LMFDB - Embedded newform 61.2.i.a.56.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [61,2,Mod(12,61)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(61, base_ring=CyclotomicField(30))

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("61.12");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	61.i (of order $15$, degree $8$, 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:	$0.487087452330$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			56.2
Character	$\chi$	$=$	61.56
Dual form			61.2.i.a.12.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.94561 + 0.866241i) q^{2} +(1.86941 + 1.35820i) q^{3} +(1.69676 - 1.88444i) q^{4} +(-1.20434 - 0.255990i) q^{5} +(-4.81367 - 1.02318i) q^{6} +(0.404506 + 3.84862i) q^{7} +(-0.352600 + 1.08519i) q^{8} +(0.722916 + 2.22491i) q^{9} +O(q^{10})$	\(q+(-1.94561 + 0.866241i) q^{2} +(1.86941 + 1.35820i) q^{3} +(1.69676 - 1.88444i) q^{4} +(-1.20434 - 0.255990i) q^{5} +(-4.81367 - 1.02318i) q^{6} +(0.404506 + 3.84862i) q^{7} +(-0.352600 + 1.08519i) q^{8} +(0.722916 + 2.22491i) q^{9} +(2.56491 - 0.545189i) q^{10} -1.98434 q^{11} +(5.73139 - 1.21824i) q^{12} +(2.72937 - 4.72741i) q^{13} +(-4.12084 - 7.13751i) q^{14} +(-1.90371 - 2.11428i) q^{15} +(0.276104 + 2.62696i) q^{16} +(3.60066 - 3.99894i) q^{17} +(-3.33381 - 3.70258i) q^{18} +(0.472909 - 4.49943i) q^{19} +(-2.52586 + 1.83515i) q^{20} +(-4.47102 + 7.74404i) q^{21} +(3.86075 - 1.71892i) q^{22} +(2.24547 + 6.91085i) q^{23} +(-2.13306 + 1.54976i) q^{24} +(-3.18283 - 1.41709i) q^{25} +(-1.21521 + 11.5620i) q^{26} +(0.471699 - 1.45174i) q^{27} +(7.93884 + 5.76791i) q^{28} +(-0.207283 - 0.359024i) q^{29} +(5.53535 + 2.46450i) q^{30} +(-2.26627 - 1.00901i) q^{31} +(-3.95380 - 6.84819i) q^{32} +(-3.70954 - 2.69514i) q^{33} +(-3.54143 + 10.8994i) q^{34} +(0.498045 - 4.73858i) q^{35} +(5.41932 + 2.41283i) q^{36} +(-5.96555 + 4.33423i) q^{37} +(2.97749 + 9.16378i) q^{38} +(11.5231 - 5.13041i) q^{39} +(0.702446 - 1.21667i) q^{40} +(-3.12409 + 2.26979i) q^{41} +(1.99066 - 18.9399i) q^{42} +(-1.69649 - 1.88414i) q^{43} +(-3.36695 + 3.73937i) q^{44} +(-0.301081 - 2.86459i) q^{45} +(-10.3553 - 11.5007i) q^{46} +(1.97577 + 3.42213i) q^{47} +(-3.05179 + 5.28586i) q^{48} +(-7.80121 + 1.65820i) q^{49} +7.42009 q^{50} +(12.1625 - 2.58521i) q^{51} +(-4.27744 - 13.1646i) q^{52} +(0.927961 - 2.85597i) q^{53} +(0.339815 + 3.23312i) q^{54} +(2.38981 + 0.507970i) q^{55} +(-4.31911 - 0.918056i) q^{56} +(6.99520 - 7.76896i) q^{57} +(0.714292 + 0.518963i) q^{58} +(-1.34010 + 0.596653i) q^{59} -7.21437 q^{60} +(1.71348 + 7.61997i) q^{61} +5.28333 q^{62} +(-8.27039 + 3.68221i) q^{63} +(9.35082 + 6.79377i) q^{64} +(-4.49725 + 4.99470i) q^{65} +(9.55196 + 2.03033i) q^{66} +(5.93084 + 1.26064i) q^{67} +(-1.42631 - 13.5705i) q^{68} +(-5.18865 + 15.9690i) q^{69} +(3.13575 + 9.65085i) q^{70} +(-8.53723 + 1.81465i) q^{71} -2.66935 q^{72} +(-6.01044 + 1.27756i) q^{73} +(7.85214 - 13.6003i) q^{74} +(-4.02532 - 6.97205i) q^{75} +(-7.67650 - 8.52561i) q^{76} +(-0.802678 - 7.63697i) q^{77} +(-17.9753 + 19.9636i) q^{78} +(-6.05353 - 6.72312i) q^{79} +(0.339951 - 3.23442i) q^{80} +(8.53141 - 6.19843i) q^{81} +(4.11208 - 7.12233i) q^{82} +(4.66057 - 2.07502i) q^{83} +(7.00694 + 21.5651i) q^{84} +(-5.36009 + 3.89433i) q^{85} +(4.93282 + 2.19623i) q^{86} +(0.100132 - 0.952694i) q^{87} +(0.699678 - 2.15339i) q^{88} +(-6.45373 - 4.68891i) q^{89} +(3.06721 + 5.31257i) q^{90} +(19.2980 + 8.59204i) q^{91} +(16.8331 + 7.49459i) q^{92} +(-2.86615 - 4.96432i) q^{93} +(-6.80846 - 4.94664i) q^{94} +(-1.72135 + 5.29776i) q^{95} +(1.90997 - 18.1721i) q^{96} +(4.08831 + 1.82023i) q^{97} +(13.7417 - 9.98393i) q^{98} +(-1.43451 - 4.41497i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 10 q^{2} - 4 q^{3} - 10 q^{4} + 2 q^{5} + q^{6} + q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) $ 32 * q - 10 * q^2 - 4 * q^3 - 10 * q^4 + 2 * q^5 + q^6 + q^7 - 4 * q^8 - 2 * q^9	\( 32 q - 10 q^{2} - 4 q^{3} - 10 q^{4} + 2 q^{5} + q^{6} + q^{7} - 4 q^{8} - 2 q^{9} + 15 q^{10} - 18 q^{11} - 53 q^{12} + 11 q^{14} + 2 q^{15} + 6 q^{16} - 24 q^{17} - 15 q^{18} + 9 q^{19} - 4 q^{20} - 3 q^{21} + q^{22} - 2 q^{23} + 15 q^{24} + 28 q^{25} + 16 q^{26} + 35 q^{27} + 4 q^{28} - 4 q^{29} + 54 q^{30} - 11 q^{31} + 34 q^{32} - 35 q^{33} + 18 q^{34} - 58 q^{35} + 65 q^{36} - 14 q^{37} - 24 q^{38} + 17 q^{39} - 60 q^{40} + 11 q^{41} + 73 q^{42} + 40 q^{43} + 29 q^{44} + 12 q^{45} - 89 q^{46} + 40 q^{47} + 43 q^{48} + q^{49} - 56 q^{50} - 9 q^{51} - 67 q^{52} + 17 q^{53} - q^{54} - 60 q^{55} - 102 q^{56} - 38 q^{57} + 73 q^{58} - 11 q^{59} - 20 q^{60} - 55 q^{61} - 74 q^{62} - 58 q^{63} + 6 q^{64} + 59 q^{65} + 34 q^{66} - 13 q^{67} - 3 q^{68} - 32 q^{69} + 44 q^{70} + 63 q^{71} + 18 q^{72} - 46 q^{73} - 10 q^{74} + q^{75} + 55 q^{76} - 31 q^{77} - 103 q^{78} - 49 q^{79} + 74 q^{80} + 48 q^{81} + 39 q^{82} + 39 q^{83} + 21 q^{85} + 74 q^{86} + 17 q^{87} + 70 q^{88} + 32 q^{89} - 60 q^{90} + 70 q^{91} + 77 q^{92} + 67 q^{93} - 64 q^{94} + 47 q^{95} - 16 q^{96} + 37 q^{97} + 127 q^{98} - 31 q^{99}+O(q^{100}) \) 32 * q - 10 * q^2 - 4 * q^3 - 10 * q^4 + 2 * q^5 + q^6 + q^7 - 4 * q^8 - 2 * q^9 + 15 * q^10 - 18 * q^11 - 53 * q^12 + 11 * q^14 + 2 * q^15 + 6 * q^16 - 24 * q^17 - 15 * q^18 + 9 * q^19 - 4 * q^20 - 3 * q^21 + q^22 - 2 * q^23 + 15 * q^24 + 28 * q^25 + 16 * q^26 + 35 * q^27 + 4 * q^28 - 4 * q^29 + 54 * q^30 - 11 * q^31 + 34 * q^32 - 35 * q^33 + 18 * q^34 - 58 * q^35 + 65 * q^36 - 14 * q^37 - 24 * q^38 + 17 * q^39 - 60 * q^40 + 11 * q^41 + 73 * q^42 + 40 * q^43 + 29 * q^44 + 12 * q^45 - 89 * q^46 + 40 * q^47 + 43 * q^48 + q^49 - 56 * q^50 - 9 * q^51 - 67 * q^52 + 17 * q^53 - q^54 - 60 * q^55 - 102 * q^56 - 38 * q^57 + 73 * q^58 - 11 * q^59 - 20 * q^60 - 55 * q^61 - 74 * q^62 - 58 * q^63 + 6 * q^64 + 59 * q^65 + 34 * q^66 - 13 * q^67 - 3 * q^68 - 32 * q^69 + 44 * q^70 + 63 * q^71 + 18 * q^72 - 46 * q^73 - 10 * q^74 + q^75 + 55 * q^76 - 31 * q^77 - 103 * q^78 - 49 * q^79 + 74 * q^80 + 48 * q^81 + 39 * q^82 + 39 * q^83 + 21 * q^85 + 74 * q^86 + 17 * q^87 + 70 * q^88 + 32 * q^89 - 60 * q^90 + 70 * q^91 + 77 * q^92 + 67 * q^93 - 64 * q^94 + 47 * q^95 - 16 * q^96 + 37 * q^97 + 127 * q^98 - 31 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/61\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{15}\right)$

Coefficient data

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

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

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

$2$	−1.94561	+	0.866241i	−1.37575	+	0.612525i	−0.955529	−	0.294896i	$-0.904715\pi$
$2$	−1.94561	+	0.866241i	−1.37575	+	0.612525i	−0.420224	+	0.907421i	$0.638048\pi$
$3$	1.86941	+	1.35820i	1.07930	+	0.784160i	0.977561	−	0.210651i	$-0.0675584\pi$
$3$	1.86941	+	1.35820i	1.07930	+	0.784160i	0.101742	+	0.994811i	$0.467558\pi$
$4$	1.69676	−	1.88444i	0.848379	−	0.942220i
$5$	−1.20434	−	0.255990i	−0.538595	−	0.114482i	−0.0694209	−	0.997587i	$-0.522115\pi$
$5$	−1.20434	−	0.255990i	−0.538595	−	0.114482i	−0.469175	+	0.883105i	$0.655448\pi$
$6$	−4.81367	−	1.02318i	−1.96517	−	0.417710i
$7$	0.404506	+	3.84862i	0.152889	+	1.45464i	0.754735	+	0.656029i	$0.227765\pi$
$7$	0.404506	+	3.84862i	0.152889	+	1.45464i	−0.601846	+	0.798612i	$0.705568\pi$
$8$	−0.352600	+	1.08519i	−0.124663	+	0.383673i
$9$	0.722916	+	2.22491i	0.240972	+	0.741635i
$10$	2.56491	−	0.545189i	0.811097	−	0.172404i
$11$	−1.98434			−0.598301			−0.299151	−	0.954206i	$-0.596703\pi$
$11$	−1.98434			−0.598301			−0.299151	+	0.954206i	$0.596703\pi$
$12$	5.73139	−	1.21824i	1.65451	−	0.351677i
$13$	2.72937	−	4.72741i	0.756991	−	1.31115i	−0.187387	−	0.982286i	$-0.560002\pi$
$13$	2.72937	−	4.72741i	0.756991	−	1.31115i	0.944378	−	0.328862i	$-0.106665\pi$
$14$	−4.12084	−	7.13751i	−1.10134	−	1.90758i
$15$	−1.90371	−	2.11428i	−0.491536	−	0.545906i
$16$	0.276104	+	2.62696i	0.0690260	+	0.656739i
$17$	3.60066	−	3.99894i	0.873288	−	0.969885i	−0.126468	−	0.991971i	$-0.540364\pi$
$17$	3.60066	−	3.99894i	0.873288	−	0.969885i	0.999756	+	0.0220861i	$0.00703079\pi$
$18$	−3.33381	−	3.70258i	−0.785788	−	0.872706i
$19$	0.472909	−	4.49943i	0.108493	−	1.03224i	−0.795868	−	0.605470i	$-0.792985\pi$
$19$	0.472909	−	4.49943i	0.108493	−	1.03224i	0.904361	−	0.426769i	$-0.140348\pi$
$20$	−2.52586	+	1.83515i	−0.564800	+	0.410351i
$21$	−4.47102	+	7.74404i	−0.975657	+	1.68989i
$22$	3.86075	−	1.71892i	0.823115	−	0.366474i
$23$	2.24547	+	6.91085i	0.468213	+	1.44101i	0.854896	+	0.518800i	$0.173621\pi$
$23$	2.24547	+	6.91085i	0.468213	+	1.44101i	−0.386683	+	0.922213i	$0.626379\pi$
$24$	−2.13306	+	1.54976i	−0.435410	+	0.316344i
$25$	−3.18283	−	1.41709i	−0.636567	−	0.283418i
$26$	−1.21521	+	11.5620i	−0.238323	+	2.26749i
$27$	0.471699	−	1.45174i	0.0907785	−	0.279387i
$28$	7.93884	+	5.76791i	1.50030	+	1.09003i
$29$	−0.207283	−	0.359024i	−0.0384914	−	0.0666691i	0.846138	−	0.532964i	$-0.178922\pi$
$29$	−0.207283	−	0.359024i	−0.0384914	−	0.0666691i	−0.884629	+	0.466295i	$0.845589\pi$
$30$	5.53535	+	2.46450i	1.01061	+	0.449953i
$31$	−2.26627	−	1.00901i	−0.407035	−	0.181224i	0.192998	−	0.981199i	$-0.438179\pi$
$31$	−2.26627	−	1.00901i	−0.407035	−	0.181224i	−0.600033	+	0.799976i	$0.704846\pi$
$32$	−3.95380	−	6.84819i	−0.698940	−	1.21060i
$33$	−3.70954	−	2.69514i	−0.645748	−	0.469164i
$34$	−3.54143	+	10.8994i	−0.607350	+	1.86923i
$35$	0.498045	−	4.73858i	0.0841849	−	0.800966i
$36$	5.41932	+	2.41283i	0.903219	+	0.402139i
$37$	−5.96555	+	4.33423i	−0.980730	+	0.712542i	−0.957872	−	0.287196i	$-0.907277\pi$
$37$	−5.96555	+	4.33423i	−0.980730	+	0.712542i	−0.0228586	+	0.999739i	$0.507277\pi$
$38$	2.97749	+	9.16378i	0.483013	+	1.48656i
$39$	11.5231	−	5.13041i	1.84517	−	0.821524i
$40$	0.702446	−	1.21667i	0.111067	−	0.192373i
$41$	−3.12409	+	2.26979i	−0.487902	+	0.354481i	−0.804377	−	0.594120i	$-0.797501\pi$
$41$	−3.12409	+	2.26979i	−0.487902	+	0.354481i	0.316475	+	0.948601i	$0.397501\pi$
$42$	1.99066	−	18.9399i	0.307165	−	2.92248i
$43$	−1.69649	−	1.88414i	−0.258712	−	0.287329i	0.599770	−	0.800172i	$-0.295259\pi$
$43$	−1.69649	−	1.88414i	−0.258712	−	0.287329i	−0.858482	+	0.512844i	$0.828592\pi$
$44$	−3.36695	+	3.73937i	−0.507586	+	0.563732i
$45$	−0.301081	−	2.86459i	−0.0448825	−	0.427028i
$46$	−10.3553	−	11.5007i	−1.52680	−	1.69568i
$47$	1.97577	+	3.42213i	0.288195	+	0.499169i	0.973379	−	0.229201i	$-0.0736114\pi$
$47$	1.97577	+	3.42213i	0.288195	+	0.499169i	−0.685184	+	0.728370i	$0.740278\pi$
$48$	−3.05179	+	5.28586i	−0.440488	+	0.762948i
$49$	−7.80121	+	1.65820i	−1.11446	+	0.236885i
$50$	7.42009			1.04936
$51$	12.1625	−	2.58521i	1.70309	−	0.362002i
$52$	−4.27744	−	13.1646i	−0.593174	−	1.82560i
$53$	0.927961	−	2.85597i	0.127465	−	0.392298i	−0.866877	−	0.498522i	$-0.833876\pi$
$53$	0.927961	−	2.85597i	0.127465	−	0.392298i	0.994342	+	0.106224i	$0.0338762\pi$
$54$	0.339815	+	3.23312i	0.0462429	+	0.439972i
$55$	2.38981	+	0.507970i	0.322242	+	0.0684947i
$56$	−4.31911	−	0.918056i	−0.577166	−	0.122680i
$57$	6.99520	−	7.76896i	0.926537	−	1.02902i
$58$	0.714292	+	0.518963i	0.0937911	+	0.0681432i
$59$	−1.34010	+	0.596653i	−0.174467	+	0.0776776i	−0.492111	−	0.870532i	$-0.663775\pi$
$59$	−1.34010	+	0.596653i	−0.174467	+	0.0776776i	0.317645	+	0.948210i	$0.397108\pi$
$60$	−7.21437			−0.931372
$61$	1.71348	+	7.61997i	0.219389	+	0.975637i
$61$	1.71348	+	7.61997i	0.219389	+	0.975637i
$62$	5.28333			0.670983
$63$	−8.27039	+	3.68221i	−1.04197	+	0.463915i
$64$	9.35082	+	6.79377i	1.16885	+	0.849221i
$65$	−4.49725	+	4.99470i	−0.557815	+	0.619516i
$66$	9.55196	+	2.03033i	1.17576	+	0.249916i
$67$	5.93084	+	1.26064i	0.724568	+	0.154012i	0.555409	−	0.831577i	$-0.312562\pi$
$67$	5.93084	+	1.26064i	0.724568	+	0.154012i	0.169159	+	0.985589i	$0.445895\pi$
$68$	−1.42631	−	13.5705i	−0.172966	−	1.64566i
$69$	−5.18865	+	15.9690i	−0.624640	+	1.92244i
$70$	3.13575	+	9.65085i	0.374794	+	1.15350i
$71$	−8.53723	+	1.81465i	−1.01318	+	0.215359i	−0.684447	−	0.729063i	$-0.739956\pi$
$71$	−8.53723	+	1.81465i	−1.01318	+	0.215359i	−0.328737	+	0.944422i	$0.606623\pi$
$72$	−2.66935			−0.314586
$73$	−6.01044	+	1.27756i	−0.703469	+	0.149527i	−0.545739	−	0.837955i	$-0.683751\pi$
$73$	−6.01044	+	1.27756i	−0.703469	+	0.149527i	−0.157730	+	0.987482i	$0.550418\pi$
$74$	7.85214	−	13.6003i	0.912793	−	1.58100i
$75$	−4.02532	−	6.97205i	−0.464804	−	0.805063i
$76$	−7.67650	−	8.52561i	−0.880554	−	0.977955i
$77$	−0.802678	−	7.63697i	−0.0914736	−	0.870314i
$78$	−17.9753	+	19.9636i	−2.03530	+	2.26043i
$79$	−6.05353	−	6.72312i	−0.681075	−	0.756411i	0.299169	−	0.954200i	$-0.403290\pi$
$79$	−6.05353	−	6.72312i	−0.681075	−	0.756411i	−0.980245	+	0.197789i	$0.936624\pi$
$80$	0.339951	−	3.23442i	0.0380077	−	0.361619i
$81$	8.53141	−	6.19843i	0.947934	−	0.688715i
$82$	4.11208	−	7.12233i	0.454103	−	0.786530i
$83$	4.66057	−	2.07502i	0.511565	−	0.227763i	−0.134686	−	0.990888i	$-0.543003\pi$
$83$	4.66057	−	2.07502i	0.511565	−	0.227763i	0.646251	+	0.763125i	$0.276336\pi$
$84$	7.00694	+	21.5651i	0.764520	+	2.35295i
$85$	−5.36009	+	3.89433i	−0.581383	+	0.422400i
$86$	4.93282	+	2.19623i	0.531920	+	0.236826i
$87$	0.100132	−	0.952694i	0.0107353	−	0.102140i
$88$	0.699678	−	2.15339i	0.0745860	−	0.229552i
$89$	−6.45373	−	4.68891i	−0.684093	−	0.497023i	0.190620	−	0.981664i	$-0.438950\pi$
$89$	−6.45373	−	4.68891i	−0.684093	−	0.497023i	−0.874713	+	0.484641i	$0.838950\pi$
$90$	3.06721	+	5.31257i	0.323313	+	0.559994i
$91$	19.2980	+	8.59204i	2.02299	+	0.900691i
$92$	16.8331	+	7.49459i	1.75497	+	0.781365i
$93$	−2.86615	−	4.96432i	−0.297206	−	0.514776i
$94$	−6.80846	−	4.94664i	−0.702239	−	0.510206i
$95$	−1.72135	+	5.29776i	−0.176607	+	0.543539i
$96$	1.90997	−	18.1721i	0.194935	−	1.85469i
$97$	4.08831	+	1.82023i	0.415105	+	0.184817i	0.603653	−	0.797247i	$-0.293711\pi$
$97$	4.08831	+	1.82023i	0.415105	+	0.184817i	−0.188548	+	0.982064i	$0.560378\pi$
$98$	13.7417	−	9.98393i	1.38812	−	1.00853i
$99$	−1.43451	−	4.41497i	−0.144174	−	0.443721i
$100$	−8.07092	+	3.59340i	−0.807092	+	0.359340i
$101$	−2.32112	+	4.02029i	−0.230960	+	0.400034i	−0.958091	−	0.286465i	$-0.907520\pi$
$101$	−2.32112	+	4.02029i	−0.230960	+	0.400034i	0.727131	+	0.686499i	$0.240853\pi$
$102$	−21.4240	+	15.5654i	−2.12129	+	1.54121i
$103$	0.0983275	−	0.935524i	0.00968850	−	0.0921799i	−0.988609	−	0.150506i	$-0.951910\pi$
$103$	0.0983275	−	0.935524i	0.00968850	−	0.0921799i	0.998298	+	0.0583262i	$0.0185763\pi$
$104$	4.16777	+	4.62877i	0.408683	+	0.453889i
$105$	7.36701	−	8.18189i	0.718946	−	0.798471i
$106$	0.668509	+	6.36044i	0.0649313	+	0.617780i
$107$	9.70753	+	10.7813i	0.938462	+	1.04227i	0.999027	+	0.0441038i	$0.0140432\pi$
$107$	9.70753	+	10.7813i	0.938462	+	1.04227i	−0.0605646	+	0.998164i	$0.519290\pi$
$108$	−1.93536	−	3.35214i	−0.186230	−	0.322560i
$109$	−0.198787	+	0.344309i	−0.0190404	+	0.0329789i	−0.875389	−	0.483420i	$-0.839394\pi$
$109$	−0.198787	+	0.344309i	−0.0190404	+	0.0329789i	0.856348	+	0.516399i	$0.172728\pi$
$110$	−5.08967	+	1.08184i	−0.485281	+	0.103150i
$111$	−17.0388			−1.61725
$112$	−9.99846	+	2.12524i	−0.944766	+	0.200816i
$113$	−1.84819	−	5.68814i	−0.173863	−	0.535095i	0.825717	−	0.564085i	$-0.190771\pi$
$113$	−1.84819	−	5.68814i	−0.173863	−	0.535095i	−0.999580	+	0.0289897i	$0.990771\pi$
$114$	−6.88014	+	21.1749i	−0.644384	+	1.98321i
$115$	−0.935197	−	8.89781i	−0.0872076	−	0.829725i
$116$	−1.02827	−	0.218565i	−0.0954722	−	0.0202933i
$117$	12.4911	+	2.65508i	1.15481	+	0.245462i
$118$	2.09047	−	2.32170i	0.192444	−	0.213730i
$119$	16.8469	+	12.2400i	1.54435	+	1.12204i
$120$	2.96565	−	1.32039i	0.270725	−	0.120535i
$121$	−7.06239			−0.642036
$122$	−9.93450	−	13.3412i	−0.899427	−	1.20785i
$123$	−8.92304			−0.804563
$124$	−5.74674	+	2.55861i	−0.516073	+	0.229770i
$125$	8.45092	+	6.13995i	0.755873	+	0.549174i
$126$	12.9013	−	14.3283i	1.14934	−	1.27647i
$127$	−2.51029	−	0.533579i	−0.222752	−	0.0473475i	0.0951833	−	0.995460i	$-0.469656\pi$
$127$	−2.51029	−	0.533579i	−0.222752	−	0.0473475i	−0.317936	+	0.948112i	$0.602990\pi$
$128$	−8.60845	−	1.82978i	−0.760887	−	0.161731i
$129$	−0.612380	−	5.82641i	−0.0539171	−	0.512987i
$130$	4.42327	−	13.6134i	0.387947	−	1.19398i
$131$	−4.15159	−	12.7773i	−0.362726	−	1.11636i	−0.951393	−	0.307980i	$-0.900347\pi$
$131$	−4.15159	−	12.7773i	−0.362726	−	1.11636i	0.588667	−	0.808376i	$-0.299653\pi$
$132$	−11.3730	+	2.41741i	−0.989895	+	0.210409i
$133$	17.5079			1.51813
$134$	−12.6311	+	2.68483i	−1.09116	+	0.231934i
$135$	−0.939714	+	1.62763i	−0.0808777	+	0.140084i
$136$	3.07002	+	5.31743i	0.263252	+	0.455966i
$137$	9.39015	+	10.4288i	0.802255	+	0.890994i	0.995935	−	0.0900705i	$-0.0287092\pi$
$137$	9.39015	+	10.4288i	0.802255	+	0.890994i	−0.193681	+	0.981065i	$0.562043\pi$
$138$	−3.73793	−	35.5641i	−0.318194	−	3.02741i
$139$	3.86611	−	4.29375i	0.327919	−	0.364191i	−0.556530	−	0.830827i	$-0.687868\pi$
$139$	3.86611	−	4.29375i	0.327919	−	0.364191i	0.884449	+	0.466637i	$0.154534\pi$
$140$	−8.08451	−	8.97876i	−0.683266	−	0.758844i
$141$	−0.954436	+	9.08085i	−0.0803780	+	0.764746i
$142$	15.0382	−	10.9259i	1.26198	−	0.916880i
$143$	−5.41600	+	9.38079i	−0.452909	+	0.784461i
$144$	−5.64513	+	2.51337i	−0.470427	+	0.209448i
$145$	0.157731	+	0.485447i	0.0130989	+	0.0403142i
$146$	10.5873	−	7.69212i	0.876211	−	0.636605i
$147$	−16.8358	−	7.49578i	−1.38859	−	0.618242i
$148$	−1.95450	+	18.5959i	−0.160659	+	1.52857i
$149$	7.04785	−	21.6911i	0.577383	−	1.77700i	−0.0505360	−	0.998722i	$-0.516093\pi$
$149$	7.04785	−	21.6911i	0.577383	−	1.77700i	0.627919	−	0.778279i	$-0.283907\pi$
$150$	13.8712	+	10.0780i	1.13258	+	0.822865i
$151$	−5.55147	−	9.61543i	−0.451772	−	0.782492i	0.546724	−	0.837313i	$-0.315875\pi$
$151$	−5.55147	−	9.61543i	−0.451772	−	0.782492i	−0.998496	+	0.0548206i	$0.982541\pi$
$152$	4.71599	+	2.09969i	0.382517	+	0.170308i
$153$	11.5002	+	5.12023i	0.929738	+	0.413946i
$154$	8.17715	+	14.1632i	0.658934	+	1.14131i
$155$	2.47106	+	1.79533i	0.198480	+	0.144204i
$156$	9.88395	−	30.4197i	0.791349	−	2.43552i
$157$	−0.905118	+	8.61162i	−0.0722363	+	0.687282i	0.897147	+	0.441731i	$0.145636\pi$
$157$	−0.905118	+	8.61162i	−0.0722363	+	0.687282i	−0.969384	+	0.245551i	$0.921031\pi$
$158$	17.6016	+	7.83676i	1.40031	+	0.623459i
$159$	5.61373	−	4.07861i	0.445198	−	0.323455i
$160$	3.00864	+	9.25965i	0.237854	+	0.732040i
$161$	−25.6889	+	11.4374i	−2.02457	+	0.901397i
$162$	−11.2294	+	19.4500i	−0.882269	+	1.52813i
$163$	−16.0936	+	11.6927i	−1.26055	+	0.915842i	−0.998785	−	0.0492895i	$-0.984304\pi$
$163$	−16.0936	+	11.6927i	−1.26055	+	0.915842i	−0.261764	+	0.965132i	$0.584304\pi$
$164$	−1.02355	+	9.73845i	−0.0799260	+	0.760445i
$165$	3.77761	+	4.19546i	0.294086	+	0.326616i
$166$	−7.27019	+	8.07436i	−0.564276	+	0.626692i
$167$	1.18071	+	11.2337i	0.0913660	+	0.869290i	0.940198	+	0.340628i	$0.110640\pi$
$167$	1.18071	+	11.2337i	0.0913660	+	0.869290i	−0.848832	+	0.528662i	$0.822694\pi$
$168$	−6.82728	−	7.58246i	−0.526736	−	0.585000i
$169$	−8.39894	−	14.5474i	−0.646072	−	1.11903i
$170$	7.05520	−	12.2200i	0.541109	−	0.937229i
$171$	10.3527	−	2.20053i	0.791689	−	0.168279i
$172$	−6.42908			−0.490213
$173$	−9.25127	+	1.96642i	−0.703361	+	0.149504i	−0.545689	−	0.837988i	$-0.683732\pi$
$173$	−9.25127	+	1.96642i	−0.703361	+	0.149504i	−0.157672	+	0.987492i	$0.550399\pi$
$174$	0.630444	+	1.94031i	0.0477939	+	0.147094i
$175$	4.16636	−	12.8227i	0.314947	−	0.969307i
$176$	−0.547885	−	5.21277i	−0.0412984	−	0.392928i
$177$	−3.31558	−	0.704748i	−0.249214	−	0.0529721i
$178$	16.6181	+	3.53230i	1.24558	+	0.264757i
$179$	1.16770	−	1.29686i	0.0872777	−	0.0969317i	−0.697924	−	0.716172i	$-0.745893\pi$
$179$	1.16770	−	1.29686i	0.0872777	−	0.0969317i	0.785202	+	0.619240i	$0.212559\pi$
$180$	−5.90902	−	4.29315i	−0.440432	−	0.319993i
$181$	20.1978	−	8.99263i	1.50129	−	0.668417i	0.518827	−	0.854879i	$-0.326369\pi$
$181$	20.1978	−	8.99263i	1.50129	−	0.668417i	0.982462	+	0.186462i	$0.0597023\pi$
$182$	−44.9892			−3.33482
$183$	−7.14628	+	16.5721i	−0.528268	+	1.22504i
$184$	−8.29135			−0.611246
$185$	8.29404	−	3.69275i	0.609790	−	0.271496i
$186$	9.87670	+	7.17584i	0.724194	+	0.526158i
$187$	−7.14493	+	7.93525i	−0.522489	+	0.580283i
$188$	9.80120	+	2.08331i	0.714826	+	0.151941i
$189$	5.77800	+	1.22815i	0.420287	+	0.0893348i
$190$	−1.24007	−	11.7985i	−0.0899641	−	0.855951i
$191$	−1.26390	+	3.88989i	−0.0914528	+	0.281463i	−0.986313	−	0.164884i	$-0.947275\pi$
$191$	−1.26390	+	3.88989i	−0.0914528	+	0.281463i	0.894860	+	0.446347i	$0.147275\pi$
$192$	8.25317	+	25.4006i	0.595621	+	1.83313i
$193$	20.8189	−	4.42519i	1.49858	−	0.318532i	0.615641	−	0.788027i	$-0.288897\pi$
$193$	20.8189	−	4.42519i	1.49858	−	0.318532i	0.882935	+	0.469494i	$0.155564\pi$
$194$	−9.53101			−0.684287
$195$	−15.1910	+	3.22895i	−1.08785	+	0.231230i
$196$	−10.1120	+	17.5145i	−0.722285	+	1.25103i
$197$	0.463455	+	0.802727i	0.0330198	+	0.0571919i	0.882063	−	0.471131i	$-0.156154\pi$
$197$	0.463455	+	0.802727i	0.0330198	+	0.0571919i	−0.849043	+	0.528323i	$0.822821\pi$
$198$	6.61542	+	7.34717i	0.470138	+	0.522141i
$199$	2.90050	+	27.5964i	0.205611	+	1.95626i	0.282635	+	0.959227i	$0.408791\pi$
$199$	2.90050	+	27.5964i	0.205611	+	1.95626i	−0.0770244	+	0.997029i	$0.524542\pi$
$200$	2.66008	−	2.95432i	0.188096	−	0.208902i
$201$	9.37496	+	10.4119i	0.661258	+	0.734402i
$202$	1.03344	−	9.83256i	0.0727128	−	0.691816i
$203$	1.29790	−	0.942979i	0.0910946	−	0.0661841i
$204$	15.7651	−	27.3059i	1.10378	−	1.91180i
$205$	4.34350	−	1.93385i	0.303363	−	0.135066i
$206$	0.619082	+	1.90534i	0.0431335	+	0.132751i
$207$	−13.7527	+	9.99193i	−0.955879	+	0.694487i
$208$	13.1723	+	5.86468i	0.913334	+	0.406642i
$209$	−0.938413	+	8.92840i	−0.0649114	+	0.617590i
$210$	−7.24582	+	22.3004i	−0.500009	+	1.53887i
$211$	1.39195	+	1.01131i	0.0958255	+	0.0696213i	0.634666	−	0.772786i	$-0.281138\pi$
$211$	1.39195	+	1.01131i	0.0958255	+	0.0696213i	−0.538841	+	0.842408i	$0.681138\pi$
$212$	−3.80738	−	6.59458i	−0.261492	−	0.452918i
$213$	−18.4242	−	8.20300i	−1.26241	−	0.562060i
$214$	−28.2263	−	12.5671i	−1.92951	−	0.859072i
$215$	1.56082	+	2.70342i	0.106447	+	0.184372i
$216$	1.40909	+	1.02377i	0.0958767	+	0.0696585i
$217$	2.96657	−	9.13018i	0.201384	−	0.619797i
$218$	0.0885071	−	0.842089i	0.00599446	−	0.0570334i
$219$	−12.9712	−	5.77513i	−0.876510	−	0.390247i
$220$	5.01217	−	3.64156i	0.337921	−	0.245514i
$221$	−9.07708	−	27.9364i	−0.610590	−	1.87920i
$222$	33.1509	−	14.7597i	2.22494	−	0.990607i
$223$	7.37302	−	12.7704i	0.493734	−	0.855172i	−0.506240	−	0.862393i	$-0.668965\pi$
$223$	7.37302	−	12.7704i	0.493734	−	0.855172i	0.999974	+	0.00722039i	$0.00229834\pi$
$224$	24.7567	−	17.9868i	1.65413	−	1.20179i
$225$	0.851968	−	8.10594i	0.0567979	−	0.540396i
$226$	8.52315	+	9.46592i	0.566952	+	0.629664i
$227$	−4.20101	+	4.66570i	−0.278831	+	0.309673i	−0.866251	−	0.499609i	$-0.833477\pi$
$227$	−4.20101	+	4.66570i	−0.278831	+	0.309673i	0.587420	+	0.809282i	$0.300144\pi$
$228$	−2.77098	−	26.3641i	−0.183512	−	1.74600i
$229$	−1.22133	−	1.35642i	−0.0807077	−	0.0896350i	0.701438	−	0.712730i	$-0.252542\pi$
$229$	−1.22133	−	1.35642i	−0.0807077	−	0.0896350i	−0.782146	+	0.623095i	$0.785875\pi$
$230$	9.52717	+	16.5015i	0.628203	+	1.08808i
$231$	8.87203	−	15.3668i	0.583737	−	1.01106i
$232$	0.462697	−	0.0983493i	0.0303776	−	0.00645695i
$233$	−11.4021			−0.746974			−0.373487	−	0.927635i	$-0.621838\pi$
$233$	−11.4021			−0.746974			−0.373487	+	0.927635i	$0.621838\pi$
$234$	−26.6028	+	5.65460i	−1.73908	+	0.369653i
$235$	−1.50346	−	4.62717i	−0.0980748	−	0.301843i
$236$	−1.14948	+	3.53772i	−0.0748245	+	0.230286i
$237$	−2.18514	−	20.7902i	−0.141940	−	1.35047i
$238$	−43.3802	−	9.22074i	−2.81192	−	0.597692i
$239$	5.69764	+	1.21107i	0.368549	+	0.0783376i	0.388464	−	0.921464i	$-0.373006\pi$
$239$	5.69764	+	1.21107i	0.368549	+	0.0783376i	−0.0199141	+	0.999802i	$0.506339\pi$
$240$	5.02850	−	5.58472i	0.324589	−	0.360492i
$241$	14.0356	+	10.1975i	0.904113	+	0.656876i	0.939519	−	0.342497i	$-0.111273\pi$
$241$	14.0356	+	10.1975i	0.904113	+	0.656876i	−0.0354063	+	0.999373i	$0.511273\pi$
$242$	13.7406	−	6.11773i	0.883282	−	0.393263i
$243$	19.7881			1.26941
$244$	17.2668	+	9.70029i	1.10539	+	0.620998i
$245$	9.81975			0.627361
$246$	17.3607	−	7.72950i	1.10688	−	0.492815i
$247$	−19.9799	−	14.5162i	−1.27129	−	0.923647i
$248$	1.89406	−	2.10356i	0.120273	−	0.133576i
$249$	11.5308	+	2.45095i	0.730736	+	0.155323i
$250$	−21.7609	−	4.62541i	−1.37628	−	0.292537i
$251$	−0.530194	−	5.04446i	−0.0334656	−	0.318403i	−0.998430	−	0.0560213i	$-0.982159\pi$
$251$	−0.530194	−	5.04446i	−0.0334656	−	0.318403i	0.964964	−	0.262382i	$-0.0845081\pi$
$252$	−7.09393	+	21.8329i	−0.446876	+	1.37534i
$253$	−4.45578	−	13.7135i	−0.280133	−	0.862160i
$254$	5.34625	−	1.13638i	0.335454	−	0.0713029i
$255$	−15.3095			−0.958717
$256$	−4.27763	+	0.909238i	−0.267352	+	0.0568274i
$257$	−10.8484	+	18.7901i	−0.676707	+	1.17209i	0.299259	+	0.954172i	$0.403260\pi$
$257$	−10.8484	+	18.7901i	−0.676707	+	1.17209i	−0.975967	+	0.217920i	$0.930073\pi$
$258$	6.23852	+	10.8054i	0.388393	+	0.672717i
$259$	−19.0939	−	21.2059i	−1.18644	−	1.31767i
$260$	1.78147	+	16.9496i	0.110482	+	1.05117i
$261$	0.648946	−	0.720728i	0.0401688	−	0.0446119i
$262$	19.1456	+	21.2633i	1.18282	+	1.31365i
$263$	0.0382994	−	0.364395i	0.00236164	−	0.0224695i	−0.993278	−	0.115757i	$-0.963071\pi$
$263$	0.0382994	−	0.364395i	0.00236164	−	0.0224695i	0.995639	+	0.0932870i	$0.0297374\pi$
$264$	4.23273	−	3.07526i	0.260506	−	0.189269i
$265$	−1.84868	+	3.20200i	−0.113563	+	0.196697i
$266$	−34.0635	+	15.1660i	−2.08857	+	0.929889i
$267$	−5.69615	−	17.5310i	−0.348599	−	1.07288i
$268$	12.4388	−	9.03732i	0.759821	−	0.552042i
$269$	−18.8038	−	8.37201i	−1.14649	−	0.510450i	−0.256551	−	0.966531i	$-0.582586\pi$
$269$	−18.8038	−	8.37201i	−1.14649	−	0.510450i	−0.889939	+	0.456080i	$0.849253\pi$
$270$	0.418394	−	3.98075i	0.0254626	−	0.242261i
$271$	−10.0125	+	30.8152i	−0.608215	+	1.87189i	−0.135248	+	0.990812i	$0.543183\pi$
$271$	−10.0125	+	30.8152i	−0.608215	+	1.87189i	−0.472967	+	0.881080i	$0.656817\pi$
$272$	11.4992	+	8.35465i	0.697240	+	0.506575i
$273$	24.4062	+	42.2727i	1.47713	+	2.55846i
$274$	−27.3034	−	12.1563i	−1.64946	−	0.734387i
$275$	6.31583	+	2.81199i	0.380859	+	0.169569i
$276$	21.2888	+	36.8732i	1.28143	+	2.21951i
$277$	−3.40946	−	2.47712i	−0.204855	−	0.148836i	0.480628	−	0.876925i	$-0.340409\pi$
$277$	−3.40946	−	2.47712i	−0.204855	−	0.148836i	−0.685483	+	0.728089i	$0.740409\pi$
$278$	−3.80251	+	11.7029i	−0.228059	+	0.701895i
$279$	0.606628	−	5.77168i	0.0363178	−	0.345541i
$280$	4.96665	+	2.21130i	0.296814	+	0.132150i
$281$	−2.97726	+	2.16310i	−0.177608	+	0.129040i	−0.673037	−	0.739608i	$-0.735011\pi$
$281$	−2.97726	+	2.16310i	−0.177608	+	0.129040i	0.495429	+	0.868648i	$0.335011\pi$
$282$	−6.00925	−	18.4946i	−0.357845	−	1.10133i
$283$	18.0382	−	8.03111i	1.07226	−	0.477400i	0.206801	−	0.978383i	$-0.433695\pi$
$283$	18.0382	−	8.03111i	1.07226	−	0.477400i	0.865457	+	0.500983i	$0.167028\pi$
$284$	−11.0660	+	19.1669i	−0.656648	+	1.13735i
$285$	−10.4133	+	7.56574i	−0.616833	+	0.448156i
$286$	2.41140	−	22.9429i	0.142589	−	1.35664i
$287$	−9.99926	−	11.1053i	−0.590238	−	0.655525i
$288$	12.3783	−	13.7475i	0.729399	−	0.810079i
$289$	−1.24977	−	11.8907i	−0.0735157	−	0.699455i
$290$	−0.727398	−	0.807857i	−0.0427143	−	0.0474390i
$291$	5.17047	+	8.95552i	0.303098	+	0.524982i
$292$	−7.79079	+	13.4940i	−0.455921	+	0.789679i
$293$	−1.67272	+	0.355547i	−0.0977212	+	0.0207713i	−0.256513	−	0.966541i	$-0.582574\pi$
$293$	−1.67272	+	0.355547i	−0.0977212	+	0.0207713i	0.158792	+	0.987312i	$0.449240\pi$
$294$	39.2490			2.28905
$295$	1.76667	−	0.375518i	0.102860	−	0.0218635i
$296$	−2.60001	−	8.00201i	−0.151123	−	0.465107i
$297$	−0.936011	+	2.88075i	−0.0543129	+	0.167158i
$298$	5.07732	+	48.3075i	0.294121	+	2.79838i
$299$	38.7992	+	8.24702i	2.24381	+	0.476937i
$300$	−19.9684	−	4.24442i	−1.15288	−	0.245052i
$301$	6.56510	−	7.29128i	0.378406	−	0.420263i
$302$	19.1303	+	13.8989i	1.10082	+	0.799794i
$303$	−9.79949	+	4.36301i	−0.562966	+	0.250649i
$304$	11.9504			0.685401
$305$	−0.112976	−	9.61564i	−0.00646901	−	0.550590i
$306$	−26.8103			−1.53264
$307$	15.9872	−	7.11797i	0.912439	−	0.406244i	0.103833	−	0.994595i	$-0.466889\pi$
$307$	15.9872	−	7.11797i	0.912439	−	0.406244i	0.808606	+	0.588351i	$0.200222\pi$
$308$	−15.7534	−	11.4455i	−0.897632	−	0.652168i
$309$	1.45445	−	1.61533i	0.0827406	−	0.0918927i
$310$	−6.36290	−	1.35248i	−0.361389	−	0.0768155i
$311$	−14.4204	−	3.06514i	−0.817704	−	0.173808i	−0.219974	−	0.975506i	$-0.570597\pi$
$311$	−14.4204	−	3.06514i	−0.817704	−	0.173808i	−0.597730	+	0.801697i	$0.703931\pi$
$312$	1.50444	+	14.3137i	0.0851719	+	0.810356i
$313$	−3.98839	+	12.2750i	−0.225437	+	0.693825i	0.772810	+	0.634638i	$0.218851\pi$
$313$	−3.98839	+	12.2750i	−0.225437	+	0.693825i	−0.998247	+	0.0591867i	$0.981149\pi$
$314$	−5.69873	−	17.5389i	−0.321598	−	0.989777i
$315$	10.9029	−	2.31749i	0.614311	−	0.130576i
$316$	−22.9407			−1.29052
$317$	14.3518	−	3.05057i	0.806078	−	0.171337i	0.213598	−	0.976922i	$-0.431482\pi$
$317$	14.3518	−	3.05057i	0.806078	−	0.171337i	0.592481	+	0.805584i	$0.298149\pi$
$318$	−7.38906	+	12.7982i	−0.414358	+	0.717689i
$319$	0.411319	+	0.712426i	0.0230295	+	0.0398882i
$320$	−9.52239	−	10.5757i	−0.532318	−	0.591199i
$321$	3.50412	+	33.3395i	0.195581	+	1.86083i
$322$	40.0730	−	44.5056i	2.23318	−	2.48020i
$323$	−16.2901	−	18.0920i	−0.906408	−	1.00667i
$324$	2.79516	−	26.5942i	0.155287	−	1.47745i
$325$	−15.3863	+	11.1788i	−0.853478	+	0.620088i
$326$	21.1832	−	36.6903i	1.17323	−	2.03209i
$327$	−0.839257	+	0.373661i	−0.0464110	+	0.0206635i
$328$	−1.36160	−	4.19057i	−0.0751816	−	0.231385i
$329$	−12.3713	+	8.98825i	−0.682050	+	0.495538i
$330$	−10.9840	−	4.89040i	−0.604650	−	0.269208i
$331$	−0.117148	+	1.11458i	−0.00643901	+	0.0612631i	−0.997270	−	0.0738473i	$-0.976472\pi$
$331$	−0.117148	+	1.11458i	−0.00643901	+	0.0612631i	0.990831	+	0.135110i	$0.0431389\pi$
$332$	3.99761	−	12.3034i	0.219398	−	0.675236i
$333$	−13.9558	−	10.1395i	−0.764775	−	0.555641i
$334$	−12.0283	−	20.8336i	−0.658158	−	1.13996i
$335$	−6.82002	−	3.03647i	−0.372617	−	0.165900i
$336$	−21.5777	−	9.60702i	−1.17716	−	0.524106i
$337$	9.71207	+	16.8218i	0.529050	+	0.916342i	0.999426	+	0.0338755i	$0.0107850\pi$
$337$	9.71207	+	16.8218i	0.529050	+	0.916342i	−0.470376	+	0.882466i	$0.655882\pi$
$338$	28.9426	+	21.0280i	1.57427	+	1.14377i
$339$	4.27064	−	13.1437i	0.231949	−	0.713866i
$340$	−1.75614	+	16.7085i	−0.0952398	+	0.906146i
$341$	4.49706	+	2.00222i	0.243530	+	0.108426i
$342$	−18.2361	+	13.2493i	−0.986094	+	0.716439i
$343$	−1.16653	−	3.59021i	−0.0629867	−	0.193853i
$344$	2.64284	−	1.17667i	0.142492	−	0.0634416i
$345$	10.3368	−	17.9038i	0.556513	−	0.963909i
$346$	16.2960	−	11.8397i	0.876076	−	0.636507i
$347$	−2.93642	+	27.9382i	−0.157635	+	1.49980i	0.574423	+	0.818559i	$0.305226\pi$
$347$	−2.93642	+	27.9382i	−0.157635	+	1.49980i	−0.732059	+	0.681242i	$0.761440\pi$
$348$	−1.62540	−	1.80518i	−0.0871303	−	0.0967680i
$349$	−7.40721	+	8.22654i	−0.396499	+	0.440356i	−0.908028	−	0.418909i	$-0.862412\pi$
$349$	−7.40721	+	8.22654i	−0.396499	+	0.440356i	0.511529	+	0.859266i	$0.329079\pi$
$350$	3.00147	+	28.5571i	0.160435	+	1.52644i
$351$	−5.57553	−	6.19225i	−0.297600	−	0.330518i
$352$	7.84569	+	13.5891i	0.418177	+	0.724304i
$353$	5.25836	−	9.10774i	0.279874	−	0.484756i	−0.691479	−	0.722397i	$-0.743041\pi$
$353$	5.25836	−	9.10774i	0.279874	−	0.484756i	0.971353	+	0.237640i	$0.0763739\pi$
$354$	7.06129	−	1.50092i	0.375304	−	0.0797732i
$355$	10.7462			0.570351
$356$	−19.7864	+	4.20572i	−1.04868	+	0.222903i
$357$	14.8693	+	45.7630i	0.786966	+	2.42203i
$358$	−1.14849	+	3.53468i	−0.0606995	+	0.186814i
$359$	1.23915	+	11.7897i	0.0653997	+	0.622236i	0.977305	+	0.211836i	$0.0679443\pi$
$359$	1.23915	+	11.7897i	0.0653997	+	0.622236i	−0.911906	+	0.410400i	$0.865389\pi$
$360$	3.21479	+	0.683325i	0.169434	+	0.0360144i
$361$	−1.43641	−	0.305319i	−0.0756007	−	0.0160694i
$362$	−31.5072	+	34.9923i	−1.65598	+	1.83915i
$363$	−13.2025	−	9.59217i	−0.692951	−	0.503458i
$364$	48.9353	−	21.7874i	2.56491	−	1.14197i
$365$	7.56564			0.396004
$366$	−0.451561	−	38.4332i	−0.0236035	−	2.00894i
$367$	−8.31934			−0.434266			−0.217133	−	0.976142i	$-0.569671\pi$
$367$	−8.31934			−0.434266			−0.217133	+	0.976142i	$0.569671\pi$
$368$	−17.5345	+	7.80687i	−0.914050	+	0.406961i
$369$	−7.30852	−	5.30995i	−0.380466	−	0.276425i
$370$	−12.9382	+	14.3693i	−0.672623	+	0.747023i
$371$	11.3669	+	2.41611i	0.590140	+	0.125438i
$372$	−14.2181	−	3.02215i	−0.737175	−	0.156691i
$373$	0.790781	+	7.52378i	0.0409451	+	0.389567i	0.995733	+	0.0922793i	$0.0294153\pi$
$373$	0.790781	+	7.52378i	0.0409451	+	0.389567i	−0.954788	+	0.297287i	$0.903918\pi$
$374$	7.02740	−	21.6281i	0.363378	−	1.11836i
$375$	7.45890	+	22.9561i	0.385176	+	1.18545i
$376$	−4.41032	+	0.937443i	−0.227445	+	0.0483449i
$377$	−2.26300			−0.116551
$378$	−12.3056	+	2.61563i	−0.632931	+	0.134534i
$379$	10.9280	−	18.9278i	0.561333	−	0.972257i	−0.436048	−	0.899923i	$-0.643622\pi$
$379$	10.9280	−	18.9278i	0.561333	−	0.972257i	0.997381	−	0.0723332i	$-0.0230445\pi$
$380$	7.06261	+	12.2328i	0.362304	+	0.627530i
$381$	−3.96805	−	4.40697i	−0.203289	−	0.225776i
$382$	−0.910524	−	8.66305i	−0.0465864	−	0.443240i
$383$	20.8527	−	23.1592i	1.06552	−	1.18338i	0.0831307	−	0.996539i	$-0.473508\pi$
$383$	20.8527	−	23.1592i	1.06552	−	1.18338i	0.982390	−	0.186842i	$-0.0598252\pi$
$384$	−13.6075	−	15.1126i	−0.694404	−	0.771214i
$385$	−0.988290	+	9.40296i	−0.0503679	+	0.479219i
$386$	−36.6721	+	26.6439i	−1.86656	+	1.35614i
$387$	2.96562	−	5.13660i	0.150751	−	0.261108i
$388$	10.3670	−	4.61569i	0.526305	−	0.234326i
$389$	−7.42504	−	22.8519i	−0.376465	−	1.15864i	−0.942485	−	0.334248i	$-0.891518\pi$
$389$	−7.42504	−	22.8519i	−0.376465	−	1.15864i	0.566021	−	0.824391i	$-0.308482\pi$
$390$	26.7587	−	19.4413i	1.35498	−	0.984451i
$391$	35.7212	+	15.9041i	1.80650	+	0.804306i
$392$	0.951244	−	9.05048i	0.0480451	−	0.457118i
$393$	9.59314	−	29.5247i	0.483910	−	1.48932i
$394$	−1.59706	−	1.16033i	−0.0804585	−	0.0584566i
$395$	5.56943	+	9.64654i	0.280229	+	0.485370i
$396$	−10.7538	−	4.78789i	−0.540397	−	0.240600i
$397$	−1.19276	−	0.531050i	−0.0598628	−	0.0266526i	0.376587	−	0.926381i	$-0.377098\pi$
$397$	−1.19276	−	0.531050i	−0.0598628	−	0.0266526i	−0.436450	+	0.899729i	$0.643764\pi$
$398$	−29.5484	−	51.1793i	−1.48113	−	2.56538i
$399$	32.7294	+	23.7793i	1.63852	+	1.19045i
$400$	2.84383	−	8.75242i	0.142192	−	0.437621i
$401$	2.08242	−	19.8129i	0.103991	−	0.989410i	−0.810756	−	0.585384i	$-0.800944\pi$
$401$	2.08242	−	19.8129i	0.103991	−	0.989410i	0.914747	−	0.404026i	$-0.132390\pi$
$402$	−27.2592	−	12.1366i	−1.35957	−	0.605318i
$403$	−10.9555	+	7.95965i	−0.545733	+	0.396498i
$404$	3.63763	+	11.1955i	0.180979	+	0.556995i
$405$	−11.8614	+	5.28104i	−0.589398	+	0.262417i
$406$	−1.70836	+	2.95896i	−0.0847843	+	0.146851i
$407$	11.8377	−	8.60058i	0.586772	−	0.426315i
$408$	−1.48304	+	14.1102i	−0.0734213	+	0.698557i
$409$	−7.27309	−	8.07759i	−0.359631	−	0.399411i	0.535993	−	0.844222i	$-0.319937\pi$
$409$	−7.27309	−	8.07759i	−0.359631	−	0.399411i	−0.895624	+	0.444811i	$0.853271\pi$
$410$	−6.77557	+	7.52503i	−0.334622	+	0.371635i
$411$	3.38955	+	32.2495i	0.167194	+	1.59075i
$412$	−1.59610	−	1.77265i	−0.0786343	−	0.0873322i
$413$	−2.83837	−	4.91620i	−0.139667	−	0.241910i
$414$	18.1020	−	31.3535i	0.889663	−	1.54094i
$415$	−6.14408	+	1.30596i	−0.301601	+	0.0641073i
$416$	−43.1656			−2.11637
$417$	13.0591	−	2.77580i	0.639508	−	0.135932i
$418$	−5.90836	−	18.1841i	−0.288987	−	0.889412i
$419$	−11.5266	+	35.4752i	−0.563111	+	1.73308i	0.110388	+	0.993889i	$0.464791\pi$
$419$	−11.5266	+	35.4752i	−0.563111	+	1.73308i	−0.673499	+	0.739188i	$0.735209\pi$
$420$	−2.91826	−	27.7654i	−0.142396	−	1.35481i
$421$	10.1823	+	2.16431i	0.496254	+	0.105482i	0.449238	−	0.893412i	$-0.351695\pi$
$421$	10.1823	+	2.16431i	0.496254	+	0.105482i	0.0470162	+	0.998894i	$0.485029\pi$
$422$	−3.58422	−	0.761849i	−0.174477	−	0.0370862i
$423$	−6.18560	+	6.86981i	−0.300754	+	0.334022i
$424$	2.77207	+	2.01403i	0.134624	+	0.0978100i
$425$	−17.1271	+	7.62549i	−0.830788	+	0.369891i
$426$	42.9521			2.08104
$427$	−28.6333	+	9.67687i	−1.38566	+	0.468296i
$428$	36.7881			1.77822
$429$	−22.8658	+	10.1805i	−1.10397	+	0.491519i
$430$	−5.37856	−	3.90775i	−0.259377	−	0.188449i
$431$	−12.8860	+	14.3113i	−0.620695	+	0.689352i	−0.968726	−	0.248131i	$-0.920184\pi$
$431$	−12.8860	+	14.3113i	−0.620695	+	0.689352i	0.348031	+	0.937483i	$0.386850\pi$
$432$	3.94389	+	0.838300i	0.189751	+	0.0403327i
$433$	−15.3817	−	3.26947i	−0.739195	−	0.157121i	−0.177100	−	0.984193i	$-0.556671\pi$
$433$	−15.3817	−	3.26947i	−0.739195	−	0.157121i	−0.562096	+	0.827072i	$0.690005\pi$
$434$	2.13714	+	20.3335i	0.102586	+	0.976040i
$435$	−0.364472	+	1.12173i	−0.0174751	+	0.0537829i
$436$	0.311537	+	0.958812i	0.0149199	+	0.0459188i
$437$	32.1568	−	6.83514i	1.53827	−	0.326969i
$438$	30.2395			1.44490
$439$	22.8168	−	4.84986i	1.08899	−	0.231471i	0.371772	−	0.928324i	$-0.378750\pi$
$439$	22.8168	−	4.84986i	1.08899	−	0.231471i	0.717214	+	0.696853i	$0.245417\pi$
$440$	−1.39389	+	2.41429i	−0.0664512	+	0.115097i
$441$	−9.32895	−	16.1582i	−0.444236	−	0.769439i
$442$	41.8601	+	46.4903i	1.99108	+	2.21132i
$443$	−1.49567	−	14.2304i	−0.0710616	−	0.676106i	−0.970835	−	0.239749i	$-0.922935\pi$
$443$	−1.49567	−	14.2304i	−0.0710616	−	0.676106i	0.899773	−	0.436357i	$-0.143732\pi$
$444$	−28.9107	+	32.1086i	−1.37204	+	1.52381i
$445$	6.57214	+	7.29910i	0.311549	+	0.346011i
$446$	−3.28273	+	31.2331i	−0.155442	+	1.47893i
$447$	42.6362	−	30.9770i	2.01662	−	1.46516i
$448$	−22.3642	+	38.7358i	−1.05661	+	1.83010i
$449$	7.26491	−	3.23455i	0.342852	−	0.152648i	−0.228085	−	0.973641i	$-0.573247\pi$
$449$	7.26491	−	3.23455i	0.342852	−	0.152648i	0.570938	+	0.820994i	$0.306580\pi$
$450$	5.36410	+	16.5090i	0.252866	+	0.778241i
$451$	6.19927	−	4.50403i	0.291912	−	0.212087i
$452$	−13.8549	−	6.16860i	−0.651680	−	0.290146i
$453$	2.68175	−	25.5152i	0.126000	−	1.19881i
$454$	4.13191	−	12.7167i	0.193920	−	0.596825i
$455$	−21.0419	−	15.2878i	−0.986458	−	0.716703i
$456$	5.96430	+	10.3305i	0.279304	+	0.483768i
$457$	−29.4136	−	13.0958i	−1.37591	−	0.612595i	−0.420343	−	0.907365i	$-0.638090\pi$
$457$	−29.4136	−	13.0958i	−1.37591	−	0.612595i	−0.955568	+	0.294770i	$0.904757\pi$
$458$	3.55122	+	1.58110i	0.165938	+	0.0738801i
$459$	−4.10699	−	7.11351i	−0.191698	−	0.332030i
$460$	−18.3542	−	13.3351i	−0.855769	−	0.621752i
$461$	9.73046	−	29.9473i	0.453193	−	1.39478i	−0.420052	−	0.907500i	$-0.637988\pi$
$461$	9.73046	−	29.9473i	0.453193	−	1.39478i	0.873244	−	0.487283i	$-0.162012\pi$
$462$	−3.95014	+	37.5831i	−0.183777	+	1.74852i
$463$	14.0725	+	6.26547i	0.654004	+	0.291181i	0.706789	−	0.707425i	$-0.250143\pi$
$463$	14.0725	+	6.26547i	0.654004	+	0.291181i	−0.0527851	+	0.998606i	$0.516810\pi$
$464$	0.885908	−	0.643650i	0.0411272	−	0.0298807i
$465$	2.18099	+	6.71241i	0.101141	+	0.311280i
$466$	22.1840	−	9.87693i	1.02765	−	0.457540i
$467$	12.3112	−	21.3237i	0.569696	−	0.986743i	−0.426900	−	0.904299i	$-0.640394\pi$
$467$	12.3112	−	21.3237i	0.569696	−	0.986743i	0.996596	−	0.0824437i	$-0.0262725\pi$
$468$	26.1978	−	19.0338i	1.21099	−	0.879838i
$469$	−2.45266	+	23.3355i	−0.113253	+	1.07753i
$470$	6.93339	+	7.70031i	0.319813	+	0.355189i
$471$	−13.3884	+	14.8693i	−0.616904	+	0.685141i
$472$	−0.174962	−	1.66465i	−0.00805326	−	0.0766216i
$473$	3.36641	+	3.73878i	0.154788	+	0.171909i
$474$	22.2607	+	38.5567i	1.02247	+	1.77097i
$475$	−7.88128	+	13.6508i	−0.361618	+	0.626341i
$476$	51.6506	−	10.9787i	2.36740	−	0.503206i
$477$	7.02510			0.321657
$478$	−12.1344	+	2.57926i	−0.555017	+	0.117972i
$479$	−2.73131	−	8.40611i	−0.124797	−	0.384085i	0.869067	−	0.494694i	$-0.164720\pi$
$479$	−2.73131	−	8.40611i	−0.124797	−	0.384085i	−0.993864	+	0.110609i	$0.964720\pi$
$480$	−6.95212	+	21.3964i	−0.317319	+	0.976608i
$481$	4.20746	+	40.0313i	0.191844	+	1.82527i
$482$	−36.1412	−	7.68206i	−1.64619	−	0.349908i
$483$	−63.5575	−	13.5096i	−2.89197	−	0.614706i
$484$	−11.9832	+	13.3087i	−0.544690	+	0.604939i
$485$	−4.45774	−	3.23874i	−0.202416	−	0.147064i
$486$	−38.4998	+	17.1412i	−1.74639	+	0.777542i
$487$	−14.6614			−0.664373			−0.332187	−	0.943214i	$-0.607786\pi$
$487$	−14.6614			−0.664373			−0.332187	+	0.943214i	$0.607786\pi$
$488$	−8.87330	−	0.827345i	−0.401675	−	0.0374522i
$489$	−45.9666			−2.07868
$490$	−19.1054	+	8.50627i	−0.863094	+	0.384274i
$491$	21.4615	+	15.5927i	0.968545	+	0.703689i	0.955120	−	0.296220i	$-0.0957263\pi$
$491$	21.4615	+	15.5927i	0.968545	+	0.703689i	0.0134259	+	0.999910i	$0.495726\pi$
$492$	−15.1402	+	16.8149i	−0.682575	+	0.758076i
$493$	−2.18207	−	0.463813i	−0.0982754	−	0.0208891i
$494$	51.4476	+	10.9355i	2.31474	+	0.492013i
$495$	0.597447	+	5.68433i	0.0268532	+	0.255492i
$496$	2.02490	−	6.23199i	0.0909206	−	0.279825i
$497$	−10.4372	−	32.1225i	−0.468174	−	1.44089i
$498$	−24.5576	+	5.21987i	−1.10045	+	0.233908i
$499$	15.8024			0.707412			0.353706	−	0.935357i	$-0.384921\pi$
$499$	15.8024			0.707412			0.353706	+	0.935357i	$0.384921\pi$
$500$	25.9095	−	5.50724i	1.15871	−	0.246291i
$501$	−13.0504	+	22.6040i	−0.583050	+	1.00987i
$502$	5.40127	+	9.35527i	0.241070	+	0.417546i
$503$	−23.2485	−	25.8201i	−1.03660	−	1.15126i	−0.988315	−	0.152427i	$-0.951291\pi$
$503$	−23.2485	−	25.8201i	−1.03660	−	1.15126i	−0.0482846	−	0.998834i	$-0.515375\pi$
$504$	−1.07977	−	10.2733i	−0.0480967	−	0.457609i
$505$	3.82456	−	4.24760i	0.170190	−	0.189016i
$506$	20.5484	+	22.8213i	0.913487	+	1.01453i
$507$	4.05728	−	38.6025i	0.180190	−	1.71440i
$508$	−5.26486	+	3.82514i	−0.233590	+	0.169713i
$509$	−13.6496	+	23.6418i	−0.605009	+	1.04791i	0.387042	+	0.922062i	$0.373497\pi$
$509$	−13.6496	+	23.6418i	−0.605009	+	1.04791i	−0.992050	+	0.125843i	$0.959836\pi$
$510$	29.7863	−	13.2617i	1.31896	−	0.587238i
$511$	−7.34810	−	22.6151i	−0.325061	−	1.00043i
$512$	21.7749	−	15.8204i	0.962324	−	0.699170i
$513$	−6.30893	−	2.80892i	−0.278546	−	0.124017i
$514$	4.83011	−	45.9555i	0.213047	−	2.02701i
$515$	−0.357904	+	1.10151i	−0.0157711	+	0.0485385i
$516$	−12.0186	−	8.73201i	−0.529088	−	0.384405i
$517$	−3.92060	−	6.79067i	−0.172428	−	0.298653i
$518$	55.5186	+	24.7185i	2.43935	+	1.08607i
$519$	−19.9652	−	8.88908i	−0.876375	−	0.390187i
$520$	−3.83447	−	6.64150i	−0.168153	−	0.291249i
$521$	11.2871	+	8.20059i	0.494499	+	0.359274i	0.806912	−	0.590672i	$-0.201137\pi$
$521$	11.2871	+	8.20059i	0.494499	+	0.359274i	−0.312413	+	0.949946i	$0.601137\pi$
$522$	−0.638272	+	1.96440i	−0.0279364	+	0.0859794i
$523$	1.81900	−	17.3067i	0.0795395	−	0.756768i	−0.879958	−	0.475051i	$-0.842430\pi$
$523$	1.81900	−	17.3067i	0.0795395	−	0.756768i	0.959498	−	0.281717i	$-0.0909038\pi$
$524$	−31.1223	−	13.8565i	−1.35958	−	0.605325i
$525$	25.2045	−	18.3121i	1.10001	−	0.799208i
$526$	0.241138	+	0.742146i	0.0105141	+	0.0323591i
$527$	−12.1951	+	5.42959i	−0.531225	+	0.236516i
$528$	6.05579	−	10.4889i	0.263545	−	0.456473i
$529$	−24.1104	+	17.5172i	−1.04828	+	0.761617i
$530$	0.823096	−	7.83124i	0.0357530	−	0.340167i
$531$	−2.29628	−	2.55027i	−0.0996500	−	0.110672i
$532$	29.7066	−	32.9926i	1.28795	−	1.43041i
$533$	2.20340	+	20.9640i	0.0954399	+	0.908050i
$534$	26.2685	+	29.1741i	1.13675	+	1.26249i
$535$	−8.93123	−	15.4693i	−0.386131	−	0.668798i
$536$	−3.45925	+	5.99159i	−0.149417	+	0.258797i
$537$	3.94430	−	0.838387i	0.170209	−	0.0361791i
$538$	43.8371			1.88995
$539$	15.4803	−	3.29043i	0.666782	−	0.141729i
$540$	1.47271	+	4.53253i	0.0633753	+	0.195049i
$541$	10.2665	−	31.5970i	0.441391	−	1.35846i	−0.445003	−	0.895529i	$-0.646798\pi$
$541$	10.2665	−	31.5970i	0.441391	−	1.35846i	0.886394	−	0.462932i	$-0.153202\pi$
$542$	−7.21305	−	68.6276i	−0.309827	−	2.94781i
$543$	49.9717	+	10.6218i	2.14449	+	0.455826i
$544$	−41.6218	−	8.84698i	−1.78452	−	0.379311i
$545$	0.327546	−	0.363777i	0.0140305	−	0.0155825i
$546$	−84.1032	−	61.1046i	−3.59928	−	2.61503i
$547$	−40.2659	+	17.9275i	−1.72165	+	0.766527i	−0.724647	+	0.689120i	$0.757997\pi$
$547$	−40.2659	+	17.9275i	−1.72165	+	0.766527i	−0.997000	+	0.0774068i	$0.975336\pi$
$548$	35.5853			1.52013
$549$	−15.7150	+	9.32093i	−0.670700	+	0.397808i
$550$	−14.7240			−0.627833
$551$	−1.71343	+	0.762867i	−0.0729945	+	0.0324992i
$552$	−15.4999	−	11.2613i	−0.659720	−	0.479315i
$553$	23.4261	−	26.0173i	0.996177	−	1.10637i
$554$	8.77927	+	1.86609i	0.372995	+	0.0792826i
$555$	20.5204	+	4.36176i	0.871045	+	0.185146i
$556$	−1.53146	−	14.5709i	−0.0649485	−	0.617944i
$557$	12.3150	−	37.9017i	0.521803	−	1.60594i	−0.248749	−	0.968568i	$-0.580019\pi$
$557$	12.3150	−	37.9017i	0.521803	−	1.60594i	0.770552	−	0.637377i	$-0.219981\pi$
$558$	3.81940	+	11.7549i	0.161688	+	0.497625i
$559$	−13.5375	+	2.87748i	−0.572573	+	0.121704i
$560$	12.5855			0.531836
$561$	−24.1345	+	5.12994i	−1.01896	+	0.216586i
$562$	3.91881	−	6.78757i	0.165305	−	0.286316i
$563$	12.7079	+	22.0107i	0.535573	+	0.927639i	0.999135	+	0.0415751i	$0.0132376\pi$
$563$	12.7079	+	22.0107i	0.535573	+	0.927639i	−0.463563	+	0.886064i	$0.653429\pi$
$564$	15.4929	+	17.2066i	0.652368	+	0.724528i
$565$	0.769736	+	7.32355i	0.0323830	+	0.308104i
$566$	−28.1384	+	31.2508i	−1.18274	+	1.31357i
$567$	27.3064	+	30.3268i	1.14676	+	1.27361i
$568$	1.04099	−	9.90437i	0.0436790	−	0.415578i
$569$	11.2939	−	8.20552i	0.473466	−	0.343993i	−0.325324	−	0.945602i	$-0.605473\pi$
$569$	11.2939	−	8.20552i	0.473466	−	0.343993i	0.798791	+	0.601609i	$0.205473\pi$
$570$	13.7065	−	23.7404i	0.574104	−	0.994377i
$571$	−20.0858	+	8.94279i	−0.840566	+	0.374244i	−0.781420	−	0.624005i	$-0.785504\pi$
$571$	−20.0858	+	8.94279i	−0.840566	+	0.374244i	−0.0591457	+	0.998249i	$0.518838\pi$
$572$	8.48790	+	26.1231i	0.354897	+	1.09226i
$573$	−7.64602	+	5.55516i	−0.319417	+	0.232070i
$574$	29.0745	+	12.9448i	1.21355	+	0.540306i
$575$	2.64633	−	25.1781i	0.110359	−	1.05000i
$576$	−8.35564	+	25.7160i	−0.348151	+	1.07150i
$577$	26.6247	+	19.3440i	1.10840	+	0.805301i	0.982411	−	0.186731i	$-0.0597893\pi$
$577$	26.6247	+	19.3440i	1.10840	+	0.805301i	0.125990	+	0.992032i	$0.459789\pi$
$578$	12.7318	+	22.0521i	0.529573	+	0.917247i
$579$	44.9293	+	20.0038i	1.86720	+	0.831330i
$580$	1.18243	+	0.526451i	0.0490977	+	0.0218597i
$581$	9.87120	+	17.0974i	0.409526	+	0.709320i
$582$	−17.8174	−	12.9451i	−0.738553	−	0.536590i
$583$	−1.84139	+	5.66722i	−0.0762626	+	0.234712i
$584$	0.732886	−	6.97295i	0.0303271	−	0.288543i
$585$	−14.3639	−	6.39520i	−0.593873	−	0.264409i
$586$	2.94647	−	2.14073i	0.121717	−	0.0884328i
$587$	7.85604	+	24.1784i	0.324253	+	0.997949i	0.971777	+	0.235903i	$0.0758049\pi$
$587$	7.85604	+	24.1784i	0.324253	+	0.997949i	−0.647523	+	0.762046i	$0.724195\pi$
$588$	−42.6917	+	19.0075i	−1.76057	+	0.783858i
$589$	−5.61171	+	9.71977i	−0.231227	+	0.400496i
$590$	−3.11196	+	2.26097i	−0.128117	+	0.0930828i
$591$	−0.223882	+	2.13009i	−0.00920926	+	0.0876202i
$592$	−13.0329	−	14.4745i	−0.535650	−	0.594900i
$593$	13.7052	−	15.2211i	0.562804	−	0.625057i	−0.392831	−	0.919611i	$-0.628504\pi$
$593$	13.7052	−	15.2211i	0.562804	−	0.625057i	0.955635	+	0.294553i	$0.0951709\pi$
$594$	−0.674308	−	6.41561i	−0.0276672	−	0.263236i
$595$	−17.1560	−	19.0537i	−0.703327	−	0.781124i
$596$	−28.9170	−	50.0858i	−1.18449	−	2.05159i
$597$	−32.0593	+	55.5284i	−1.31210	+	2.27263i
$598$	−82.6319	+	17.5640i	−3.37907	+	0.718243i
$599$	24.3177			0.993593			0.496797	−	0.867867i	$-0.334510\pi$
$599$	24.3177			0.993593			0.496797	+	0.867867i	$0.334510\pi$
$600$	8.98534	−	1.90989i	0.366825	−	0.0779710i
$601$	−6.20409	−	19.0942i	−0.253070	−	0.778870i	−0.994204	−	0.107513i	$-0.965711\pi$
$601$	−6.20409	−	19.0942i	−0.253070	−	0.778870i	0.741133	−	0.671358i	$-0.234289\pi$
$602$	−6.45711	+	19.8729i	−0.263172	+	0.809961i
$603$	1.48269	+	14.1069i	0.0603800	+	0.574477i
$604$	−27.5392	−	5.85364i	−1.12055	−	0.238181i
$605$	8.50549	+	1.80790i	0.345797	+	0.0735015i
$606$	15.2865	−	16.9774i	0.620974	−	0.689661i
$607$	−0.0186590	−	0.0135565i	−0.000757344	−	0.000550243i	0.587407	−	0.809292i	$-0.300149\pi$
$607$	−0.0186590	−	0.0135565i	−0.000757344	−	0.000550243i	−0.588164	+	0.808742i	$0.700149\pi$
$608$	−32.6827	+	14.5513i	−1.32546	+	0.590133i
$609$	3.70706			0.150218
$610$	8.54927	+	18.6104i	0.346150	+	0.753513i
$611$	21.5704			0.872646
$612$	29.1619	−	12.9837i	1.17880	−	0.524835i
$613$	−33.7387	−	24.5126i	−1.36269	−	0.990056i	−0.998268	−	0.0588237i	$-0.981265\pi$
$613$	−33.7387	−	24.5126i	−1.36269	−	0.990056i	−0.364427	−	0.931232i	$-0.618735\pi$
$614$	−24.9390	+	27.6976i	−1.00646	+	1.11778i
$615$	10.7463	+	2.28420i	0.433334	+	0.0921080i
$616$	8.57060	+	1.82174i	0.345319	+	0.0733999i
$617$	−4.43511	−	42.1972i	−0.178551	−	1.69880i	−0.606572	−	0.795028i	$-0.707456\pi$
$617$	−4.43511	−	42.1972i	−0.178551	−	1.69880i	0.428021	−	0.903769i	$-0.359211\pi$
$618$	−1.43052	+	4.40269i	−0.0575440	+	0.177102i
$619$	0.767447	+	2.36196i	0.0308463	+	0.0949351i	0.965294	−	0.261164i	$-0.0841064\pi$
$619$	0.767447	+	2.36196i	0.0308463	+	0.0949351i	−0.934448	+	0.356099i	$0.884106\pi$
$620$	7.57598	−	1.61033i	0.304259	−	0.0646722i
$621$	11.0919			0.445104
$622$	30.7115	−	6.52794i	1.23142	−	0.261747i
$623$	15.4352	−	26.7346i	0.618400	−	1.07110i
$624$	16.6589	+	28.8541i	0.666891	+	1.15509i
$625$	3.05042	+	3.38784i	0.122017	+	0.135514i
$626$	−2.87326	−	27.3373i	−0.114839	−	1.09262i
$627$	−13.8809	+	15.4163i	−0.554348	+	0.615666i
$628$	14.6923	+	16.3175i	0.586287	+	0.651138i
$629$	−4.14762	+	39.4619i	−0.165376	+	1.57345i
$630$	−19.2053	+	13.9535i	−0.765159	+	0.555921i
$631$	−8.73991	+	15.1380i	−0.347930	+	0.602633i	−0.985882	−	0.167444i	$-0.946449\pi$
$631$	−8.73991	+	15.1380i	−0.347930	+	0.602633i	0.637951	+	0.770077i	$0.279782\pi$
$632$	9.43035	−	4.19866i	0.375119	−	0.167014i
$633$	1.22855	+	3.78109i	0.0488305	+	0.150285i
$634$	−25.2805	+	18.3674i	−1.00402	+	0.729461i
$635$	2.88664	+	1.28522i	0.114553	+	0.0510023i
$636$	1.83924	−	17.4992i	0.0729304	−	0.693887i
$637$	−13.4534	+	41.4053i	−0.533044	+	1.64054i
$638$	−1.41740	−	1.02980i	−0.0561153	−	0.0407702i
$639$	−10.2091	−	17.6827i	−0.403866	−	0.699517i
$640$	9.89906	+	4.40735i	0.391295	+	0.174216i
$641$	35.5364	+	15.8218i	1.40360	+	0.624925i	0.962190	−	0.272378i	$-0.0878101\pi$
$641$	35.5364	+	15.8218i	1.40360	+	0.624925i	0.441415	+	0.897303i	$0.354477\pi$
$642$	−35.6976	−	61.8301i	−1.40887	−	2.44024i
$643$	−7.93799	−	5.76729i	−0.313044	−	0.227440i	0.420158	−	0.907451i	$-0.361975\pi$
$643$	−7.93799	−	5.76729i	−0.313044	−	0.227440i	−0.733201	+	0.680012i	$0.761975\pi$
$644$	−22.0347	+	67.8159i	−0.868289	+	2.67232i
$645$	−0.753988	+	7.17371i	−0.0296882	+	0.282465i
$646$	47.3663	+	21.0888i	1.86360	+	0.829729i
$647$	−29.8155	+	21.6622i	−1.17217	+	0.851629i	−0.991267	−	0.131873i	$-0.957901\pi$
$647$	−29.8155	+	21.6622i	−1.17217	+	0.851629i	−0.180900	+	0.983502i	$0.557901\pi$
$648$	3.71831	+	11.4438i	0.146069	+	0.449554i
$649$	2.65922	−	1.18396i	0.104384	−	0.0464746i
$650$	20.2522	−	35.0778i	0.794356	−	1.37586i
$651$	17.9464	−	13.0388i	0.703374	−	0.511031i
$652$	−5.27278	+	50.1671i	−0.206498	+	1.96470i
$653$	14.6834	+	16.3076i	0.574607	+	0.638166i	0.958460	−	0.285228i	$-0.0920694\pi$
$653$	14.6834	+	16.3076i	0.574607	+	0.638166i	−0.383852	+	0.923395i	$0.625403\pi$
$654$	1.30918	−	1.45400i	0.0511932	−	0.0568558i
$655$	1.72906	+	16.4509i	0.0675599	+	0.642790i
$656$	−6.82520	−	7.58016i	−0.266479	−	0.295955i
$657$	−7.18749	−	12.4491i	−0.280411	−	0.485686i
$658$	16.2836	−	28.2041i	0.634803	−	1.09951i
$659$	1.97929	−	0.420712i	0.0771023	−	0.0163886i	−0.169199	−	0.985582i	$-0.554118\pi$
$659$	1.97929	−	0.420712i	0.0771023	−	0.0163886i	0.246301	+	0.969193i	$0.420785\pi$
$660$	14.3158			0.557241
$661$	38.0775	−	8.09362i	1.48104	−	0.314805i	0.604685	−	0.796465i	$-0.293299\pi$
$661$	38.0775	−	8.09362i	1.48104	−	0.314805i	0.876358	+	0.481660i	$0.159966\pi$
$662$	−0.737575	−	2.27002i	−0.0286667	−	0.0882270i
$663$	20.9745	−	64.5530i	0.814584	−	2.50703i
$664$	0.608476	+	5.78927i	0.0236135	+	0.224667i
$665$	−21.0854	−	4.48183i	−0.817656	−	0.173798i
$666$	35.9358	+	7.63840i	1.39249	+	0.295982i
$667$	2.01571	−	2.23868i	0.0780488	−	0.0866819i
$668$	23.1726	+	16.8359i	0.896576	+	0.651400i
$669$	31.1281	−	13.8591i	1.20348	−	0.535824i
$670$	15.8994			0.614247
$671$	−3.40013	−	15.1206i	−0.131261	−	0.583725i
$672$	70.7102			2.72770
$673$	−30.4872	+	13.5738i	−1.17519	+	0.523230i	−0.899033	−	0.437881i	$-0.855729\pi$
$673$	−30.4872	+	13.5738i	−1.17519	+	0.523230i	−0.276161	+	0.961111i	$0.589062\pi$
$674$	−33.4676	−	24.3156i	−1.28912	−	0.936603i
$675$	−3.55858	+	3.95220i	−0.136970	+	0.152120i
$676$	−41.6647	−	8.85610i	−1.60249	−	0.340619i
$677$	−23.8568	−	5.07092i	−0.916892	−	0.194891i	−0.274784	−	0.961506i	$-0.588606\pi$
$677$	−23.8568	−	5.07092i	−0.916892	−	0.194891i	−0.642108	+	0.766615i	$0.721940\pi$
$678$	3.07659	+	29.2718i	0.118156	+	1.12418i
$679$	−5.35164	+	16.4706i	−0.205377	+	0.632085i
$680$	−2.33613	−	7.18986i	−0.0895864	−	0.275719i
$681$	−14.1904	+	3.01626i	−0.543777	+	0.115583i
$682$	−10.4839			−0.401450
$683$	−12.9711	+	2.75710i	−0.496326	+	0.105497i	−0.449272	−	0.893395i	$-0.648317\pi$
$683$	−12.9711	+	2.75710i	−0.496326	+	0.105497i	−0.0470542	+	0.998892i	$0.514983\pi$
$684$	13.4192	−	23.2428i	0.513097	−	0.888710i
$685$	−8.63923	−	14.9636i	−0.330088	−	0.571729i
$686$	5.37960	+	5.97465i	0.205394	+	0.228113i
$687$	−0.440862	−	4.19452i	−0.0168199	−	0.160031i
$688$	4.48115	−	4.97682i	0.170842	−	0.189739i
$689$	−10.9686	−	12.1819i	−0.417870	−	0.464092i
$690$	−4.60230	+	43.7880i	−0.175207	+	1.66698i
$691$	6.43016	−	4.67178i	0.244615	−	0.177723i	−0.458722	−	0.888580i	$-0.651693\pi$
$691$	6.43016	−	4.67178i	0.244615	−	0.177723i	0.703337	+	0.710857i	$0.251693\pi$
$692$	−11.9916	+	20.7700i	−0.455851	+	0.789557i
$693$	16.4113	−	7.30677i	0.623413	−	0.277561i
$694$	−18.4881	−	56.9004i	−0.701797	−	2.15991i
$695$	−5.75524	+	4.18143i	−0.218309	+	0.158611i
$696$	0.998548	+	0.444582i	0.0378499	+	0.0168518i
$697$	−2.17206	+	20.6658i	−0.0822727	+	0.782772i
$698$	7.28536	−	22.4220i	0.275755	−	0.848687i
$699$	−21.3151	−	15.4863i	−0.806211	−	0.585747i
$700$	−17.0944	−	29.6083i	−0.646107	−	1.11909i
$701$	−20.9030	−	9.30662i	−0.789495	−	0.351506i	−0.0279432	−	0.999610i	$-0.508896\pi$
$701$	−20.9030	−	9.30662i	−0.789495	−	0.351506i	−0.761552	+	0.648103i	$0.775562\pi$
$702$	16.2118	+	7.21795i	0.611874	+	0.272424i
$703$	16.6804	+	28.8913i	0.629112	+	1.08965i
$704$	−18.5552	−	13.4811i	−0.699326	−	0.508090i
$705$	3.47407	−	10.6921i	0.130841	−	0.402687i
$706$	−2.34121	+	22.2751i	−0.0881125	+	0.838335i
$707$	−16.4115	−	7.30686i	−0.617217	−	0.274803i
$708$	−6.95379	+	5.05222i	−0.261339	+	0.189874i
$709$	12.4938	+	38.4519i	0.469214	+	1.44409i	0.853604	+	0.520922i	$0.174412\pi$
$709$	12.4938	+	38.4519i	0.469214	+	1.44409i	−0.384390	+	0.923171i	$0.625588\pi$
$710$	−20.9080	+	9.30882i	−0.784662	+	0.349354i
$711$	10.5821	−	18.3288i	0.396861	−	0.687383i
$712$	7.36394	−	5.35022i	0.275975	−	0.200508i
$713$	1.88427	−	17.9276i	0.0705663	−	0.671394i
$714$	−68.5716	−	76.1565i	−2.56623	−	2.85008i
$715$	8.92407	−	9.91119i	0.333741	−	0.370657i
$716$	−0.462554	−	4.40091i	−0.0172865	−	0.164470i
$717$	9.00632	+	10.0025i	0.336347	+	0.373552i
$718$	−12.6236	−	21.8647i	−0.471109	−	0.815985i
$719$	5.40177	−	9.35614i	0.201452	−	0.348925i	−0.747544	−	0.664212i	$-0.768767\pi$
$719$	5.40177	−	9.35614i	0.201452	−	0.348925i	0.948996	+	0.315287i	$0.102101\pi$
$720$	7.44203	−	1.58185i	0.277348	−	0.0589521i
$721$	3.64025			0.135570
$722$	3.05918	−	0.650248i	0.113851	−	0.0241997i
$723$	12.3880	+	38.1264i	0.460716	+	1.41794i
$724$	17.3247	−	53.3198i	0.643866	−	1.98162i
$725$	0.150977	+	1.43645i	0.00560715	+	0.0533484i
$726$	33.9960	+	7.22607i	1.26171	+	0.268185i
$727$	36.8424	+	7.83110i	1.36641	+	0.290440i	0.831995	−	0.554782i	$-0.187199\pi$
$727$	36.8424	+	7.83110i	1.36641	+	0.290440i	0.534415	+	0.845222i	$0.320532\pi$
$728$	−16.1285	+	17.9125i	−0.597762	+	0.663882i
$729$	11.3977	+	8.28095i	0.422139	+	0.306702i
$730$	−14.7198	+	6.55366i	−0.544803	+	0.242562i
$731$	−13.6430			−0.504606
$732$	19.1036	+	41.5856i	0.706090	+	1.53705i
$733$	2.42808			0.0896831			0.0448416	−	0.998994i	$-0.485722\pi$
$733$	2.42808			0.0896831			0.0448416	+	0.998994i	$0.485722\pi$
$734$	16.1862	−	7.20655i	0.597442	−	0.265999i
$735$	18.3571	+	13.3372i	0.677113	+	0.491951i
$736$	38.4487	−	42.7016i	1.41724	−	1.57400i
$737$	−11.7688	−	2.50154i	−0.433510	−	0.0921453i
$738$	18.8192	+	4.00015i	0.692745	+	0.147247i
$739$	−0.144334	−	1.37325i	−0.00530942	−	0.0505158i	0.991546	−	0.129753i	$-0.0414183\pi$
$739$	−0.144334	−	1.37325i	−0.00530942	−	0.0505158i	−0.996856	+	0.0792369i	$0.974752\pi$
$740$	7.11422	−	21.8953i	0.261524	−	0.804888i
$741$	−17.6346	−	54.2736i	−0.647822	−	1.99379i
$742$	−24.2085	+	5.14567i	−0.888722	+	0.188904i
$743$	−33.5407			−1.23049			−0.615245	−	0.788336i	$-0.710943\pi$
$743$	−33.5407			−1.23049			−0.615245	+	0.788336i	$0.710943\pi$
$744$	6.39783	−	1.35990i	0.234556	−	0.0498564i
$745$	−14.0407	+	24.3192i	−0.514410	+	0.890985i
$746$	−8.05596	−	13.9533i	−0.294950	−	0.510868i
$747$	7.98593	+	8.86927i	0.292190	+	0.324510i
$748$	2.83029	+	26.9284i	0.103486	+	0.984600i
$749$	−37.5664	+	41.7217i	−1.37265	+	1.52448i
$750$	−34.3976	−	38.2025i	−1.25602	−	1.39496i
$751$	2.83605	−	26.9833i	0.103489	−	0.984633i	−0.812373	−	0.583139i	$-0.801824\pi$
$751$	2.83605	−	26.9833i	0.103489	−	0.984633i	0.915862	−	0.401494i	$-0.131509\pi$
$752$	−8.44427	+	6.13512i	−0.307931	+	0.223725i
$753$	5.86026	−	10.1503i	0.213560	−	0.369896i
$754$	4.40292	−	1.96031i	0.160345	−	0.0713901i
$755$	4.22439	+	13.0013i	0.153741	+	0.473167i
$756$	12.1182	−	8.80442i	0.440736	−	0.320214i
$757$	3.14580	+	1.40060i	0.114336	+	0.0509057i	0.463107	−	0.886302i	$-0.346734\pi$
$757$	3.14580	+	1.40060i	0.114336	+	0.0509057i	−0.348771	+	0.937208i	$0.613401\pi$
$758$	−4.86553	+	46.2924i	−0.176724	+	1.68142i
$759$	10.2960	−	31.6880i	0.373723	−	1.15020i
$760$	−5.14214	−	3.73598i	−0.186525	−	0.135518i
$761$	13.2840	+	23.0085i	0.481543	+	0.834057i	0.999776	−	0.0211827i	$-0.00674317\pi$
$761$	13.2840	+	23.0085i	0.481543	+	0.834057i	−0.518233	+	0.855240i	$0.673410\pi$
$762$	11.5378	+	5.13694i	0.417969	+	0.186092i
$763$	−1.40553	−	0.625781i	−0.0508835	−	0.0226548i
$764$	5.18574	+	8.98196i	0.187613	+	0.324956i
$765$	−12.5394	−	9.11042i	−0.453363	−	0.329388i
$766$	−20.5096	+	63.1222i	−0.741043	+	2.28070i
$767$	−0.837019	+	7.96371i	−0.0302230	+	0.287553i
$768$	−9.23156	−	4.11016i	−0.333115	−	0.148313i
$769$	11.1719	−	8.11685i	0.402869	−	0.292701i	−0.367840	−	0.929889i	$-0.619903\pi$
$769$	11.1719	−	8.11685i	0.402869	−	0.292701i	0.770708	+	0.637188i	$0.219903\pi$
$770$	−6.22240	−	19.1506i	−0.224240	−	0.690139i
$771$	−45.8009	+	20.3919i	−1.64948	+	0.734395i
$772$	26.9856	−	46.7405i	0.971233	−	1.68223i
$773$	10.7009	−	7.77468i	0.384885	−	0.279636i	−0.378471	−	0.925613i	$-0.623550\pi$
$773$	10.7009	−	7.77468i	0.384885	−	0.279636i	0.763356	+	0.645978i	$0.223550\pi$
$774$	−1.32040	+	12.5628i	−0.0474608	+	0.451559i
$775$	5.78332	+	6.42302i	0.207743	+	0.230722i
$776$	−3.41684	+	3.79478i	−0.122657	+	0.136225i
$777$	−6.89230	−	65.5759i	−0.247260	−	2.35252i
$778$	34.2415	+	38.0290i	1.22762	+	1.36341i
$779$	8.73533	+	15.1300i	0.312976	+	0.542090i
$780$	−19.6907	+	34.1053i	−0.705041	+	1.22117i
$781$	16.9408	−	3.60087i	0.606189	−	0.128849i
$782$	−83.2763			−2.97796
$783$	−0.618984	+	0.131569i	−0.0221207	+	0.00470190i
$784$	−6.50996	−	20.0356i	−0.232498	−	0.715557i
$785$	3.29455	−	10.1396i	0.117588	−	0.361897i
$786$	6.91096	+	65.7534i	0.246506	+	2.34535i
$787$	13.7088	+	2.91390i	0.488666	+	0.103869i	0.445654	−	0.895205i	$-0.352971\pi$
$787$	13.7088	+	2.91390i	0.488666	+	0.103869i	0.0430124	+	0.999075i	$0.486305\pi$
$788$	2.29906	+	0.488681i	0.0819007	+	0.0174085i
$789$	0.566520	−	0.629184i	0.0201686	−	0.0223995i
$790$	−19.1922	−	13.9439i	−0.682826	−	0.496102i
$791$	21.1439	−	9.41386i	0.751790	−	0.334718i
$792$	5.29689			0.188217
$793$	40.6995	+	12.6974i	1.44528	+	0.450898i
$794$	2.78066			0.0986819
$795$	−7.80490	+	3.47496i	−0.276811	+	0.123244i
$796$	56.9252	+	41.3586i	2.01766	+	1.46592i
$797$	−6.51823	+	7.23922i	−0.230887	+	0.256426i	−0.847445	−	0.530884i	$-0.821860\pi$
$797$	−6.51823	+	7.23922i	−0.230887	+	0.256426i	0.616557	+	0.787310i	$0.288527\pi$
$798$	−84.2771	−	17.9137i	−2.98338	−	0.634136i
$799$	20.7989	+	4.42095i	0.735814	+	0.156402i
$800$	2.87981	+	27.3995i	0.101817	+	0.968720i
$801$	5.76687	−	17.7486i	0.203762	−	0.627116i
$802$	13.1112	+	40.3521i	0.462972	+	1.42488i
$803$	11.9268	−	2.53511i	0.420887	−	0.0894622i
$804$	35.5277			1.25297
$805$	33.8660	−	7.19843i	1.19362	−	0.253711i
$806$	14.4202	−	24.9765i	0.507929	−	0.879758i
$807$	−23.7811	−	41.1901i	−0.837136	−	1.44996i
$808$	−3.54436	−	3.93641i	−0.124690	−	0.138482i
$809$	−3.66154	−	34.8372i	−0.128733	−	1.22481i	−0.847969	−	0.530045i	$-0.822175\pi$
$809$	−3.66154	−	34.8372i	−0.128733	−	1.22481i	0.719237	−	0.694765i	$-0.244492\pi$
$810$	18.5030	−	20.5497i	0.650130	−	0.722042i
$811$	−11.7247	−	13.0216i	−0.411711	−	0.457251i	0.501247	−	0.865304i	$-0.332875\pi$
$811$	−11.7247	−	13.0216i	−0.411711	−	0.457251i	−0.912958	+	0.408053i	$0.866208\pi$
$812$	0.425233	−	4.04582i	0.0149227	−	0.141980i
$813$	−60.5708	+	44.0072i	−2.12431	+	1.54340i
$814$	−15.5813	+	26.9876i	−0.546125	+	0.945917i
$815$	22.3753	−	9.96213i	0.783773	−	0.348958i
$816$	10.1493	+	31.2365i	0.355298	+	1.09350i
$817$	−9.27985	+	6.74220i	−0.324661	+	0.235880i
$818$	21.1477	+	9.41558i	0.739413	+	0.329208i
$819$	−5.16563	+	49.1477i	−0.180502	+	1.71736i
$820$	3.72564	−	11.4663i	0.130105	−	0.400422i
$821$	10.2058	+	7.41496i	0.356185	+	0.258784i	0.751459	−	0.659780i	$-0.229350\pi$
$821$	10.2058	+	7.41496i	0.356185	+	0.258784i	−0.395274	+	0.918563i	$0.629350\pi$
$822$	−34.5305	−	59.8086i	−1.20439	−	2.08607i
$823$	−37.3573	−	16.6325i	−1.30219	−	0.579774i	−0.365790	−	0.930698i	$-0.619201\pi$
$823$	−37.3573	−	16.6325i	−1.30219	−	0.579774i	−0.936404	+	0.350924i	$0.885868\pi$
$824$	0.980552	+	0.436570i	0.0341591	+	0.0152086i
$825$	7.98760	+	13.8349i	0.278093	+	0.481670i
$826$	9.78097	+	7.10629i	0.340323	+	0.247259i
$827$	−3.64368	+	11.2141i	−0.126703	+	0.389952i	−0.994208	−	0.107477i	$-0.965723\pi$
$827$	−3.64368	+	11.2141i	−0.126703	+	0.389952i	0.867504	+	0.497429i	$0.165723\pi$
$828$	−4.50582	+	42.8700i	−0.156588	+	1.48984i
$829$	12.6123	+	5.61538i	0.438045	+	0.195030i	0.613896	−	0.789387i	$-0.289601\pi$
$829$	12.6123	+	5.61538i	0.438045	+	0.195030i	−0.175852	+	0.984417i	$0.556268\pi$
$830$	10.8227	−	7.86315i	0.375661	−	0.272934i
$831$	−3.00924	−	9.26150i	−0.104389	−	0.321278i
$832$	57.6388	−	25.6624i	1.99826	−	0.889685i
$833$	−21.4585	+	37.1671i	−0.743491	+	1.28776i
$834$	−23.0034	+	16.7130i	−0.796543	+	0.578722i
$835$	1.45374	−	13.8314i	0.0503087	−	0.478655i
$836$	15.2328	+	16.9177i	0.526837	+	0.585112i
$837$	−2.53382	+	2.81409i	−0.0875816	+	0.0972692i
$838$	−8.30383	−	79.0056i	−0.286851	−	2.72920i
$839$	7.79560	+	8.65789i	0.269134	+	0.298903i	0.862529	−	0.506008i	$-0.168879\pi$
$839$	7.79560	+	8.65789i	0.269134	+	0.298903i	−0.593395	+	0.804912i	$0.702213\pi$
$840$	6.28131	+	10.8795i	0.216726	+	0.375380i
$841$	14.4141	−	24.9659i	0.497037	−	0.860893i
$842$	−21.6856	+	4.60941i	−0.747334	+	0.158851i
$843$	−8.50364			−0.292881
$844$	4.26755	−	0.907095i	0.146895	−	0.0312235i
$845$	6.39117	+	19.6700i	0.219863	+	0.676668i
$846$	6.08385	−	18.7242i	0.209167	−	0.643751i
$847$	−2.85678	−	27.1805i	−0.0981601	−	0.933931i
$848$	7.75872	+	1.64917i	0.266436	+	0.0566326i
$849$	44.6286	+	9.48610i	1.53165	+	0.325562i
$850$	26.7172	−	29.6725i	0.916392	−	1.01776i
$851$	−43.3487	−	31.4947i	−1.48597	−	1.07962i
$852$	−46.7195	+	20.8009i	−1.60058	+	0.712626i
$853$	−18.2376			−0.624444			−0.312222	−	0.950009i	$-0.601073\pi$
$853$	−18.2376			−0.624444			−0.312222	+	0.950009i	$0.601073\pi$
$854$	47.3266	−	43.6307i	1.61948	−	1.49301i
$855$	−13.0314			−0.445665
$856$	−15.1226	+	6.73304i	−0.516881	+	0.230130i
$857$	40.7310	+	29.5928i	1.39134	+	1.01087i	0.995716	+	0.0924606i	$0.0294732\pi$
$857$	40.7310	+	29.5928i	1.39134	+	1.01087i	0.395629	+	0.918411i	$0.370527\pi$
$858$	35.6690	−	39.6145i	1.21772	−	1.35242i
$859$	−49.8985	−	10.6063i	−1.70252	−	0.361881i	−0.748848	−	0.662741i	$-0.769393\pi$
$859$	−49.8985	−	10.6063i	−1.70252	−	0.361881i	−0.953668	+	0.300860i	$0.902726\pi$
$860$	7.74278	+	1.64578i	0.264027	+	0.0561206i
$861$	−3.60942	−	34.3414i	−0.123009	−	1.17035i
$862$	12.6740	−	39.0066i	0.431678	−	1.32857i
$863$	9.13512	+	28.1150i	0.310963	+	0.957046i	0.977384	+	0.211470i	$0.0678252\pi$
$863$	9.13512	+	28.1150i	0.310963	+	0.957046i	−0.666421	+	0.745575i	$0.732175\pi$
$864$	−11.8068	+	2.50961i	−0.401675	+	0.0853787i
$865$	11.6450			0.395943
$866$	32.7588	−	6.96311i	1.11319	−	0.236616i
$867$	13.8137	−	23.9261i	0.469139	−	0.812572i
$868$	−12.1717	−	21.0820i	−0.413135	−	0.715571i
$869$	12.0123	+	13.3410i	0.407488	+	0.452561i
$870$	−0.262568	−	2.49817i	−0.00890190	−	0.0846959i
$871$	22.1470	−	24.5968i	0.750424	−	0.833430i
$872$	−0.303549	−	0.337125i	−0.0102795	−	0.0114165i
$873$	−1.09434	+	10.4120i	−0.0370379	+	0.352392i
$874$	−56.6437	+	41.1540i	−1.91600	+	1.39206i
$875$	−20.2119	+	35.0080i	−0.683286	+	1.18349i
$876$	−32.8918	+	14.6444i	−1.11131	+	0.494788i
$877$	−1.77511	−	5.46322i	−0.0599411	−	0.184480i	0.916602	−	0.399800i	$-0.130920\pi$
$877$	−1.77511	−	5.46322i	−0.0599411	−	0.184480i	−0.976543	+	0.215320i	$0.930920\pi$
$878$	−40.1914	+	29.2007i	−1.35639	+	0.985477i
$879$	−3.60990	−	1.60723i	−0.121759	−	0.0542105i
$880$	−0.674578	+	6.41818i	−0.0227400	+	0.216357i
$881$	−10.8991	+	33.5439i	−0.367199	+	1.13012i	0.581393	+	0.813623i	$0.302508\pi$
$881$	−10.8991	+	33.5439i	−0.367199	+	1.13012i	−0.948593	+	0.316500i	$0.897492\pi$
$882$	32.1474	+	23.3564i	1.08246	+	0.786452i
$883$	20.2089	+	35.0028i	0.680083	+	1.17794i	0.974955	+	0.222401i	$0.0713896\pi$
$883$	20.2089	+	35.0028i	0.680083	+	1.17794i	−0.294872	+	0.955537i	$0.595277\pi$
$884$	−68.0461	−	30.2961i	−2.28864	−	1.01897i
$885$	3.81266	+	1.69751i	0.128161	+	0.0570610i
$886$	15.2369	+	26.3911i	0.511895	+	0.886628i
$887$	−18.8828	−	13.7192i	−0.634023	−	0.460644i	0.223769	−	0.974642i	$-0.428164\pi$
$887$	−18.8828	−	13.7192i	−0.634023	−	0.460644i	−0.857792	+	0.513998i	$0.828164\pi$
$888$	6.00788	−	18.4904i	0.201611	−	0.620496i
$889$	1.03811	−	9.87699i	0.0348172	−	0.331264i
$890$	−19.1096	−	8.50814i	−0.640555	−	0.285194i
$891$	−16.9292	+	12.2998i	−0.567150	+	0.412059i
$892$	−11.5549	−	35.5624i	−0.386887	−	1.19072i
$893$	16.3320	−	7.27147i	0.546529	−	0.243330i
$894$	−56.1198	+	97.2024i	−1.87693	+	3.25093i
$895$	−1.73828	+	1.26293i	−0.0581043	+	0.0422153i
$896$	3.55997	−	33.8708i	0.118930	−	1.13154i
$897$	61.3303	+	68.1142i	2.04776	+	2.27427i
$898$	−11.3328	+	12.5863i	−0.378179	+	0.420011i
$899$	0.107500	+	1.02280i	0.00358533	+	0.0341122i
$900$	−13.8296	−	15.3593i	−0.460986	−	0.511977i
$901$	−8.07957	−	13.9942i	−0.269170	−	0.466216i
$902$	−8.15977	+	14.1331i	−0.271691	+	0.470582i
$903$	22.1759	−	4.71363i	0.737968	−	0.156860i
$904$	6.82439			0.226976
$905$	−26.6269	+	5.65973i	−0.885109	+	0.188136i
$906$	16.8846	+	51.9656i	0.560955	+	1.72644i
$907$	0.499891	−	1.53850i	0.0165986	−	0.0510852i	−0.942414	−	0.334448i	$-0.891450\pi$
$907$	0.499891	−	1.53850i	0.0165986	−	0.0510852i	0.959013	+	0.283363i	$0.0914501\pi$
$908$	1.66413	+	15.8331i	0.0552260	+	0.525441i
$909$	−10.6227	−	2.25793i	−0.352334	−	0.0748909i
$910$	54.1821	+	11.5168i	1.79612	+	0.381777i
$911$	−24.3368	+	27.0288i	−0.806314	+	0.895503i	−0.996270	−	0.0862900i	$-0.972499\pi$
$911$	−24.3368	+	27.0288i	−0.806314	+	0.895503i	0.189956	+	0.981793i	$0.439166\pi$
$912$	22.3401	+	16.2310i	0.739755	+	0.537464i
$913$	−9.24817	+	4.11755i	−0.306070	+	0.136271i
$914$	68.5715			2.26814
$915$	12.8488	−	18.1290i	0.424768	−	0.599326i
$916$	−4.62840			−0.152927
$917$	47.4955	−	21.1464i	1.56844	−	0.698315i
$918$	14.1526	+	10.2825i	0.467106	+	0.339372i
$919$	11.4978	−	12.7696i	0.379277	−	0.421230i	−0.523037	−	0.852310i	$-0.675201\pi$
$919$	11.4978	−	12.7696i	0.379277	−	0.421230i	0.902313	+	0.431081i	$0.141868\pi$
$920$	9.98557	+	2.12250i	0.329214	+	0.0699767i
$921$	39.5543	+	8.40753i	1.30336	+	0.277037i
$922$	7.00988	+	66.6946i	0.230858	+	2.19647i
$923$	−14.7227	+	45.3119i	−0.484604	+	1.49146i
$924$	−13.9042	−	42.7926i	−0.457413	−	1.40777i
$925$	25.1293	−	5.34140i	0.826247	−	0.175624i
$926$	−32.8069			−1.07810
$927$	2.15253	−	0.457535i	0.0706985	−	0.0150274i
$928$	−1.63911	+	2.83902i	−0.0538064	+	0.0931954i
$929$	−11.5819	−	20.0604i	−0.379990	−	0.658162i	0.611071	−	0.791576i	$-0.290739\pi$
$929$	−11.5819	−	20.0604i	−0.379990	−	0.658162i	−0.991060	+	0.133415i	$0.957406\pi$
$930$	−10.0579	−	11.1705i	−0.329812	−	0.366294i
$931$	3.77168	+	35.8852i	0.123612	+	1.17609i
$932$	−19.3465	+	21.4865i	−0.633717	+	0.703814i
$933$	−22.7945	−	25.3158i	−0.746257	−	0.828802i
$934$	−5.48140	+	52.1520i	−0.179357	+	1.70647i
$935$	10.6362	−	7.72768i	0.347842	−	0.252722i
$936$	−7.28564	+	12.6191i	−0.238139	+	0.412468i
$937$	2.44613	−	1.08909i	0.0799116	−	0.0355789i	−0.366392	−	0.930461i	$-0.619407\pi$
$937$	2.44613	−	1.08909i	0.0799116	−	0.0355789i	0.446303	+	0.894882i	$0.352740\pi$
$938$	−15.4422	−	47.5263i	−0.504207	−	1.55179i
$939$	−24.1279	+	17.5299i	−0.787384	+	0.572068i
$940$	−11.2706	−	5.01801i	−0.367608	−	0.163669i
$941$	5.08037	−	48.3365i	0.165615	−	1.57572i	−0.524108	−	0.851652i	$-0.675601\pi$
$941$	5.08037	−	48.3365i	0.165615	−	1.57572i	0.689723	−	0.724073i	$-0.257732\pi$
$942$	13.1681	−	40.5274i	0.429041	−	1.32045i
$943$	−22.7012	−	16.4934i	−0.739254	−	0.537099i
$944$	−1.93739	−	3.35565i	−0.0630566	−	0.109217i
$945$	−6.64425	−	2.95821i	−0.216138	−	0.0962307i
$946$	−9.78840	−	4.35808i	−0.318248	−	0.141693i
$947$	−27.8693	−	48.2710i	−0.905630	−	1.56860i	−0.820070	−	0.572263i	$-0.806065\pi$
$947$	−27.8693	−	48.2710i	−0.905630	−	1.56860i	−0.0855598	−	0.996333i	$-0.527268\pi$
$948$	−42.8855	−	31.1582i	−1.39286	−	1.01197i
$949$	−10.3652	+	31.9008i	−0.336468	+	1.03554i
$950$	3.50903	−	33.3862i	0.113848	−	1.08319i
$951$	30.9727	+	13.7899i	1.00436	+	0.447169i
$952$	−19.2229	+	13.9663i	−0.623018	+	0.452649i
$953$	−8.35678	−	25.7195i	−0.270703	−	0.833137i	−0.990325	−	0.138771i	$-0.955685\pi$
$953$	−8.35678	−	25.7195i	−0.270703	−	0.833137i	0.719622	−	0.694366i	$-0.244315\pi$
$954$	−13.6681	+	6.08543i	−0.442521	+	0.197023i
$955$	2.51794	−	4.36119i	0.0814785	−	0.141125i
$956$	11.9497	−	8.68196i	0.386481	−	0.280795i
$957$	−0.198696	+	1.89047i	−0.00642294	+	0.0611102i
$958$	12.5958	+	13.9890i	0.406951	+	0.451965i
$959$	−36.3382	+	40.3576i	−1.17342	+	1.30322i
$960$	−3.43729	−	32.7036i	−0.110938	−	1.05550i
$961$	−16.6252	−	18.4641i	−0.536295	−	0.595616i
$962$	−42.8628	−	74.2406i	−1.38195	−	2.39361i
$963$	−16.9697	+	29.3923i	−0.546840	+	0.947154i
$964$	43.0315	−	9.14664i	1.38595	−	0.294593i
$965$	−26.2057			−0.843593
$966$	135.360	−	28.7718i	4.35515	−	0.925716i
$967$	−6.20814	−	19.1067i	−0.199640	−	0.614430i	−0.999891	−	0.0147641i	$-0.995300\pi$
$967$	−6.20814	−	19.1067i	−0.199640	−	0.614430i	0.800251	−	0.599666i	$-0.204700\pi$
$968$	2.49020	−	7.66404i	0.0800380	−	0.246332i
$969$	−5.88024	−	55.9467i	−0.188901	−	1.79727i
$970$	11.4785	+	2.43984i	0.368554	+	0.0783385i
$971$	−20.4636	−	4.34968i	−0.656710	−	0.139588i	−0.132508	−	0.991182i	$-0.542303\pi$
$971$	−20.4636	−	4.34968i	−0.656710	−	0.139588i	−0.524202	+	0.851594i	$0.675636\pi$
$972$	33.5756	−	37.2894i	1.07694	−	1.19606i
$973$	18.0889	+	13.1423i	0.579902	+	0.421323i
$974$	28.5254	−	12.7003i	0.914013	−	0.406945i
$975$	−43.9463			−1.40741
$976$	−19.5442	+	6.60515i	−0.625595	+	0.211426i
$977$	60.1275			1.92365			0.961824	−	0.273669i	$-0.0882372\pi$
$977$	60.1275			1.92365			0.961824	+	0.273669i	$0.0882372\pi$
$978$	89.4330	−	39.8181i	2.85975	−	1.27324i
$979$	12.8064	+	9.30439i	0.409294	+	0.297369i
$980$	16.6617	−	18.5047i	0.532240	−	0.591112i
$981$	−0.909762	−	0.193376i	−0.0290465	−	0.00617402i
$982$	−55.2628	−	11.7465i	−1.76351	−	0.374845i
$983$	3.48984	+	33.2036i	0.111309	+	1.05903i	0.897490	+	0.441035i	$0.145388\pi$
$983$	3.48984	+	33.2036i	0.111309	+	1.05903i	−0.786182	+	0.617996i	$0.787945\pi$
$984$	3.14626	−	9.68320i	0.100299	−	0.308689i
$985$	−0.352665	−	1.08539i	−0.0112369	−	0.0345835i
$986$	4.64722	−	0.987797i	0.147998	−	0.0314579i
$987$	−35.3348			−1.12472
$988$	−61.2561	+	13.0204i	−1.94882	+	0.414233i
$989$	9.21161	−	15.9550i	0.292912	−	0.507339i
$990$	−6.08639	−	10.5419i	−0.193438	−	0.335045i
$991$	−20.1793	−	22.4114i	−0.641018	−	0.711922i	0.331838	−	0.943337i	$-0.392331\pi$
$991$	−20.1793	−	22.4114i	−0.641018	−	0.711922i	−0.972855	+	0.231414i	$0.925665\pi$
$992$	2.05051	+	19.5093i	0.0651038	+	0.619421i
$993$	−1.73283	+	1.92450i	−0.0549897	+	0.0610723i
$994$	48.1326	+	53.4567i	1.52667	+	1.69554i
$995$	3.57121	−	33.9778i	0.113215	−	1.07717i
$996$	24.1837	−	17.5705i	0.766289	−	0.556742i
$997$	18.2499	−	31.6097i	0.577979	−	1.00109i	−0.417732	−	0.908570i	$-0.637175\pi$
$997$	18.2499	−	31.6097i	0.577979	−	1.00109i	0.995711	−	0.0925188i	$-0.0294918\pi$
$998$	−30.7453	+	13.6887i	−0.973224	+	0.433307i
$999$	3.47822	+	10.7049i	0.110046	+	0.338687i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	61.2.i.a.56.2	yes	32
3.2	odd	2		549.2.bl.b.361.3		32
4.3	odd	2		976.2.bw.c.849.1		32
61.12	even	15	inner	61.2.i.a.12.2	✓	32
61.16	even	15		3721.2.a.j.1.4		16
61.45	even	30		3721.2.a.l.1.13		16
183.134	odd	30		549.2.bl.b.73.3		32
244.195	odd	30		976.2.bw.c.561.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.i.a.12.2	✓	32	61.12	even	15	inner
61.2.i.a.56.2	yes	32	1.1	even	1	trivial
549.2.bl.b.73.3		32	183.134	odd	30
549.2.bl.b.361.3		32	3.2	odd	2
976.2.bw.c.561.1		32	244.195	odd	30
976.2.bw.c.849.1		32	4.3	odd	2
3721.2.a.j.1.4		16	61.16	even	15
3721.2.a.l.1.13		16	61.45	even	30

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	61.i (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.94561 + 0.866241i) q^{2} +(1.86941 + 1.35820i) q^{3} +(1.69676 - 1.88444i) q^{4} +(-1.20434 - 0.255990i) q^{5} +(-4.81367 - 1.02318i) q^{6} +(0.404506 + 3.84862i) q^{7} +(-0.352600 + 1.08519i) q^{8} +(0.722916 + 2.22491i) q^{9} +O(q^{10})\)	\(q+(-1.94561 + 0.866241i) q^{2} +(1.86941 + 1.35820i) q^{3} +(1.69676 - 1.88444i) q^{4} +(-1.20434 - 0.255990i) q^{5} +(-4.81367 - 1.02318i) q^{6} +(0.404506 + 3.84862i) q^{7} +(-0.352600 + 1.08519i) q^{8} +(0.722916 + 2.22491i) q^{9} +(2.56491 - 0.545189i) q^{10} -1.98434 q^{11} +(5.73139 - 1.21824i) q^{12} +(2.72937 - 4.72741i) q^{13} +(-4.12084 - 7.13751i) q^{14} +(-1.90371 - 2.11428i) q^{15} +(0.276104 + 2.62696i) q^{16} +(3.60066 - 3.99894i) q^{17} +(-3.33381 - 3.70258i) q^{18} +(0.472909 - 4.49943i) q^{19} +(-2.52586 + 1.83515i) q^{20} +(-4.47102 + 7.74404i) q^{21} +(3.86075 - 1.71892i) q^{22} +(2.24547 + 6.91085i) q^{23} +(-2.13306 + 1.54976i) q^{24} +(-3.18283 - 1.41709i) q^{25} +(-1.21521 + 11.5620i) q^{26} +(0.471699 - 1.45174i) q^{27} +(7.93884 + 5.76791i) q^{28} +(-0.207283 - 0.359024i) q^{29} +(5.53535 + 2.46450i) q^{30} +(-2.26627 - 1.00901i) q^{31} +(-3.95380 - 6.84819i) q^{32} +(-3.70954 - 2.69514i) q^{33} +(-3.54143 + 10.8994i) q^{34} +(0.498045 - 4.73858i) q^{35} +(5.41932 + 2.41283i) q^{36} +(-5.96555 + 4.33423i) q^{37} +(2.97749 + 9.16378i) q^{38} +(11.5231 - 5.13041i) q^{39} +(0.702446 - 1.21667i) q^{40} +(-3.12409 + 2.26979i) q^{41} +(1.99066 - 18.9399i) q^{42} +(-1.69649 - 1.88414i) q^{43} +(-3.36695 + 3.73937i) q^{44} +(-0.301081 - 2.86459i) q^{45} +(-10.3553 - 11.5007i) q^{46} +(1.97577 + 3.42213i) q^{47} +(-3.05179 + 5.28586i) q^{48} +(-7.80121 + 1.65820i) q^{49} +7.42009 q^{50} +(12.1625 - 2.58521i) q^{51} +(-4.27744 - 13.1646i) q^{52} +(0.927961 - 2.85597i) q^{53} +(0.339815 + 3.23312i) q^{54} +(2.38981 + 0.507970i) q^{55} +(-4.31911 - 0.918056i) q^{56} +(6.99520 - 7.76896i) q^{57} +(0.714292 + 0.518963i) q^{58} +(-1.34010 + 0.596653i) q^{59} -7.21437 q^{60} +(1.71348 + 7.61997i) q^{61} +5.28333 q^{62} +(-8.27039 + 3.68221i) q^{63} +(9.35082 + 6.79377i) q^{64} +(-4.49725 + 4.99470i) q^{65} +(9.55196 + 2.03033i) q^{66} +(5.93084 + 1.26064i) q^{67} +(-1.42631 - 13.5705i) q^{68} +(-5.18865 + 15.9690i) q^{69} +(3.13575 + 9.65085i) q^{70} +(-8.53723 + 1.81465i) q^{71} -2.66935 q^{72} +(-6.01044 + 1.27756i) q^{73} +(7.85214 - 13.6003i) q^{74} +(-4.02532 - 6.97205i) q^{75} +(-7.67650 - 8.52561i) q^{76} +(-0.802678 - 7.63697i) q^{77} +(-17.9753 + 19.9636i) q^{78} +(-6.05353 - 6.72312i) q^{79} +(0.339951 - 3.23442i) q^{80} +(8.53141 - 6.19843i) q^{81} +(4.11208 - 7.12233i) q^{82} +(4.66057 - 2.07502i) q^{83} +(7.00694 + 21.5651i) q^{84} +(-5.36009 + 3.89433i) q^{85} +(4.93282 + 2.19623i) q^{86} +(0.100132 - 0.952694i) q^{87} +(0.699678 - 2.15339i) q^{88} +(-6.45373 - 4.68891i) q^{89} +(3.06721 + 5.31257i) q^{90} +(19.2980 + 8.59204i) q^{91} +(16.8331 + 7.49459i) q^{92} +(-2.86615 - 4.96432i) q^{93} +(-6.80846 - 4.94664i) q^{94} +(-1.72135 + 5.29776i) q^{95} +(1.90997 - 18.1721i) q^{96} +(4.08831 + 1.82023i) q^{97} +(13.7417 - 9.98393i) q^{98} +(-1.43451 - 4.41497i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 10 q^{2} - 4 q^{3} - 10 q^{4} + 2 q^{5} + q^{6} + q^{7} - 4 q^{8} - 2 q^{9}+O(q^{10}) \) 32 * q - 10 * q^2 - 4 * q^3 - 10 * q^4 + 2 * q^5 + q^6 + q^7 - 4 * q^8 - 2 * q^9	\( 32 q - 10 q^{2} - 4 q^{3} - 10 q^{4} + 2 q^{5} + q^{6} + q^{7} - 4 q^{8} - 2 q^{9} + 15 q^{10} - 18 q^{11} - 53 q^{12} + 11 q^{14} + 2 q^{15} + 6 q^{16} - 24 q^{17} - 15 q^{18} + 9 q^{19} - 4 q^{20} - 3 q^{21} + q^{22} - 2 q^{23} + 15 q^{24} + 28 q^{25} + 16 q^{26} + 35 q^{27} + 4 q^{28} - 4 q^{29} + 54 q^{30} - 11 q^{31} + 34 q^{32} - 35 q^{33} + 18 q^{34} - 58 q^{35} + 65 q^{36} - 14 q^{37} - 24 q^{38} + 17 q^{39} - 60 q^{40} + 11 q^{41} + 73 q^{42} + 40 q^{43} + 29 q^{44} + 12 q^{45} - 89 q^{46} + 40 q^{47} + 43 q^{48} + q^{49} - 56 q^{50} - 9 q^{51} - 67 q^{52} + 17 q^{53} - q^{54} - 60 q^{55} - 102 q^{56} - 38 q^{57} + 73 q^{58} - 11 q^{59} - 20 q^{60} - 55 q^{61} - 74 q^{62} - 58 q^{63} + 6 q^{64} + 59 q^{65} + 34 q^{66} - 13 q^{67} - 3 q^{68} - 32 q^{69} + 44 q^{70} + 63 q^{71} + 18 q^{72} - 46 q^{73} - 10 q^{74} + q^{75} + 55 q^{76} - 31 q^{77} - 103 q^{78} - 49 q^{79} + 74 q^{80} + 48 q^{81} + 39 q^{82} + 39 q^{83} + 21 q^{85} + 74 q^{86} + 17 q^{87} + 70 q^{88} + 32 q^{89} - 60 q^{90} + 70 q^{91} + 77 q^{92} + 67 q^{93} - 64 q^{94} + 47 q^{95} - 16 q^{96} + 37 q^{97} + 127 q^{98} - 31 q^{99}+O(q^{100}) \) 32 * q - 10 * q^2 - 4 * q^3 - 10 * q^4 + 2 * q^5 + q^6 + q^7 - 4 * q^8 - 2 * q^9 + 15 * q^10 - 18 * q^11 - 53 * q^12 + 11 * q^14 + 2 * q^15 + 6 * q^16 - 24 * q^17 - 15 * q^18 + 9 * q^19 - 4 * q^20 - 3 * q^21 + q^22 - 2 * q^23 + 15 * q^24 + 28 * q^25 + 16 * q^26 + 35 * q^27 + 4 * q^28 - 4 * q^29 + 54 * q^30 - 11 * q^31 + 34 * q^32 - 35 * q^33 + 18 * q^34 - 58 * q^35 + 65 * q^36 - 14 * q^37 - 24 * q^38 + 17 * q^39 - 60 * q^40 + 11 * q^41 + 73 * q^42 + 40 * q^43 + 29 * q^44 + 12 * q^45 - 89 * q^46 + 40 * q^47 + 43 * q^48 + q^49 - 56 * q^50 - 9 * q^51 - 67 * q^52 + 17 * q^53 - q^54 - 60 * q^55 - 102 * q^56 - 38 * q^57 + 73 * q^58 - 11 * q^59 - 20 * q^60 - 55 * q^61 - 74 * q^62 - 58 * q^63 + 6 * q^64 + 59 * q^65 + 34 * q^66 - 13 * q^67 - 3 * q^68 - 32 * q^69 + 44 * q^70 + 63 * q^71 + 18 * q^72 - 46 * q^73 - 10 * q^74 + q^75 + 55 * q^76 - 31 * q^77 - 103 * q^78 - 49 * q^79 + 74 * q^80 + 48 * q^81 + 39 * q^82 + 39 * q^83 + 21 * q^85 + 74 * q^86 + 17 * q^87 + 70 * q^88 + 32 * q^89 - 60 * q^90 + 70 * q^91 + 77 * q^92 + 67 * q^93 - 64 * q^94 + 47 * q^95 - 16 * q^96 + 37 * q^97 + 127 * q^98 - 31 * q^99

Introduction

L-functions

Modular forms

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