.00147293i
$371$	−21.4094	−	9.67685i	−1.11152	−	0.502397i
$372$	−3.84332	−	16.8387i	−0.199267	−	0.873046i
$373$	−11.1993	+	19.3977i	−0.579875	+	1.00437i	0.415618	+	0.909539i	$0.363565\pi$
$373$	−11.1993	+	19.3977i	−0.579875	+	1.00437i	−0.995493	+	0.0948341i	$0.969768\pi$
$374$	−4.76371	−	8.25099i	−0.246326	−	0.426648i
$375$	−10.5725	+	9.80983i	−0.545961	+	0.506578i
$376$	−10.9831	+	7.48816i	−0.566411	+	0.386172i
$377$	−2.00551	+	2.51483i	−0.103289	+	0.129520i
$378$	8.70555	−	8.48027i	0.447765	−	0.436178i
$379$	−5.48454	−	6.87740i	−0.281722	−	0.353268i	0.620756	−	0.784004i	$-0.286826\pi$
$379$	−5.48454	−	6.87740i	−0.281722	−	0.353268i	−0.902478	+	0.430735i	$0.858254\pi$
$380$	−4.86366	−	1.50024i	−0.249501	−	0.0769608i
$381$	8.57908	−	21.8591i	0.439520	−	1.11988i
$382$	−0.334318	−	4.46117i	−0.0171052	−	0.228253i
$383$	11.6823	+	29.7660i	0.596937	+	1.52097i	0.835300	+	0.549795i	$0.185294\pi$
$383$	11.6823	+	29.7660i	0.596937	+	1.52097i	−0.238363	+	0.971176i	$0.576611\pi$
$384$	5.32427	−	2.56403i	0.271703	−	0.130845i
$385$	−5.06521	−	12.0377i	−0.258147	−	0.613496i
$386$	−3.84295	−	1.85067i	−0.195601	−	0.0941965i
$387$	0.446751	−	5.96148i	0.0227096	−	0.303039i
$388$	8.14078	−	2.51110i	0.413286	−	0.127482i
$389$	0.293603	+	0.200175i	0.0148862	+	0.0101493i	0.570740	−	0.821131i	$-0.306656\pi$
$389$	0.293603	+	0.200175i	0.0148862	+	0.0101493i	−0.555854	+	0.831280i	$0.687609\pi$
$390$	1.52312	−	0.229573i	0.0771261	−	0.0116249i
$391$	6.96377			0.352173
$392$	11.3560	+	17.6322i	0.573566	+	0.890560i
$393$	−1.35223			−0.0682111
$394$	2.67362	−	0.402983i	0.134695	−	0.0203020i
$395$	3.87931	+	2.64487i	0.195189	+	0.133078i
$396$	−3.21007	+	0.990177i	−0.161312	+	0.0497583i
$397$	2.55586	−	34.1055i	0.128275	−	1.71171i	−0.447653	−	0.894207i	$-0.647740\pi$
$397$	2.55586	−	34.1055i	0.128275	−	1.71171i	0.575928	−	0.817501i	$-0.304641\pi$
$398$	−14.7066	−	7.08234i	−0.737176	−	0.355005i
$399$	−29.5608	−	8.33759i	−1.47989	−	0.417402i
$400$	−3.77838	+	1.81957i	−0.188919	+	0.0909787i
$401$	6.69412	+	17.0563i	0.334288	+	0.851753i	0.994885	+	0.101012i	$0.0322081\pi$
$401$	6.69412	+	17.0563i	0.334288	+	0.851753i	−0.660597	+	0.750741i	$0.729697\pi$
$402$	1.59744	+	21.3164i	0.0796732	+	1.06317i
$403$	−3.32161	+	8.46331i	−0.165461	+	0.421588i
$404$	−6.38393	−	1.96918i	−0.317612	−	0.0979704i
$405$	5.29558	+	6.64044i	0.263139	+	0.329966i
$406$	−2.90458	+	7.96436i	−0.144152	+	0.395265i
$407$	−0.133457	+	0.167349i	−0.00661521	+	0.00829521i
$408$	−7.41675	+	5.05666i	−0.367184	+	0.250342i
$409$	−12.5531	+	11.6476i	−0.620711	+	0.575936i	−0.926561	−	0.376144i	$-0.877250\pi$
$409$	−12.5531	+	11.6476i	−0.620711	+	0.575936i	0.305850	+	0.952080i	$0.401059\pi$
$410$	−3.65428	−	6.32940i	−0.180472	−	0.312587i
$411$	−16.0996	+	27.8852i	−0.794132	+	1.37548i
$412$	2.86162	+	12.5376i	0.140982	+	0.617681i
$413$	7.63377	−	10.0646i	0.375633	−	0.495245i
$414$	−0.538026	+	2.35725i	−0.0264425	+	0.115852i
$415$	7.06120	+	6.55184i	0.346621	+	0.321617i
$416$	−4.97065	−	0.749205i	−0.243706	−	0.0367328i
$417$	−16.4662	−	2.48188i	−0.806353	−	0.121538i
$418$	27.0612	+	25.1091i	1.32361	+	1.22813i
$419$	−4.21683	+	18.4751i	−0.206005	+	0.902569i	0.761189	+	0.648531i	$0.224616\pi$
$419$	−4.21683	+	18.4751i	−0.206005	+	0.902569i	−0.967194	+	0.254038i	$0.918241\pi$
$420$	−3.66978	+	1.87842i	−0.179067	+	0.0916573i
$421$	5.97720	+	26.1878i	0.291311	+	1.27632i	0.882703	+	0.469931i	$0.155721\pi$
$421$	5.97720	+	26.1878i	0.291311	+	1.27632i	−0.591392	+	0.806384i	$0.701421\pi$
$422$	7.11064	−	12.3160i	0.346141	−	0.599533i
$423$	−1.22885	−	2.12842i	−0.0597485	−	0.103487i
$424$	19.5035	−	18.0966i	0.947176	−	0.878850i
$425$	−5.68214	+	3.87402i	−0.275624	+	0.187918i
$426$	1.08931	−	1.36596i	0.0527774	−	0.0661807i
$427$	12.1663	+	19.9379i	0.588767	+	0.964865i
$428$	−3.38940	−	4.25017i	−0.163833	−	0.205440i
$429$	10.8412	+	3.34405i	0.523416	+	0.161452i
$430$	−3.22153	+	8.20831i	−0.155356	+	0.395840i
$431$	0.764783	+	10.2053i	0.0368383	+	0.491573i	0.984858	+	0.173362i	$0.0554630\pi$
$431$	0.764783	+	10.2053i	0.0368383	+	0.491573i	−0.948020	+	0.318211i	$0.896918\pi$
$432$	1.63270	+	4.16006i	0.0785535	+	0.200151i
$433$	11.3432	−	5.46262i	0.545122	−	0.262517i	−0.140992	−	0.990011i	$-0.545029\pi$
$433$	11.3432	−	5.46262i	0.545122	−	0.262517i	0.686114	+	0.727494i	$0.259315\pi$
$434$	−1.20975	+	23.9313i	−0.0580700	+	1.14874i
$435$	−4.48121	−	2.15804i	−0.214858	−	0.103470i
$436$	−0.677184	+	9.03639i	−0.0324312	+	0.432764i
$437$	−25.7837	+	7.95321i	−1.23340	+	0.380454i
$438$	−14.9406	−	10.1863i	−0.713888	−	0.486721i
$439$	9.80290	−	1.47755i	0.467867	−	0.0705196i	0.0891221	−	0.996021i	$-0.471594\pi$
$439$	9.80290	−	1.47755i	0.467867	−	0.0705196i	0.378745	+	0.925501i	$0.376356\pi$
$440$	14.7893			0.705052
$441$	−3.40776	+	1.85010i	−0.162274	+	0.0881000i
$442$	1.58314			0.0753022
$443$	2.64225	−	0.398255i	0.125537	−	0.0189217i	−0.0859732	−	0.996297i	$-0.527400\pi$
$443$	2.64225	−	0.398255i	0.125537	−	0.0189217i	0.211510	+	0.977376i	$0.432162\pi$
$444$	0.0558273	+	0.0380624i	0.00264945	+	0.00180636i
$445$	−3.09244	+	0.953891i	−0.146596	+	0.0452188i
$446$	−0.210381	+	2.80734i	−0.00996184	+	0.132931i
$447$	−2.33446	−	1.12422i	−0.110416	−	0.0531737i
$448$	−18.0994	+	3.17944i	−0.855117	+	0.150215i
$449$	−34.1589	+	16.4500i	−1.61206	+	0.776325i	−0.999896	−	0.0144086i	$-0.995413\pi$
$449$	−34.1589	+	16.4500i	−1.61206	+	0.776325i	−0.612160	+	0.790734i	$0.709699\pi$
$450$	−0.872354	−	2.22272i	−0.0411232	−	0.104780i
$451$	−4.02279	−	53.6805i	−0.189426	−	2.52771i
$452$	−1.31319	+	3.34595i	−0.0617672	+	0.157380i
$453$	−27.8421	−	8.58814i	−1.30813	−	0.403506i
$454$	9.43731	+	11.8340i	0.442915	+	0.555398i
$455$	2.15311	+	0.271222i	0.100939	+	0.0127151i
$456$	21.6857	−	27.1931i	1.01553	−	1.27343i
$457$	26.5972	−	18.1336i	1.24416	−	0.848256i	0.251346	−	0.967897i	$-0.419127\pi$
$457$	26.5972	−	18.1336i	1.24416	−	0.848256i	0.992817	+	0.119641i	$0.0381745\pi$
$458$	−12.0149	+	11.1482i	−0.561419	+	0.520921i
$459$	3.66429	+	6.34673i	0.171034	+	0.296240i
$460$	−1.81085	+	3.13649i	−0.0844315	+	0.146240i
$461$	−2.33376	−	10.2249i	−0.108694	−	0.476220i	−0.999751	−	0.0223276i	$-0.992892\pi$
$461$	−2.33376	−	10.2249i	−0.108694	−	0.476220i	0.891057	−	0.453892i	$-0.149965\pi$
$462$	29.8919	−	0.726269i	1.39070	−	0.0337891i
$463$	−3.73114	+	16.3472i	−0.173401	+	0.759718i	0.811181	+	0.584795i	$0.198825\pi$
$463$	−3.73114	+	16.3472i	−0.173401	+	0.759718i	−0.984582	+	0.174923i	$0.944032\pi$
$464$	−2.28516	−	2.12032i	−0.106086	−	0.0984335i
$465$	−13.9015	−	2.09531i	−0.644666	−	0.0971678i
$466$	25.4196	+	3.83139i	1.17754	+	0.177486i
$467$	−7.76185	−	7.20195i	−0.359176	−	0.333266i	0.479858	−	0.877346i	$-0.340688\pi$
$467$	−7.76185	−	7.20195i	−0.359176	−	0.333266i	−0.839033	+	0.544080i	$0.816879\pi$
$468$	0.124213	−	0.544211i	0.00574173	−	0.0251562i
$469$	−5.98638	+	29.5154i	−0.276425	+	1.36289i
$470$	0.806661	+	3.53421i	0.0372085	+	0.163021i
$471$	−7.57683	+	13.1235i	−0.349122	+	0.604697i
$472$	7.15241	+	12.3883i	0.329216	+	0.570219i
$473$	−47.6100	+	44.1756i	−2.18911	+	2.03120i
$474$	−8.88171	+	6.05545i	−0.407950	+	0.278136i
$475$	16.6139	−	20.8332i	0.762300	−	0.955894i
$476$	−4.01741	+	1.34691i	−0.184138	+	0.0617355i
$477$	3.06701	+	3.84591i	0.140429	+	0.176092i
$478$	−20.4945	−	6.32170i	−0.937395	−	0.289148i
$479$	0.888116	−	2.26288i	0.0405791	−	0.103394i	−0.909148	−	0.416474i	$-0.863266\pi$
$479$	0.888116	−	2.26288i	0.0405791	−	0.103394i	0.949727	+	0.313080i	$0.101361\pi$
$480$	−0.580867	−	7.75113i	−0.0265128	−	0.353789i
$481$	−0.0129943	−	0.0331089i	−0.000592489	−	0.00150964i
$482$	−21.6442	+	10.4233i	−0.985866	+	0.474768i
$483$	−10.4646	+	19.1869i	−0.476154	+	0.873032i
$484$	22.8947	+	11.0255i	1.04067	+	0.501160i
$485$	0.518205	−	6.91496i	0.0235305	−	0.313992i
$486$	−5.41360	+	1.66987i	−0.245566	+	0.0757470i
$487$	−34.2805	−	23.3721i	−1.55340	−	1.05909i	−0.968824	−	0.247749i	$-0.920309\pi$
$487$	−34.2805	−	23.3721i	−1.55340	−	1.05909i	−0.584574	−	0.811340i	$-0.698738\pi$
$488$	−26.1542	+	3.94212i	−1.18395	+	0.178451i
$489$	0.778659			0.0352122
$490$	5.60750	−	1.12609i	0.253321	−	0.0508717i
$491$	1.98108			0.0894051			0.0447025	−	0.999000i	$-0.485766\pi$
$491$	1.98108			0.0894051			0.0447025	+	0.999000i	$0.485766\pi$
$492$	−16.8029	+	2.53263i	−0.757533	+	0.114180i
$493$	−4.22376	−	2.87971i	−0.190228	−	0.129696i
$494$	−5.86164	+	1.80808i	−0.263728	+	0.0813492i
$495$	−0.204339	+	2.72671i	−0.00918434	+	0.122556i
$496$	−7.93864	−	3.82305i	−0.356456	−	0.171660i
$497$	1.99949	−	1.43559i	0.0896893	−	0.0643950i
$498$	−19.8699	+	9.56884i	−0.890391	+	0.428790i
$499$	−7.23962	−	18.4462i	−0.324090	−	0.825767i	−0.996343	−	0.0854459i	$-0.972769\pi$
$499$	−7.23962	−	18.4462i	−0.324090	−	0.825767i	0.672253	−	0.740322i	$-0.265327\pi$
$500$	−0.576122	−	7.68781i	−0.0257649	−	0.343809i
$501$	−11.9224	+	30.3778i	−0.532654	+	1.35718i
$502$	−21.3088	−	6.57290i	−0.951059	−	0.293363i
$503$	−3.05255	−	3.82777i	−0.136106	−	0.170672i	0.709107	−	0.705101i	$-0.249098\pi$
$503$	−3.05255	−	3.82777i	−0.136106	−	0.170672i	−0.845214	+	0.534429i	$0.820527\pi$
$504$	−0.434404	−	4.36951i	−0.0193499	−	0.194633i
$505$	−3.39045	+	4.25149i	−0.150873	+	0.189189i
$506$	21.7036	−	14.7972i	0.964841	−	0.657818i
$507$	−1.38194	+	1.28225i	−0.0613742	+	0.0569469i
$508$	6.27608	+	10.8705i	0.278456	+	0.482300i
$509$	−5.06327	+	8.76984i	−0.224425	+	0.388716i	−0.956147	−	0.292888i	$-0.905384\pi$
$509$	−5.06327	+	8.76984i	−0.224425	+	0.388716i	0.731721	+	0.681604i	$0.238717\pi$
$510$	0.544728	+	2.38661i	0.0241210	+	0.105681i
$511$	−16.3632	−	19.5264i	−0.723867	−	0.863796i
$512$	2.37629	−	10.4112i	0.105018	−	0.460115i
$513$	−20.8157	−	19.3141i	−0.919034	−	0.852739i
$514$	25.7876	+	3.88686i	1.13744	+	0.171442i
$515$	10.3506	+	1.56010i	0.456103	+	0.0687464i
$516$	15.0289	+	13.9448i	0.661612	+	0.613886i
$517$	−5.94144	+	26.0311i	−0.261304	+	1.14485i
$518$	−0.0602088	−	0.0718477i	−0.00264542	−	0.00315681i
$519$	3.17199	+	13.8974i	0.139235	+	0.610028i
$520$	−1.22874	+	2.12824i	−0.0538839	+	0.0933297i
$521$	6.39289	+	11.0728i	0.280078	+	0.485109i	0.971404	−	0.237434i	$-0.0763064\pi$
$521$	6.39289	+	11.0728i	0.280078	+	0.485109i	−0.691326	+	0.722543i	$0.742973\pi$
$522$	1.30111	−	1.20726i	0.0569483	−	0.0528403i
$523$	−14.0054	+	9.54872i	−0.612413	+	0.417536i	−0.829413	−	0.558635i	$-0.811325\pi$
$523$	−14.0054	+	9.54872i	−0.612413	+	0.417536i	0.217000	+	0.976172i	$0.430373\pi$
$524$	0.450668	−	0.565120i	0.0196875	−	0.0246874i
$525$	−2.13520	−	21.4772i	−0.0931879	−	0.937342i
$526$	−16.9044	−	21.1975i	−0.737069	−	0.924255i
$527$	−13.8074	−	4.25901i	−0.601458	−	0.185525i
$528$	−4.01696	+	10.2350i	−0.174816	+	0.445423i
$529$	−0.283996	−	3.78966i	−0.0123476	−	0.164768i
$530$	−2.65080	−	6.75414i	−0.115144	−	0.293381i
$531$	−2.38287	+	1.14753i	−0.103408	+	0.0497985i
$532$	13.3364	−	9.57521i	0.578204	−	0.415138i
$533$	8.05908	+	3.88105i	0.349077	+	0.168107i
$534$	0.553700	−	7.38861i	0.0239609	−	0.319736i
$535$	−4.22825	+	1.30424i	−0.182803	+	0.0563873i
$536$	−28.1783	−	19.2116i	−1.21712	−	0.829817i
$537$	−34.3015	+	5.17012i	−1.48022	+	0.223107i
$538$	−4.14266			−0.178603
$539$	40.8104	+	10.4474i	1.75783	+	0.450001i
$540$	−3.81143			−0.164018
$541$	29.3659	−	4.42620i	1.26254	−	0.190297i	0.516552	−	0.856256i	$-0.327215\pi$
$541$	29.3659	−	4.42620i	1.26254	−	0.190297i	0.745989	+	0.665958i	$0.231977\pi$
$542$	10.0724	+	6.86728i	0.432649	+	0.294975i
$543$	−41.4062	+	12.7721i	−1.77691	+	0.548104i
$544$	0.597013	−	7.96659i	0.0255967	−	0.341565i
$545$	6.64545	+	3.20028i	0.284660	+	0.137085i
$546$	−2.37901	+	4.36192i	−0.101812	+	0.186673i
$547$	−29.8806	+	14.3897i	−1.27760	+	0.615261i	−0.944773	−	0.327726i	$-0.893718\pi$
$547$	−29.8806	+	14.3897i	−1.27760	+	0.615261i	−0.332830	+	0.942987i	$0.608003\pi$
$548$	−6.28808	−	16.0218i	−0.268614	−	0.684416i
$549$	−0.365446	−	4.87654i	−0.0155969	−	0.208126i
$550$	−9.47733	+	24.1478i	−0.404115	+	1.02967i
$551$	18.9275	+	5.83836i	0.806339	+	0.248723i
$552$	−15.4308	−	19.3496i	−0.656778	−	0.823573i
$553$	−14.3593	+	4.81420i	−0.610618	+	0.204721i
$554$	2.33461	−	2.92751i	0.0991880	−	0.124378i
$555$	0.0454412	−	0.0309813i	0.00192887	−	0.00131508i
$556$	6.52502	−	6.05433i	0.276723	−	0.256761i
$557$	11.5123	+	19.9399i	0.487793	+	0.844882i	0.999901	−	0.0140385i	$-0.00446874\pi$
$557$	11.5123	+	19.9399i	0.487793	+	0.844882i	−0.512108	+	0.858921i	$0.671135\pi$
$558$	2.50844	−	4.34475i	0.106191	−	0.183928i
$559$	−2.40147	−	10.5215i	−0.101571	−	0.445014i
$560$	−0.418054	+	2.06118i	−0.0176660	+	0.0871009i
$561$	−4.01217	+	17.5785i	−0.169394	+	0.742164i
$562$	−15.2385	−	14.1393i	−0.642799	−	0.596431i
$563$	9.03328	+	1.36155i	0.380707	+	0.0573824i	0.336608	−	0.941645i	$-0.390720\pi$
$563$	9.03328	+	1.36155i	0.380707	+	0.0573824i	0.0440990	+	0.999027i	$0.485958\pi$
$564$	8.33436	+	1.25620i	0.350940	+	0.0528957i
$565$	2.14470	+	1.98999i	0.0902283	+	0.0837196i
$566$	−3.03242	+	13.2859i	−0.127462	+	0.558448i
$567$	−27.3886	+	0.665447i	−1.15021	+	0.0279461i
$568$	0.620260	+	2.71754i	0.0260255	+	0.114025i
$569$	−6.81662	+	11.8067i	−0.285767	+	0.494964i	−0.972795	−	0.231668i	$-0.925582\pi$
$569$	−6.81662	+	11.8067i	−0.285767	+	0.494964i	0.687028	+	0.726631i	$0.258915\pi$
$570$	−4.74259	−	8.21440i	−0.198645	−	0.344063i
$571$	−0.253857	+	0.235545i	−0.0106236	+	0.00985724i	−0.685467	−	0.728104i	$-0.740402\pi$
$571$	−0.253857	+	0.235545i	−0.0106236	+	0.00985724i	0.674843	+	0.737961i	$0.264211\pi$
$572$	−5.01064	+	3.41620i	−0.209506	+	0.142838i
$573$	−5.27871	+	6.61929i	−0.220521	+	0.276525i
$574$	23.3899	+	2.94637i	0.976274	+	0.122979i
$575$	−11.8219	−	14.8242i	−0.493006	−	0.618210i
$576$	3.67657	+	1.13407i	0.153190	+	0.0472529i
$577$	10.9359	−	27.8643i	0.455268	−	1.16000i	−0.500462	−	0.865759i	$-0.666836\pi$
$577$	10.9359	−	27.8643i	0.455268	−	1.16000i	0.955730	−	0.294245i	$-0.0950683\pi$
$578$	−1.07749	−	14.3781i	−0.0448176	−	0.598049i
$579$	2.94908	+	7.51414i	0.122560	+	0.312277i
$580$	2.39537	−	1.15355i	0.0994622	−	0.0478985i
$581$	−30.6026	+	5.37583i	−1.26961	+	0.223027i
$582$	14.3040	+	6.88844i	0.592920	+	0.285535i
$583$	3.99369	−	53.2922i	0.165402	−	2.20714i
$584$	27.5680	−	8.50360i	1.14077	−	0.351881i
$585$	−0.375408	−	0.255949i	−0.0155212	−	0.0105822i
$586$	−11.0746	+	1.66922i	−0.457485	+	0.0689548i
$587$	44.9498			1.85528			0.927638	−	0.373481i	$-0.121836\pi$
$587$	44.9498			1.85528			0.927638	+	0.373481i	$0.121836\pi$
$588$	2.32597	−	13.0929i	0.0959212	−	0.539944i
$589$	55.9865			2.30688
$590$	3.85749	−	0.581423i	0.158810	−	0.0239368i
$591$	−4.22782	−	2.88248i	−0.173909	−	0.118569i
$592$	0.0329386	−	0.0101602i	0.00135377	−	0.000417582i
$593$	−0.312753	+	4.17340i	−0.0128432	+	0.171381i	0.987094	+	0.160144i	$0.0511959\pi$
$593$	−0.312753	+	4.17340i	−0.0128432	+	0.171381i	−0.999937	+	0.0112368i	$0.996423\pi$
$594$	24.9063	+	11.9943i	1.02192	+	0.492131i
$595$	−0.174124	+	3.44451i	−0.00713837	+	0.141211i
$596$	1.24785	−	0.600934i	0.0511140	−	0.0246152i
$597$	11.2859	+	28.7559i	0.461900	+	1.17690i
$598$	0.326185	+	4.35264i	0.0133387	+	0.177993i
$599$	4.68167	−	11.9287i	0.191288	−	0.487394i	−0.802765	−	0.596296i	$-0.796638\pi$
$599$	4.68167	−	11.9287i	0.191288	−	0.487394i	0.994052	+	0.108903i	$0.0347336\pi$
$600$	23.3552	+	7.20414i	0.953474	+	0.294108i
$601$	16.7125	+	20.9568i	0.681718	+	0.854847i	0.995511	−	0.0946439i	$-0.0301712\pi$
$601$	16.7125	+	20.9568i	0.681718	+	0.854847i	−0.313793	+	0.949491i	$0.601600\pi$
$602$	−14.8157	−	24.2798i	−0.603842	−	0.989570i
$603$	3.93139	−	4.92981i	0.160099	−	0.200757i
$604$	12.8683	−	8.77343i	0.523602	−	0.356986i
$605$	15.1623	−	14.0685i	0.616434	−	0.571967i
$606$	−6.22500	−	10.7820i	−0.252873	−	0.437990i
$607$	0.524112	−	0.907789i	0.0212731	−	0.0368460i	−0.855193	−	0.518310i	$-0.826561\pi$
$607$	0.524112	−	0.907789i	0.0212731	−	0.0368460i	0.876466	+	0.481464i	$0.159895\pi$
$608$	6.88804	+	30.1785i	0.279347	+	1.22390i
$609$	14.2814	−	7.31007i	0.578711	−	0.296219i
$610$	−1.60506	+	7.03223i	−0.0649870	+	0.284727i
$611$	−3.25236	−	3.01775i	−0.131576	−	0.122085i
$612$	0.877231	+	0.132221i	0.0354600	+	0.00534473i
$613$	32.3453	+	4.87527i	1.30641	+	0.196910i	0.765101	−	0.643911i	$-0.222689\pi$
$613$	32.3453	+	4.87527i	1.30641	+	0.196910i	0.541313	+	0.840821i	$0.317927\pi$
$614$	12.0292	+	11.1614i	0.485457	+	0.450438i
$615$	−3.07777	+	13.4846i	−0.124108	+	0.543752i
$616$	−28.8287	+	38.0085i	−1.16154	+	1.53141i
$617$	2.36818	+	10.3757i	0.0953395	+	0.417710i	0.999964	−	0.00850006i	$-0.00270568\pi$
$617$	2.36818	+	10.3757i	0.0953395	+	0.417710i	−0.904624	+	0.426210i	$0.859849\pi$
$618$	−11.9827	+	20.7547i	−0.482016	+	0.834876i
$619$	8.11574	+	14.0569i	0.326199	+	0.564994i	0.981754	−	0.190154i	$-0.0608986\pi$
$619$	8.11574	+	14.0569i	0.326199	+	0.564994i	−0.655555	+	0.755147i	$0.727565\pi$
$620$	5.50872	−	5.11134i	0.221235	−	0.205276i
$621$	−16.6946	+	11.3822i	−0.669930	+	0.456750i
$622$	−0.489600	+	0.613939i	−0.0196312	+	0.0246167i
$623$	3.57658	−	9.80699i	0.143293	−	0.392909i
$624$	−1.13912	−	1.42842i	−0.0456015	−	0.0571825i
$625$	14.6786	+	4.52774i	0.587142	+	0.181109i
$626$	7.01901	−	17.8841i	0.280536	−	0.714794i
$627$	−5.22085	−	69.6674i	−0.208501	−	2.78225i
$628$	−2.95932	−	7.54023i	−0.118090	−	0.300888i
$629$	0.0509286	−	0.0245259i	0.00203066	−	0.000977912i
$630$	−1.15252	−	0.325066i	−0.0459174	−	0.0129509i
$631$	−5.35256	−	2.57766i	−0.213082	−	0.102615i	0.324299	−	0.945955i	$-0.394872\pi$
$631$	−5.35256	−	2.57766i	−0.213082	−	0.102615i	−0.537380	+	0.843340i	$0.680586\pi$
$632$	1.28164	−	17.1023i	0.0509809	−	0.680293i
$633$	−25.7179	+	7.93293i	−1.02220	+	0.315306i
$634$	11.9097	+	8.11987i	0.472993	+	0.322481i
$635$	10.1029	−	1.52276i	0.400920	−	0.0604289i
$636$	−16.8698			−0.668930
$637$	−4.89408	+	5.00479i	−0.193911	+	0.198297i
$638$	−19.2830			−0.763421
$639$	−0.509603	+	0.0768103i	−0.0201596	+	0.00303857i
$640$	2.12440	+	1.44839i	0.0839742	+	0.0572526i
$641$	−0.428867	+	0.132288i	−0.0169392	+	0.00522507i	−0.303213	−	0.952923i	$-0.598059\pi$
$641$	−0.428867	+	0.132288i	−0.0169392	+	0.00522507i	0.286274	+	0.958148i	$0.407583\pi$
$642$	0.757066	−	10.1023i	0.0298790	−	0.398708i
$643$	−0.449577	−	0.216505i	−0.0177296	−	0.00853812i	0.424998	−	0.905194i	$-0.360275\pi$
$643$	−0.449577	−	0.216505i	−0.0177296	−	0.00853812i	−0.442728	+	0.896656i	$0.645989\pi$
$644$	−4.53090	−	10.7679i	−0.178542	−	0.424313i
$645$	15.0351	−	7.24053i	0.592007	−	0.285095i
$646$	−3.56165	−	9.07493i	−0.140131	−	0.357048i
$647$	0.522170	+	6.96787i	0.0205286	+	0.273935i	0.998017	+	0.0629459i	$0.0200496\pi$
$647$	0.522170	+	6.96787i	0.0205286	+	0.273935i	−0.977488	+	0.210990i	$0.932331\pi$
$648$	11.3345	−	28.8799i	0.445262	−	1.13451i
$649$	27.4566	+	8.46924i	1.07777	+	0.332447i
$650$	−2.68757	−	3.37011i	−0.105415	−	0.132187i
$651$	32.4831	−	31.6425i	1.27311	−	1.24017i
$652$	−0.259509	+	0.325414i	−0.0101632	+	0.0127442i
$653$	−37.1150	+	25.3045i	−1.45242	+	0.990243i	−0.457539	+	0.889189i	$0.651269\pi$
$653$	−37.1150	+	25.3045i	−1.45242	+	0.990243i	−0.994881	+	0.101054i	$0.967778\pi$
$654$	−12.3792	+	11.4862i	−0.484063	+	0.449145i
$655$	−0.294172	−	0.509521i	−0.0114942	−	0.0199086i
$656$	−4.33443	+	7.50746i	−0.169231	+	0.293117i
$657$	1.18691	+	5.20021i	0.0463060	+	0.202880i
$658$	−10.6554	−	4.81611i	−0.415389	−	0.187752i
$659$	4.41733	−	19.3536i	0.172075	−	0.753908i	−0.813068	−	0.582169i	$-0.802204\pi$
$659$	4.41733	−	19.3536i	0.172075	−	0.753908i	0.985142	−	0.171739i	$-0.0549387\pi$
$660$	−6.87405	−	6.37819i	−0.267572	−	0.248271i
$661$	−35.4776	−	5.34739i	−1.37992	−	0.207989i	−0.583195	−	0.812333i	$-0.698197\pi$
$661$	−35.4776	−	5.34739i	−1.37992	−	0.207989i	−0.796724	+	0.604343i	$0.793436\pi$
$662$	−34.8751	−	5.25658i	−1.35546	−	0.204303i
$663$	−2.19628	−	2.03785i	−0.0852963	−	0.0791434i
$664$	7.82954	−	34.3034i	0.303845	−	1.33123i
$665$	−3.28921	−	12.9523i	−0.127550	−	0.502269i
$666$	0.00436727	+	0.0191343i	0.000169228	+	0.000741438i
$667$	7.04715	−	12.2060i	0.272867	−	0.472619i
$668$	−8.72191	−	15.1068i	−0.337461	−	0.584499i
$669$	3.90553	−	3.62380i	0.150996	−	0.140104i
$670$	−7.68450	+	5.23920i	−0.296878	+	0.202408i
$671$	−33.1246	+	41.5369i	−1.27876	+	1.60351i
$672$	21.0527	+	13.6164i	0.812126	+	0.525265i
$673$	28.4122	+	35.6278i	1.09521	+	1.37335i	0.921420	+	0.388568i	$0.127030\pi$
$673$	28.4122	+	35.6278i	1.09521	+	1.37335i	0.173790	+	0.984783i	$0.444399\pi$
$674$	1.32408	+	0.408424i	0.0510016	+	0.0157319i
$675$	7.29004	−	18.5747i	0.280594	−	0.714941i
$676$	−0.0753055	−	1.00488i	−0.00289637	−	0.0386493i
$677$	8.78829	+	22.3922i	0.337761	+	0.860602i	0.994330	+	0.106336i	$0.0339119\pi$
$677$	8.78829	+	22.3922i	0.337761	+	0.860602i	−0.656569	+	0.754266i	$0.727993\pi$
$678$	−6.03509	+	2.90635i	−0.231776	+	0.111618i
$679$	16.7613	+	14.8111i	0.643241	+	0.568398i
$680$	−3.51883	−	1.69458i	−0.134941	−	0.0649841i
$681$	2.14066	−	28.5651i	0.0820303	−	1.09462i
$682$	−52.0825	+	16.0653i	−1.99434	+	0.615173i
$683$	−4.65114	−	3.17109i	−0.177971	−	0.121339i	0.471058	−	0.882102i	$-0.343872\pi$
$683$	−4.65114	−	3.17109i	−0.177971	−	0.121339i	−0.649029	+	0.760764i	$0.724825\pi$
$684$	−3.39899	+	0.512316i	−0.129964	+	0.0195889i
$685$	−14.0095			−0.535277
$686$	−8.03662	+	16.6064i	−0.306840	+	0.634034i
$687$	31.0184			1.18342
$688$	10.3423	−	1.55885i	0.394295	−	0.0594304i
$689$	7.33716	+	5.00239i	0.279524	+	0.190576i
$690$	−6.44945	+	1.98939i	−0.245526	+	0.0757348i
$691$	−0.980159	+	13.0793i	−0.0372870	+	0.497561i	0.947029	+	0.321148i	$0.104069\pi$
$691$	−0.980159	+	13.0793i	−0.0372870	+	0.497561i	−0.984316	+	0.176413i	$0.943551\pi$
$692$	−6.86510	−	3.30606i	−0.260972	−	0.125677i
$693$	−6.60933	−	5.84032i	−0.251068	−	0.221855i
$694$	−17.5498	+	8.45152i	−0.666180	+	0.320815i
$695$	−2.64697	−	6.74437i	−0.100405	−	0.255829i
$696$	1.35770	+	18.1172i	0.0514633	+	0.686731i
$697$	−5.19363	+	13.2332i	−0.196723	+	0.501242i
$698$	8.86292	+	2.73385i	0.335466	+	0.103478i
$699$	−30.3326	−	38.0359i	−1.14729	−	1.43865i
$700$	9.68729	+	6.26553i	0.366145	+	0.236815i
$701$	23.6411	−	29.6450i	0.892911	−	1.11968i	−0.0992936	−	0.995058i	$-0.531658\pi$
$701$	23.6411	−	29.6450i	0.892911	−	1.11968i	0.992205	−	0.124617i	$-0.0397703\pi$
$702$	−3.79533	+	2.58761i	−0.143245	+	0.0976630i
$703$	−0.160555	+	0.148973i	−0.00605543	+	0.00561862i
$704$	−20.8998	−	36.1995i	−0.787690	−	1.36432i
$705$	3.43024	−	5.94134i	0.129190	−	0.223764i
$706$	3.01757	+	13.2208i	0.113568	+	0.497573i
$707$	−4.31734	−	17.0009i	−0.162370	−	0.639383i
$708$	2.01829	−	8.84271i	0.0758520	−	0.332329i
$709$	−17.9900	−	16.6923i	−0.675628	−	0.626891i	0.265831	−	0.964020i	$-0.414354\pi$
$709$	−17.9900	−	16.6923i	−0.675628	−	0.626891i	−0.941459	+	0.337129i	$0.890544\pi$
$710$	0.751666	+	0.113295i	0.0282095	+	0.00425190i
$711$	3.13545	+	0.472593i	0.117589	+	0.0177236i
$712$	8.66549	+	8.04040i	0.324753	+	0.301327i
$713$	8.86478	−	38.8391i	0.331989	−	1.45454i
$714$	−7.19543	−	3.25226i	−0.269282	−	0.121713i
$715$	1.09840	+	4.81243i	0.0410780	+	0.179975i
$716$	9.27122	−	16.0582i	0.346482	−	0.600124i
$717$	20.2944	+	35.1509i	0.757908	+	1.31274i
$718$	−13.5730	+	12.5939i	−0.506540	+	0.470001i
$719$	14.0498	−	9.57900i	0.523969	−	0.357236i	−0.272267	−	0.962222i	$-0.587773\pi$
$719$	14.0498	−	9.57900i	0.523969	−	0.357236i	0.796237	+	0.604985i	$0.206821\pi$
$720$	0.274546	−	0.344269i	0.0102317	−	0.0128302i
$721$	−24.1859	+	23.5600i	−0.900730	+	0.877420i
$722$	11.7509	+	14.7351i	0.437322	+	0.548385i
$723$	43.4439	+	13.4007i	1.61570	+	0.498376i
$724$	8.46206	−	21.5610i	0.314490	−	0.801307i
$725$	1.04016	+	13.8800i	0.0386307	+	0.515490i
$726$	17.3009	+	44.0821i	0.642098	+	1.63604i
$727$	3.28882	−	1.58381i	0.121976	−	0.0587404i	−0.371901	−	0.928273i	$-0.621294\pi$
$727$	3.28882	−	1.58381i	0.121976	−	0.0587404i	0.493876	+	0.869532i	$0.335580\pi$
$728$	−3.07441	−	7.30645i	−0.113945	−	0.270795i
$729$	−18.3288	−	8.82667i	−0.678844	−	0.326914i
$730$	0.587946	−	7.84559i	0.0217608	−	0.290378i
$731$	16.3896	−	5.05552i	0.606191	−	0.186985i
$732$	13.8566	+	9.44726i	0.512154	+	0.349181i
$733$	−17.0571	+	2.57095i	−0.630019	+	0.0949601i	−0.456287	−	0.889833i	$-0.650821\pi$
$733$	−17.0571	+	2.57095i	−0.630019	+	0.0949601i	−0.173732	+	0.984793i	$0.555583\pi$
$734$	9.14757			0.337643
$735$	−9.22878	−	5.65586i	−0.340409	−	0.208620i
$736$	22.0261			0.811894
$737$	−67.7380	+	10.2099i	−2.49516	+	0.376085i
$738$	−4.07818	−	2.78045i	−0.150120	−	0.102350i
$739$	−37.9734	+	11.7133i	−1.39688	+	0.430879i	−0.899600	−	0.436714i	$-0.856142\pi$
$739$	−37.9734	+	11.7133i	−1.39688	+	0.430879i	−0.497275	+	0.867593i	$0.665666\pi$
$740$	−0.00219693	+	0.0293160i	−8.07607e−5	+	0.00107768i
$741$	10.4592	+	5.03689i	0.384228	+	0.185035i
$742$	22.5253	+	6.35325i	0.826932	+	0.233235i
$743$	−1.18474	+	0.570539i	−0.0434638	+	0.0209310i	−0.455489	−	0.890241i	$-0.650536\pi$
$743$	−1.18474	+	0.570539i	−0.0434638	+	0.0209310i	0.412026	+	0.911172i	$0.364821\pi$
$744$	18.7611	+	47.8026i	0.687817	+	1.75253i
$745$	−0.0842466	−	1.12419i	−0.00308656	−	0.0411872i
$746$	8.15153	−	20.7698i	0.298449	−	0.760435i
$747$	6.21636	+	1.91749i	0.227445	+	0.0701574i
$748$	−6.00917	−	7.53526i	−0.219717	−	0.275516i
$749$	4.89021	−	13.4090i	0.178684	−	0.489953i
$750$	8.95763	−	11.2325i	0.327087	−	0.410154i
$751$	−2.88788	+	1.96893i	−0.105380	+	0.0718471i	−0.614864	−	0.788633i	$-0.710789\pi$
$751$	−2.88788	+	1.96893i	−0.105380	+	0.0718471i	0.509483	+	0.860481i	$0.329837\pi$
$752$	3.15199	−	2.92462i	0.114941	−	0.106650i
$753$	21.1008	+	36.5477i	0.768957	+	1.33187i
$754$	1.60209	−	2.77491i	0.0583448	−	0.101056i
$755$	−2.82091	−	12.3592i	−0.102663	−	0.449797i
$756$	7.42961	−	9.79539i	0.270212	−	0.356255i
$757$	−5.08981	+	22.2999i	−0.184992	+	0.810504i	0.794214	+	0.607638i	$0.207883\pi$
$757$	−5.08981	+	22.2999i	−0.184992	+	0.810504i	−0.979206	+	0.202866i	$0.934974\pi$
$758$	6.42343	+	5.96007i	0.233310	+	0.216480i
$759$	−49.1565	−	7.40915i	−1.78427	−	0.268935i
$760$	14.9640	+	2.25545i	0.542800	+	0.0818139i
$761$	13.4478	+	12.4778i	0.487484	+	0.452319i	0.885214	−	0.465183i	$-0.154012\pi$
$761$	13.4478	+	12.4778i	0.487484	+	0.452319i	−0.397731	+	0.917502i	$0.630202\pi$
$762$	−5.20517	+	22.8053i	−0.188563	+	0.826150i
$763$	−21.1787	+	10.8405i	−0.766720	+	0.392453i
$764$	−1.00704	−	4.41212i	−0.0364333	−	0.159625i
$765$	0.361048	−	0.625354i	0.0130537	−	0.0226097i
$766$	−15.9265	−	27.5856i	−0.575449	−	0.996706i
$767$	−3.49994	+	3.24747i	−0.126376	+	0.117259i
$768$	−26.5013	+	18.0682i	−0.956282	+	0.651982i
$769$	11.1513	−	13.9833i	0.402127	−	0.504251i	−0.538999	−	0.842306i	$-0.681197\pi$
$769$	11.1513	−	13.9833i	0.402127	−	0.504251i	0.941126	+	0.338055i	$0.109769\pi$
$770$	6.77651	+	11.1053i	0.244208	+	0.400206i
$771$	−30.7718	−	38.5866i	−1.10822	−	1.38966i
$772$	−4.12315	−	1.27182i	−0.148395	−	0.0457739i
$773$	−4.15978	+	10.5989i	−0.149617	+	0.381218i	−0.985958	−	0.166991i	$-0.946595\pi$
$773$	−4.15978	+	10.5989i	−0.149617	+	0.381218i	0.836342	+	0.548209i	$0.184690\pi$
$774$	0.445028	+	5.93849i	0.0159962	+	0.213454i
$775$	14.3733	+	36.6227i	0.516305	+	1.31552i
$776$	−22.8211	+	10.9901i	−0.819230	+	0.394521i
$777$	−0.00895643	+	0.177176i	−0.000321310	+	0.00635615i
$778$	−0.318923	−	0.153585i	−0.0114339	−	0.00550629i
$779$	4.11628	−	54.9279i	0.147481	−	1.96800i
$780$	1.48897	−	0.459285i	0.0533136	−	0.0164451i
$781$	4.62603	+	3.15398i	0.165533	+	0.112858i
$782$	−6.85943	+	1.03389i	−0.245293	+	0.0369719i
$783$	14.8326			0.530075
$784$	−4.48234	−	5.09226i	−0.160083	−	0.181866i
$785$	−6.59322			−0.235322
$786$	1.33197	−	0.200762i	0.0475099	−	0.00716096i
$787$	5.69855	+	3.88520i	0.203131	+	0.138493i	0.660613	−	0.750726i	$-0.270296\pi$
$787$	5.69855	+	3.88520i	0.203131	+	0.138493i	−0.457482	+	0.889219i	$0.651249\pi$
$788$	2.61367	−	0.806212i	0.0931083	−	0.0287201i
$789$	−3.83443	+	51.1669i	−0.136509	+	1.82159i
$790$	−4.21386	−	2.02929i	−0.149923	−	0.0721989i
$791$	−9.29495	+	1.63280i	−0.330490	+	0.0580557i
$792$	8.99883	−	4.33361i	0.319759	−	0.153988i
$793$	−3.22524	−	8.21779i	−0.114532	−	0.291822i
$794$	2.54600	+	33.9740i	0.0903541	+	1.20569i
$795$	−5.01662	+	12.7821i	−0.177921	+	0.453336i
$796$	−15.7789	−	4.86715i	−0.559268	−	0.172511i
$797$	15.1720	+	19.0251i	0.537420	+	0.673904i	0.974206	−	0.225662i	$-0.0724545\pi$
$797$	15.1720	+	19.0251i	0.537420	+	0.673904i	−0.436785	+	0.899566i	$0.643883\pi$
$798$	30.3557	+	3.82385i	1.07458	+	0.135363i
$799$	4.39633	−	5.51283i	0.155531	−	0.195030i
$800$	−17.9724	+	12.2534i	−0.635420	+	0.433222i
$801$	−1.60214	+	1.48657i	−0.0566088	+	0.0525253i
$802$	−9.12613	−	15.8069i	−0.322255	−	0.558162i
$803$	28.9742	−	50.1848i	1.02248	−	1.77098i
$804$	4.81183	+	21.0820i	0.169700	+	0.743506i
$805$	−9.50612	+	0.230965i	−0.335047	+	0.00814046i
$806$	2.01531	−	8.82965i	0.0709863	−	0.311011i
$807$	5.74708	+	5.33251i	0.202307	+	0.187713i
$808$	19.6413	+	2.96045i	0.690979	+	0.104148i
$809$	43.1020	+	6.49658i	1.51538	+	0.228407i	0.853458	−	0.521162i	$-0.174501\pi$
$809$	43.1020	+	6.49658i	1.51538	+	0.228407i	0.661926	+	0.749569i	$0.269739\pi$
$810$	−6.20212	−	5.75472i	−0.217920	−	0.202200i
$811$	4.79328	−	21.0007i	0.168315	−	0.737435i	−0.818357	−	0.574710i	$-0.805115\pi$
$811$	4.79328	−	21.0007i	0.168315	−	0.737435i	0.986672	−	0.162724i	$-0.0520281\pi$
$812$	−1.70466	+	8.40470i	−0.0598219	+	0.294947i
$813$	−5.13374	−	22.4924i	−0.180048	−	0.788842i
$814$	0.106611	−	0.184656i	0.00373672	−	0.00647219i
$815$	0.169394	+	0.293398i	0.00593360	+	0.0102773i
$816$	2.12850	−	1.97496i	0.0745124	−	0.0691374i
$817$	−54.9093	+	37.4365i	−1.92103	+	1.30974i
$818$	10.6357	−	13.3368i	0.371870	−	0.466310i
$819$	1.38957	−	0.465879i	0.0485556	−	0.0162791i
$820$	−4.60968	−	5.78036i	−0.160977	−	0.201859i
$821$	2.63683	+	0.813354i	0.0920259	+	0.0283862i	0.340426	−	0.940271i	$-0.389429\pi$
$821$	2.63683	+	0.813354i	0.0920259	+	0.0283862i	−0.248400	+	0.968657i	$0.579905\pi$
$822$	11.7183	−	29.8577i	0.408722	−	1.04141i
$823$	2.05200	+	27.3820i	0.0715282	+	0.954478i	0.911354	+	0.411623i	$0.135038\pi$
$823$	2.05200	+	27.3820i	0.0715282	+	0.954478i	−0.839826	+	0.542855i	$0.817343\pi$
$824$	−13.9689	−	35.5923i	−0.486631	−	1.23992i
$825$	44.2314	−	21.3007i	1.53994	−	0.741596i
$826$	−6.02513	+	11.0471i	−0.209641	+	0.384379i
$827$	29.9413	+	14.4190i	1.04116	+	0.501397i	0.874707	−	0.484652i	$-0.161054\pi$
$827$	29.9413	+	14.4190i	1.04116	+	0.501397i	0.166455	+	0.986049i	$0.446768\pi$
$828$	−0.182784	+	2.43908i	−0.00635217	+	0.0847639i
$829$	−20.7416	+	6.39793i	−0.720385	+	0.222209i	−0.633206	−	0.773983i	$-0.718261\pi$
$829$	−20.7416	+	6.39793i	−0.720385	+	0.222209i	−0.0871788	+	0.996193i	$0.527785\pi$
$830$	−7.92814	−	5.40531i	−0.275190	−	0.187621i
$831$	−7.00713	+	1.05616i	−0.243075	+	0.0366376i
$832$	6.94568			0.240798
$833$	−8.51297	−	7.16186i	−0.294957	−	0.248144i
$834$	16.5879			0.574394
$835$	−14.0400	+	2.11619i	−0.485874	+	0.0732338i
$836$	30.8551	+	21.0367i	1.06715	+	0.727568i
$837$	40.0623	−	12.3576i	1.38475	−	0.427140i
$838$	1.41069	−	18.8244i	0.0487315	−	0.650277i
$839$	40.9517	+	19.7213i	1.41381	+	0.680855i	0.975911	−	0.218168i	$-0.0700082\pi$
$839$	40.9517	+	19.7213i	1.41381	+	0.680855i	0.437900	+	0.899024i	$0.355722\pi$
$840$	9.95676	−	7.14874i	0.343541	−	0.246655i
$841$	16.8063	−	8.09346i	0.579526	−	0.279085i
$842$	−9.77567	−	24.9080i	−0.336892	−	0.858386i
$843$	2.93994	+	39.2307i	0.101257	+	1.35118i
$844$	5.25590	−	13.3918i	0.180915	−	0.460965i
$845$	−0.783788	−	0.241767i	−0.0269631	−	0.00831702i
$846$	1.52643	+	1.91409i	0.0524799	+	0.0658077i
$847$	6.60038	+	66.3908i	0.226792	+	2.28122i
$848$	−5.36585	+	6.72857i	−0.184264	+	0.231060i
$849$	21.3087	−	14.5281i	0.731314	−	0.498602i
$850$	5.02184	−	4.65959i	0.172248	−	0.159823i
$851$	0.0779241	+	0.134969i	0.00267120	+	0.00462666i
$852$	0.883696	−	1.53061i	0.0302749	−	0.0524377i
$853$	−4.57131	−	20.0282i	−0.156519	−	0.685754i	−0.990904	−	0.134572i	$-0.957034\pi$
$853$	−4.57131	−	20.0282i	−0.156519	−	0.685754i	0.834385	−	0.551182i	$-0.185823\pi$
$854$	−14.9441	−	17.8329i	−0.511377	−	0.610230i
$855$	−0.622591	+	2.72775i	−0.0212922	+	0.0932871i
$856$	11.8482	+	10.9935i	0.404963	+	0.375751i
$857$	−1.44403	−	0.217653i	−0.0493272	−	0.00743488i	0.124332	−	0.992241i	$-0.460321\pi$
$857$	−1.44403	−	0.217653i	−0.0493272	−	0.00743488i	−0.173660	+	0.984806i	$0.555559\pi$
$858$	−11.1752	−	1.68439i	−0.381515	−	0.0575041i
$859$	6.71164	+	6.22749i	0.228998	+	0.212479i	0.786324	−	0.617815i	$-0.211982\pi$
$859$	6.71164	+	6.22749i	0.228998	+	0.212479i	−0.557325	+	0.830294i	$0.688172\pi$
$860$	−1.98492	+	8.69652i	−0.0676853	+	0.296549i
$861$	−28.6560	−	34.1954i	−0.976593	−	1.16538i
$862$	−2.26848	−	9.93886i	−0.0772647	−	0.338519i
$863$	−25.3009	+	43.8224i	−0.861252	+	1.49173i	0.00946909	+	0.999955i	$0.496986\pi$
$863$	−25.3009	+	43.8224i	−0.861252	+	1.49173i	−0.870721	+	0.491777i	$0.836347\pi$
$864$	11.5900	+	20.0745i	0.394300	+	0.682947i
$865$	−4.54648	+	4.21852i	−0.154585	+	0.143434i
$866$	−10.3623	+	7.06487i	−0.352124	+	0.240074i
$867$	−17.0130	+	21.3336i	−0.577790	+	0.724526i
$868$	2.39803	+	24.1209i	0.0813946	+	0.818718i
$869$	−21.4783	−	26.9330i	−0.728602	−	0.913638i
$870$	4.73447	+	1.46039i	0.160514	+	0.0495119i
$871$	4.15865	−	10.5961i	0.140910	−	0.359034i
$872$	−2.01341	−	26.8670i	−0.0681825	−	0.909832i
$873$	−1.71093	−	4.35939i	−0.0579063	−	0.147543i
$874$	24.2166	−	11.6621i	0.819137	−	0.394476i
$875$	16.4422	−	11.8051i	0.555847	−	0.399086i
$876$	−16.4809	−	7.93679i	−0.556839	−	0.268159i
$877$	−0.206222	+	2.75184i	−0.00696362	+	0.0929230i	−0.999603	−	0.0281874i	$-0.991026\pi$
$877$	−0.206222	+	2.75184i	−0.00696362	+	0.0929230i	0.992639	+	0.121110i	$0.0386455\pi$
$878$	−9.43665	+	2.91082i	−0.318472	+	0.0982355i
$879$	17.5123	+	11.9397i	0.590675	+	0.402716i
$880$	−4.73043	+	0.712997i	−0.159463	+	0.0240351i
$881$	−21.9086			−0.738121			−0.369060	−	0.929405i	$-0.620320\pi$
$881$	−21.9086			−0.738121			−0.369060	+	0.929405i	$0.620320\pi$
$882$	3.08202	−	2.32832i	0.103777	−	0.0783986i
$883$	27.2639			0.917503			0.458751	−	0.888565i	$-0.348297\pi$
$883$	27.2639			0.917503			0.458751	+	0.888565i	$0.348297\pi$
$884$	1.58362	−	0.238692i	0.0532628	−	0.00802808i
$885$	−6.09989	−	4.15883i	−0.205046	−	0.139798i
$886$	−2.54353	+	0.784575i	−0.0854516	+	0.0263583i
$887$	3.18977	−	42.5645i	0.107102	−	1.42918i	−0.641991	−	0.766712i	$-0.721891\pi$
$887$	3.18977	−	42.5645i	0.107102	−	1.42918i	0.749093	−	0.662465i	$-0.230489\pi$
$888$	−0.180999	−	0.0871644i	−0.00607392	−	0.00292504i
$889$	−15.7800	+	28.9327i	−0.529243	+	0.970371i
$890$	2.90448	−	1.39872i	0.0973584	−	0.0468853i
$891$	−22.7669	−	58.0091i	−0.762720	−	1.94338i
$892$	0.212822	+	2.83991i	0.00712581	+	0.0950873i
$893$	−9.98151	+	25.4325i	−0.334018	+	0.851065i
$894$	2.46639	+	0.760782i	0.0824885	+	0.0254443i
$895$	−9.41022	−	11.8000i	−0.314549	−	0.394432i
$896$	−7.86345	+	2.63636i	−0.262699	+	0.0880748i
$897$	5.15029	−	6.45826i	0.171963	−	0.215635i
$898$	31.2047	−	21.2750i	1.04132	−	0.709957i
$899$	−21.4378	+	19.8914i	−0.714991	+	0.663415i
$900$	−1.20774	−	2.09187i	−0.0402581	−	0.0697290i
$901$	−7.05651	+	12.2222i	−0.235086	+	0.407182i
$902$	11.9323	+	52.2789i	0.397303	+	1.74070i
$903$	−10.6997	+	52.7542i	−0.356065	+	1.75555i
$904$	2.37807	−	10.4190i	0.0790934	−	0.346531i
$905$	−13.8202	−	12.8233i	−0.459400	−	0.426261i
$906$	28.7000	+	4.32582i	0.953492	+	0.143716i
$907$	−21.0502	−	3.17281i	−0.698960	−	0.105351i	−0.210057	−	0.977689i	$-0.567365\pi$
$907$	−21.0502	−	3.17281i	−0.698960	−	0.105351i	−0.488903	+	0.872338i	$0.662603\pi$
$908$	11.2244	+	10.4147i	0.372495	+	0.345625i
$909$	−0.817198	+	3.58038i	−0.0271047	+	0.118754i
$910$	−2.16111	+	0.0525074i	−0.0716402	+	0.00174060i
$911$	1.81425	+	7.94875i	0.0601088	+	0.263354i	0.996049	−	0.0888051i	$-0.0283048\pi$
$911$	1.81425	+	7.94875i	0.0601088	+	0.263354i	−0.935940	+	0.352159i	$0.885448\pi$
$912$	−5.62530	+	9.74330i	−0.186272	+	0.322633i
$913$	−35.3375	−	61.2064i	−1.16950	−	2.02563i
$914$	−23.5064	+	21.8107i	−0.777522	+	0.721435i
$915$	11.2787	−	7.68970i	0.372863	−	0.254214i
$916$	−10.3377	+	12.9631i	−0.341568	+	0.428312i
$917$	1.88290	+	0.237185i	0.0621788	+	0.00783253i
$918$	−4.55166	−	5.70760i	−0.150227	−	0.188379i
$919$	33.5089	+	10.3361i	1.10536	+	0.340958i	0.793132	−	0.609050i	$-0.208449\pi$
$919$	33.5089	+	10.3361i	1.10536	+	0.340958i	0.312226	+	0.950008i	$0.398925\pi$
$920$	3.93402	−	10.0237i	0.129701	−	0.330472i
$921$	−2.32076	−	30.9683i	−0.0764715	−	1.02044i
$922$	3.81685	+	9.72518i	0.125701	+	0.320282i
$923$	−0.838217	+	0.403664i	−0.0275902	+	0.0132868i
$924$	29.7915	−	5.23334i	0.980069	−	0.172164i
$925$	−0.138667	−	0.0667786i	−0.00455935	−	0.00219567i
$926$	1.24821	−	16.6562i	0.0410187	−	0.547357i
$927$	6.75517	−	2.08369i	0.221869	−	0.0684375i
$928$	−13.3596	−	9.10840i	−0.438550	−	0.298998i
$929$	−10.9822	+	1.65530i	−0.360314	+	0.0543086i	−0.326705	−	0.945126i	$-0.605938\pi$
$929$	−10.9822	+	1.65530i	−0.360314	+	0.0543086i	−0.0336094	+	0.999435i	$0.510700\pi$
$930$	14.0043			0.459219
$931$	39.6991	+	16.7946i	1.30109	+	0.550421i
$932$	26.0050			0.851822
$933$	1.46949	−	0.221491i	0.0481091	−	0.00725128i
$934$	8.71481	+	5.94165i	0.285157	+	0.194417i
$935$	−7.49640	+	2.31233i	−0.245158	+	0.0756213i
$936$	−0.124027	+	1.65502i	−0.00405394	+	0.0540960i
$937$	−25.5349	−	12.2970i	−0.834189	−	0.401724i	−0.0325043	−	0.999472i	$-0.510348\pi$
$937$	−25.5349	−	12.2970i	−0.834189	−	0.401724i	−0.801684	+	0.597747i	$0.796063\pi$
$938$	1.51461	−	29.9619i	0.0494537	−	0.978292i
$939$	−32.7582	+	15.7755i	−1.06902	+	0.514815i
$940$	1.33976	+	3.41366i	0.0436983	+	0.111341i
$941$	−1.89783	−	25.3248i	−0.0618675	−	0.825564i	−0.938693	−	0.344755i	$-0.887962\pi$
$941$	−1.89783	−	25.3248i	−0.0618675	−	0.825564i	0.876825	−	0.480809i	$-0.159657\pi$
$942$	5.51490	−	14.0517i	0.179685	−	0.457830i
$943$	−37.4530	−	11.5527i	−1.21964	−	0.376209i
$944$	−2.88498	−	3.61765i	−0.0938980	−	0.117744i
$945$	−5.21255	−	8.54227i	−0.169564	−	0.277880i
$946$	40.3380	−	50.5823i	1.31150	−	1.64457i
$947$	10.3648	−	7.06661i	0.336811	−	0.229634i	−0.383089	−	0.923711i	$-0.625140\pi$
$947$	10.3648	−	7.06661i	0.336811	−	0.229634i	0.719900	+	0.694077i	$0.244187\pi$
$948$	−7.97142	+	7.39639i	−0.258900	+	0.240224i
$949$	4.81455	+	8.33904i	0.156287	+	0.270697i
$950$	−13.2719	+	22.9877i	−0.430599	+	0.745819i
$951$	−6.07013	−	26.5950i	−0.196838	−	0.862402i
$952$	11.2143	−	5.74016i	0.363458	−	0.186040i
$953$	−6.44079	+	28.2189i	−0.208638	+	0.914101i	0.756837	+	0.653604i	$0.226744\pi$
$953$	−6.44079	+	28.2189i	−0.208638	+	0.914101i	−0.965475	+	0.260497i	$0.916113\pi$
$954$	−3.59205	−	3.33294i	−0.116297	−	0.107908i
$955$	−3.64250	−	0.549019i	−0.117869	−	0.0177658i
$956$	−21.4538	−	3.23364i	−0.693866	−	0.104583i
$957$	26.7512	+	24.8214i	0.864742	+	0.802363i
$958$	−0.538845	+	2.36083i	−0.0174093	+	0.0762751i
$959$	27.3087	−	36.0045i	0.881845	−	1.16265i
$960$	2.38988	+	10.4707i	0.0771330	+	0.337942i
$961$	−25.8304	+	44.7395i	−0.833237	+	1.44321i
$962$	0.0177152	+	0.0306836i	0.000571161	+	0.000989280i
$963$	−2.19058	+	2.03256i	−0.0705906	+	0.0654985i
$964$	−20.0792	+	13.6898i	−0.646708	+	0.440918i
$965$	−2.18977	+	2.74588i	−0.0704911	+	0.0883930i
$966$	7.45915	−	20.4530i	0.239994	−	0.658065i
$967$	2.25512	+	2.82783i	0.0725198	+	0.0909370i	0.816768	−	0.576966i	$-0.195764\pi$
$967$	2.25512	+	2.82783i	0.0725198	+	0.0909370i	−0.744248	+	0.667903i	$0.767192\pi$
$968$	−72.1962	−	22.2696i	−2.32047	−	0.715772i
$969$	−6.74038	+	17.1742i	−0.216532	+	0.551715i
$970$	0.516206	+	6.88829i	0.0165744	+	0.221170i
$971$	−14.1220	−	35.9822i	−0.453196	−	1.15472i	−0.956789	−	0.290783i	$-0.906084\pi$
$971$	−14.1220	−	35.9822i	−0.453196	−	1.15472i	0.503593	−	0.863941i	$-0.332011\pi$
$972$	−5.16347	+	2.48660i	−0.165618	+	0.0797577i
$973$	22.4928	+	6.34406i	0.721086	+	0.203381i
$974$	37.2369	+	17.9323i	1.19315	+	0.574589i
$975$	−0.609621	+	8.13483i	−0.0195235	+	0.260523i
$976$	8.17551	−	2.52181i	0.261692	−	0.0807212i
$977$	−46.9675	−	32.0219i	−1.50262	−	1.02447i	−0.985713	−	0.168432i	$-0.946130\pi$
$977$	−46.9675	−	32.0219i	−1.50262	−	1.02447i	−0.516911	−	0.856039i	$-0.672918\pi$
$978$	−0.766992	+	0.115605i	−0.0245257	+	0.00369665i
$979$	23.7443			0.758870
$980$	5.43942	−	1.97189i	0.173756	−	0.0629896i
$981$	4.98130			0.159041
$982$	−1.95140	+	0.294126i	−0.0622717	+	0.00938595i
$983$	−22.0589	−	15.0395i	−0.703569	−	0.479685i	0.157926	−	0.987451i	$-0.449519\pi$
$983$	−22.0589	−	15.0395i	−0.703569	−	0.479685i	−0.861495	+	0.507766i	$0.830472\pi$
$984$	48.2781	−	14.8918i	1.53905	−	0.474734i
$985$	0.166374	−	2.22011i	0.00530113	−	0.0707387i
$986$	4.58801	+	2.20947i	0.146112	+	0.0703639i
$987$	8.58271	+	20.3972i	0.273191	+	0.649249i
$988$	−5.59081	+	2.69239i	−0.177867	+	0.0856564i
$989$	17.2764	+	44.0195i	0.549357	+	1.39974i
$990$	−0.203550	−	2.71619i	−0.00646926	−	0.0863262i
$991$	21.3370	−	54.3658i	0.677792	−	1.72699i	−0.00881873	−	0.999961i	$-0.502807\pi$
$991$	21.3370	−	54.3658i	0.677792	−	1.72699i	0.686611	−	0.727025i	$-0.259098\pi$
$992$	−43.6721	−	13.4711i	−1.38659	−	0.427707i
$993$	41.6157	+	52.1844i	1.32063	+	1.65602i
$994$	−1.75639	+	1.71094i	−0.0557093	+	0.0542676i
$995$	−8.38004	+	10.5082i	−0.265665	+	0.333133i
$996$	−18.4332	+	12.5676i	−0.584079	+	0.398218i
$997$	11.5924	−	10.7562i	0.367137	−	0.340653i	−0.474933	−	0.880022i	$-0.657528\pi$
$997$	11.5924	−	10.7562i	0.367137	−	0.340653i	0.842069	+	0.539369i	$0.181337\pi$
$998$	9.86981	+	17.0950i	0.312423	+	0.541133i
$999$	−0.0820062	+	0.142039i	−0.00259456	+	0.00449391i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.b.534.10	yes	348
49.39	even	21	inner	637.2.bl.b.235.10	✓	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.b.235.10	✓	348	49.39	even	21	inner
637.2.bl.b.534.10	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)

\(f(q)\)	\(=\)	\(q+(-0.985016 + 0.148467i) q^{2} +(1.55762 + 1.06197i) q^{3} +(-0.962931 + 0.297025i) q^{4} +(-0.0612958 + 0.817935i) q^{5} +(-1.69195 - 0.814798i) q^{6} +(-1.98261 - 1.75193i) q^{7} +(2.69939 - 1.29996i) q^{8} +(0.202377 + 0.515649i) q^{9} +O(q^{10})\)	\(q+(-0.985016 + 0.148467i) q^{2} +(1.55762 + 1.06197i) q^{3} +(-0.962931 + 0.297025i) q^{4} +(-0.0612958 + 0.817935i) q^{5} +(-1.69195 - 0.814798i) q^{6} +(-1.98261 - 1.75193i) q^{7} +(2.69939 - 1.29996i) q^{8} +(0.202377 + 0.515649i) q^{9} +(-0.0610593 - 0.814780i) q^{10} +(2.19864 - 5.60206i) q^{11} +(-1.81531 - 0.559948i) q^{12} +(0.623490 + 0.781831i) q^{13} +(2.21301 + 1.43133i) q^{14} +(-0.964094 + 1.20894i) q^{15} +(-0.800742 + 0.545936i) q^{16} +(-1.16502 + 1.08098i) q^{17} +(-0.275902 - 0.477876i) q^{18} +(3.07896 - 5.33291i) q^{19} +(-0.183923 - 0.805821i) q^{20} +(-1.22766 - 4.83430i) q^{21} +(-1.33398 + 5.84454i) q^{22} +(-3.21205 - 2.98035i) q^{23} +(5.58513 + 0.841823i) q^{24} +(4.27889 + 0.644939i) q^{25} +(-0.730224 - 0.677549i) q^{26} +(1.02611 - 4.49567i) q^{27} +(2.42948 + 1.09810i) q^{28} +(0.715759 + 3.13595i) q^{29} +(0.770161 - 1.33396i) q^{30} +(4.54590 + 7.87372i) q^{31} +(-3.68490 + 3.41909i) q^{32} +(9.37384 - 6.39097i) q^{33} +(0.987070 - 1.23775i) q^{34} +(1.55449 - 1.51426i) q^{35} +(-0.348036 - 0.436423i) q^{36} +(-0.0339874 - 0.0104837i) q^{37} +(-2.24106 + 5.71013i) q^{38} +(0.140880 + 1.87992i) q^{39} +(0.897820 + 2.28761i) q^{40} +(8.05908 - 3.88105i) q^{41} +(1.92700 + 4.57960i) q^{42} +(-9.72337 - 4.68253i) q^{43} +(-0.453193 + 6.04744i) q^{44} +(-0.434172 + 0.133924i) q^{45} +(3.60640 + 2.45881i) q^{46} +(-4.38718 + 0.661262i) q^{47} -1.82701 q^{48} +(0.861493 + 6.94679i) q^{49} -4.31053 q^{50} +(-2.96261 + 0.446541i) q^{51} +(-0.832601 - 0.567658i) q^{52} +(8.48568 - 2.61748i) q^{53} +(-0.343273 + 4.58065i) q^{54} +(4.44735 + 2.14173i) q^{55} +(-7.62928 - 2.15183i) q^{56} +(10.4592 - 5.03689i) q^{57} +(-1.17062 - 2.98269i) q^{58} +(0.356798 + 4.76113i) q^{59} +(0.569272 - 1.45048i) q^{60} +(-8.43583 - 2.60211i) q^{61} +(-5.64677 - 7.08083i) q^{62} +(0.502145 - 1.37688i) q^{63} +(4.33056 - 5.43035i) q^{64} +(-0.677705 + 0.462051i) q^{65} +(-8.28453 + 7.68692i) q^{66} +(-5.69146 - 9.85789i) q^{67} +(0.800753 - 1.38694i) q^{68} +(-1.83812 - 8.05332i) q^{69} +(-1.30638 + 1.72236i) q^{70} +(-0.207022 + 0.907025i) q^{71} +(1.21662 + 1.12886i) q^{72} +(9.52154 + 1.43514i) q^{73} +(0.0350347 + 0.00528063i) q^{74} +(5.97997 + 5.54861i) q^{75} +(-1.38082 + 6.04975i) q^{76} +(-14.1735 + 7.25483i) q^{77} +(-0.417876 - 1.83083i) q^{78} +(2.86210 - 4.95730i) q^{79} +(-0.397458 - 0.688418i) q^{80} +(7.59073 - 7.04317i) q^{81} +(-7.36212 + 5.01941i) q^{82} +(7.32215 - 9.18168i) q^{83} +(2.61806 + 4.29045i) q^{84} +(-0.812758 - 1.01917i) q^{85} +(10.2729 + 3.16876i) q^{86} +(-2.21539 + 5.64471i) q^{87} +(-1.34744 - 17.9803i) q^{88} +(1.44145 + 3.67276i) q^{89} +(0.407783 - 0.196378i) q^{90} +(0.133575 - 2.64238i) q^{91} +(3.97822 + 1.91581i) q^{92} +(-1.28086 + 17.0918i) q^{93} +(4.22327 - 1.30271i) q^{94} +(4.17325 + 2.84527i) q^{95} +(-9.37062 + 1.41239i) q^{96} -8.45417 q^{97} +(-1.87996 - 6.71479i) q^{98} +3.33365 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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Database

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