LMFDB - Embedded newform 125.2.g.a.11.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [125,2,Mod(6,125)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(125, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("125.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 125 = 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	125.g (of order $25$, degree $20$, 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:	$0.998130025266$
Analytic rank:	$0$
Dimension:	$220$
Relative dimension:	$11$ over $\Q(\zeta_{25})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{25}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	125.11
Dual form			125.2.g.a.91.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.992063 + 0.931610i) q^{2} +(-0.836274 - 1.31776i) q^{3} +(-0.00928759 + 0.147622i) q^{4} +(-0.216983 - 2.22552i) q^{5} +(2.05727 + 0.528217i) q^{6} +(0.230945 - 0.710774i) q^{7} +(-1.86327 - 2.25231i) q^{8} +(0.240210 - 0.510472i) q^{9} +O(q^{10})$	\(q+(-0.992063 + 0.931610i) q^{2} +(-0.836274 - 1.31776i) q^{3} +(-0.00928759 + 0.147622i) q^{4} +(-0.216983 - 2.22552i) q^{5} +(2.05727 + 0.528217i) q^{6} +(0.230945 - 0.710774i) q^{7} +(-1.86327 - 2.25231i) q^{8} +(0.240210 - 0.510472i) q^{9} +(2.28857 + 2.00571i) q^{10} +(2.10398 - 1.97577i) q^{11} +(0.202297 - 0.111214i) q^{12} +(0.774088 - 1.64502i) q^{13} +(0.433053 + 0.920283i) q^{14} +(-2.75123 + 2.14707i) q^{15} +(3.65326 + 0.461514i) q^{16} +(-0.104204 - 1.65627i) q^{17} +(0.237257 + 0.730202i) q^{18} +(-2.32836 + 3.66890i) q^{19} +(0.330550 - 0.0113618i) q^{20} +(-1.12976 + 0.290073i) q^{21} +(-0.246637 + 3.92018i) q^{22} +(0.0876365 - 0.459407i) q^{23} +(-1.40979 + 4.33888i) q^{24} +(-4.90584 + 0.965799i) q^{25} +(0.764573 + 2.35311i) q^{26} +(-5.51879 + 0.697185i) q^{27} +(0.102781 + 0.0406939i) q^{28} +(1.88834 + 0.747646i) q^{29} +(0.729163 - 4.69310i) q^{30} +(0.117523 + 1.86798i) q^{31} +(0.675502 - 0.490781i) q^{32} +(-4.36309 - 1.12025i) q^{33} +(1.64637 + 1.54605i) q^{34} +(-1.63195 - 0.359745i) q^{35} +(0.0731259 + 0.0402013i) q^{36} +(0.279059 + 0.0352534i) q^{37} +(-1.10811 - 5.80890i) q^{38} +(-2.81509 + 0.355628i) q^{39} +(-4.60824 + 4.63545i) q^{40} +(-1.16480 - 6.10607i) q^{41} +(0.850559 - 1.34027i) q^{42} +(9.41267 + 6.83871i) q^{43} +(0.272126 + 0.328944i) q^{44} +(-1.18818 - 0.423827i) q^{45} +(0.341047 + 0.537403i) q^{46} +(-6.47852 + 7.83118i) q^{47} +(-2.44696 - 5.20006i) q^{48} +(5.21125 + 3.78620i) q^{49} +(3.96715 - 5.52846i) q^{50} +(-2.09541 + 1.52241i) q^{51} +(0.235652 + 0.129551i) q^{52} +(9.85881 - 2.53131i) q^{53} +(4.82548 - 5.83301i) q^{54} +(-4.85364 - 4.25373i) q^{55} +(-2.03119 + 0.804207i) q^{56} +6.78186 q^{57} +(-2.56986 + 1.01748i) q^{58} +(11.0341 - 6.06603i) q^{59} +(-0.291402 - 0.426083i) q^{60} +(2.57035 - 13.4743i) q^{61} +(-1.85682 - 1.74367i) q^{62} +(-0.307355 - 0.288626i) q^{63} +(-1.59291 + 8.35033i) q^{64} +(-3.82898 - 1.36580i) q^{65} +(5.37210 - 2.95334i) q^{66} +(3.29017 - 1.30267i) q^{67} +0.245469 q^{68} +(-0.678674 + 0.268706i) q^{69} +(1.95414 - 1.16345i) q^{70} +(-6.28157 + 7.59311i) q^{71} +(-1.59731 + 0.410121i) q^{72} +(12.7554 + 7.01232i) q^{73} +(-0.309687 + 0.225001i) q^{74} +(5.37531 + 5.65702i) q^{75} +(-0.519986 - 0.377792i) q^{76} +(-0.918424 - 1.95175i) q^{77} +(2.46144 - 2.97537i) q^{78} +(-4.15423 - 6.54601i) q^{79} +(0.234410 - 8.23052i) q^{80} +(4.45510 + 5.38529i) q^{81} +(6.84402 + 4.97247i) q^{82} +(-5.15184 + 8.11800i) q^{83} +(-0.0323284 - 0.169471i) q^{84} +(-3.66344 + 0.591289i) q^{85} +(-15.7090 + 1.98451i) q^{86} +(-0.593952 - 3.11360i) q^{87} +(-8.37033 - 1.05742i) q^{88} +(-11.0801 - 6.09135i) q^{89} +(1.57359 - 0.686461i) q^{90} +(-0.990467 - 0.930110i) q^{91} +(0.0670046 + 0.0172038i) q^{92} +(2.36326 - 1.71701i) q^{93} +(-0.868504 - 13.8045i) q^{94} +(8.67041 + 4.38570i) q^{95} +(-1.21163 - 0.479720i) q^{96} +(-11.5300 - 4.56507i) q^{97} +(-8.69715 + 1.09871i) q^{98} +(-0.503178 - 1.54862i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9}+O(q^{10}) $ 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9	\( 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9} - 20 q^{10} - 15 q^{11} - 100 q^{12} - 20 q^{13} - 10 q^{14} - 15 q^{17} + 10 q^{18} - 10 q^{19} + 5 q^{20} - 5 q^{21} + 25 q^{22} - 90 q^{23} + 15 q^{24} - 45 q^{25} + 15 q^{26} + 10 q^{27} + 30 q^{28} - 10 q^{29} + 40 q^{30} - 10 q^{31} + 20 q^{32} + 15 q^{33} + 5 q^{34} + 10 q^{35} - 210 q^{36} + 20 q^{37} + 30 q^{38} + 45 q^{40} - 5 q^{41} + 70 q^{42} + 25 q^{43} + 15 q^{44} - 100 q^{45} - 100 q^{47} + 105 q^{48} - 20 q^{49} + 60 q^{50} + 25 q^{51} + 85 q^{52} + 20 q^{53} + 60 q^{54} + 15 q^{55} - 105 q^{56} + 40 q^{57} - 225 q^{58} + 5 q^{59} - 35 q^{60} + 65 q^{62} + 85 q^{63} + 45 q^{64} + 45 q^{65} + 55 q^{66} - 105 q^{67} + 80 q^{68} + 40 q^{69} + 95 q^{70} - 85 q^{71} + 160 q^{72} + 40 q^{73} + 35 q^{74} + 55 q^{75} + 35 q^{76} + 75 q^{77} - 10 q^{78} - 330 q^{80} + 55 q^{81} - 95 q^{82} + 50 q^{83} + 115 q^{84} + 85 q^{85} + 40 q^{86} + 95 q^{87} + 165 q^{88} + 55 q^{89} + 170 q^{90} - 105 q^{91} + 155 q^{92} - 185 q^{93} + 60 q^{94} + 30 q^{95} + 135 q^{96} + 65 q^{97} + 135 q^{98} + 45 q^{99}+O(q^{100}) \) 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9 - 20 * q^10 - 15 * q^11 - 100 * q^12 - 20 * q^13 - 10 * q^14 - 15 * q^17 + 10 * q^18 - 10 * q^19 + 5 * q^20 - 5 * q^21 + 25 * q^22 - 90 * q^23 + 15 * q^24 - 45 * q^25 + 15 * q^26 + 10 * q^27 + 30 * q^28 - 10 * q^29 + 40 * q^30 - 10 * q^31 + 20 * q^32 + 15 * q^33 + 5 * q^34 + 10 * q^35 - 210 * q^36 + 20 * q^37 + 30 * q^38 + 45 * q^40 - 5 * q^41 + 70 * q^42 + 25 * q^43 + 15 * q^44 - 100 * q^45 - 100 * q^47 + 105 * q^48 - 20 * q^49 + 60 * q^50 + 25 * q^51 + 85 * q^52 + 20 * q^53 + 60 * q^54 + 15 * q^55 - 105 * q^56 + 40 * q^57 - 225 * q^58 + 5 * q^59 - 35 * q^60 + 65 * q^62 + 85 * q^63 + 45 * q^64 + 45 * q^65 + 55 * q^66 - 105 * q^67 + 80 * q^68 + 40 * q^69 + 95 * q^70 - 85 * q^71 + 160 * q^72 + 40 * q^73 + 35 * q^74 + 55 * q^75 + 35 * q^76 + 75 * q^77 - 10 * q^78 - 330 * q^80 + 55 * q^81 - 95 * q^82 + 50 * q^83 + 115 * q^84 + 85 * q^85 + 40 * q^86 + 95 * q^87 + 165 * q^88 + 55 * q^89 + 170 * q^90 - 105 * q^91 + 155 * q^92 - 185 * q^93 + 60 * q^94 + 30 * q^95 + 135 * q^96 + 65 * q^97 + 135 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/125\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{19}{25}\right)$

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 $

$2$	−0.992063	+	0.931610i	−0.701495	+	0.658747i	−0.950845	−	0.309666i	$-0.899783\pi$
$2$	−0.992063	+	0.931610i	−0.701495	+	0.658747i	0.249351	+	0.968413i	$0.419783\pi$
$3$	−0.836274	−	1.31776i	−0.482823	−	0.760807i	0.512368	−	0.858766i	$-0.328769\pi$
$3$	−0.836274	−	1.31776i	−0.482823	−	0.760807i	−0.995190	+	0.0979593i	$0.968769\pi$
$4$	−0.00928759	+	0.147622i	−0.00464379	+	0.0738110i
$5$	−0.216983	−	2.22552i	−0.0970378	−	0.995281i
$5$	−0.216983	−	2.22552i	−0.0970378	−	0.995281i
$6$	2.05727	+	0.528217i	0.839877	+	0.215644i
$7$	0.230945	−	0.710774i	0.0872889	−	0.268647i	−0.897879	−	0.440243i	$-0.854892\pi$
$7$	0.230945	−	0.710774i	0.0872889	−	0.268647i	0.985167	+	0.171596i	$0.0548923\pi$
$8$	−1.86327	−	2.25231i	−0.658766	−	0.796311i
$9$	0.240210	−	0.510472i	0.0800699	−	0.170157i
$10$	2.28857	+	2.00571i	0.723710	+	0.634261i
$11$	2.10398	−	1.97577i	0.634374	−	0.595717i	−0.299161	−	0.954203i	$-0.596707\pi$
$11$	2.10398	−	1.97577i	0.634374	−	0.595717i	0.933535	+	0.358485i	$0.116707\pi$
$12$	0.202297	−	0.111214i	0.0583980	−	0.0321046i
$13$	0.774088	−	1.64502i	0.214693	−	0.456247i	−0.768251	−	0.640148i	$-0.778873\pi$
$13$	0.774088	−	1.64502i	0.214693	−	0.456247i	0.982945	+	0.183902i	$0.0588728\pi$
$14$	0.433053	+	0.920283i	0.115738	+	0.245956i
$15$	−2.75123	+	2.14707i	−0.710364	+	0.554371i
$16$	3.65326	+	0.461514i	0.913314	+	0.115378i
$17$	−0.104204	−	1.65627i	−0.0252731	−	0.401704i	−0.990244	−	0.139346i	$-0.955500\pi$
$17$	−0.104204	−	1.65627i	−0.0252731	−	0.401704i	0.964971	−	0.262358i	$-0.0845001\pi$
$18$	0.237257	+	0.730202i	0.0559220	+	0.172110i
$19$	−2.32836	+	3.66890i	−0.534162	+	0.841704i	−0.999046	−	0.0436674i	$-0.986096\pi$
$19$	−2.32836	+	3.66890i	−0.534162	+	0.841704i	0.464885	+	0.885371i	$0.346096\pi$
$20$	0.330550	−	0.0113618i	0.0739133	−	0.00254058i
$21$	−1.12976	+	0.290073i	−0.246534	+	0.0632991i
$22$	−0.246637	+	3.92018i	−0.0525831	+	0.835785i
$23$	0.0876365	−	0.459407i	0.0182735	−	0.0957929i	−0.971982	−	0.235055i	$-0.924473\pi$
$23$	0.0876365	−	0.459407i	0.0182735	−	0.0957929i	0.990256	+	0.139262i	$0.0444730\pi$
$24$	−1.40979	+	4.33888i	−0.287772	+	0.885670i
$25$	−4.90584	+	0.965799i	−0.981167	+	0.193160i
$26$	0.764573	+	2.35311i	0.149945	+	0.461483i
$27$	−5.51879	+	0.697185i	−1.06209	+	0.134173i
$28$	0.102781	+	0.0406939i	0.0194238	+	0.00769042i
$29$	1.88834	+	0.747646i	0.350655	+	0.138834i	0.536848	−	0.843679i	$-0.319615\pi$
$29$	1.88834	+	0.747646i	0.350655	+	0.138834i	−0.186193	+	0.982513i	$0.559615\pi$
$30$	0.729163	−	4.69310i	0.133126	−	0.856839i
$31$	0.117523	+	1.86798i	0.0211078	+	0.335500i	0.994382	+	0.105853i	$0.0337572\pi$
$31$	0.117523	+	1.86798i	0.0211078	+	0.335500i	−0.973274	+	0.229647i	$0.926243\pi$
$32$	0.675502	−	0.490781i	0.119413	−	0.0867587i
$33$	−4.36309	−	1.12025i	−0.759516	−	0.195011i
$34$	1.64637	+	1.54605i	0.282350	+	0.265145i
$35$	−1.63195	−	0.359745i	−0.275850	−	0.0608079i
$36$	0.0731259	+	0.0402013i	0.0121876	+	0.00670021i
$37$	0.279059	+	0.0352534i	0.0458770	+	0.00579562i	0.148238	−	0.988952i	$-0.452640\pi$
$37$	0.279059	+	0.0352534i	0.0458770	+	0.00579562i	−0.102361	+	0.994747i	$0.532640\pi$
$38$	−1.10811	−	5.80890i	−0.179759	−	0.942328i
$39$	−2.81509	+	0.355628i	−0.450774	+	0.0569461i
$40$	−4.60824	+	4.63545i	−0.728628	+	0.732929i
$41$	−1.16480	−	6.10607i	−0.181910	−	0.953608i	−0.949760	−	0.312978i	$-0.898673\pi$
$41$	−1.16480	−	6.10607i	−0.181910	−	0.953608i	0.767850	−	0.640630i	$-0.221327\pi$
$42$	0.850559	−	1.34027i	0.131244	−	0.206808i
$43$	9.41267	+	6.83871i	1.43542	+	1.04289i	0.988975	+	0.148082i	$0.0473099\pi$
$43$	9.41267	+	6.83871i	1.43542	+	1.04289i	0.446444	+	0.894811i	$0.352690\pi$
$44$	0.272126	+	0.328944i	0.0410246	+	0.0495902i
$45$	−1.18818	−	0.423827i	−0.177124	−	0.0631803i
$46$	0.341047	+	0.537403i	0.0502846	+	0.0792358i
$47$	−6.47852	+	7.83118i	−0.944989	+	1.14230i	0.0446913	+	0.999001i	$0.485770\pi$
$47$	−6.47852	+	7.83118i	−0.944989	+	1.14230i	−0.989680	+	0.143294i	$0.954230\pi$
$48$	−2.44696	−	5.20006i	−0.353188	−	0.750563i
$49$	5.21125	+	3.78620i	0.744465	+	0.540885i
$50$	3.96715	−	5.52846i	0.561040	−	0.781842i
$51$	−2.09541	+	1.52241i	−0.293417	+	0.213180i
$52$	0.235652	+	0.129551i	0.0326790	+	0.0179654i
$53$	9.85881	−	2.53131i	1.35421	−	0.347703i	0.499279	−	0.866441i	$-0.333598\pi$
$53$	9.85881	−	2.53131i	1.35421	−	0.347703i	0.854933	+	0.518739i	$0.173598\pi$
$54$	4.82548	−	5.83301i	0.656665	−	0.793772i
$55$	−4.85364	−	4.25373i	−0.654464	−	0.573573i
$56$	−2.03119	+	0.804207i	−0.271430	+	0.107467i
$57$	6.78186			0.898280
$58$	−2.56986	+	1.01748i	−0.337440	+	0.133602i
$59$	11.0341	−	6.06603i	1.43651	−	0.789730i	0.442271	−	0.896881i	$-0.354173\pi$
$59$	11.0341	−	6.06603i	1.43651	−	0.789730i	0.994243	+	0.107151i	$0.0341729\pi$
$60$	−0.291402	−	0.426083i	−0.0376199	−	0.0550071i
$61$	2.57035	−	13.4743i	0.329100	−	1.72520i	−0.305351	−	0.952240i	$-0.598774\pi$
$61$	2.57035	−	13.4743i	0.329100	−	1.72520i	0.634451	−	0.772963i	$-0.281226\pi$
$62$	−1.85682	−	1.74367i	−0.235816	−	0.221446i
$63$	−0.307355	−	0.288626i	−0.0387231	−	0.0363634i
$64$	−1.59291	+	8.35033i	−0.199114	+	1.04379i
$65$	−3.82898	−	1.36580i	−0.474927	−	0.169407i
$66$	5.37210	−	2.95334i	0.661259	−	0.363530i
$67$	3.29017	−	1.30267i	0.401958	−	0.159147i	−0.158442	−	0.987368i	$-0.550647\pi$
$67$	3.29017	−	1.30267i	0.401958	−	0.159147i	0.560401	+	0.828222i	$0.310647\pi$
$68$	0.245469			0.0297675
$69$	−0.678674	+	0.268706i	−0.0817027	+	0.0323484i
$70$	1.95414	−	1.16345i	0.233564	−	0.139059i
$71$	−6.28157	+	7.59311i	−0.745485	+	0.901136i	−0.997786	−	0.0665124i	$-0.978813\pi$
$71$	−6.28157	+	7.59311i	−0.745485	+	0.901136i	0.252301	+	0.967649i	$0.418813\pi$
$72$	−1.59731	+	0.410121i	−0.188245	+	0.0483332i
$73$	12.7554	+	7.01232i	1.49290	+	0.820730i	0.998814	−	0.0486810i	$-0.0155018\pi$
$73$	12.7554	+	7.01232i	1.49290	+	0.820730i	0.494089	+	0.869411i	$0.335502\pi$
$74$	−0.309687	+	0.225001i	−0.0360003	+	0.0261558i
$75$	5.37531	+	5.65702i	0.620687	+	0.653217i
$76$	−0.519986	−	0.377792i	−0.0596465	−	0.0433357i
$77$	−0.918424	−	1.95175i	−0.104664	−	0.222423i
$78$	2.46144	−	2.97537i	0.278703	−	0.336894i
$79$	−4.15423	−	6.54601i	−0.467387	−	0.736484i	0.526101	−	0.850422i	$-0.323653\pi$
$79$	−4.15423	−	6.54601i	−0.467387	−	0.736484i	−0.993488	+	0.113938i	$0.963653\pi$
$80$	0.234410	−	8.23052i	0.0262079	−	0.920200i
$81$	4.45510	+	5.38529i	0.495011	+	0.598365i
$82$	6.84402	+	4.97247i	0.755796	+	0.549118i
$83$	−5.15184	+	8.11800i	−0.565488	+	0.891066i	−0.999954	−	0.00962214i	$-0.996937\pi$
$83$	−5.15184	+	8.11800i	−0.565488	+	0.891066i	0.434466	+	0.900688i	$0.356937\pi$
$84$	−0.0323284	−	0.169471i	−0.00352732	−	0.0184909i
$85$	−3.66344	+	0.591289i	−0.397356	+	0.0641343i
$86$	−15.7090	+	1.98451i	−1.69394	+	0.213995i
$87$	−0.593952	−	3.11360i	−0.0636783	−	0.333813i
$88$	−8.37033	−	1.05742i	−0.892280	−	0.112721i
$89$	−11.0801	−	6.09135i	−1.17449	−	0.645682i	−0.229669	−	0.973269i	$-0.573764\pi$
$89$	−11.0801	−	6.09135i	−1.17449	−	0.645682i	−0.944821	+	0.327587i	$0.893764\pi$
$90$	1.57359	−	0.686461i	0.165871	−	0.0723593i
$91$	−0.990467	−	0.930110i	−0.103829	−	0.0975021i
$92$	0.0670046	+	0.0172038i	0.00698571	+	0.00179363i
$93$	2.36326	−	1.71701i	0.245059	−	0.178046i
$94$	−0.868504	−	13.8045i	−0.0895794	−	1.42382i
$95$	8.67041	+	4.38570i	0.889566	+	0.449964i
$96$	−1.21163	−	0.479720i	−0.123662	−	0.0489612i
$97$	−11.5300	−	4.56507i	−1.17070	−	0.463512i	−0.299334	−	0.954148i	$-0.596764\pi$
$97$	−11.5300	−	4.56507i	−1.17070	−	0.463512i	−0.871365	+	0.490636i	$0.836764\pi$
$98$	−8.69715	+	1.09871i	−0.878545	+	0.110986i
$99$	−0.503178	−	1.54862i	−0.0505713	−	0.155642i
$100$	−0.0970097	−	0.733179i	−0.00970097	−	0.0733179i
$101$	−0.0242442	+	0.0746160i	−0.00241239	+	0.00742457i	−0.952255	−	0.305302i	$-0.901242\pi$
$101$	−0.0242442	+	0.0746160i	−0.00241239	+	0.00742457i	0.949843	+	0.312727i	$0.101242\pi$
$102$	0.660495	−	3.46243i	0.0653987	−	0.342832i
$103$	−0.397420	+	6.31681i	−0.0391589	+	0.622413i	0.928686	+	0.370867i	$0.120939\pi$
$103$	−0.397420	+	6.31681i	−0.0391589	+	0.622413i	−0.967845	+	0.251547i	$0.919061\pi$
$104$	−5.14743	+	1.32163i	−0.504747	+	0.129597i
$105$	0.890701	+	2.45136i	0.0869235	+	0.239228i
$106$	−7.42237	+	11.6958i	−0.720924	+	1.13600i
$107$	2.50633	+	7.71370i	0.242296	+	0.745711i	0.996069	+	0.0885764i	$0.0282317\pi$
$107$	2.50633	+	7.71370i	0.242296	+	0.745711i	−0.753773	+	0.657135i	$0.771768\pi$
$108$	−0.0516636	−	0.821169i	−0.00497133	−	0.0790170i
$109$	10.2906	+	1.30000i	0.985661	+	0.124518i	0.601606	−	0.798793i	$-0.294528\pi$
$109$	10.2906	+	1.30000i	0.985661	+	0.124518i	0.384054	+	0.923311i	$0.374528\pi$
$110$	8.77793	−	0.301719i	0.836943	−	0.0287678i
$111$	−0.186914	−	0.397213i	−0.0177411	−	0.0377018i
$112$	1.17173	−	2.49006i	0.110718	−	0.235288i
$113$	−2.91819	+	1.60429i	−0.274520	+	0.150919i	−0.613067	−	0.790031i	$-0.710065\pi$
$113$	−2.91819	+	1.60429i	−0.274520	+	0.150919i	0.338547	+	0.940949i	$0.390065\pi$
$114$	−6.72804	+	6.31805i	−0.630138	+	0.591739i
$115$	−1.04143	−	0.0953528i	−0.0971140	−	0.00889170i
$116$	−0.127907	+	0.271816i	−0.0118759	+	0.0252375i
$117$	−0.653793	−	0.790300i	−0.0604432	−	0.0730632i
$118$	−5.29533	+	16.2973i	−0.487474	+	1.50029i
$119$	−1.20130	−	0.308441i	−0.110123	−	0.0282747i
$120$	9.96215	+	2.19604i	0.909415	+	0.200470i
$121$	−0.167625	+	2.66432i	−0.0152386	+	0.242211i
$122$	10.0028	+	15.7619i	0.905611	+	1.42702i
$123$	−7.07222	+	6.64126i	−0.637681	+	0.598822i
$124$	−0.276847			−0.0248616
$125$	3.21388	+	10.7085i	0.287459	+	0.957793i
$126$	0.573802			0.0511183
$127$	3.56600	−	3.34870i	0.316432	−	0.297149i	−0.510013	−	0.860166i	$-0.670360\pi$
$127$	3.56600	−	3.34870i	0.316432	−	0.297149i	0.826445	+	0.563017i	$0.190360\pi$
$128$	−5.30418	−	8.35806i	−0.468828	−	0.738755i
$129$	1.14018	−	18.1226i	0.100387	−	1.59561i
$130$	5.07099	−	2.21215i	0.444755	−	0.194019i
$131$	14.5915	+	3.74646i	1.27486	+	0.327330i	0.824677	−	0.565604i	$-0.191357\pi$
$131$	14.5915	+	3.74646i	1.27486	+	0.327330i	0.450188	+	0.892934i	$0.351357\pi$
$132$	0.205896	−	0.633683i	0.0179210	−	0.0551550i
$133$	2.07004	+	2.50225i	0.179495	+	0.216973i
$134$	−2.05048	+	4.35749i	−0.177134	+	0.376429i
$135$	2.74908	+	12.1309i	0.236603	+	1.04406i
$136$	−3.53626	+	3.32077i	−0.303232	+	0.284754i
$137$	−1.80025	+	0.989696i	−0.153806	+	0.0845554i	−0.556798	−	0.830648i	$-0.687970\pi$
$137$	−1.80025	+	0.989696i	−0.153806	+	0.0845554i	0.402992	+	0.915203i	$0.367970\pi$
$138$	0.422959	−	0.898833i	0.0360046	−	0.0765137i
$139$	−4.70928	−	10.0077i	−0.399436	−	0.848844i	−0.998829	−	0.0483889i	$-0.984591\pi$
$139$	−4.70928	−	10.0077i	−0.399436	−	0.848844i	0.599393	−	0.800455i	$-0.295409\pi$
$140$	0.0682631	−	0.237571i	0.00576928	−	0.0200784i
$141$	15.7374	+	1.98810i	1.32533	+	0.167428i
$142$	−0.842101	−	13.3848i	−0.0706676	−	1.12323i
$143$	−1.62152	−	4.99051i	−0.135598	−	0.417328i
$144$	1.11314	−	1.75402i	0.0927615	−	0.146169i
$145$	1.25416	−	4.36475i	0.104152	−	0.362473i
$146$	−19.1869	+	4.92635i	−1.58792	+	0.407708i
$147$	0.631252	−	10.0335i	0.0520648	−	0.827546i
$148$	−0.00779595	+	0.0408678i	−0.000640824	+	0.00335931i
$149$	−6.58318	+	20.2609i	−0.539315	+	1.65984i	0.194821	+	0.980839i	$0.437587\pi$
$149$	−6.58318	+	20.2609i	−0.539315	+	1.65984i	−0.734136	+	0.679002i	$0.762413\pi$
$150$	−10.6028	−	0.604438i	−0.865714	−	0.0493522i
$151$	−5.98279	−	18.4131i	−0.486873	−	1.49844i	−0.829250	−	0.558878i	$-0.811232\pi$
$151$	−5.98279	−	18.4131i	−0.486873	−	1.49844i	0.342377	−	0.939563i	$-0.388768\pi$
$152$	12.6019	−	1.59198i	1.02215	−	0.129127i
$153$	−0.870509	−	0.344659i	−0.0703764	−	0.0278640i
$154$	2.72940	+	1.08065i	0.219942	+	0.0870810i
$155$	4.13172	−	0.666871i	0.331868	−	0.0535644i
$156$	−0.0263532	−	0.418871i	−0.00210994	−	0.0335365i
$157$	9.92267	−	7.20924i	0.791915	−	0.575360i	−0.116616	−	0.993177i	$-0.537205\pi$
$157$	9.92267	−	7.20924i	0.791915	−	0.575360i	0.908531	+	0.417817i	$0.137205\pi$
$158$	10.2196	+	2.62394i	0.813027	+	0.208750i
$159$	−11.5803	−	10.8746i	−0.918379	−	0.862415i
$160$	−1.23881	−	1.39685i	−0.0979368	−	0.110431i
$161$	−0.306295	−	0.168387i	−0.0241394	−	0.0132708i
$162$	−9.43673	−	1.19214i	−0.741419	−	0.0936630i
$163$	0.259525	+	1.36048i	0.0203276	+	0.106561i	0.991005	−	0.133825i	$-0.0427260\pi$
$163$	0.259525	+	1.36048i	0.0203276	+	0.106561i	−0.970677	+	0.240386i	$0.922726\pi$
$164$	0.912208	−	0.115239i	0.0712315	−	0.00899863i
$165$	−1.54642	+	9.95320i	−0.120388	+	0.774855i
$166$	−2.45185	−	12.8531i	−0.190301	−	0.997592i
$167$	5.11920	−	8.06657i	0.396136	−	0.624210i	−0.586458	−	0.809980i	$-0.699478\pi$
$167$	5.11920	−	8.06657i	0.396136	−	0.624210i	0.982593	+	0.185770i	$0.0594780\pi$
$168$	2.75838	+	2.00408i	0.212814	+	0.154618i
$169$	6.17963	+	7.46989i	0.475356	+	0.574607i
$170$	3.08351	−	3.99949i	0.236495	−	0.306747i
$171$	1.31358	+	2.06987i	0.100452	+	0.158287i
$172$	−1.09696	+	1.32600i	−0.0836428	+	0.101107i
$173$	−8.12791	−	17.2727i	−0.617954	−	1.31322i	−0.931533	−	0.363656i	$-0.881528\pi$
$173$	−8.12791	−	17.2727i	−0.617954	−	1.31322i	0.313580	−	0.949562i	$-0.398472\pi$
$174$	3.48990	+	2.53556i	0.264569	+	0.192220i
$175$	−0.446511	+	3.70999i	−0.0337531	+	0.280449i
$176$	8.59823	−	6.24698i	0.648116	−	0.470884i
$177$	−17.2211	−	9.46736i	−1.29441	−	0.711610i
$178$	16.6669	−	4.27934i	1.24924	−	0.320750i
$179$	−11.4270	+	13.8129i	−0.854097	+	1.03243i	0.144979	+	0.989435i	$0.453689\pi$
$179$	−11.4270	+	13.8129i	−0.854097	+	1.03243i	−0.999075	+	0.0429909i	$0.986311\pi$
$180$	0.0736015	−	0.171466i	0.00548593	−	0.0127803i
$181$	10.1154	−	4.00498i	0.751874	−	0.297688i	0.0392454	−	0.999230i	$-0.487505\pi$
$181$	10.1154	−	4.00498i	0.751874	−	0.297688i	0.712628	+	0.701542i	$0.247505\pi$
$182$	1.84911			0.137065
$183$	−19.9053	+	7.88107i	−1.47144	+	0.582586i
$184$	−1.19802	+	0.658614i	−0.0883188	+	0.0485537i
$185$	0.0179058	−	0.628700i	0.00131646	−	0.0462229i
$186$	−0.744923	+	3.90502i	−0.0546204	+	0.286330i
$187$	−3.49165	−	3.27888i	−0.255335	−	0.239775i
$188$	−1.09588	−	1.02910i	−0.0799256	−	0.0750551i
$189$	−0.778993	+	4.08362i	−0.0566634	+	0.297040i
$190$	−12.6874	+	3.72654i	−0.920438	+	0.270352i
$191$	−15.7281	+	8.64660i	−1.13805	+	0.625646i	−0.935395	−	0.353605i	$-0.884956\pi$
$191$	−15.7281	+	8.64660i	−1.13805	+	0.625646i	−0.202651	+	0.979251i	$0.564956\pi$
$192$	12.3358	−	4.88409i	0.890260	−	0.352479i
$193$	12.9078			0.929126			0.464563	−	0.885540i	$-0.346211\pi$
$193$	12.9078			0.929126			0.464563	+	0.885540i	$0.346211\pi$
$194$	15.6914	−	6.21266i	1.12658	−	0.446043i
$195$	1.40228	+	6.18785i	0.100419	+	0.443121i
$196$	−0.607326	+	0.734131i	−0.0433804	+	0.0524379i
$197$	16.8542	−	4.32743i	1.20081	−	0.308316i	0.405261	−	0.914201i	$-0.367181\pi$
$197$	16.8542	−	4.32743i	1.20081	−	0.308316i	0.795553	+	0.605885i	$0.207181\pi$
$198$	1.94190	+	1.06757i	0.138005	+	0.0758686i
$199$	1.05155	−	0.763999i	0.0745427	−	0.0541585i	−0.549890	−	0.835237i	$-0.685330\pi$
$199$	1.05155	−	0.763999i	0.0745427	−	0.0541585i	0.624433	+	0.781079i	$0.285330\pi$
$200$	11.3162	+	9.24991i	0.800174	+	0.654067i
$201$	−4.46808	−	3.24625i	−0.315154	−	0.228973i
$202$	−0.0454612	−	0.0966099i	−0.00319864	−	0.00679745i
$203$	0.967509	−	1.16952i	0.0679058	−	0.0820840i
$204$	−0.205279	−	0.323469i	−0.0143724	−	0.0226473i
$205$	−13.3364	+	3.91718i	−0.931455	+	0.273588i
$206$	−5.49053	−	6.63691i	−0.382543	−	0.462416i
$207$	−0.213463	−	0.155090i	−0.0148367	−	0.0107795i
$208$	3.58714	−	5.65243i	0.248724	−	0.391926i
$209$	2.35009	+	12.3196i	0.162559	+	0.852165i
$210$	−3.16734	−	1.60212i	−0.218567	−	0.110557i
$211$	1.13978	−	0.143988i	0.0784658	−	0.00991254i	−0.0860023	−	0.996295i	$-0.527409\pi$
$211$	1.13978	−	0.143988i	0.0784658	−	0.00991254i	0.164468	+	0.986382i	$0.447409\pi$
$212$	0.282113	+	1.47889i	0.0193756	+	0.101570i
$213$	15.2590	+	1.92766i	1.04553	+	0.132081i
$214$	−9.67259	−	5.31755i	−0.661205	−	0.363500i
$215$	13.1773	−	22.4319i	0.898682	−	1.52985i
$216$	11.8533	+	11.1310i	0.806513	+	0.757366i
$217$	1.35486	+	0.347868i	0.0919736	+	0.0236148i
$218$	−11.4200	+	8.29713i	−0.773462	+	0.561953i
$219$	−1.42644	−	22.6727i	−0.0963902	−	1.53208i
$220$	0.673023	−	0.676996i	0.0453752	−	0.0456431i
$221$	−2.80526	−	1.11068i	−0.188702	−	0.0747124i
$222$	0.555479	+	0.219930i	0.0372813	+	0.0147607i
$223$	−19.3997	+	2.45075i	−1.29910	+	0.164114i	−0.744286	−	0.667861i	$-0.767210\pi$
$223$	−19.3997	+	2.45075i	−1.29910	+	0.164114i	−0.554813	+	0.831975i	$0.687210\pi$
$224$	−0.192831	−	0.593473i	−0.0128841	−	0.0396531i
$225$	−0.685417	+	2.73628i	−0.0456944	+	0.182419i
$226$	1.40046	−	4.31017i	0.0931572	−	0.286708i
$227$	0.283451	−	1.48590i	0.0188133	−	0.0986228i	−0.971642	−	0.236456i	$-0.924014\pi$
$227$	0.283451	−	1.48590i	0.0188133	−	0.0986228i	0.990455	+	0.137834i	$0.0440139\pi$
$228$	−0.0629871	+	1.00115i	−0.00417142	+	0.0663029i
$229$	−16.4576	+	4.22559i	−1.08755	+	0.279235i	−0.749574	−	0.661921i	$-0.769742\pi$
$229$	−16.4576	+	4.22559i	−1.08755	+	0.279235i	−0.337974	+	0.941155i	$0.609742\pi$
$230$	1.12200	−	0.875612i	0.0739824	−	0.0577361i
$231$	−1.80388	+	2.84246i	−0.118686	+	0.187020i
$232$	−1.83456	−	5.64618i	−0.120444	−	0.370690i
$233$	−0.0137329	−	0.218278i	−0.000899671	−	0.0142999i	0.997551	−	0.0699388i	$-0.0222804\pi$
$233$	−0.0137329	−	0.218278i	−0.000899671	−	0.0142999i	−0.998451	+	0.0556390i	$0.982280\pi$
$234$	1.38485	+	0.174948i	0.0905308	+	0.0114367i
$235$	18.8341	+	12.7188i	1.22860	+	0.829683i
$236$	0.793000	+	1.68521i	0.0516199	+	0.109698i
$237$	−5.15198	+	10.9485i	−0.334657	+	0.711183i
$238$	1.47911	−	0.813148i	0.0958765	−	0.0527085i
$239$	14.1152	−	13.2550i	0.913033	−	0.857395i	−0.0771716	−	0.997018i	$-0.524589\pi$
$239$	14.1152	−	13.2550i	0.913033	−	0.857395i	0.990205	+	0.139623i	$0.0445889\pi$
$240$	−11.0419	+	6.57407i	−0.712749	+	0.424355i
$241$	−4.55117	+	9.67172i	−0.293166	+	0.623010i	−0.996099	−	0.0882465i	$-0.971874\pi$
$241$	−4.55117	+	9.67172i	−0.293166	+	0.623010i	0.702932	+	0.711257i	$0.251874\pi$
$242$	−2.31581	−	2.79934i	−0.148866	−	0.179948i
$243$	−1.78604	+	5.49687i	−0.114575	+	0.352625i
$244$	1.96523	+	0.504584i	0.125811	+	0.0323027i
$245$	7.29549	−	12.4193i	0.466092	−	0.793438i
$246$	0.829033	−	13.1771i	0.0528572	−	0.840141i
$247$	4.23307	+	6.67025i	0.269344	+	0.424418i
$248$	3.98829	−	3.74525i	0.253257	−	0.237824i
$249$	15.0059			0.950960
$250$	−13.1645	−	7.62938i	−0.832594	−	0.482524i
$251$	8.99770			0.567930			0.283965	−	0.958835i	$-0.408350\pi$
$251$	8.99770			0.567930			0.283965	+	0.958835i	$0.408350\pi$
$252$	0.0454621	−	0.0426917i	0.00286384	−	0.00268933i
$253$	−0.723296	−	1.13973i	−0.0454733	−	0.0716544i
$254$	−0.418021	+	6.64425i	−0.0262289	+	0.416897i
$255$	3.84281	+	4.33304i	0.240646	+	0.271346i
$256$	−3.41913	−	0.877884i	−0.213696	−	0.0548678i
$257$	−5.97350	+	18.3846i	−0.372617	+	1.14680i	0.572456	+	0.819936i	$0.305991\pi$
$257$	−5.97350	+	18.3846i	−0.372617	+	1.14680i	−0.945072	+	0.326861i	$0.894009\pi$
$258$	15.7521	+	19.0410i	0.980683	+	1.18544i
$259$	0.0895044	−	0.190206i	0.00556153	−	0.0118189i
$260$	0.237184	−	0.552557i	0.0147096	−	0.0342681i
$261$	0.835249	−	0.784351i	0.0517006	−	0.0485501i
$262$	−17.9659	+	9.87685i	−1.10994	+	0.610194i
$263$	9.19263	−	19.5353i	0.566842	−	1.20460i	−0.391817	−	0.920043i	$-0.628153\pi$
$263$	9.19263	−	19.5353i	0.566842	−	1.20460i	0.958659	−	0.284557i	$-0.0918466\pi$
$264$	5.60646	+	11.9143i	0.345054	+	0.733277i
$265$	−7.77267	−	21.3917i	−0.477471	−	1.31408i
$266$	−4.38473	−	0.553920i	−0.268845	−	0.0339630i
$267$	1.23910	+	19.6949i	0.0758317	+	1.20531i
$268$	0.161745	+	0.497800i	0.00988015	+	0.0304080i
$269$	−6.24077	+	9.83388i	−0.380506	+	0.599582i	−0.979566	−	0.201122i	$-0.935541\pi$
$269$	−6.24077	+	9.83388i	−0.380506	+	0.599582i	0.599060	+	0.800704i	$0.295541\pi$
$270$	−14.0285	−	9.47352i	−0.853747	−	0.576540i
$271$	0.255258	−	0.0655392i	0.0155058	−	0.00398123i	−0.240929	−	0.970543i	$-0.577452\pi$
$271$	0.255258	−	0.0655392i	0.0155058	−	0.00398123i	0.256435	+	0.966562i	$0.417452\pi$
$272$	0.383708	−	6.09887i	0.0232657	−	0.369798i
$273$	−0.397357	+	2.08302i	−0.0240492	+	0.126070i
$274$	0.863952	−	2.65897i	0.0521932	−	0.160634i
$275$	−8.41359	+	11.7248i	−0.507359	+	0.707034i
$276$	−0.0333637	−	0.102683i	−0.00200826	−	0.00618078i
$277$	−16.1648	+	2.04209i	−0.971249	+	0.122697i	−0.594917	−	0.803787i	$-0.702815\pi$
$277$	−16.1648	+	2.04209i	−0.971249	+	0.122697i	−0.376332	+	0.926485i	$0.622815\pi$
$278$	13.9952	+	5.54109i	0.839376	+	0.332332i
$279$	0.981782	+	0.388715i	0.0587778	+	0.0232718i
$280$	2.23051	+	4.34595i	0.133298	+	0.259720i
$281$	0.455711	+	7.24331i	0.0271854	+	0.432100i	0.987954	+	0.154748i	$0.0494567\pi$
$281$	0.455711	+	7.24331i	0.0271854	+	0.432100i	−0.960769	+	0.277352i	$0.910543\pi$
$282$	−17.4646	+	12.6888i	−1.04000	+	0.755607i
$283$	1.32987	+	0.341451i	0.0790523	+	0.0202972i	0.288009	−	0.957628i	$-0.407007\pi$
$283$	1.32987	+	0.341451i	0.0790523	+	0.0202972i	−0.208957	+	0.977925i	$0.567007\pi$
$284$	−1.06257	−	0.997819i	−0.0630519	−	0.0592097i
$285$	−1.47155	−	15.0931i	−0.0871671	−	0.894040i
$286$	6.25786	+	3.44029i	0.370035	+	0.203428i
$287$	−4.60904	−	0.582257i	−0.272063	−	0.0343696i
$288$	−0.0882676	−	0.462715i	−0.00520122	−	0.0272657i
$289$	14.1336	−	1.78549i	0.831387	−	0.105029i
$290$	2.82204	+	5.49849i	0.165716	+	0.322883i
$291$	3.62662	+	19.0114i	0.212596	+	1.11447i
$292$	−1.15364	+	1.81785i	−0.0675117	+	0.106381i
$293$	−26.0294	−	18.9115i	−1.52065	−	1.10482i	−0.961163	−	0.275982i	$-0.910997\pi$
$293$	−26.0294	−	18.9115i	−1.52065	−	1.10482i	−0.559490	−	0.828837i	$-0.689003\pi$
$294$	8.72103	+	10.5419i	0.508621	+	0.614817i
$295$	−15.8943	−	23.2403i	−0.925399	−	1.35310i
$296$	−0.440561	−	0.694213i	−0.0256071	−	0.0403503i
$297$	−10.2339	+	12.3707i	−0.593834	+	0.717822i
$298$	−12.3444	−	26.2331i	−0.715089	−	1.51964i
$299$	−0.687895	−	0.499785i	−0.0397820	−	0.0289033i
$300$	−0.885025	+	0.740974i	−0.0510969	+	0.0427801i
$301$	7.03459	−	5.11093i	0.405467	−	0.294589i
$302$	23.0892	+	12.6934i	1.32863	+	0.730422i
$303$	0.118601	−	0.0304514i	0.00681342	−	0.00174939i
$304$	−10.1993	+	12.3289i	−0.584972	+	0.707110i
$305$	−30.5449	−	2.79667i	−1.74900	−	0.160137i
$306$	1.18469	−	0.469051i	0.0677240	−	0.0268138i
$307$	0.0749696			0.00427874			0.00213937	−	0.999998i	$-0.499319\pi$
$307$	0.0749696			0.00427874			0.00213937	+	0.999998i	$0.499319\pi$
$308$	0.296651	−	0.117452i	0.0169033	−	0.00669248i
$309$	8.65636	−	4.75888i	0.492443	−	0.270723i
$310$	−3.47767	+	4.51073i	−0.197518	+	0.256192i
$311$	0.159459	−	0.835911i	0.00904206	−	0.0474002i	−0.977480	−	0.211027i	$-0.932319\pi$
$311$	0.159459	−	0.835911i	0.00904206	−	0.0474002i	0.986522	+	0.163627i	$0.0523193\pi$
$312$	6.04625	+	5.67780i	0.342301	+	0.321442i
$313$	3.46052	+	3.24965i	0.195600	+	0.183681i	0.776159	−	0.630538i	$-0.217166\pi$
$313$	3.46052	+	3.24965i	0.195600	+	0.183681i	−0.580558	+	0.814219i	$0.697166\pi$
$314$	−3.12772	+	16.3961i	−0.176507	+	0.925284i
$315$	−0.575650	+	0.746650i	−0.0324342	+	0.0420690i
$316$	1.00492	−	0.552458i	0.0565311	−	0.0310782i
$317$	−21.8442	+	8.64873i	−1.22689	+	0.485761i	−0.890077	−	0.455810i	$-0.849350\pi$
$317$	−21.8442	+	8.64873i	−1.22689	+	0.485761i	−0.336815	+	0.941571i	$0.609350\pi$
$318$	21.6193			1.21235
$319$	5.45020	−	2.15789i	0.305153	−	0.120819i
$320$	18.9294	+	1.73317i	1.05819	+	0.0968869i
$321$	8.06879	−	9.75349i	0.450356	−	0.544387i
$322$	0.460735	−	0.118297i	0.0256758	−	0.00659242i
$323$	6.31931	+	3.47407i	0.351616	+	0.193302i
$324$	−0.836364	+	0.607654i	−0.0464647	+	0.0337586i
$325$	−2.20879	+	8.81781i	−0.122522	+	0.489124i
$326$	−1.52490	−	1.10790i	−0.0844563	−	0.0613611i
$327$	−6.89267	−	14.6477i	−0.381165	−	0.810018i
$328$	−11.5824	+	14.0007i	−0.639532	+	0.773061i
$329$	4.07002	+	6.41333i	0.224388	+	0.353578i
$330$	−7.73835	−	11.3149i	−0.425982	−	0.622862i
$331$	−9.26063	−	11.1942i	−0.509010	−	0.615288i	0.451927	−	0.892055i	$-0.350737\pi$
$331$	−9.26063	−	11.1942i	−0.509010	−	0.615288i	−0.960937	+	0.276767i	$0.910737\pi$
$332$	−1.15055	−	0.835921i	−0.0631445	−	0.0458771i
$333$	0.0850285	−	0.133984i	0.00465954	−	0.00734225i
$334$	2.43632	+	12.7716i	0.133310	+	0.698833i
$335$	−3.61302	−	7.03967i	−0.197401	−	0.384618i
$336$	−4.26118	+	0.538312i	−0.232466	+	0.0293673i
$337$	2.63880	+	13.8331i	0.143744	+	0.753534i	0.979030	+	0.203718i	$0.0653024\pi$
$337$	2.63880	+	13.8331i	0.143744	+	0.753534i	−0.835285	+	0.549817i	$0.814698\pi$
$338$	−13.0896	−	1.65360i	−0.711981	−	0.0899441i
$339$	4.55447	+	2.50384i	0.247365	+	0.135990i
$340$	−0.0532627	−	0.546296i	−0.00288858	−	0.0296270i
$341$	3.93797	+	3.69800i	0.213253	+	0.200258i
$342$	−3.23146	−	0.829697i	−0.174737	−	0.0448649i
$343$	8.12699	−	5.90460i	0.438816	−	0.318819i
$344$	−2.13549	−	33.9426i	−0.115138	−	1.83006i
$345$	0.745270	+	1.45209i	0.0401240	+	0.0781782i
$346$	24.1548	+	9.56356i	1.29857	+	0.514140i
$347$	4.99350	+	1.97707i	0.268065	+	0.106134i	0.498312	−	0.866998i	$-0.333953\pi$
$347$	4.99350	+	1.97707i	0.268065	+	0.106134i	−0.230247	+	0.973132i	$0.573953\pi$
$348$	0.465153	−	0.0587625i	0.0249348	−	0.00315000i
$349$	−6.37041	−	19.6061i	−0.341000	−	1.04949i	−0.963690	−	0.267022i	$-0.913960\pi$
$349$	−6.37041	−	19.6061i	−0.341000	−	1.04949i	0.622690	−	0.782468i	$-0.286040\pi$
$350$	−3.01329	−	4.09652i	−0.161067	−	0.218968i
$351$	−3.12514	+	9.61820i	−0.166808	+	0.513382i
$352$	0.451574	−	2.36723i	0.0240690	−	0.126174i
$353$	0.384713	−	6.11485i	0.0204762	−	0.325460i	−0.974433	−	0.224680i	$-0.927866\pi$
$353$	0.384713	−	6.11485i	0.0204762	−	0.325460i	0.994909	−	0.100780i	$-0.0321338\pi$
$354$	25.9043	−	6.65108i	1.37680	−	0.353501i
$355$	18.2616	+	12.3321i	0.969224	+	0.654522i
$356$	1.00212	−	1.57909i	0.0531125	−	0.0836919i
$357$	0.598164	+	1.84096i	0.0316582	+	0.0974339i
$358$	−1.53190	−	24.3488i	−0.0809633	−	1.28688i
$359$	−13.1903	−	1.66632i	−0.696158	−	0.0879453i	−0.230713	−	0.973022i	$-0.574106\pi$
$359$	−13.1903	−	1.66632i	−0.696158	−	0.0879453i	−0.465445	+	0.885077i	$0.654106\pi$
$360$	1.25932	+	3.46586i	0.0663720	+	0.182667i
$361$	0.0502048	+	0.106691i	0.00264236	+	0.00561530i
$362$	−6.30407	+	13.3968i	−0.331334	+	0.704121i
$363$	3.65111	−	2.00721i	0.191634	−	0.105351i
$364$	0.146504	−	0.137576i	0.00767888	−	0.00721095i
$365$	12.8383	−	29.9088i	0.671989	−	1.56550i
$366$	12.4053	−	26.3625i	0.648433	−	1.37799i
$367$	8.72646	+	10.5485i	0.455517	+	0.550626i	0.947407	−	0.320032i	$-0.103694\pi$
$367$	8.72646	+	10.5485i	0.455517	+	0.550626i	−0.491889	+	0.870658i	$0.663694\pi$
$368$	0.532181	−	1.63789i	0.0277419	−	0.0853807i
$369$	−3.39677	−	0.872142i	−0.176829	−	0.0454019i
$370$	0.567939	+	0.640391i	0.0295257	+	0.0332923i
$371$	0.477647	−	7.59198i	0.0247982	−	0.394156i
$372$	0.231520	+	0.364817i	0.0120037	+	0.0189149i
$373$	−2.79672	+	2.62630i	−0.144809	+	0.135984i	−0.753566	−	0.657372i	$-0.771668\pi$
$373$	−2.79672	+	2.62630i	−0.144809	+	0.135984i	0.608758	+	0.793356i	$0.291668\pi$
$374$	6.51857			0.337067
$375$	11.4234	−	13.1903i	0.589904	−	0.681145i
$376$	29.7095			1.53215
$377$	2.69163	−	2.52761i	0.138626	−	0.130179i
$378$	−3.03153	−	4.77693i	−0.155925	−	0.245699i
$379$	1.42383	−	22.6312i	0.0731374	−	1.16249i	−0.774735	−	0.632286i	$-0.782117\pi$
$379$	1.42383	−	22.6312i	0.0731374	−	1.16249i	0.847873	−	0.530200i	$-0.177883\pi$
$380$	−0.727953	+	1.23921i	−0.0373432	+	0.0635702i
$381$	−7.39493	−	1.89869i	−0.378853	−	0.0972730i
$382$	7.54803	−	23.2304i	0.386191	−	1.18857i
$383$	10.7910	+	13.0440i	0.551393	+	0.666520i	0.970411	−	0.241458i	$-0.0776256\pi$
$383$	10.7910	+	13.0440i	0.551393	+	0.666520i	−0.419018	+	0.907978i	$0.637626\pi$
$384$	−6.57813	+	13.9792i	−0.335689	+	0.713375i
$385$	−4.14437	+	2.46746i	−0.211216	+	0.125754i
$386$	−12.8054	+	12.0251i	−0.651777	+	0.612060i
$387$	5.75198	−	3.16218i	0.292390	−	0.160743i
$388$	0.780990	−	1.65969i	0.0396488	−	0.0842579i
$389$	4.39390	+	9.33751i	0.222779	+	0.473430i	0.984704	−	0.174235i	$-0.0557453\pi$
$389$	4.39390	+	9.33751i	0.222779	+	0.473430i	−0.761925	+	0.647666i	$0.775745\pi$
$390$	−7.15581	−	4.83236i	−0.362349	−	0.244696i
$391$	−0.770032	−	0.0972777i	−0.0389422	−	0.00491955i
$392$	−1.18230	−	18.7921i	−0.0597150	−	0.949142i
$393$	−7.26556	−	22.3611i	−0.366499	−	1.12797i
$394$	−12.6890	+	19.9946i	−0.639262	+	1.00732i
$395$	−13.6669	+	10.6657i	−0.687654	+	0.536648i
$396$	0.233284	−	0.0598971i	0.0117230	−	0.00300994i
$397$	1.36945	−	21.7668i	0.0687309	−	1.09245i	−0.800917	−	0.598775i	$-0.795654\pi$
$397$	1.36945	−	21.7668i	0.0687309	−	1.09245i	0.869648	−	0.493672i	$-0.164346\pi$
$398$	−0.331460	+	1.73757i	−0.0166146	+	0.0870967i
$399$	1.56623	−	4.82037i	0.0784098	−	0.241321i
$400$	−18.3680	+	1.26420i	−0.918401	+	0.0632100i
$401$	−4.73579	−	14.5752i	−0.236494	−	0.727853i	−0.996920	−	0.0784285i	$-0.975010\pi$
$401$	−4.73579	−	14.5752i	−0.236494	−	0.727853i	0.760426	−	0.649425i	$-0.224990\pi$
$402$	7.45686	−	0.942021i	0.371915	−	0.0469837i
$403$	3.16384	+	1.25265i	0.157602	+	0.0623991i
$404$	−0.0107898	−	0.00427198i	−0.000536812	−	0.000212539i
$405$	11.0184	−	11.0834i	0.547507	−	0.550739i
$406$	0.129703	+	2.06158i	0.00643707	+	0.102314i
$407$	0.656788	−	0.477184i	0.0325558	−	0.0236531i
$408$	7.33325	+	1.88286i	0.363050	+	0.0932154i
$409$	11.7369	+	11.0217i	0.580354	+	0.544988i	0.918151	−	0.396230i	$-0.129682\pi$
$409$	11.7369	+	11.0217i	0.580354	+	0.544988i	−0.337797	+	0.941219i	$0.609682\pi$
$410$	9.58128	−	16.3104i	0.473186	−	0.805514i
$411$	2.80968	+	1.54463i	0.138591	+	0.0761912i
$412$	−0.928808	−	0.117336i	−0.0457591	−	0.00578072i
$413$	−1.76332	−	9.24365i	−0.0867674	−	0.454850i
$414$	0.356252	−	0.0450051i	0.0175088	−	0.00221188i
$415$	19.1846	+	9.70403i	0.941735	+	0.476352i
$416$	−0.284447	−	1.49112i	−0.0139462	−	0.0731083i
$417$	−9.24949	+	14.5749i	−0.452950	+	0.713734i
$418$	−13.8085	−	10.0325i	−0.675396	−	0.490704i
$419$	19.5259	+	23.6027i	0.953900	+	1.15307i	0.988125	+	0.153653i	$0.0491038\pi$
$419$	19.5259	+	23.6027i	0.953900	+	1.15307i	−0.0342246	+	0.999414i	$0.510896\pi$
$420$	−0.370147	+	0.108720i	−0.0180613	+	0.00530499i
$421$	20.9003	+	32.9335i	1.01862	+	1.60508i	0.771639	+	0.636061i	$0.219437\pi$
$421$	20.9003	+	32.9335i	1.01862	+	1.60508i	0.246978	+	0.969021i	$0.420563\pi$
$422$	−0.996596	+	1.20468i	−0.0485135	+	0.0586428i
$423$	2.44139	+	5.18823i	0.118705	+	0.252260i
$424$	−24.0709	−	17.4885i	−1.16899	−	0.849319i
$425$	2.11083	+	8.02474i	0.102390	+	0.389257i
$426$	−16.9337	+	12.3031i	−0.820440	+	0.596085i
$427$	−8.98356	−	4.93875i	−0.434745	−	0.239003i
$428$	−1.16199	+	0.298348i	−0.0561668	+	0.0144212i
$429$	−5.22025	+	6.31020i	−0.252036	+	0.304659i
$430$	7.82513	+	34.5300i	0.377361	+	1.66518i
$431$	1.92549	−	0.762356i	0.0927477	−	0.0367214i	−0.321293	−	0.946980i	$-0.604117\pi$
$431$	1.92549	−	0.762356i	0.0927477	−	0.0367214i	0.414040	+	0.910259i	$0.364117\pi$
$432$	−20.4833			−0.985504
$433$	−11.7794	+	4.66378i	−0.566081	+	0.224127i	−0.633693	−	0.773584i	$-0.718462\pi$
$433$	−11.7794	+	4.66378i	−0.566081	+	0.224127i	0.0676126	+	0.997712i	$0.478462\pi$
$434$	−1.66818	+	0.917089i	−0.0800752	+	0.0440217i
$435$	−6.80050	+	1.99745i	−0.326059	+	0.0957703i
$436$	−0.287484	+	1.50704i	−0.0137680	+	0.0721743i
$437$	1.48147	+	1.39119i	0.0708683	+	0.0665497i
$438$	22.5372	+	21.1639i	1.07687	+	1.01125i
$439$	−0.514083	+	2.69491i	−0.0245358	+	0.128621i	−0.992448	−	0.122669i	$-0.960855\pi$
$439$	−0.514083	+	2.69491i	−0.0245358	+	0.128621i	0.967912	+	0.251290i	$0.0808548\pi$
$440$	−0.537080	+	18.8577i	−0.0256043	+	0.899007i
$441$	3.18454	−	1.75072i	0.151645	−	0.0833674i
$442$	3.81771	−	1.51154i	0.181590	−	0.0718966i
$443$	4.98511			0.236850			0.118425	−	0.992963i	$-0.462216\pi$
$443$	4.98511			0.236850			0.118425	+	0.992963i	$0.462216\pi$
$444$	0.0603734	−	0.0239035i	0.00286519	−	0.00113441i
$445$	−11.1522	+	25.9807i	−0.528664	+	1.23160i
$446$	16.9626	−	20.5042i	0.803201	−	0.970903i
$447$	32.2043	−	8.26866i	1.52321	−	0.391094i
$448$	5.56733	+	3.06066i	0.263031	+	0.144603i
$449$	−26.7050	+	19.4023i	−1.26029	+	0.915652i	−0.998772	−	0.0495476i	$-0.984222\pi$
$449$	−26.7050	+	19.4023i	−1.26029	+	0.915652i	−0.261515	+	0.965199i	$0.584222\pi$
$450$	−1.86917	−	3.35311i	−0.0881136	−	0.158067i
$451$	−14.5149	−	10.5457i	−0.683480	−	0.496577i
$452$	−0.209725	−	0.445689i	−0.00986465	−	0.0209634i
$453$	−19.2608	+	23.2823i	−0.904951	+	1.09390i
$454$	1.10308	+	1.73818i	0.0517701	+	0.0815766i
$455$	−1.85506	+	2.40612i	−0.0869666	+	0.112801i
$456$	−12.6364	−	15.2748i	−0.591756	−	0.715310i
$457$	−3.43152	−	2.49314i	−0.160520	−	0.116624i	0.504626	−	0.863338i	$-0.331630\pi$
$457$	−3.43152	−	2.49314i	−0.160520	−	0.116624i	−0.665145	+	0.746714i	$0.731630\pi$
$458$	12.3904	−	19.5241i	0.578964	−	0.912301i
$459$	1.72980	+	9.06794i	0.0807402	+	0.423255i
$460$	0.0237486	−	0.152853i	0.00110728	−	0.00712679i
$461$	−9.31437	+	1.17668i	−0.433814	+	0.0548034i	−0.339208	−	0.940711i	$-0.610159\pi$
$461$	−9.31437	+	1.17668i	−0.433814	+	0.0548034i	−0.0946056	+	0.995515i	$0.530159\pi$
$462$	−0.858498	−	4.50041i	−0.0399410	−	0.209378i
$463$	−3.93902	−	0.497613i	−0.183062	−	0.0231261i	0.0332679	−	0.999446i	$-0.489409\pi$
$463$	−3.93902	−	0.497613i	−0.183062	−	0.0231261i	−0.216329	+	0.976320i	$0.569409\pi$
$464$	6.55353	+	3.60284i	0.304240	+	0.167257i
$465$	−4.33402	−	4.88692i	−0.200986	−	0.226625i
$466$	0.216974	+	0.203752i	0.0100511	+	0.00943862i
$467$	24.8452	+	6.37915i	1.14970	+	0.295192i	0.775004	−	0.631957i	$-0.217748\pi$
$467$	24.8452	+	6.37915i	1.14970	+	0.295192i	0.374693	+	0.927149i	$0.377748\pi$
$468$	0.122738	−	0.0891742i	0.00567356	−	0.00412208i
$469$	−0.166058	−	2.63941i	−0.00766784	−	0.121877i
$470$	−30.5336	+	4.92821i	−1.40841	+	0.227321i
$471$	−17.7981	−	7.04676i	−0.820093	−	0.324698i
$472$	−34.2220	−	13.5495i	−1.57520	−	0.623664i
$473$	33.3158	−	4.20877i	1.53186	−	0.193519i
$474$	−5.08865	−	15.6613i	−0.233730	−	0.719345i
$475$	7.87911	−	20.2478i	0.361519	−	0.929031i
$476$	0.0566898	−	0.174473i	0.00259837	−	0.00799697i
$477$	1.07602	−	5.64069i	0.0492675	−	0.258269i
$478$	−1.65463	+	26.2996i	−0.0756811	+	1.20292i
$479$	−31.0129	+	7.96276i	−1.41702	+	0.363828i	−0.878078	−	0.478517i	$-0.841174\pi$
$479$	−31.0129	+	7.96276i	−1.41702	+	0.363828i	−0.538938	+	0.842345i	$0.681174\pi$
$480$	−0.804720	+	2.80060i	−0.0367303	+	0.127829i
$481$	0.274009	−	0.431769i	0.0124937	−	0.0196870i
$482$	−4.49522	−	13.8349i	−0.204752	−	0.630161i
$483$	0.0342533	+	0.544440i	0.00155858	+	0.0247729i
$484$	−0.391756	−	0.0494903i	−0.0178071	−	0.00224956i
$485$	−7.65780	+	26.6508i	−0.347723	+	1.21015i
$486$	−3.34907	−	7.11714i	−0.151917	−	0.322840i
$487$	14.9302	−	31.7283i	0.676553	−	1.43775i	−0.211207	−	0.977441i	$-0.567739\pi$
$487$	14.9302	−	31.7283i	0.676553	−	1.43775i	0.887760	−	0.460307i	$-0.152261\pi$
$488$	−35.1375	+	19.3170i	−1.59060	+	0.874439i
$489$	1.57574	−	1.47972i	0.0712576	−	0.0669153i
$490$	4.33232	+	19.1172i	0.195714	+	0.863629i
$491$	−9.09217	+	19.3218i	−0.410324	+	0.871982i	0.587696	+	0.809082i	$0.300035\pi$
$491$	−9.09217	+	19.3218i	−0.410324	+	0.871982i	−0.998020	+	0.0629005i	$0.979965\pi$
$492$	−0.914712	−	1.10570i	−0.0412384	−	0.0498487i
$493$	1.04153	−	3.20550i	0.0469081	−	0.144368i
$494$	−10.4135	−	2.67374i	−0.468527	−	0.120297i
$495$	−3.33730	+	1.45586i	−0.150001	+	0.0654358i
$496$	−0.432756	+	6.87846i	−0.0194313	+	0.308852i
$497$	3.94629	+	6.21837i	0.177015	+	0.278932i
$498$	−14.8868	+	13.9796i	−0.667093	+	0.626442i
$499$	29.1157			1.30340			0.651699	−	0.758478i	$-0.274056\pi$
$499$	29.1157			1.30340			0.651699	+	0.758478i	$0.274056\pi$
$500$	−1.61065	+	0.374984i	−0.0720305	+	0.0167698i
$501$	−14.9108			−0.666166
$502$	−8.92629	+	8.38234i	−0.398400	+	0.374122i
$503$	−17.9537	−	28.2905i	−0.800516	−	1.26141i	−0.961596	−	0.274470i	$-0.911498\pi$
$503$	−17.9537	−	28.2905i	−0.800516	−	1.26141i	0.161080	−	0.986941i	$-0.448502\pi$
$504$	−0.0773879	+	1.23005i	−0.00344713	+	0.0547906i
$505$	0.171320	+	0.0377654i	0.00762362	+	0.00168054i
$506$	1.77934	+	0.456857i	0.0791014	+	0.0203098i
$507$	4.67563	−	14.3901i	0.207652	−	0.639088i
$508$	0.461222	+	0.557522i	0.0204634	+	0.0247360i
$509$	−10.0359	+	21.3274i	−0.444833	+	0.945319i	0.549144	+	0.835728i	$0.314954\pi$
$509$	−10.0359	+	21.3274i	−0.444833	+	0.945319i	−0.993977	+	0.109591i	$0.965046\pi$
$510$	−7.84902	−	0.718651i	−0.347560	−	0.0318224i
$511$	7.92996	−	7.44673i	0.350801	−	0.329424i
$512$	21.5591	−	11.8522i	0.952786	−	0.523798i
$513$	10.2918	−	21.8712i	0.454394	−	0.965636i
$514$	−11.2011	−	23.8036i	−0.494061	−	1.04993i
$515$	14.1444	−	0.486177i	0.623276	−	0.0214235i
$516$	2.66471	+	0.336631i	0.117307	+	0.0148194i
$517$	1.84194	+	29.2767i	0.0810082	+	1.28759i
$518$	0.0884041	+	0.272080i	0.00388426	+	0.0119545i
$519$	−15.9640	+	25.1553i	−0.700744	+	1.10420i
$520$	4.05822	+	11.1689i	0.177965	+	0.489789i
$521$	16.4062	−	4.21239i	0.718768	−	0.184548i	0.128446	−	0.991716i	$-0.459001\pi$
$521$	16.4062	−	4.21239i	0.718768	−	0.184548i	0.590321	+	0.807168i	$0.299001\pi$
$522$	−0.0979110	+	1.55625i	−0.00428545	+	0.0681153i
$523$	−6.74641	+	35.3659i	−0.295000	+	1.54644i	0.458319	+	0.888788i	$0.348452\pi$
$523$	−6.74641	+	35.3659i	−0.295000	+	1.54644i	−0.753319	+	0.657655i	$0.771548\pi$
$524$	−0.688579	+	2.11923i	−0.0300807	+	0.0925790i
$525$	5.26227	−	2.51417i	0.229664	−	0.109727i
$526$	9.07963	+	27.9442i	0.395891	+	1.21843i
$527$	3.08163	−	0.389301i	0.134238	−	0.0169582i
$528$	−15.4225	−	6.10619i	−0.671177	−	0.265738i
$529$	21.1815	+	8.38634i	0.920934	+	0.364624i
$530$	27.6397	+	13.9808i	1.20059	+	0.607288i
$531$	−0.446046	−	7.08970i	−0.0193568	−	0.307667i
$532$	−0.388613	+	0.282344i	−0.0168485	+	0.0122411i
$533$	−10.9463	−	2.81052i	−0.474135	−	0.121737i
$534$	−19.5773	−	18.3843i	−0.847190	−	0.795565i
$535$	16.6231	−	7.25162i	0.718680	−	0.313515i
$536$	−9.06449	−	4.98325i	−0.391526	−	0.215243i
$537$	27.7582	+	3.50667i	1.19785	+	0.151324i
$538$	−2.97010	−	15.5698i	−0.128050	−	0.671261i
$539$	18.4450	−	2.33015i	0.794484	−	0.100367i
$540$	−1.81631	+	0.293158i	−0.0781617	+	0.0126155i
$541$	−1.62748	−	8.53153i	−0.0699707	−	0.366799i	0.930029	−	0.367486i	$-0.119781\pi$
$541$	−1.62748	−	8.53153i	−0.0699707	−	0.366799i	−1.00000		0.000686715i	$0.999781\pi$
$542$	−0.192176	+	0.302820i	−0.00825465	+	0.0130072i
$543$	−13.7369	−	9.98041i	−0.589505	−	0.428300i
$544$	−0.883255	−	1.06767i	−0.0378692	−	0.0457760i
$545$	0.660294	−	23.1840i	0.0282839	−	0.993092i
$546$	−1.54636	−	2.43667i	−0.0661780	−	0.104280i
$547$	−5.99512	+	7.24686i	−0.256333	+	0.309853i	−0.882943	−	0.469479i	$-0.844442\pi$
$547$	−5.99512	+	7.24686i	−0.256333	+	0.309853i	0.626611	+	0.779332i	$0.284442\pi$
$548$	−0.129381	−	0.274948i	−0.00552688	−	0.0117452i
$549$	−6.26081	−	4.54874i	−0.267205	−	0.194136i
$550$	−2.57614	−	19.4700i	−0.109847	−	0.830202i
$551$	−7.13976	+	5.18734i	−0.304164	+	0.220988i
$552$	1.86976	+	1.02791i	0.0795823	+	0.0437508i
$553$	−5.61214	+	1.44095i	−0.238652	+	0.0612755i
$554$	14.1341	−	17.0852i	0.600500	−	0.725879i
$555$	−0.843447	+	0.502169i	−0.0358023	+	0.0213159i
$556$	1.52110	−	0.602245i	0.0645089	−	0.0255409i
$557$	−0.828621			−0.0351098			−0.0175549	−	0.999846i	$-0.505588\pi$
$557$	−0.828621			−0.0351098			−0.0175549	+	0.999846i	$0.505588\pi$
$558$	−1.33612	+	0.529008i	−0.0565625	+	0.0223947i
$559$	18.5361	−	10.1903i	0.783992	−	0.431003i
$560$	−5.79591	−	2.06741i	−0.244922	−	0.0873639i
$561$	−1.40079	+	7.34318i	−0.0591412	+	0.310029i
$562$	−7.20003	−	6.76128i	−0.303715	−	0.285207i
$563$	26.7587	+	25.1281i	1.12774	+	1.05902i	0.997718	+	0.0675120i	$0.0215061\pi$
$563$	26.7587	+	25.1281i	1.12774	+	1.05902i	0.130026	+	0.991511i	$0.458494\pi$
$564$	−0.439649	+	2.30472i	−0.0185126	+	0.0970463i
$565$	4.20357	+	6.14638i	0.176845	+	0.258580i
$566$	−1.63741	+	0.900174i	−0.0688255	+	0.0378371i
$567$	4.85661	−	1.92287i	0.203958	−	0.0807528i
$568$	28.8063			1.20868
$569$	2.29337	−	0.908008i	0.0961429	−	0.0380657i	−0.319561	−	0.947566i	$-0.603535\pi$
$569$	2.29337	−	0.908008i	0.0961429	−	0.0380657i	0.415704	+	0.909500i	$0.363535\pi$
$570$	15.5208	+	13.6024i	0.650094	+	0.569743i
$571$	−6.15676	+	7.44224i	−0.257652	+	0.311448i	−0.883439	−	0.468546i	$-0.844778\pi$
$571$	−6.15676	+	7.44224i	−0.257652	+	0.311448i	0.625787	+	0.779994i	$0.284778\pi$
$572$	0.751769	−	0.193022i	0.0314331	−	0.00807064i
$573$	24.5471	+	13.4949i	1.02547	+	0.563757i
$574$	5.11490	−	3.71619i	0.213492	−	0.155111i
$575$	0.0137640	+	2.33841i	0.000574000	+	0.0975186i
$576$	3.87997	+	2.81897i	0.161666	+	0.117457i
$577$	18.2092	+	38.6965i	0.758059	+	1.61096i	0.791239	+	0.611508i	$0.209437\pi$
$577$	18.2092	+	38.6965i	0.758059	+	1.61096i	−0.0331797	+	0.999449i	$0.510563\pi$
$578$	−12.3580	+	14.9383i	−0.514027	+	0.621351i
$579$	−10.7945	−	17.0094i	−0.448603	−	0.706886i
$580$	0.632685	+	0.225679i	0.0262708	+	0.00937083i
$581$	4.58028	+	5.53660i	0.190022	+	0.229697i
$582$	−21.3091	−	15.4819i	−0.883289	−	0.641747i
$583$	15.7415	−	24.8046i	0.651945	−	1.02730i
$584$	−7.97280	−	41.7949i	−0.329917	−	1.72948i
$585$	−1.61696	+	1.62651i	−0.0668532	+	0.0672478i
$586$	43.4409	−	5.48786i	1.79453	−	0.226701i
$587$	−6.30714	−	33.0632i	−0.260324	−	1.36466i	−0.836781	−	0.547538i	$-0.815565\pi$
$587$	−6.30714	−	33.0632i	−0.260324	−	1.36466i	0.576457	−	0.817127i	$-0.304435\pi$
$588$	1.47530	+	0.186373i	0.0608402	+	0.00768590i
$589$	−7.12708	−	3.91815i	−0.293666	−	0.161444i
$590$	37.4190	+	8.24858i	1.54051	+	0.339589i
$591$	−19.7972	−	18.5908i	−0.814349	−	0.764725i
$592$	1.00320	+	0.257579i	0.0412315	+	0.0105864i
$593$	−7.67260	+	5.57447i	−0.315076	+	0.228916i	−0.734071	−	0.679072i	$-0.762382\pi$
$593$	−7.67260	+	5.57447i	−0.315076	+	0.228916i	0.418996	+	0.907988i	$0.362382\pi$
$594$	−1.37195	−	21.8066i	−0.0562920	−	0.894735i
$595$	−0.425778	+	2.74043i	−0.0174552	+	0.112347i
$596$	−2.92982	−	1.16000i	−0.120010	−	0.0475153i
$597$	−1.88615	−	0.746781i	−0.0771951	−	0.0305637i
$598$	1.14804	−	0.145031i	0.0469468	−	0.00593076i
$599$	1.21034	+	3.72504i	0.0494532	+	0.152201i	0.972734	−	0.231926i	$-0.0745026\pi$
$599$	1.21034	+	3.72504i	0.0494532	+	0.152201i	−0.923280	+	0.384127i	$0.874503\pi$
$600$	2.72570	−	22.6474i	0.111276	−	0.924577i
$601$	−12.4204	+	38.2261i	−0.506639	+	1.55927i	0.291359	+	0.956614i	$0.405893\pi$
$601$	−12.4204	+	38.2261i	−0.506639	+	1.55927i	−0.797998	+	0.602661i	$0.794107\pi$
$602$	−2.21737	+	11.6238i	−0.0903732	+	0.473753i
$603$	0.125355	−	1.99245i	0.00510483	−	0.0811390i
$604$	2.77375	−	0.712178i	0.112862	−	0.0289781i
$605$	5.96586	−	0.205061i	0.242547	−	0.00833693i
$606$	−0.0892904	+	0.140699i	−0.00362717	+	0.00571551i
$607$	0.718310	+	2.21073i	0.0291553	+	0.0897308i	0.964575	−	0.263808i	$-0.0849784\pi$
$607$	0.718310	+	2.21073i	0.0291553	+	0.0897308i	−0.935420	+	0.353538i	$0.884978\pi$
$608$	0.227818	+	3.62106i	0.00923924	+	0.146854i
$609$	−2.35024	−	0.296904i	−0.0952365	−	0.0120312i
$610$	32.9079	−	25.6815i	1.33240	−	1.03981i
$611$	7.86751	+	16.7193i	0.318285	+	0.676391i
$612$	0.0589641	−	0.125305i	0.00238348	−	0.00506516i
$613$	−38.3070	+	21.0594i	−1.54720	+	0.850582i	−0.547297	+	0.836939i	$0.684343\pi$
$613$	−38.3070	+	21.0594i	−1.54720	+	0.850582i	−0.999907	+	0.0136435i	$0.995657\pi$
$614$	−0.0743746	+	0.0698424i	−0.00300151	+	0.00281861i
$615$	16.3148	+	14.2983i	0.657875	+	0.576563i
$616$	−2.68467	+	5.70521i	−0.108168	+	0.229869i
$617$	−9.68808	−	11.7109i	−0.390028	−	0.471462i	0.538554	−	0.842591i	$-0.318971\pi$
$617$	−9.68808	−	11.7109i	−0.390028	−	0.471462i	−0.928581	+	0.371129i	$0.878971\pi$
$618$	−4.15425	+	12.7855i	−0.167108	+	0.514306i
$619$	−37.2534	−	9.56505i	−1.49734	−	0.384452i	−0.590886	−	0.806755i	$-0.701222\pi$
$619$	−37.2534	−	9.56505i	−1.49734	−	0.384452i	−0.906454	+	0.422304i	$0.861222\pi$
$620$	0.0600711	+	0.616127i	0.00241251	+	0.0247442i
$621$	−0.163356	+	2.59647i	−0.00655524	+	0.104193i
$622$	0.620550	+	0.977830i	0.0248818	+	0.0392074i
$623$	−6.88847	+	6.46870i	−0.275981	+	0.259163i
$624$	−10.4484			−0.418269
$625$	23.1345	−	9.47610i	0.925379	−	0.379044i
$626$	−6.46046			−0.258212
$627$	14.2689	−	13.3994i	0.569846	−	0.535121i
$628$	0.972085	+	1.53176i	0.0387904	+	0.0611239i
$629$	0.0293101	−	0.465870i	0.00116867	−	0.0185755i
$630$	−0.124505	−	1.27701i	−0.00496041	−	0.0508771i
$631$	−43.8705	−	11.2640i	−1.74646	−	0.448414i	−0.765628	−	0.643283i	$-0.777572\pi$
$631$	−43.8705	−	11.2640i	−1.74646	−	0.448414i	−0.980829	+	0.194869i	$0.937572\pi$
$632$	−7.00319	+	21.5536i	−0.278572	+	0.857356i
$633$	−1.14291	−	1.38154i	−0.0454266	−	0.0549114i
$634$	13.6136	−	28.9304i	0.540665	−	1.14897i
$635$	−8.22635	−	7.20958i	−0.326453	−	0.286104i
$636$	1.71289	−	1.60851i	0.0679205	−	0.0637816i
$637$	10.2623	−	5.64177i	0.406609	−	0.223535i
$638$	−3.39664	+	7.21822i	−0.134474	+	0.285772i
$639$	2.36717	+	5.03050i	0.0936440	+	0.199004i
$640$	−17.4501	+	13.6181i	−0.689774	+	0.538303i
$641$	−31.1484	−	3.93496i	−1.23029	−	0.155422i	−0.516811	−	0.856099i	$-0.672881\pi$
$641$	−31.1484	−	3.93496i	−1.23029	−	0.155422i	−0.713478	+	0.700678i	$0.752881\pi$
$642$	1.08169	+	17.1930i	0.0426911	+	0.678555i
$643$	2.87206	+	8.83929i	0.113263	+	0.348588i	0.991581	−	0.129490i	$-0.0413339\pi$
$643$	2.87206	+	8.83929i	0.113263	+	0.348588i	−0.878318	+	0.478077i	$0.841334\pi$
$644$	0.0277024	−	0.0436520i	0.00109163	−	0.00172013i
$645$	−40.5796	+	1.39482i	−1.59782	+	0.0549210i
$646$	−9.50563	+	2.44063i	−0.373994	+	0.0960253i
$647$	1.47746	−	23.4835i	0.0580848	−	0.923232i	−0.855813	−	0.517286i	$-0.826942\pi$
$647$	1.47746	−	23.4835i	0.0580848	−	0.923232i	0.913897	−	0.405945i	$-0.133058\pi$
$648$	3.82827	−	20.0685i	0.150389	−	0.788365i
$649$	11.2304	−	34.5636i	0.440832	−	1.35674i
$650$	−6.02350	−	10.8056i	−0.236261	−	0.423829i
$651$	−0.674625	−	2.07628i	−0.0264406	−	0.0813759i
$652$	−0.203247	+	0.0256760i	−0.00795975	+	0.00100555i
$653$	9.64663	+	3.81937i	0.377502	+	0.149463i	0.549210	−	0.835684i	$-0.314929\pi$
$653$	9.64663	+	3.81937i	0.377502	+	0.149463i	−0.171708	+	0.985148i	$0.554929\pi$
$654$	20.4839	+	8.11014i	0.800982	+	0.317131i
$655$	5.17169	−	33.2865i	0.202075	−	1.30061i
$656$	−1.43726	−	22.8446i	−0.0561156	−	0.891932i
$657$	6.64356	−	4.82683i	0.259190	−	0.188312i
$658$	−10.0124	−	2.57076i	−0.390326	−	0.100219i
$659$	−27.8288	−	26.1330i	−1.08406	−	1.01800i	−0.999768	−	0.0215546i	$-0.993138\pi$
$659$	−27.8288	−	26.1330i	−1.08406	−	1.01800i	−0.0842880	−	0.996441i	$-0.526862\pi$
$660$	−1.45495	−	0.320726i	−0.0566338	−	0.0124843i
$661$	−2.26555	−	1.24549i	−0.0881195	−	0.0484441i	0.437085	−	0.899420i	$-0.356011\pi$
$661$	−2.26555	−	1.24549i	−0.0881195	−	0.0484441i	−0.525204	+	0.850976i	$0.676011\pi$
$662$	19.6157	+	2.47804i	0.762387	+	0.0963119i
$663$	0.882357	+	4.62548i	0.0342679	+	0.179639i
$664$	27.8835	−	3.52250i	1.08209	−	0.136700i
$665$	5.11963	−	5.14985i	0.198531	−	0.199703i
$666$	0.0404666	+	0.212134i	0.00156805	+	0.00822001i
$667$	0.508961	−	0.801993i	0.0197070	−	0.0310533i
$668$	1.14326	+	0.830625i	0.0442340	+	0.0321378i
$669$	19.4529	+	23.5146i	0.752094	+	0.909125i
$670$	10.1426	+	3.61787i	0.391842	+	0.139770i
$671$	−21.2141	−	33.4280i	−0.818961	−	1.29048i
$672$	−0.620793	+	0.750410i	−0.0239476	+	0.0289477i
$673$	5.21821	+	11.0893i	0.201147	+	0.427460i	0.979796	−	0.200001i	$-0.0640945\pi$
$673$	5.21821	+	11.0893i	0.201147	+	0.427460i	−0.778649	+	0.627460i	$0.784094\pi$
$674$	−15.5049	−	11.2649i	−0.597225	−	0.433909i
$675$	26.4009	−	8.75031i	1.01617	−	0.336800i
$676$	−1.16011	+	0.842872i	−0.0446198	+	0.0324182i
$677$	−0.497166	−	0.273319i	−0.0191077	−	0.0105045i	0.472171	−	0.881507i	$-0.343470\pi$
$677$	−0.497166	−	0.273319i	−0.0191077	−	0.0105045i	−0.491279	+	0.871002i	$0.663470\pi$
$678$	−6.85092	+	1.75902i	−0.263108	+	0.0675547i
$679$	−5.90753	+	7.14098i	−0.226710	+	0.274046i
$680$	8.15774	+	7.14946i	0.312835	+	0.274169i
$681$	−2.19510	+	0.869101i	−0.0841164	+	0.0333040i
$682$	−7.35181			−0.281515
$683$	−20.0091	+	7.92217i	−0.765628	+	0.303133i	−0.718288	−	0.695745i	$-0.755074\pi$
$683$	−20.0091	+	7.92217i	−0.765628	+	0.303133i	−0.0473393	+	0.998879i	$0.515074\pi$
$684$	−0.317758	+	0.174689i	−0.0121498	+	0.00667939i
$685$	2.59321	+	3.79174i	0.0990813	+	0.144875i
$686$	−2.56170	+	13.4289i	−0.0978063	+	0.512719i
$687$	19.3313	+	18.1533i	0.737537	+	0.692593i
$688$	31.2308	+	29.3276i	1.19066	+	1.11811i
$689$	3.46753	−	18.1774i	0.132102	−	0.692504i
$690$	−2.09214	−	0.746269i	−0.0796464	−	0.0284100i
$691$	−15.8006	+	8.68643i	−0.601082	+	0.330447i	−0.753076	−	0.657934i	$-0.771431\pi$
$691$	−15.8006	+	8.68643i	−0.601082	+	0.330447i	0.151994	+	0.988381i	$0.451431\pi$
$692$	2.62532	−	1.03944i	0.0997996	−	0.0395134i
$693$	−1.21693			−0.0462272
$694$	−6.79572	+	2.69062i	−0.257962	+	0.102134i
$695$	−21.2505	+	12.6521i	−0.806077	+	0.479920i
$696$	−5.90610	+	7.13925i	−0.223870	+	0.270612i
$697$	−9.99191	+	2.56549i	−0.378471	+	0.0971747i
$698$	24.5851	+	13.5158i	0.930559	+	0.511579i
$699$	−0.276153	+	0.200637i	−0.0104450	+	0.00758877i
$700$	−0.543529	−	0.100372i	−0.0205435	−	0.00379369i
$701$	17.2096	+	12.5035i	0.649998	+	0.472251i	0.863270	−	0.504742i	$-0.168412\pi$
$701$	17.2096	+	12.5035i	0.649998	+	0.472251i	−0.213273	+	0.976993i	$0.568412\pi$
$702$	−5.86007	−	12.4533i	−0.221174	−	0.470019i
$703$	−0.779090	+	0.941758i	−0.0293839	+	0.0355191i
$704$	13.1469	+	20.7162i	0.495492	+	0.780770i
$705$	1.00979	−	35.4552i	0.0380308	−	1.33532i
$706$	5.31499	+	6.42472i	0.200032	+	0.241797i
$707$	0.0474361	+	0.0344643i	0.00178402	+	0.00129616i
$708$	1.55753	−	2.45428i	0.0585356	−	0.0922374i
$709$	5.87621	+	30.8042i	0.220686	+	1.15688i	0.904256	+	0.426991i	$0.140426\pi$
$709$	5.87621	+	30.8042i	0.220686	+	1.15688i	−0.683570	+	0.729885i	$0.739574\pi$
$710$	−29.6054	+	4.77839i	−1.11107	+	0.179330i
$711$	−4.33944	+	0.548199i	−0.162742	+	0.0205591i
$712$	6.92567	+	36.3057i	0.259551	+	1.36061i
$713$	0.868463	+	0.109712i	0.0325242	+	0.00410876i
$714$	−2.30847	−	1.26909i	−0.0863924	−	0.0474946i
$715$	−10.7546	+	4.69157i	−0.402200	+	0.175455i
$716$	−1.93296	−	1.81517i	−0.0722381	−	0.0678361i
$717$	−29.2710	−	7.51551i	−1.09315	−	0.280672i
$718$	14.6380	−	10.6351i	0.546285	−	0.396899i
$719$	0.615330	+	9.78038i	0.0229479	+	0.364747i	0.992696	+	0.120640i	$0.0384947\pi$
$719$	0.615330	+	9.78038i	0.0229479	+	0.364747i	−0.969748	+	0.244107i	$0.921505\pi$
$720$	−4.14514	−	2.09671i	−0.154480	−	0.0781398i
$721$	4.39804	+	1.74131i	0.163792	+	0.0648497i
$722$	−0.149200	−	0.0590726i	−0.00555266	−	0.00219846i
$723$	16.5510	−	2.09088i	0.615538	−	0.0777605i
$724$	0.497275	+	1.53046i	0.0184811	+	0.0568789i
$725$	−9.98595	−	1.84407i	−0.370869	−	0.0684872i
$726$	−1.75219	+	5.39269i	−0.0650299	+	0.200142i
$727$	−4.91421	+	25.7612i	−0.182258	+	0.955429i	0.767170	+	0.641444i	$0.221664\pi$
$727$	−4.91421	+	25.7612i	−0.182258	+	0.955429i	−0.949428	+	0.313985i	$0.898336\pi$
$728$	−0.249386	+	3.96388i	−0.00924287	+	0.146911i
$729$	29.0461	−	7.45777i	1.07578	−	0.276214i
$730$	15.1269	+	41.6318i	0.559872	+	1.54086i
$731$	10.3459	−	16.3025i	0.382657	−	0.602971i
$732$	−0.978547	−	3.01166i	−0.0361681	−	0.111314i
$733$	−2.59819	−	41.2971i	−0.0959664	−	1.52534i	−0.691715	−	0.722171i	$-0.743144\pi$
$733$	−2.59819	−	41.2971i	−0.0959664	−	1.52534i	0.595748	−	0.803171i	$-0.296856\pi$
$734$	−18.4843	−	2.33511i	−0.682267	−	0.0861903i
$735$	−22.4666	+	0.772232i	−0.828693	+	0.0284842i
$736$	−0.166269	−	0.353340i	−0.00612877	−	0.0130243i
$737$	4.34868	−	9.24142i	0.160186	−	0.340412i
$738$	4.18231	−	2.29924i	0.153953	−	0.0846363i
$739$	15.0880	−	14.1686i	0.555023	−	0.521201i	−0.355491	−	0.934680i	$-0.615686\pi$
$739$	15.0880	−	14.1686i	0.555023	−	0.521201i	0.910514	+	0.413479i	$0.135686\pi$
$740$	0.0926436	+	0.00848238i	0.00340565	+	0.000311819i
$741$	5.24976	−	11.1563i	0.192855	−	0.409837i
$742$	6.59891	+	7.97671i	0.242254	+	0.292834i
$743$	−11.9111	+	36.6585i	−0.436975	+	1.34487i	0.454075	+	0.890964i	$0.349970\pi$
$743$	−11.9111	+	36.6585i	−0.436975	+	1.34487i	−0.891049	+	0.453906i	$0.850030\pi$
$744$	−8.27064	−	2.12354i	−0.303216	−	0.0778527i
$745$	46.5195	+	10.2547i	1.70434	+	0.375702i
$746$	0.327842	−	5.21090i	0.0120032	−	0.190785i
$747$	2.90649	+	4.57989i	0.106343	+	0.167569i
$748$	0.516463	−	0.484991i	0.0188838	−	0.0177330i
$749$	6.06152			0.221483
$750$	0.955440	+	23.7278i	0.0348877	+	0.866417i
$751$	−32.4190			−1.18298			−0.591492	−	0.806311i	$-0.701461\pi$
$751$	−32.4190			−1.18298			−0.591492	+	0.806311i	$0.701461\pi$
$752$	−27.2819	+	25.6194i	−0.994868	+	0.934243i
$753$	−7.52454	−	11.8568i	−0.274209	−	0.432085i
$754$	−0.315523	+	5.01510i	−0.0114907	+	0.182639i
$755$	−39.6806	+	17.3101i	−1.44412	+	0.629981i
$756$	−0.595597	−	0.152923i	−0.0216617	−	0.00556177i
$757$	3.55803	−	10.9505i	0.129319	−	0.398003i	−0.865344	−	0.501178i	$-0.832900\pi$
$757$	3.55803	−	10.9505i	0.129319	−	0.398003i	0.994663	+	0.103175i	$0.0329003\pi$
$758$	19.6709	+	23.7780i	0.714479	+	0.863656i
$759$	−0.897016	+	1.90626i	−0.0325596	+	0.0691927i
$760$	−6.27737	−	27.7002i	−0.227704	−	1.00479i
$761$	20.6888	−	19.4281i	0.749969	−	0.704268i	−0.212047	−	0.977259i	$-0.568013\pi$
$761$	20.6888	−	19.4281i	0.749969	−	0.704268i	0.962016	+	0.272992i	$0.0880131\pi$
$762$	9.10508	−	5.00556i	0.329842	−	0.181332i
$763$	3.30057	−	7.01406i	0.119489	−	0.253926i
$764$	−1.13035	−	2.40212i	−0.0408947	−	0.0869057i
$765$	−0.578157	+	2.01212i	−0.0209033	+	0.0727482i
$766$	−22.8573	−	2.88755i	−0.825868	−	0.104331i
$767$	−1.43741	−	22.8469i	−0.0519017	−	0.824954i
$768$	1.70249	+	5.23974i	0.0614334	+	0.189073i
$769$	−28.9402	+	45.6024i	−1.04361	+	1.64446i	−0.329910	+	0.944012i	$0.607018\pi$
$769$	−28.9402	+	45.6024i	−1.04361	+	1.64446i	−0.713699	+	0.700452i	$0.752982\pi$
$770$	1.81276	−	6.30881i	0.0653274	−	0.227354i
$771$	29.2218	−	7.50289i	1.05240	−	0.270210i
$772$	−0.119883	+	1.90548i	−0.00431467	+	0.0685797i
$773$	8.28532	−	43.4332i	0.298002	−	1.56218i	−0.446636	−	0.894716i	$-0.647378\pi$
$773$	8.28532	−	43.4332i	0.298002	−	1.56218i	0.744639	−	0.667468i	$-0.232622\pi$
$774$	−2.76042	+	8.49568i	−0.0992211	+	0.305371i
$775$	−2.38065	−	9.05051i	−0.0855153	−	0.325104i
$776$	11.2017	+	34.4751i	0.402116	+	1.23759i
$777$	−0.325496	+	0.0411197i	−0.0116771	+	0.00147516i
$778$	−13.0579	−	5.17000i	−0.468150	−	0.185354i
$779$	25.1146	+	9.94359i	0.899825	+	0.356266i
$780$	−0.926486	+	0.149537i	−0.0331735	+	0.00535430i
$781$	1.78594	+	28.3867i	0.0639060	+	1.01576i
$782$	0.854546	−	0.620864i	0.0305585	−	0.0222020i
$783$	−10.9426	−	2.80958i	−0.391056	−	0.100406i
$784$	17.2907	+	16.2370i	0.617524	+	0.579894i
$785$	−18.1973	−	20.5188i	−0.649490	−	0.732346i
$786$	28.0397	+	15.4150i	1.00014	+	0.549833i
$787$	−23.0846	−	2.91626i	−0.822876	−	0.103953i	−0.297391	−	0.954756i	$-0.596116\pi$
$787$	−23.0846	−	2.91626i	−0.822876	−	0.103953i	−0.525486	+	0.850802i	$0.676116\pi$
$788$	0.482288	+	2.52824i	0.0171808	+	0.0900650i
$789$	−33.4304	+	4.22324i	−1.19015	+	0.150351i
$790$	3.62215	−	23.3132i	0.128870	−	0.829446i
$791$	0.466347	+	2.44468i	0.0165814	+	0.0869227i
$792$	−2.55042	+	4.01881i	−0.0906251	+	0.142802i
$793$	−20.1758	−	14.6586i	−0.716463	−	0.520541i
$794$	18.9196	+	22.8699i	0.671432	+	0.811622i
$795$	−21.6889	+	28.1318i	−0.769228	+	0.997732i
$796$	0.103017	+	0.162328i	0.00365133	+	0.00575357i
$797$	18.9459	−	22.9017i	0.671100	−	0.811220i	−0.319562	−	0.947565i	$-0.603536\pi$
$797$	18.9459	−	22.9017i	0.671100	−	0.811220i	0.990661	+	0.136345i	$0.0435356\pi$
$798$	2.93690	+	6.24124i	0.103965	+	0.220937i
$799$	13.6456	+	9.91412i	0.482747	+	0.350736i
$800$	−2.83991	+	3.06009i	−0.100406	+	0.108191i
$801$	−5.77101	+	4.19289i	−0.203909	+	0.148148i
$802$	18.2766	+	10.0477i	0.645371	+	0.354796i
$803$	40.6918	−	10.4479i	1.43598	−	0.368698i
$804$	0.520716	−	0.629438i	0.0183642	−	0.0221986i
$805$	−0.308287	+	0.718202i	−0.0108657	+	0.0253133i
$806$	−4.30572	+	1.70475i	−0.151662	+	0.0600474i
$807$	18.1776			0.639883
$808$	0.213232	−	0.0844244i	0.00750146	−	0.00297004i
$809$	−12.9254	+	7.10581i	−0.454433	+	0.249827i	−0.692494	−	0.721423i	$-0.743488\pi$
$809$	−12.9254	+	7.10581i	−0.454433	+	0.249827i	0.238061	+	0.971250i	$0.423488\pi$
$810$	−0.605505	+	21.2603i	−0.0212753	+	0.747009i
$811$	6.48053	−	33.9721i	0.227562	−	1.19292i	−0.666682	−	0.745342i	$-0.732286\pi$
$811$	6.48053	−	33.9721i	0.227562	−	1.19292i	0.894244	−	0.447580i	$-0.147714\pi$
$812$	0.163661	+	0.153687i	0.00574336	+	0.00539337i
$813$	−0.299831	−	0.281560i	−0.0105155	−	0.00987473i
$814$	−0.207026	+	1.08527i	−0.00725625	+	0.0380386i
$815$	2.97145	−	0.872777i	0.104085	−	0.0305720i
$816$	−8.35770	+	4.59469i	−0.292578	+	0.160846i
$817$	−47.0066	+	18.6112i	−1.64455	+	0.651125i
$818$	−21.9117			−0.766125
$819$	−0.712715	+	0.282184i	−0.0249043	+	0.00986030i
$820$	−0.454399	−	2.00513i	−0.0158683	−	0.0700221i
$821$	18.8718	−	22.8121i	0.658631	−	0.796148i	−0.330403	−	0.943840i	$-0.607184\pi$
$821$	18.8718	−	22.8121i	0.658631	−	0.796148i	0.989033	+	0.147692i	$0.0471845\pi$
$822$	−4.22638	+	1.08515i	−0.147412	+	0.0378489i
$823$	0.365565	+	0.200971i	0.0127428	+	0.00700542i	0.488112	−	0.872781i	$-0.337686\pi$
$823$	0.365565	+	0.200971i	0.0127428	+	0.00700542i	−0.475370	+	0.879786i	$0.657686\pi$
$824$	14.9679	−	10.8748i	0.521431	−	0.378842i
$825$	22.4865	+	1.28190i	0.782881	+	0.0446301i
$826$	10.3608	+	7.52756i	0.360498	+	0.261917i
$827$	8.18341	+	17.3906i	0.284565	+	0.604732i	0.995094	−	0.0989366i	$-0.0315441\pi$
$827$	8.18341	+	17.3906i	0.284565	+	0.604732i	−0.710529	+	0.703668i	$0.751544\pi$
$828$	0.0248772	−	0.0300714i	0.000864543	−	0.00104505i
$829$	0.883967	+	1.39291i	0.0307015	+	0.0483778i	0.859332	−	0.511418i	$-0.170880\pi$
$829$	0.883967	+	1.39291i	0.0307015	+	0.0483778i	−0.828631	+	0.559796i	$0.810880\pi$
$830$	−28.0727	+	8.24554i	−0.974418	+	0.286207i
$831$	16.2092	+	19.5935i	0.562290	+	0.679692i
$832$	12.5034	+	9.08426i	0.433478	+	0.314940i
$833$	5.72793	−	9.02577i	0.198461	−	0.312724i
$834$	−4.40200	−	23.0761i	−0.152429	−	0.799060i
$835$	−19.0630	−	9.64255i	−0.659704	−	0.333694i
$836$	−1.84047	+	0.232505i	−0.0636540	+	0.00804137i
$837$	−1.95092	−	10.2271i	−0.0674335	−	0.353499i
$838$	−41.3594	−	5.22490i	−1.42874	−	0.180491i
$839$	0.421518	+	0.231732i	0.0145524	+	0.00800027i	0.489013	−	0.872276i	$-0.337357\pi$
$839$	0.421518	+	0.231732i	0.0145524	+	0.00800027i	−0.474461	+	0.880277i	$0.657357\pi$
$840$	3.86159	−	6.57367i	0.133238	−	0.226813i
$841$	−18.1332	−	17.0283i	−0.625284	−	0.587181i
$842$	−51.4156	−	13.2013i	−1.77190	−	0.454946i
$843$	9.16382	−	6.65791i	0.315619	−	0.229310i
$844$	0.0106700	+	0.169594i	0.000367275	+	0.00583767i
$845$	15.2835	−	15.3737i	0.525768	−	0.528872i
$846$	−7.25542	−	2.87262i	−0.249446	−	0.0987628i
$847$	1.85502	+	0.734455i	0.0637393	+	0.0252362i
$848$	37.1850	−	4.69756i	1.27694	−	0.161315i
$849$	−0.662182	−	2.03799i	−0.0227260	−	0.0699435i
$850$	−9.57000	−	5.99458i	−0.328248	−	0.205613i
$851$	0.0406514	−	0.125112i	0.00139351	−	0.00428879i
$852$	−0.426284	+	2.23466i	−0.0146042	+	0.0765581i
$853$	−0.0375333	+	0.596575i	−0.00128512	+	0.0204263i	−0.998617	−	0.0525741i	$-0.983257\pi$
$853$	−0.0375333	+	0.596575i	−0.00128512	+	0.0204263i	0.997332	+	0.0730004i	$0.0232574\pi$
$854$	13.5132	−	3.46961i	0.462414	−	0.118728i
$855$	4.32149	−	3.37251i	0.147792	−	0.115337i
$856$	12.7036	−	20.0177i	0.434201	−	0.684192i
$857$	4.66813	+	14.3670i	0.159460	+	0.490768i	0.998585	−	0.0531701i	$-0.0169326\pi$
$857$	4.66813	+	14.3670i	0.159460	+	0.490768i	−0.839125	+	0.543938i	$0.816933\pi$
$858$	−0.699822	−	11.1233i	−0.0238915	−	0.379745i
$859$	−16.3384	−	2.06401i	−0.557458	−	0.0704233i	−0.158444	−	0.987368i	$-0.550648\pi$
$859$	−16.3384	−	2.06401i	−0.557458	−	0.0704233i	−0.399014	+	0.916945i	$0.630648\pi$
$860$	3.18906	+	2.15359i	0.108746	+	0.0734368i
$861$	3.08715	+	6.56052i	0.105210	+	0.223582i
$862$	−1.19999	+	2.55011i	−0.0408719	+	0.0868572i
$863$	−23.3555	+	12.8398i	−0.795029	+	0.437071i	−0.826850	−	0.562423i	$-0.809869\pi$
$863$	−23.3555	+	12.8398i	−0.795029	+	0.437071i	0.0318209	+	0.999494i	$0.489869\pi$
$864$	−3.38579	+	3.17947i	−0.115187	+	0.108168i
$865$	−36.6770	+	21.8367i	−1.24706	+	0.742469i
$866$	7.34106	−	15.6005i	0.249459	−	0.530128i
$867$	−14.1724	−	17.1315i	−0.481319	−	0.581815i
$868$	−0.0639363	+	0.196776i	−0.00217014	+	0.00667900i
$869$	−21.6738	−	5.56490i	−0.735235	−	0.188776i
$870$	4.88568	−	8.31700i	0.165640	−	0.281973i
$871$	0.403961	−	6.42078i	0.0136877	−	0.217560i
$872$	−16.2462	−	25.5998i	−0.550164	−	0.866920i
$873$	−5.09997	+	4.78919i	−0.172608	+	0.162089i
$874$	−2.76576			−0.0935532
$875$	8.35352	+	0.188713i	0.282401	+	0.00637965i
$876$	3.36024			0.113532
$877$	−3.00019	+	2.81737i	−0.101309	+	0.0951357i	−0.733547	−	0.679639i	$-0.762137\pi$
$877$	−3.00019	+	2.81737i	−0.101309	+	0.0951357i	0.632238	+	0.774774i	$0.282137\pi$
$878$	−2.00061	−	3.15245i	−0.0675172	−	0.106390i
$879$	−3.15300	+	50.1155i	−0.106348	+	1.69035i
$880$	−15.7684	−	17.7800i	−0.531554	−	0.599364i
$881$	37.2073	+	9.55322i	1.25355	+	0.321856i	0.816375	−	0.577522i	$-0.195980\pi$
$881$	37.2073	+	9.55322i	1.25355	+	0.321856i	0.437172	+	0.899378i	$0.355980\pi$
$882$	−1.52828	+	4.70357i	−0.0514599	+	0.158377i
$883$	−0.747203	−	0.903214i	−0.0251454	−	0.0303956i	0.757791	−	0.652498i	$-0.226279\pi$
$883$	−0.747203	−	0.903214i	−0.0251454	−	0.0303956i	−0.782936	+	0.622102i	$0.786279\pi$
$884$	0.190015	−	0.403802i	0.00639089	−	0.0135813i
$885$	−17.3331	+	40.3800i	−0.582645	+	1.35736i
$886$	−4.94555	+	4.64418i	−0.166149	+	0.156024i
$887$	−6.10296	+	3.35513i	−0.204917	+	0.112654i	−0.580908	−	0.813969i	$-0.697302\pi$
$887$	−6.10296	+	3.35513i	−0.204917	+	0.112654i	0.375991	+	0.926623i	$0.377302\pi$
$888$	−0.546374	+	1.16110i	−0.0183351	+	0.0389641i
$889$	−1.55662	−	3.30799i	−0.0522074	−	0.110946i
$890$	−13.1402	−	36.1640i	−0.440460	−	1.21222i
$891$	20.0135	+	2.52830i	0.670479	+	0.0847012i
$892$	−0.181608	−	2.88658i	−0.00608069	−	0.0966499i
$893$	−13.6475	−	42.0028i	−0.456698	−	1.40557i
$894$	−24.2456	+	38.2049i	−0.810893	+	1.27776i
$895$	33.2203	+	22.4339i	1.11043	+	0.749882i
$896$	−7.16567	+	1.83983i	−0.239388	+	0.0614644i
$897$	−0.0833264	+	1.32443i	−0.00278219	+	0.0442216i
$898$	8.41767	−	44.1270i	0.280901	−	1.47254i
$899$	−1.17466	+	3.61525i	−0.0391773	+	0.120575i
$900$	−0.397570	−	0.126596i	−0.0132523	−	0.00421987i
$901$	−5.21985	−	16.0651i	−0.173899	−	0.535205i
$902$	24.2242	−	3.06022i	0.806577	−	0.101894i
$903$	−12.6178	−	4.99574i	−0.419894	−	0.166248i
$904$	9.05073	+	3.58344i	0.301023	+	0.119183i
$905$	−11.1080	−	21.6430i	−0.369243	−	0.719439i
$906$	−2.58208	−	41.0410i	−0.0857840	−	1.36350i
$907$	26.0338	−	18.9147i	0.864438	−	0.628051i	−0.0646509	−	0.997908i	$-0.520593\pi$
$907$	26.0338	−	18.9147i	0.864438	−	0.628051i	0.929089	+	0.369857i	$0.120593\pi$
$908$	0.216719	+	0.0556440i	0.00719208	+	0.00184661i
$909$	0.0322657	+	0.0302995i	0.00107018	+	0.00100497i
$910$	−0.401225	−	4.11521i	−0.0133005	−	0.136418i
$911$	12.9688	+	7.12966i	0.429676	+	0.236216i	0.681889	−	0.731455i	$-0.261159\pi$
$911$	12.9688	+	7.12966i	0.429676	+	0.236216i	−0.252214	+	0.967672i	$0.581159\pi$
$912$	24.7759	+	3.12992i	0.820412	+	0.103642i
$913$	5.19993	+	27.2590i	0.172092	+	0.902140i
$914$	5.72692	−	0.723478i	0.189430	−	0.0239305i
$915$	21.8586	+	42.5895i	0.722622	+	1.40797i
$916$	−0.470939	−	2.46875i	−0.0155603	−	0.0815697i
$917$	6.03271	−	9.50603i	0.199218	−	0.313917i
$918$	−10.1639	−	7.38447i	−0.335457	−	0.243724i
$919$	2.73802	+	3.30970i	0.0903189	+	0.109177i	0.813737	−	0.581234i	$-0.197430\pi$
$919$	2.73802	+	3.30970i	0.0903189	+	0.109177i	−0.723418	+	0.690411i	$0.757430\pi$
$920$	1.72571	+	2.52329i	0.0568948	+	0.0831905i
$921$	−0.0626951	−	0.0987917i	−0.00206587	−	0.00325530i
$922$	8.14424	−	9.84470i	0.268216	−	0.324218i
$923$	7.62834	+	16.2110i	0.251090	+	0.533593i
$924$	−0.402855	−	0.292691i	−0.0132530	−	0.00962884i
$925$	−1.40307	+	0.0965677i	−0.0461325	+	0.00317513i
$926$	4.37133	−	3.17596i	0.143651	−	0.104369i
$927$	3.12909	+	1.72023i	0.102773	+	0.0564998i
$928$	1.64251	−	0.421724i	0.0539179	−	0.0138438i
$929$	10.9299	−	13.2120i	0.358600	−	0.433473i	−0.560103	−	0.828423i	$-0.689238\pi$
$929$	10.9299	−	13.2120i	0.358600	−	0.433473i	0.918702	+	0.394951i	$0.129238\pi$
$930$	8.85233	+	0.810513i	0.290279	+	0.0265778i
$931$	−26.0248	+	10.3040i	−0.852930	+	0.337699i
$932$	0.0323501			0.00105966
$933$	−1.23488	+	0.488923i	−0.0404281	+	0.0160066i
$934$	−30.5909	+	16.8175i	−1.00096	+	0.550284i
$935$	−6.53956	+	8.48218i	−0.213866	+	0.277397i
$936$	−0.561805	+	2.94508i	−0.0183632	+	0.0962631i
$937$	−9.45153	−	8.87557i	−0.308768	−	0.289952i	0.514635	−	0.857409i	$-0.327927\pi$
$937$	−9.45153	−	8.87557i	−0.308768	−	0.289952i	−0.823403	+	0.567457i	$0.807927\pi$
$938$	2.62364	+	2.46376i	0.0856650	+	0.0804448i
$939$	1.38830	−	7.27772i	0.0453055	−	0.237499i
$940$	−2.05250	+	2.66221i	−0.0669451	+	0.0868316i
$941$	41.4946	−	22.8119i	1.35269	−	0.743646i	0.370020	−	0.929024i	$-0.379351\pi$
$941$	41.4946	−	22.8119i	1.35269	−	0.743646i	0.982667	+	0.185378i	$0.0593510\pi$
$942$	24.2217	−	9.59003i	0.789184	−	0.312460i
$943$	−2.90725			−0.0946730
$944$	43.1099	−	17.0684i	1.40311	−	0.555529i
$945$	9.25719	+	0.847583i	0.301137	+	0.0275719i
$946$	−29.1305	+	35.2127i	−0.947113	+	1.14486i
$947$	−32.6897	+	8.39329i	−1.06227	+	0.272745i	−0.739101	−	0.673595i	$-0.764749\pi$
$947$	−32.6897	+	8.39329i	−1.06227	+	0.272745i	−0.323172	+	0.946340i	$0.604749\pi$
$948$	−1.56839	−	0.862231i	−0.0509390	−	0.0280040i
$949$	21.4092	−	15.5547i	0.694972	−	0.504927i
$950$	11.0464	+	27.4273i	0.358393	+	0.889860i
$951$	29.6646	+	21.5526i	0.961942	+	0.698892i
$952$	1.54364	+	3.28040i	0.0500296	+	0.106318i
$953$	29.0137	−	35.0716i	0.939847	−	1.13608i	−0.0506733	−	0.998715i	$-0.516137\pi$
$953$	29.0137	−	35.0716i	0.939847	−	1.13608i	0.990521	−	0.137365i	$-0.0438633\pi$
$954$	4.18744	+	6.59835i	0.135573	+	0.213630i
$955$	22.6559	+	33.1270i	0.733127	+	1.07196i
$956$	1.82563	+	2.20681i	0.0590452	+	0.0713734i
$957$	−7.40143	−	5.37745i	−0.239254	−	0.173828i
$958$	23.3486	−	36.7915i	0.754359	−	1.18868i
$959$	0.287692	+	1.50814i	0.00929007	+	0.0487003i
$960$	−13.5463	−	26.3938i	−0.437205	−	0.851855i
$961$	27.2800	−	3.44627i	0.880000	−	0.111170i
$962$	0.130406	+	0.683611i	0.00420445	+	0.0220405i
$963$	4.53967	+	0.573493i	0.146289	+	0.0184806i
$964$	−1.38549	−	0.761679i	−0.0446236	−	0.0245320i
$965$	−2.80078	−	28.7266i	−0.0901604	−	0.924742i
$966$	−0.541187	−	0.508209i	−0.0174124	−	0.0163513i
$967$	27.9975	+	7.18854i	0.900340	+	0.231168i	0.670368	−	0.742029i	$-0.266136\pi$
$967$	27.9975	+	7.18854i	0.900340	+	0.231168i	0.229972	+	0.973197i	$0.426136\pi$
$968$	6.31320	−	4.58681i	0.202914	−	0.147426i
$969$	−0.706694	−	11.2326i	−0.0227023	−	0.360842i
$970$	−17.2311	−	33.5734i	−0.553259	−	1.07798i
$971$	1.95692	+	0.774799i	0.0628005	+	0.0248645i	0.399315	−	0.916814i	$-0.369248\pi$
$971$	1.95692	+	0.774799i	0.0628005	+	0.0248645i	−0.336514	+	0.941678i	$0.609248\pi$
$972$	−0.794871	−	0.314712i	−0.0254955	−	0.0100944i
$973$	−8.20081	+	1.03600i	−0.262906	+	0.0332128i
$974$	14.7467	+	45.3857i	0.472515	+	1.45425i
$975$	13.4669	−	4.46346i	0.431285	−	0.142945i
$976$	15.6087	−	48.0387i	0.499623	−	1.53768i
$977$	−3.05336	+	16.0063i	−0.0976857	+	0.512086i	0.899487	+	0.436947i	$0.143940\pi$
$977$	−3.05336	+	16.0063i	−0.0976857	+	0.512086i	−0.997173	+	0.0751395i	$0.976060\pi$
$978$	−0.184715	+	2.93595i	−0.00590652	+	0.0938815i
$979$	−35.3475	+	9.07569i	−1.12971	+	0.290060i
$980$	1.76560	+	1.19232i	0.0564000	+	0.0380872i
$981$	3.13552	−	4.94079i	0.100109	−	0.157747i
$982$	−8.98040	−	27.6388i	−0.286576	−	0.881991i
$983$	−0.0134387	−	0.213603i	−0.000428629	−	0.00681286i	0.997807	−	0.0661966i	$-0.0210864\pi$
$983$	−0.0134387	−	0.213603i	−0.000428629	−	0.00681286i	−0.998235	+	0.0593837i	$0.981086\pi$
$984$	28.1356	+	3.55436i	0.896931	+	0.113309i
$985$	−13.2878	−	36.5703i	−0.423386	−	1.16523i
$986$	1.95301	+	4.15036i	0.0621965	+	0.132174i
$987$	5.04756	−	10.7266i	0.160665	−	0.341431i
$988$	−1.02399	+	0.562943i	−0.0325775	+	0.0179096i
$989$	3.96664	−	3.72492i	0.126132	−	0.118446i
$990$	1.95453	−	4.55336i	0.0621189	−	0.144715i
$991$	−25.5584	+	54.3143i	−0.811888	+	1.72535i	−0.132991	+	0.991117i	$0.542458\pi$
$991$	−25.5584	+	54.3143i	−0.811888	+	1.72535i	−0.678898	+	0.734233i	$0.737542\pi$
$992$	0.996158	+	1.20415i	0.0316280	+	0.0382317i
$993$	−7.00678	+	21.5646i	−0.222353	+	0.684333i
$994$	−9.70806	−	2.49261i	−0.307921	−	0.0790607i
$995$	−1.92846	−	2.17448i	−0.0611364	−	0.0689355i
$996$	−0.139369	+	2.21520i	−0.00441606	+	0.0701913i
$997$	−12.5291	−	19.7427i	−0.396801	−	0.625258i	0.585916	−	0.810372i	$-0.300735\pi$
$997$	−12.5291	−	19.7427i	−0.396801	−	0.625258i	−0.982717	+	0.185113i	$0.940735\pi$
$998$	−28.8846	+	27.1245i	−0.914327	+	0.858610i
$999$	−1.56465			−0.0495032

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	125.2.g.a.11.5	✓	220
5.2	odd	4		625.2.h.b.199.8		440
5.3	odd	4		625.2.h.b.199.15		440
5.4	even	2		625.2.g.a.426.7		220
125.34	even	50		625.2.g.a.201.7		220
125.62	odd	100		625.2.h.b.424.15		440
125.63	odd	100		625.2.h.b.424.8		440
125.91	even	25	inner	125.2.g.a.91.5	yes	220

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.g.a.11.5	✓	220	1.1	even	1	trivial
125.2.g.a.91.5	yes	220	125.91	even	25	inner
625.2.g.a.201.7		220	125.34	even	50
625.2.g.a.426.7		220	5.4	even	2
625.2.h.b.199.8		440	5.2	odd	4
625.2.h.b.199.15		440	5.3	odd	4
625.2.h.b.424.8		440	125.63	odd	100
625.2.h.b.424.15		440	125.62	odd	100

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:	\( N \)	\(=\)	\( 125 = 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	125.g (of order \(25\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.992063 + 0.931610i) q^{2} +(-0.836274 - 1.31776i) q^{3} +(-0.00928759 + 0.147622i) q^{4} +(-0.216983 - 2.22552i) q^{5} +(2.05727 + 0.528217i) q^{6} +(0.230945 - 0.710774i) q^{7} +(-1.86327 - 2.25231i) q^{8} +(0.240210 - 0.510472i) q^{9} +O(q^{10})\)	\(q+(-0.992063 + 0.931610i) q^{2} +(-0.836274 - 1.31776i) q^{3} +(-0.00928759 + 0.147622i) q^{4} +(-0.216983 - 2.22552i) q^{5} +(2.05727 + 0.528217i) q^{6} +(0.230945 - 0.710774i) q^{7} +(-1.86327 - 2.25231i) q^{8} +(0.240210 - 0.510472i) q^{9} +(2.28857 + 2.00571i) q^{10} +(2.10398 - 1.97577i) q^{11} +(0.202297 - 0.111214i) q^{12} +(0.774088 - 1.64502i) q^{13} +(0.433053 + 0.920283i) q^{14} +(-2.75123 + 2.14707i) q^{15} +(3.65326 + 0.461514i) q^{16} +(-0.104204 - 1.65627i) q^{17} +(0.237257 + 0.730202i) q^{18} +(-2.32836 + 3.66890i) q^{19} +(0.330550 - 0.0113618i) q^{20} +(-1.12976 + 0.290073i) q^{21} +(-0.246637 + 3.92018i) q^{22} +(0.0876365 - 0.459407i) q^{23} +(-1.40979 + 4.33888i) q^{24} +(-4.90584 + 0.965799i) q^{25} +(0.764573 + 2.35311i) q^{26} +(-5.51879 + 0.697185i) q^{27} +(0.102781 + 0.0406939i) q^{28} +(1.88834 + 0.747646i) q^{29} +(0.729163 - 4.69310i) q^{30} +(0.117523 + 1.86798i) q^{31} +(0.675502 - 0.490781i) q^{32} +(-4.36309 - 1.12025i) q^{33} +(1.64637 + 1.54605i) q^{34} +(-1.63195 - 0.359745i) q^{35} +(0.0731259 + 0.0402013i) q^{36} +(0.279059 + 0.0352534i) q^{37} +(-1.10811 - 5.80890i) q^{38} +(-2.81509 + 0.355628i) q^{39} +(-4.60824 + 4.63545i) q^{40} +(-1.16480 - 6.10607i) q^{41} +(0.850559 - 1.34027i) q^{42} +(9.41267 + 6.83871i) q^{43} +(0.272126 + 0.328944i) q^{44} +(-1.18818 - 0.423827i) q^{45} +(0.341047 + 0.537403i) q^{46} +(-6.47852 + 7.83118i) q^{47} +(-2.44696 - 5.20006i) q^{48} +(5.21125 + 3.78620i) q^{49} +(3.96715 - 5.52846i) q^{50} +(-2.09541 + 1.52241i) q^{51} +(0.235652 + 0.129551i) q^{52} +(9.85881 - 2.53131i) q^{53} +(4.82548 - 5.83301i) q^{54} +(-4.85364 - 4.25373i) q^{55} +(-2.03119 + 0.804207i) q^{56} +6.78186 q^{57} +(-2.56986 + 1.01748i) q^{58} +(11.0341 - 6.06603i) q^{59} +(-0.291402 - 0.426083i) q^{60} +(2.57035 - 13.4743i) q^{61} +(-1.85682 - 1.74367i) q^{62} +(-0.307355 - 0.288626i) q^{63} +(-1.59291 + 8.35033i) q^{64} +(-3.82898 - 1.36580i) q^{65} +(5.37210 - 2.95334i) q^{66} +(3.29017 - 1.30267i) q^{67} +0.245469 q^{68} +(-0.678674 + 0.268706i) q^{69} +(1.95414 - 1.16345i) q^{70} +(-6.28157 + 7.59311i) q^{71} +(-1.59731 + 0.410121i) q^{72} +(12.7554 + 7.01232i) q^{73} +(-0.309687 + 0.225001i) q^{74} +(5.37531 + 5.65702i) q^{75} +(-0.519986 - 0.377792i) q^{76} +(-0.918424 - 1.95175i) q^{77} +(2.46144 - 2.97537i) q^{78} +(-4.15423 - 6.54601i) q^{79} +(0.234410 - 8.23052i) q^{80} +(4.45510 + 5.38529i) q^{81} +(6.84402 + 4.97247i) q^{82} +(-5.15184 + 8.11800i) q^{83} +(-0.0323284 - 0.169471i) q^{84} +(-3.66344 + 0.591289i) q^{85} +(-15.7090 + 1.98451i) q^{86} +(-0.593952 - 3.11360i) q^{87} +(-8.37033 - 1.05742i) q^{88} +(-11.0801 - 6.09135i) q^{89} +(1.57359 - 0.686461i) q^{90} +(-0.990467 - 0.930110i) q^{91} +(0.0670046 + 0.0172038i) q^{92} +(2.36326 - 1.71701i) q^{93} +(-0.868504 - 13.8045i) q^{94} +(8.67041 + 4.38570i) q^{95} +(-1.21163 - 0.479720i) q^{96} +(-11.5300 - 4.56507i) q^{97} +(-8.69715 + 1.09871i) q^{98} +(-0.503178 - 1.54862i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9}+O(q^{10}) \) 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9	\( 220 q - 20 q^{2} - 20 q^{3} - 20 q^{4} - 15 q^{5} - 20 q^{6} - 15 q^{7} - 5 q^{8} - 20 q^{9} - 20 q^{10} - 15 q^{11} - 100 q^{12} - 20 q^{13} - 10 q^{14} - 15 q^{17} + 10 q^{18} - 10 q^{19} + 5 q^{20} - 5 q^{21} + 25 q^{22} - 90 q^{23} + 15 q^{24} - 45 q^{25} + 15 q^{26} + 10 q^{27} + 30 q^{28} - 10 q^{29} + 40 q^{30} - 10 q^{31} + 20 q^{32} + 15 q^{33} + 5 q^{34} + 10 q^{35} - 210 q^{36} + 20 q^{37} + 30 q^{38} + 45 q^{40} - 5 q^{41} + 70 q^{42} + 25 q^{43} + 15 q^{44} - 100 q^{45} - 100 q^{47} + 105 q^{48} - 20 q^{49} + 60 q^{50} + 25 q^{51} + 85 q^{52} + 20 q^{53} + 60 q^{54} + 15 q^{55} - 105 q^{56} + 40 q^{57} - 225 q^{58} + 5 q^{59} - 35 q^{60} + 65 q^{62} + 85 q^{63} + 45 q^{64} + 45 q^{65} + 55 q^{66} - 105 q^{67} + 80 q^{68} + 40 q^{69} + 95 q^{70} - 85 q^{71} + 160 q^{72} + 40 q^{73} + 35 q^{74} + 55 q^{75} + 35 q^{76} + 75 q^{77} - 10 q^{78} - 330 q^{80} + 55 q^{81} - 95 q^{82} + 50 q^{83} + 115 q^{84} + 85 q^{85} + 40 q^{86} + 95 q^{87} + 165 q^{88} + 55 q^{89} + 170 q^{90} - 105 q^{91} + 155 q^{92} - 185 q^{93} + 60 q^{94} + 30 q^{95} + 135 q^{96} + 65 q^{97} + 135 q^{98} + 45 q^{99}+O(q^{100}) \) 220 * q - 20 * q^2 - 20 * q^3 - 20 * q^4 - 15 * q^5 - 20 * q^6 - 15 * q^7 - 5 * q^8 - 20 * q^9 - 20 * q^10 - 15 * q^11 - 100 * q^12 - 20 * q^13 - 10 * q^14 - 15 * q^17 + 10 * q^18 - 10 * q^19 + 5 * q^20 - 5 * q^21 + 25 * q^22 - 90 * q^23 + 15 * q^24 - 45 * q^25 + 15 * q^26 + 10 * q^27 + 30 * q^28 - 10 * q^29 + 40 * q^30 - 10 * q^31 + 20 * q^32 + 15 * q^33 + 5 * q^34 + 10 * q^35 - 210 * q^36 + 20 * q^37 + 30 * q^38 + 45 * q^40 - 5 * q^41 + 70 * q^42 + 25 * q^43 + 15 * q^44 - 100 * q^45 - 100 * q^47 + 105 * q^48 - 20 * q^49 + 60 * q^50 + 25 * q^51 + 85 * q^52 + 20 * q^53 + 60 * q^54 + 15 * q^55 - 105 * q^56 + 40 * q^57 - 225 * q^58 + 5 * q^59 - 35 * q^60 + 65 * q^62 + 85 * q^63 + 45 * q^64 + 45 * q^65 + 55 * q^66 - 105 * q^67 + 80 * q^68 + 40 * q^69 + 95 * q^70 - 85 * q^71 + 160 * q^72 + 40 * q^73 + 35 * q^74 + 55 * q^75 + 35 * q^76 + 75 * q^77 - 10 * q^78 - 330 * q^80 + 55 * q^81 - 95 * q^82 + 50 * q^83 + 115 * q^84 + 85 * q^85 + 40 * q^86 + 95 * q^87 + 165 * q^88 + 55 * q^89 + 170 * q^90 - 105 * q^91 + 155 * q^92 - 185 * q^93 + 60 * q^94 + 30 * q^95 + 135 * q^96 + 65 * q^97 + 135 * q^98 + 45 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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