LMFDB - Embedded newform 600.2.b.f.251.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [600,2,Mod(251,600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(600, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("600.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.b (of order $2$, degree $1$, 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:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.1649659456.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{5} + 4x^{4} - 4x^{3} - 8x + 16 $ x^8 - x^7 - 2x^5 + 4x^4 - 4x^3 - 8x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 120)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.3
Root			$-0.578647 - 1.29041i$ of defining polynomial
Character	$\chi$	$=$	600.251
Dual form			600.2.b.f.251.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.578647 - 1.29041i) q^{2} +(-0.751690 - 1.56044i) q^{3} +(-1.33034 + 1.49339i) q^{4} +(-1.57865 + 1.87293i) q^{6} +4.28591i q^{7} +(2.69688 + 0.852541i) q^{8} +(-1.86993 + 2.34593i) q^{9} +O(q^{10})$	\(q+(-0.578647 - 1.29041i) q^{2} +(-0.751690 - 1.56044i) q^{3} +(-1.33034 + 1.49339i) q^{4} +(-1.57865 + 1.87293i) q^{6} +4.28591i q^{7} +(2.69688 + 0.852541i) q^{8} +(-1.86993 + 2.34593i) q^{9} -2.44673i q^{11} +(3.33034 + 0.953342i) q^{12} -2.71493i q^{13} +(5.53060 - 2.48003i) q^{14} +(-0.460411 - 3.97341i) q^{16} -1.16504i q^{17} +(4.10924 + 1.05551i) q^{18} +6.05444 q^{19} +(6.68789 - 3.22167i) q^{21} +(-3.15729 + 1.41579i) q^{22} +7.55782 q^{23} +(-0.696882 - 4.84916i) q^{24} +(-3.50338 + 1.57098i) q^{26} +(5.06628 + 1.15449i) q^{27} +(-6.40052 - 5.70170i) q^{28} +0.733092 q^{29} -0.469799i q^{31} +(-4.86093 + 2.89332i) q^{32} +(-3.81797 + 1.83918i) q^{33} +(-1.50338 + 0.674144i) q^{34} +(-1.01575 - 5.91340i) q^{36} -1.36664i q^{37} +(-3.50338 - 7.81273i) q^{38} +(-4.23647 + 2.04078i) q^{39} -4.69186i q^{41} +(-8.02722 - 6.76594i) q^{42} +1.50338 q^{43} +(3.65391 + 3.25497i) q^{44} +(-4.37330 - 9.75271i) q^{46} +4.07812 q^{47} +(-5.85418 + 3.70522i) q^{48} -11.3690 q^{49} +(-1.81797 + 0.875746i) q^{51} +(4.05444 + 3.61177i) q^{52} -1.00676 q^{53} +(-1.44181 - 7.20563i) q^{54} +(-3.65391 + 11.5586i) q^{56} +(-4.55106 - 9.44757i) q^{57} +(-0.424201 - 0.945992i) q^{58} +1.63484i q^{59} +10.9336i q^{61} +(-0.606236 + 0.271848i) q^{62} +(-10.0544 - 8.01433i) q^{63} +(6.54635 + 4.59841i) q^{64} +(4.58256 + 3.86252i) q^{66} +9.97632 q^{67} +(1.73985 + 1.54989i) q^{68} +(-5.68113 - 11.7935i) q^{69} +11.6359 q^{71} +(-7.04297 + 4.73250i) q^{72} +9.63593 q^{73} +(-1.76353 + 0.790800i) q^{74} +(-8.05444 + 9.04162i) q^{76} +10.4865 q^{77} +(5.08487 + 4.28591i) q^{78} +3.61177i q^{79} +(-2.00676 - 8.77342i) q^{81} +(-6.05444 + 2.71493i) q^{82} -5.45095i q^{83} +(-4.08594 + 14.2735i) q^{84} +(-0.869925 - 1.93998i) q^{86} +(-0.551058 - 1.14394i) q^{87} +(2.08594 - 6.59854i) q^{88} -7.75993i q^{89} +11.6359 q^{91} +(-10.0544 + 11.2867i) q^{92} +(-0.733092 + 0.353143i) q^{93} +(-2.35979 - 5.26246i) q^{94} +(8.16876 + 5.41030i) q^{96} -17.1156 q^{97} +(6.57865 + 14.6707i) q^{98} +(5.73985 + 4.57520i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + q^{2} + q^{4} - 7 q^{6} + 7 q^{8}+O(q^{10}) $ 8 * q + q^2 + q^4 - 7 * q^6 + 7 * q^8	$ 8 q + q^{2} + q^{4} - 7 q^{6} + 7 q^{8} + 15 q^{12} + 6 q^{14} - 7 q^{16} - 11 q^{18} - 4 q^{19} + 4 q^{21} - 14 q^{22} - 4 q^{23} + 9 q^{24} - 16 q^{26} + 12 q^{27} + 2 q^{28} + 11 q^{32} + 4 q^{33} - 19 q^{36} - 16 q^{38} - 16 q^{39} - 38 q^{42} + 30 q^{44} - 8 q^{46} + 28 q^{47} - 21 q^{48} - 16 q^{49} + 20 q^{51} - 20 q^{52} + 16 q^{53} - 15 q^{54} - 30 q^{56} + 4 q^{57} + 2 q^{58} - 34 q^{62} - 28 q^{63} + 25 q^{64} + 18 q^{66} + 32 q^{67} - 16 q^{68} - 20 q^{69} + 24 q^{71} - 41 q^{72} + 8 q^{73} - 32 q^{74} - 12 q^{76} + 12 q^{78} + 8 q^{81} + 4 q^{82} - 2 q^{84} + 8 q^{86} + 36 q^{87} - 14 q^{88} + 24 q^{91} - 28 q^{92} - 40 q^{94} + 17 q^{96} - 8 q^{97} + 47 q^{98} + 16 q^{99}+O(q^{100}) $ 8 * q + q^2 + q^4 - 7 * q^6 + 7 * q^8 + 15 * q^12 + 6 * q^14 - 7 * q^16 - 11 * q^18 - 4 * q^19 + 4 * q^21 - 14 * q^22 - 4 * q^23 + 9 * q^24 - 16 * q^26 + 12 * q^27 + 2 * q^28 + 11 * q^32 + 4 * q^33 - 19 * q^36 - 16 * q^38 - 16 * q^39 - 38 * q^42 + 30 * q^44 - 8 * q^46 + 28 * q^47 - 21 * q^48 - 16 * q^49 + 20 * q^51 - 20 * q^52 + 16 * q^53 - 15 * q^54 - 30 * q^56 + 4 * q^57 + 2 * q^58 - 34 * q^62 - 28 * q^63 + 25 * q^64 + 18 * q^66 + 32 * q^67 - 16 * q^68 - 20 * q^69 + 24 * q^71 - 41 * q^72 + 8 * q^73 - 32 * q^74 - 12 * q^76 + 12 * q^78 + 8 * q^81 + 4 * q^82 - 2 * q^84 + 8 * q^86 + 36 * q^87 - 14 * q^88 + 24 * q^91 - 28 * q^92 - 40 * q^94 + 17 * q^96 - 8 * q^97 + 47 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.578647	−	1.29041i	−0.409165	−	0.912460i
$2$	−0.578647	−	1.29041i	−0.409165	−	0.912460i
$3$	−0.751690	−	1.56044i	−0.433988	−	0.900919i
$3$	−0.751690	−	1.56044i	−0.433988	−	0.900919i
$4$	−1.33034	+	1.49339i	−0.665168	+	0.746694i
$5$		0			0
$5$		0			0
$6$	−1.57865	+	1.87293i	−0.644480	+	0.764621i
$7$			4.28591i			1.61992i	0.586484	+	0.809961i	$0.300512\pi$
$7$			4.28591i			1.61992i	−0.586484	+	0.809961i	$0.699488\pi$
$8$	2.69688	+	0.852541i	0.953492	+	0.301419i
$9$	−1.86993	+	2.34593i	−0.623308	+	0.781976i
$10$		0			0
$11$		−	2.44673i		−	0.737717i	−0.929486	−	0.368858i	$-0.879749\pi$
$11$		−	2.44673i		−	0.737717i	0.929486	−	0.368858i	$-0.120251\pi$
$12$	3.33034	+	0.953342i	0.961385	+	0.275206i
$13$		−	2.71493i		−	0.752985i	−0.926420	−	0.376493i	$-0.877130\pi$
$13$		−	2.71493i		−	0.752985i	0.926420	−	0.376493i	$-0.122870\pi$
$14$	5.53060	−	2.48003i	1.47811	−	0.662815i
$15$		0			0
$16$	−0.460411	−	3.97341i	−0.115103	−	0.993354i
$17$		−	1.16504i		−	0.282563i	−0.989969	−	0.141281i	$-0.954878\pi$
$17$		−	1.16504i		−	0.282563i	0.989969	−	0.141281i	$-0.0451222\pi$
$18$	4.10924	+	1.05551i	0.968558	+	0.248787i
$19$	6.05444			1.38898			0.694492	−	0.719501i	$-0.255629\pi$
$19$	6.05444			1.38898			0.694492	+	0.719501i	$0.255629\pi$
$20$		0			0
$21$	6.68789	−	3.22167i	1.45942	−	0.703027i
$22$	−3.15729	+	1.41579i	−0.673137	+	0.301848i
$23$	7.55782			1.57591			0.787957	−	0.615731i	$-0.211139\pi$
$23$	7.55782			1.57591			0.787957	+	0.615731i	$0.211139\pi$
$24$	−0.696882	−	4.84916i	−0.142250	−	0.989831i
$25$		0			0
$26$	−3.50338	+	1.57098i	−0.687069	+	0.308095i
$27$	5.06628	+	1.15449i	0.975005	+	0.222182i
$28$	−6.40052	−	5.70170i	−1.20959	−	1.07752i
$29$	0.733092			0.136132			0.0680659	−	0.997681i	$-0.478317\pi$
$29$	0.733092			0.136132			0.0680659	+	0.997681i	$0.478317\pi$
$30$		0			0
$31$		−	0.469799i		−	0.0843784i	−0.999110	−	0.0421892i	$-0.986567\pi$
$31$		−	0.469799i		−	0.0843784i	0.999110	−	0.0421892i	$-0.0134332\pi$
$32$	−4.86093	+	2.89332i	−0.859300	+	0.511472i
$33$	−3.81797	+	1.83918i	−0.664623	+	0.320160i
$34$	−1.50338	+	0.674144i	−0.257827	+	0.115615i
$35$		0			0
$36$	−1.01575	−	5.91340i	−0.169292	−	0.985566i
$37$		−	1.36664i		−	0.224674i	−0.993670	−	0.112337i	$-0.964166\pi$
$37$		−	1.36664i		−	0.224674i	0.993670	−	0.112337i	$-0.0358336\pi$
$38$	−3.50338	−	7.81273i	−0.568323	−	1.26739i
$39$	−4.23647	+	2.04078i	−0.678378	+	0.326787i
$40$		0			0
$41$		−	4.69186i		−	0.732745i	−0.930468	−	0.366372i	$-0.880600\pi$
$41$		−	4.69186i		−	0.732745i	0.930468	−	0.366372i	$-0.119400\pi$
$42$	−8.02722	−	6.76594i	−1.23863	−	1.04401i
$43$	1.50338			0.229263			0.114632	−	0.993408i	$-0.463431\pi$
$43$	1.50338			0.229263			0.114632	+	0.993408i	$0.463431\pi$
$44$	3.65391	+	3.25497i	0.550848	+	0.490706i
$45$		0			0
$46$	−4.37330	−	9.75271i	−0.644809	−	1.43796i
$47$	4.07812			0.594854			0.297427	−	0.954745i	$-0.403871\pi$
$47$	4.07812			0.594854			0.297427	+	0.954745i	$0.403871\pi$
$48$	−5.85418	+	3.70522i	−0.844977	+	0.534802i
$49$	−11.3690			−1.62415
$50$		0			0
$51$	−1.81797	+	0.875746i	−0.254566	+	0.122629i
$52$	4.05444	+	3.61177i	0.562249	+	0.500862i
$53$	−1.00676			−0.138289			−0.0691445	−	0.997607i	$-0.522027\pi$
$53$	−1.00676			−0.138289			−0.0691445	+	0.997607i	$0.522027\pi$
$54$	−1.44181	−	7.20563i	−0.196206	−	0.980563i
$55$		0			0
$56$	−3.65391	+	11.5586i	−0.488275	+	1.54458i
$57$	−4.55106	−	9.44757i	−0.602802	−	1.25136i
$58$	−0.424201	−	0.945992i	−0.0557003	−	0.124215i
$59$			1.63484i			0.212837i	0.994321	+	0.106419i	$0.0339384\pi$
$59$			1.63484i			0.212837i	−0.994321	+	0.106419i	$0.966062\pi$
$60$		0			0
$61$			10.9336i			1.39990i	0.714190	+	0.699952i	$0.246795\pi$
$61$			10.9336i			1.39990i	−0.714190	+	0.699952i	$0.753205\pi$
$62$	−0.606236	+	0.271848i	−0.0769920	+	0.0345247i
$63$	−10.0544	−	8.01433i	−1.26674	−	1.00971i
$64$	6.54635	+	4.59841i	0.818293	+	0.574801i
$65$		0			0
$66$	4.58256	+	3.86252i	0.564074	+	0.475443i
$67$	9.97632			1.21880			0.609401	−	0.792862i	$-0.291410\pi$
$67$	9.97632			1.21880			0.609401	+	0.792862i	$0.291410\pi$
$68$	1.73985	+	1.54989i	0.210988	+	0.187952i
$69$	−5.68113	−	11.7935i	−0.683928	−	1.41977i
$70$		0			0
$71$	11.6359			1.38093			0.690465	−	0.723365i	$-0.257406\pi$
$71$	11.6359			1.38093			0.690465	+	0.723365i	$0.257406\pi$
$72$	−7.04297	+	4.73250i	−0.830022	+	0.557731i
$73$	9.63593			1.12780			0.563900	−	0.825843i	$-0.309300\pi$
$73$	9.63593			1.12780			0.563900	+	0.825843i	$0.309300\pi$
$74$	−1.76353	+	0.790800i	−0.205006	+	0.0919287i
$75$		0			0
$76$	−8.05444	+	9.04162i	−0.923907	+	1.03714i
$77$	10.4865			1.19504
$78$	5.08487	+	4.28591i	0.575749	+	0.485284i
$79$			3.61177i			0.406355i	0.979142	+	0.203178i	$0.0651269\pi$
$79$			3.61177i			0.406355i	−0.979142	+	0.203178i	$0.934873\pi$
$80$		0			0
$81$	−2.00676	−	8.77342i	−0.222973	−	0.974825i
$82$	−6.05444	+	2.71493i	−0.668601	+	0.299814i
$83$		−	5.45095i		−	0.598319i	−0.954203	−	0.299160i	$-0.903294\pi$
$83$		−	5.45095i		−	0.598319i	0.954203	−	0.299160i	$-0.0967063\pi$
$84$	−4.08594	+	14.2735i	−0.445812	+	1.55737i
$85$		0			0
$86$	−0.869925	−	1.93998i	−0.0938065	−	0.209194i
$87$	−0.551058	−	1.14394i	−0.0590796	−	0.122644i
$88$	2.08594	−	6.59854i	0.222362	−	0.703407i
$89$		−	7.75993i		−	0.822551i	−0.911511	−	0.411275i	$-0.865083\pi$
$89$		−	7.75993i		−	0.822551i	0.911511	−	0.411275i	$-0.134917\pi$
$90$		0			0
$91$	11.6359			1.21978
$92$	−10.0544	+	11.2867i	−1.04825	+	1.17672i
$93$	−0.733092	+	0.353143i	−0.0760181	+	0.0366192i
$94$	−2.35979	−	5.26246i	−0.243393	−	0.542781i
$95$		0			0
$96$	8.16876	+	5.41030i	0.833721	+	0.552186i
$97$	−17.1156			−1.73783			−0.868915	−	0.494962i	$-0.835182\pi$
$97$	−17.1156			−1.73783			−0.868915	+	0.494962i	$0.835182\pi$
$98$	6.57865	+	14.6707i	0.664544	+	1.48197i
$99$	5.73985	+	4.57520i	0.576877	+	0.459825i
$100$		0			0
$101$	−5.36226			−0.533565			−0.266783	−	0.963757i	$-0.585961\pi$
$101$	−5.36226			−0.533565			−0.266783	+	0.963757i	$0.585961\pi$
$102$	2.18203	+	1.83918i	0.216054	+	0.182106i
$103$			13.0910i			1.28990i	0.764225	+	0.644949i	$0.223122\pi$
$103$			13.0910i			1.28990i	−0.764225	+	0.644949i	$0.776878\pi$
$104$	2.31459	−	7.32184i	0.226964	−	0.717965i
$105$		0			0
$106$	0.582557	+	1.29914i	0.0565830	+	0.126183i
$107$		−	8.82622i		−	0.853263i	−0.904425	−	0.426632i	$-0.859700\pi$
$107$		−	8.82622i		−	0.853263i	0.904425	−	0.426632i	$-0.140300\pi$
$108$	−8.46395	+	6.03005i	−0.814444	+	0.580242i
$109$		−	0.780183i		−	0.0747280i	−0.999302	−	0.0373640i	$-0.988104\pi$
$109$		−	0.780183i		−	0.0747280i	0.999302	−	0.0373640i	$-0.0118961\pi$
$110$		0			0
$111$	−2.13255	+	1.02729i	−0.202413	+	0.0975058i
$112$	17.0297	−	1.97328i	1.60916	−	0.186457i
$113$			2.91653i			0.274364i	0.990546	+	0.137182i	$0.0438045\pi$
$113$			2.91653i			0.274364i	−0.990546	+	0.137182i	$0.956195\pi$
$114$	−9.55782	+	11.3395i	−0.895172	+	1.06205i
$115$		0			0
$116$	−0.975259	+	1.09479i	−0.0905505	+	0.101649i
$117$	6.36902	+	5.07671i	0.588816	+	0.469342i
$118$	2.10961	−	0.945992i	0.194206	−	0.0870856i
$119$	4.99324			0.457730
$120$		0			0
$121$	5.01352			0.455774
$122$	14.1089	−	6.32669i	1.27736	−	0.572792i
$123$	−7.32134	+	3.52682i	−0.660143	+	0.318003i
$124$	0.701592	+	0.624991i	0.0630048	+	0.0561258i
$125$		0			0
$126$	−4.52384	+	17.6119i	−0.403016	+	1.56899i
$127$			2.93762i			0.260672i	0.991470	+	0.130336i	$0.0416056\pi$
$127$			2.93762i			0.260672i	−0.991470	+	0.130336i	$0.958394\pi$
$128$	2.14582	−	11.1083i	0.189666	−	0.981849i
$129$	−1.13007	−	2.34593i	−0.0994975	−	0.206547i
$130$		0			0
$131$		−	7.87658i		−	0.688180i	−0.938937	−	0.344090i	$-0.888187\pi$
$131$		−	7.87658i		−	0.688180i	0.938937	−	0.344090i	$-0.111813\pi$
$132$	2.33257	−	8.14843i	0.203024	−	0.709230i
$133$			25.9488i			2.25004i
$134$	−5.77276	−	12.8736i	−0.498691	−	1.11211i
$135$		0			0
$136$	0.993241	−	3.14197i	0.0851697	−	0.269421i
$137$		−	2.51333i		−	0.214728i	−0.994220	−	0.107364i	$-0.965759\pi$
$137$		−	2.51333i		−	0.214728i	0.994220	−	0.107364i	$-0.0342410\pi$
$138$	−11.9311	+	14.1553i	−1.01564	+	1.20498i
$139$	2.57474			0.218386			0.109193	−	0.994021i	$-0.465173\pi$
$139$	2.57474			0.218386			0.109193	+	0.994021i	$0.465173\pi$
$140$		0			0
$141$	−3.06548	−	6.36364i	−0.258160	−	0.535915i
$142$	−6.73309	−	15.0152i	−0.565029	−	1.26004i
$143$	−6.64269			−0.555490
$144$	10.1823	+	6.34990i	0.848523	+	0.529158i
$145$		0			0
$146$	−5.57580	−	12.4343i	−0.461456	−	1.02907i
$147$	8.54598	+	17.7406i	0.704860	+	1.46322i
$148$	2.04092	+	1.81809i	0.167763	+	0.149446i
$149$	16.1224			1.32080			0.660399	−	0.750915i	$-0.270387\pi$
$149$	16.1224			1.32080			0.660399	+	0.750915i	$0.270387\pi$
$150$		0			0
$151$			17.8468i			1.45235i	0.687511	+	0.726174i	$0.258703\pi$
$151$			17.8468i			1.45235i	−0.687511	+	0.726174i	$0.741297\pi$
$152$	16.3281	+	5.16166i	1.32438	+	0.418666i
$153$	2.73309	+	2.17853i	0.220957	+	0.176124i
$154$	−6.06795	−	13.5319i	−0.488970	−	1.09043i
$155$		0			0
$156$	2.58825	−	9.04162i	0.207226	−	0.723909i
$157$		−	23.2338i		−	1.85426i	−0.374737	−	0.927131i	$-0.622267\pi$
$157$		−	23.2338i		−	1.85426i	0.374737	−	0.927131i	$-0.377733\pi$
$158$	4.66067	−	2.08994i	0.370783	−	0.166266i
$159$	0.756770	+	1.57098i	0.0600158	+	0.124587i
$160$		0			0
$161$			32.3921i			2.55286i
$162$	−10.1601	+	7.66626i	−0.798256	+	0.602318i
$163$	−6.96956			−0.545898			−0.272949	−	0.962028i	$-0.587999\pi$
$163$	−6.96956			−0.545898			−0.272949	+	0.962028i	$0.587999\pi$
$164$	7.00676	+	6.24175i	0.547136	+	0.487399i
$165$		0			0
$166$	−7.03398	+	3.15417i	−0.545943	+	0.244811i
$167$	−9.93540			−0.768825			−0.384412	−	0.923162i	$-0.625596\pi$
$167$	−9.93540			−0.768825			−0.384412	+	0.923162i	$0.625596\pi$
$168$	20.7831	−	2.98677i	1.60345	−	0.230435i
$169$	5.62917			0.433013
$170$		0			0
$171$	−11.3213	+	14.2033i	−0.865765	+	1.08615i
$172$	−2.00000	+	2.24513i	−0.152499	+	0.171189i
$173$	8.01352			0.609256			0.304628	−	0.952471i	$-0.401468\pi$
$173$	8.01352			0.609256			0.304628	+	0.952471i	$0.401468\pi$
$174$	−1.15729	+	1.37303i	−0.0877342	+	0.104089i
$175$		0			0
$176$	−9.72187	+	1.12650i	−0.732813	+	0.0849132i
$177$	2.55106	−	1.22889i	0.191749	−	0.0923690i
$178$	−10.0135	+	4.49025i	−0.750545	+	0.336559i
$179$			23.5020i			1.75663i	0.478087	+	0.878313i	$0.341330\pi$
$179$			23.5020i			1.75663i	−0.478087	+	0.878313i	$0.658670\pi$
$180$		0			0
$181$		−	9.92011i		−	0.737356i	−0.929557	−	0.368678i	$-0.879811\pi$
$181$		−	9.92011i		−	0.737356i	0.929557	−	0.368678i	$-0.120189\pi$
$182$	−6.73309	−	15.0152i	−0.499090	−	1.11300i
$183$	17.0612	−	8.21868i	1.26120	−	0.607542i
$184$	20.3825	+	6.44335i	1.50262	+	0.475010i
$185$		0			0
$186$	0.879902	+	0.741647i	0.0645176	+	0.0543802i
$187$	−2.85053			−0.208451
$188$	−5.42526	+	6.09020i	−0.395678	+	0.444174i
$189$	−4.94804	+	21.7136i	−0.359917	+	1.57943i
$190$		0			0
$191$	−22.4865			−1.62706			−0.813532	−	0.581521i	$-0.802458\pi$
$191$	−22.4865			−1.62706			−0.813532	+	0.581521i	$0.802458\pi$
$192$	2.25470	−	13.6717i	0.162719	−	0.986672i
$193$	13.1156			0.944084			0.472042	−	0.881576i	$-0.343517\pi$
$193$	13.1156			0.944084			0.472042	+	0.881576i	$0.343517\pi$
$194$	9.90390	+	22.0863i	0.711059	+	1.58570i
$195$		0			0
$196$	15.1246	−	16.9784i	1.08033	−	1.21274i
$197$	−24.2786			−1.72978			−0.864890	−	0.501961i	$-0.832612\pi$
$197$	−24.2786			−1.72978			−0.864890	+	0.501961i	$0.832612\pi$
$198$	2.58256	−	10.0542i	0.183534	−	0.714521i
$199$		−	1.81809i		−	0.128881i	−0.997922	−	0.0644404i	$-0.979474\pi$
$199$		−	1.81809i		−	0.128881i	0.997922	−	0.0644404i	$-0.0205262\pi$
$200$		0			0
$201$	−7.49910	−	15.5674i	−0.528946	−	1.09804i
$202$	3.10286	+	6.91954i	0.218316	+	0.486857i
$203$			3.14197i			0.220523i
$204$	1.11068	−	3.87996i	0.0777630	−	0.271652i
$205$		0			0
$206$	16.8929	−	7.57509i	1.17698	−	0.527781i
$207$	−14.1326	+	17.7301i	−0.982280	+	1.23233i
$208$	−10.7875	+	1.24998i	−0.747981	+	0.0866707i
$209$		−	14.8136i		−	1.02468i
$210$		0			0
$211$	1.06120			0.0730557			0.0365279	−	0.999333i	$-0.488370\pi$
$211$	1.06120			0.0730557			0.0365279	+	0.999333i	$0.488370\pi$
$212$	1.33933	−	1.50348i	0.0919854	−	0.103259i
$213$	−8.74661	−	18.1571i	−0.599308	−	1.24411i
$214$	−11.3895	+	5.10726i	−0.778569	+	0.349125i
$215$		0			0
$216$	12.6789	+	7.43273i	0.862690	+	0.505733i
$217$	2.01352			0.136686
$218$	−1.00676	+	0.451450i	−0.0681863	+	0.0305761i
$219$	−7.24323	−	15.0363i	−0.489452	−	1.01606i
$220$		0			0
$221$	−3.16299			−0.212766
$222$	2.55962	+	2.15744i	0.171790	+	0.144798i
$223$		−	5.22551i		−	0.349926i	−0.984575	−	0.174963i	$-0.944019\pi$
$223$		−	5.22551i		−	0.349926i	0.984575	−	0.174963i	$-0.0559806\pi$
$224$	−12.4005	−	20.8335i	−0.828545	−	1.39200i
$225$		0			0
$226$	3.76353	−	1.68764i	0.250346	−	0.112260i
$227$			13.8951i			0.922248i	0.887336	+	0.461124i	$0.152554\pi$
$227$			13.8951i			0.922248i	−0.887336	+	0.461124i	$0.847446\pi$
$228$	20.1633	+	5.77195i	1.33535	+	0.382257i
$229$		−	0.233312i		−	0.0154177i	−0.999970	−	0.00770885i	$-0.997546\pi$
$229$		−	0.233312i		−	0.0154177i	0.999970	−	0.00770885i	$-0.00245383\pi$
$230$		0			0
$231$	−7.88256	−	16.3635i	−0.518635	−	1.07664i
$232$	1.97706	+	0.624991i	0.129801	+	0.0410327i
$233$		−	8.62188i		−	0.564838i	−0.959291	−	0.282419i	$-0.908863\pi$
$233$		−	8.62188i		−	0.564838i	0.959291	−	0.282419i	$-0.0911369\pi$
$234$	2.86564	−	11.1563i	0.187333	−	0.729310i
$235$		0			0
$236$	−2.44144	−	2.17488i	−0.158924	−	0.141573i
$237$	5.63593	−	2.71493i	0.366093	−	0.176353i
$238$	−2.88932	−	6.44335i	−0.187287	−	0.417660i
$239$	−20.1089			−1.30073			−0.650367	−	0.759620i	$-0.725385\pi$
$239$	−20.1089			−1.30073			−0.650367	+	0.759620i	$0.725385\pi$
$240$		0			0
$241$	−9.12420			−0.587741			−0.293871	−	0.955845i	$-0.594943\pi$
$241$	−9.12420			−0.587741			−0.293871	+	0.955845i	$0.594943\pi$
$242$	−2.90105	−	6.46951i	−0.186487	−	0.415876i
$243$	−12.1819	+	9.72631i	−0.781470	+	0.623943i
$244$	−16.3281	−	14.5454i	−1.04530	−	0.931172i
$245$		0			0
$246$	8.78753	+	7.40678i	0.560272	+	0.472239i
$247$		−	16.4374i		−	1.04588i
$248$	0.400523	−	1.26699i	0.0254332	−	0.0804542i
$249$	−8.50586	+	4.09742i	−0.539037	+	0.259663i
$250$		0			0
$251$		−	13.3064i		−	0.839895i	−0.907548	−	0.419947i	$-0.862049\pi$
$251$		−	13.3064i		−	0.839895i	0.907548	−	0.419947i	$-0.137951\pi$
$252$	25.3443	−	4.35341i	1.59654	−	0.274239i
$253$		−	18.4919i		−	1.16258i
$254$	3.79075	−	1.69984i	0.237853	−	0.106658i
$255$		0			0
$256$	−15.5760	+	3.65881i	−0.973503	+	0.228675i
$257$			30.2136i			1.88467i	0.334668	+	0.942336i	$0.391376\pi$
$257$			30.2136i			1.88467i	−0.334668	+	0.942336i	$0.608624\pi$
$258$	−2.37330	+	2.81573i	−0.147755	+	0.175300i
$259$	5.85729			0.363954
$260$		0			0
$261$	−1.37083	+	1.71978i	−0.0848521	+	0.106452i
$262$	−10.1641	+	4.55776i	−0.627937	+	0.281579i
$263$	−14.9286			−0.920540			−0.460270	−	0.887779i	$-0.652247\pi$
$263$	−14.9286			−0.920540			−0.460270	+	0.887779i	$0.652247\pi$
$264$	−11.8646	+	1.70508i	−0.730214	+	0.104941i
$265$		0			0
$266$	33.4847	−	15.0152i	2.05308	−	0.920639i
$267$	−12.1089	+	5.83306i	−0.741051	+	0.356977i
$268$	−13.2719	+	14.8985i	−0.810708	+	0.910071i
$269$	−4.85053			−0.295742			−0.147871	−	0.989007i	$-0.547242\pi$
$269$	−4.85053			−0.295742			−0.147871	+	0.989007i	$0.547242\pi$
$270$		0			0
$271$		−	14.8802i		−	0.903906i	−0.892042	−	0.451953i	$-0.850728\pi$
$271$		−	14.8802i		−	0.903906i	0.892042	−	0.451953i	$-0.149272\pi$
$272$	−4.62917	+	0.536396i	−0.280685	+	0.0325238i
$273$	−8.74661	−	18.1571i	−0.529369	−	1.09892i
$274$	−3.24323	+	1.45433i	−0.195931	+	0.0878591i
$275$		0			0
$276$	25.1701	+	7.20518i	1.51506	+	0.433701i
$277$			19.6832i			1.18265i	0.806434	+	0.591324i	$0.201395\pi$
$277$			19.6832i			1.18265i	−0.806434	+	0.591324i	$0.798605\pi$
$278$	−1.48986	−	3.32247i	−0.0893560	−	0.199269i
$279$	1.10212	+	0.878490i	0.0659819	+	0.0525938i
$280$		0			0
$281$			2.29836i			0.137109i	0.997647	+	0.0685544i	$0.0218387\pi$
$281$			2.29836i			0.137109i	−0.997647	+	0.0685544i	$0.978161\pi$
$282$	−6.43790	+	7.63803i	−0.383372	+	0.454838i
$283$	21.6123			1.28472			0.642358	−	0.766405i	$-0.277956\pi$
$283$	21.6123			1.28472			0.642358	+	0.766405i	$0.277956\pi$
$284$	−15.4797	+	17.3770i	−0.918551	+	1.03113i
$285$		0			0
$286$	3.84377	+	8.57182i	0.227287	+	0.506862i
$287$	20.1089			1.18699
$288$	2.30205	−	16.8137i	0.135650	−	0.990757i
$289$	15.6427			0.920158
$290$		0			0
$291$	12.8656	+	26.7079i	0.754197	+	1.56564i
$292$	−12.8190	+	14.3902i	−0.750177	+	0.842121i
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$	17.9477	−	21.2934i	1.04673	−	1.24186i
$295$		0			0
$296$	1.16511	−	3.68566i	0.0677209	−	0.214225i
$297$	2.82472	−	12.3958i	0.163907	−	0.719278i
$298$	−9.32917	−	20.8046i	−0.540424	−	1.20518i
$299$		−	20.5189i		−	1.18664i
$300$		0			0
$301$			6.44335i			0.371388i
$302$	23.0297	−	10.3270i	1.32521	−	0.594250i
$303$	4.03076	+	8.36747i	0.231561	+	0.480699i
$304$	−2.78753	−	24.0568i	−0.159876	−	1.37975i
$305$		0			0
$306$	1.22971	−	4.78742i	0.0702980	−	0.273679i
$307$	4.98308			0.284399			0.142200	−	0.989838i	$-0.454582\pi$
$307$	4.98308			0.284399			0.142200	+	0.989838i	$0.454582\pi$
$308$	−13.9505	+	15.6603i	−0.794905	+	0.892331i
$309$	20.4277	−	9.84040i	1.16209	−	0.559801i
$310$		0			0
$311$	11.0886			0.628777			0.314388	−	0.949294i	$-0.398201\pi$
$311$	11.0886			0.628777			0.314388	+	0.949294i	$0.398201\pi$
$312$	−13.1651	+	1.89198i	−0.745328	+	0.107113i
$313$	−11.2583			−0.636359			−0.318180	−	0.948030i	$-0.603072\pi$
$313$	−11.2583			−0.636359			−0.318180	+	0.948030i	$0.603072\pi$
$314$	−29.9813	+	13.4442i	−1.69194	+	0.758699i
$315$		0			0
$316$	−5.39376	−	4.80486i	−0.303423	−	0.270295i
$317$	−27.2110			−1.52832			−0.764161	−	0.645026i	$-0.776847\pi$
$317$	−27.2110			−1.52832			−0.764161	+	0.645026i	$0.776847\pi$
$318$	1.58932	−	1.88559i	0.0891244	−	0.105739i
$319$		−	1.79368i		−	0.100427i
$320$		0			0
$321$	−13.7728	+	6.63458i	−0.768721	+	0.370306i
$322$	41.7992	−	18.7436i	2.32938	−	1.04454i
$323$		−	7.05364i		−	0.392475i
$324$	15.7718	+	8.67473i	0.876210	+	0.481930i
$325$		0			0
$326$	4.03291	+	8.99362i	0.223362	+	0.498111i
$327$	−1.21743	+	0.586455i	−0.0673238	+	0.0324311i
$328$	4.00000	−	12.6534i	0.220863	−	0.698666i
$329$			17.4784i			0.963617i
$330$		0			0
$331$	−18.3195			−1.00693			−0.503467	−	0.864015i	$-0.667942\pi$
$331$	−18.3195			−1.00693			−0.503467	+	0.864015i	$0.667942\pi$
$332$	8.14037	+	7.25159i	0.446761	+	0.397983i
$333$	3.20603	+	2.55551i	0.175690	+	0.140041i
$334$	5.74909	+	12.8208i	0.314576	+	0.701522i
$335$		0			0
$336$	−15.8802	−	25.0905i	−0.866337	−	1.36880i
$337$	−2.54733			−0.138762			−0.0693810	−	0.997590i	$-0.522102\pi$
$337$	−2.54733			−0.138762			−0.0693810	+	0.997590i	$0.522102\pi$
$338$	−3.25730	−	7.26396i	−0.177174	−	0.395107i
$339$	4.55106	−	2.19232i	0.247180	−	0.119071i
$340$		0			0
$341$	−1.14947			−0.0622474
$342$	24.8792	+	6.39054i	1.34531	+	0.345561i
$343$		−	18.7252i		−	1.01107i
$344$	4.05444	+	1.28169i	0.218601	+	0.0691042i
$345$		0			0
$346$	−4.63699	−	10.3408i	−0.249286	−	0.555922i
$347$		−	29.3727i		−	1.57681i	−0.615156	−	0.788405i	$-0.710907\pi$
$347$		−	29.3727i		−	1.57681i	0.615156	−	0.788405i	$-0.289093\pi$
$348$	2.44144	+	0.698887i	0.130875	+	0.0374643i
$349$		−	23.5131i		−	1.25863i	−0.777152	−	0.629313i	$-0.783336\pi$
$349$		−	23.5131i		−	1.25863i	0.777152	−	0.629313i	$-0.216664\pi$
$350$		0			0
$351$	3.13436	−	13.7546i	0.167300	−	0.734165i
$352$	7.07918	+	11.8934i	0.377321	+	0.633920i
$353$			31.0677i			1.65357i	0.562522	+	0.826783i	$0.309831\pi$
$353$			31.0677i			1.65357i	−0.562522	+	0.826783i	$0.690169\pi$
$354$	−3.06194	−	2.58083i	−0.162740	−	0.137169i
$355$		0			0
$356$	11.5886	+	10.3233i	0.614193	+	0.547134i
$357$	−3.75337	−	7.79164i	−0.198649	−	0.412377i
$358$	30.3274	−	13.5994i	1.60285	−	0.718749i
$359$	11.3979			0.601556			0.300778	−	0.953694i	$-0.402754\pi$
$359$	11.3979			0.601556			0.300778	+	0.953694i	$0.402754\pi$
$360$		0			0
$361$	17.6562			0.929274
$362$	−12.8010	+	5.74024i	−0.672808	+	0.301700i
$363$	−3.76861	−	7.82328i	−0.197801	−	0.410616i
$364$	−15.4797	+	17.3770i	−0.811357	+	0.910800i
$365$		0			0
$366$	−20.4779	−	17.2603i	−1.07040	−	0.902210i
$367$		−	21.0209i		−	1.09728i	−0.836059	−	0.548640i	$-0.815146\pi$
$367$		−	21.0209i		−	1.09728i	0.836059	−	0.548640i	$-0.184854\pi$
$368$	−3.47970	−	30.0303i	−0.181392	−	1.56544i
$369$	11.0068	+	8.77342i	0.572989	+	0.456726i
$370$		0			0
$371$		−	4.31488i		−	0.224017i
$372$	0.447879	−	1.56459i	0.0232215	−	0.0811202i
$373$			10.3471i			0.535755i	0.963453	+	0.267878i	$0.0863223\pi$
$373$			10.3471i			0.535755i	−0.963453	+	0.267878i	$0.913678\pi$
$374$	1.64945	+	3.67836i	0.0852910	+	0.190204i
$375$		0			0
$376$	10.9982	+	3.47676i	0.567189	+	0.179300i
$377$		−	1.99029i		−	0.102505i
$378$	30.8827	−	6.17948i	1.58843	−	0.317838i
$379$	−17.5341			−0.900668			−0.450334	−	0.892860i	$-0.648695\pi$
$379$	−17.5341			−0.900668			−0.450334	+	0.892860i	$0.648695\pi$
$380$		0			0
$381$	4.58397	−	2.20818i	0.234844	−	0.113128i
$382$	13.0117	+	29.0168i	0.665737	+	1.48463i
$383$	24.7343			1.26386			0.631932	−	0.775023i	$-0.282262\pi$
$383$	24.7343			1.26386			0.631932	+	0.775023i	$0.282262\pi$
$384$	−18.9469	+	5.00161i	−0.966878	+	0.255237i
$385$		0			0
$386$	−7.58932	−	16.9246i	−0.386286	−	0.861439i
$387$	−2.81121	+	3.52682i	−0.142902	+	0.179278i
$388$	22.7695	−	25.5603i	1.15595	−	1.29763i
$389$	−24.2313			−1.22857			−0.614287	−	0.789083i	$-0.710556\pi$
$389$	−24.2313			−1.22857			−0.614287	+	0.789083i	$0.710556\pi$
$390$		0			0
$391$		−	8.80513i		−	0.445295i
$392$	−30.6609	−	9.69256i	−1.54861	−	0.489548i
$393$	−12.2909	+	5.92075i	−0.619994	+	0.298662i
$394$	14.0487	+	31.3295i	0.707765	+	1.57836i
$395$		0			0
$396$	−14.4685	+	2.48526i	−0.727068	+	0.124889i
$397$			21.8856i			1.09840i	0.835689	+	0.549202i	$0.185068\pi$
$397$			21.8856i			1.09840i	−0.835689	+	0.549202i	$0.814932\pi$
$398$	−2.34609	+	1.05203i	−0.117599	+	0.0527335i
$399$	40.4914	−	19.5054i	2.02711	−	0.976493i
$400$		0			0
$401$			21.4163i			1.06948i	0.845016	+	0.534740i	$0.179591\pi$
$401$			21.4163i			1.06948i	−0.845016	+	0.534740i	$0.820409\pi$
$402$	−15.7491	+	18.6850i	−0.785493	+	0.931922i
$403$	−1.27547			−0.0635357
$404$	7.13362	−	8.00794i	0.354911	−	0.398410i
$405$		0			0
$406$	4.05444	−	1.81809i	0.201218	−	0.0902302i
$407$	−3.34379			−0.165746
$408$	−5.64945	+	0.811893i	−0.279689	+	0.0401947i
$409$	−21.5455			−1.06536			−0.532679	−	0.846317i	$-0.678815\pi$
$409$	−21.5455			−1.06536			−0.532679	+	0.846317i	$0.678815\pi$
$410$		0			0
$411$	−3.92188	+	1.88924i	−0.193452	+	0.0931894i
$412$	−19.5500	−	17.4155i	−0.963159	−	0.857999i
$413$	−7.00676			−0.344780
$414$	31.0569	+	7.97738i	1.52636	+	0.392067i
$415$		0			0
$416$	7.85516	+	13.1971i	0.385131	+	0.647040i
$417$	−1.93540	−	4.01771i	−0.0947771	−	0.196748i
$418$	−19.1156	+	8.57182i	−0.934976	+	0.419261i
$419$		−	14.6547i		−	0.715930i	−0.933735	−	0.357965i	$-0.883471\pi$
$419$		−	14.6547i		−	0.715930i	0.933735	−	0.357965i	$-0.116529\pi$
$420$		0			0
$421$		−	19.0967i		−	0.930718i	−0.885122	−	0.465359i	$-0.845925\pi$
$421$		−	19.0967i		−	0.930718i	0.885122	−	0.465359i	$-0.154075\pi$
$422$	−0.614057	−	1.36938i	−0.0298918	−	0.0666605i
$423$	−7.62577	+	9.56697i	−0.370778	+	0.465162i
$424$	−2.71511	−	0.858303i	−0.131857	−	0.0416829i
$425$		0			0
$426$	−18.3690	+	21.7933i	−0.889982	+	1.05589i
$427$	−46.8604			−2.26774
$428$	13.1810	+	11.7418i	0.637126	+	0.567564i
$429$	4.99324	+	10.3655i	0.241076	+	0.500451i
$430$		0			0
$431$	27.8537			1.34166			0.670832	−	0.741609i	$-0.265937\pi$
$431$	27.8537			1.34166			0.670832	+	0.741609i	$0.265937\pi$
$432$	2.25470	−	20.6620i	0.108479	−	0.994099i
$433$	−24.0750			−1.15697			−0.578486	−	0.815692i	$-0.696356\pi$
$433$	−24.0750			−1.15697			−0.578486	+	0.815692i	$0.696356\pi$
$434$	−1.16511	−	2.59827i	−0.0559273	−	0.124721i
$435$		0			0
$436$	1.16511	+	1.03791i	0.0557989	+	0.0497067i
$437$	45.7583			2.18892
$438$	−15.2117	+	18.0474i	−0.726845	+	0.862340i
$439$			24.6249i			1.17528i	0.809122	+	0.587641i	$0.199943\pi$
$439$			24.6249i			1.17528i	−0.809122	+	0.587641i	$0.800057\pi$
$440$		0			0
$441$	21.2592	−	26.6709i	1.01234	−	1.27004i
$442$	1.83025	+	4.08156i	0.0870562	+	0.194140i
$443$			7.61113i			0.361616i	0.983518	+	0.180808i	$0.0578712\pi$
$443$			7.61113i			0.361616i	−0.983518	+	0.180808i	$0.942129\pi$
$444$	1.30287	−	4.55136i	0.0618316	−	0.215998i
$445$		0			0
$446$	−6.74307	+	3.02372i	−0.319294	+	0.143177i
$447$	−12.1190	−	25.1580i	−0.573211	−	1.18993i
$448$	−19.7084	+	28.0571i	−0.931132	+	1.32557i
$449$		−	11.2946i		−	0.533026i	−0.963831	−	0.266513i	$-0.914128\pi$
$449$		−	11.2946i		−	0.533026i	0.963831	−	0.266513i	$-0.0858715\pi$
$450$		0			0
$451$	−11.4797			−0.540558
$452$	−4.35551	−	3.87996i	−0.204866	−	0.182498i
$453$	27.8487	−	13.4152i	1.30845	−	0.630302i
$454$	17.9304	−	8.04033i	0.841514	−	0.377351i
$455$		0			0
$456$	−4.21923	−	29.3589i	−0.197584	−	1.37486i
$457$	29.5067			1.38027			0.690133	−	0.723682i	$-0.257552\pi$
$457$	29.5067			1.38027			0.690133	+	0.723682i	$0.257552\pi$
$458$	−0.301069	+	0.135005i	−0.0140680	+	0.00630838i
$459$	1.34502	−	5.90240i	0.0627803	−	0.275500i
$460$		0			0
$461$	−28.9508			−1.34838			−0.674188	−	0.738560i	$-0.735506\pi$
$461$	−28.9508			−1.34838			−0.674188	+	0.738560i	$0.735506\pi$
$462$	−16.5544	+	19.6404i	−0.770181	+	0.913755i
$463$			22.6025i			1.05043i	0.850971	+	0.525213i	$0.176014\pi$
$463$			22.6025i			1.05043i	−0.850971	+	0.525213i	$0.823986\pi$
$464$	−0.337524	−	2.91288i	−0.0156691	−	0.135227i
$465$		0			0
$466$	−11.1258	+	4.98902i	−0.515392	+	0.231112i
$467$		−	13.6141i		−	0.629984i	−0.949094	−	0.314992i	$-0.897998\pi$
$467$		−	13.6141i		−	0.629984i	0.949094	−	0.314992i	$-0.102002\pi$
$468$	−16.0544	+	2.75769i	−0.742117	+	0.127474i
$469$			42.7576i			1.97436i
$470$		0			0
$471$	−36.2549	+	17.4646i	−1.67054	+	0.804728i
$472$	−1.39376	+	4.40896i	−0.0641532	+	0.202939i
$473$		−	3.67836i		−	0.169131i
$474$	−6.76459	−	5.70170i	−0.310708	−	0.261888i
$475$		0			0
$476$	−6.64269	+	7.45684i	−0.304467	+	0.341784i
$477$	1.88256	−	2.36178i	0.0861967	−	0.108139i
$478$	11.6359	+	25.9488i	0.532215	+	1.18687i
$479$	−0.411425			−0.0187985			−0.00939924	−	0.999956i	$-0.502992\pi$
$479$	−0.411425			−0.0187985			−0.00939924	+	0.999956i	$0.502992\pi$
$480$		0			0
$481$	−3.71032			−0.169176
$482$	5.27968	+	11.7740i	0.240483	+	0.536290i
$483$	50.5459	−	24.3488i	2.29992	−	1.10791i
$484$	−6.66966	+	7.48712i	−0.303167	+	0.340324i
$485$		0			0
$486$	19.6000	+	10.0916i	0.889073	+	0.457765i
$487$			32.2250i			1.46025i	0.683312	+	0.730126i	$0.260539\pi$
$487$			32.2250i			1.46025i	−0.683312	+	0.730126i	$0.739461\pi$
$488$	−9.32134	+	29.4866i	−0.421957	+	1.33480i
$489$	5.23895	+	10.8756i	0.236913	+	0.491810i
$490$		0			0
$491$		−	14.1605i		−	0.639055i	−0.947577	−	0.319528i	$-0.896476\pi$
$491$		−	14.1605i		−	0.639055i	0.947577	−	0.319528i	$-0.103524\pi$
$492$	4.47294	−	15.6255i	0.201656	−	0.704450i
$493$		−	0.854079i		−	0.0384658i
$494$	−21.2110	+	9.51142i	−0.954328	+	0.427939i
$495$		0			0
$496$	−1.86671	+	0.216301i	−0.0838176	+	0.00971219i
$497$			49.8706i			2.23700i
$498$	10.2093	+	8.60512i	0.457488	+	0.385605i
$499$	−14.6018			−0.653665			−0.326833	−	0.945082i	$-0.605981\pi$
$499$	−14.6018			−0.653665			−0.326833	+	0.945082i	$0.605981\pi$
$500$		0			0
$501$	7.46834	+	15.5036i	0.333661	+	0.692648i
$502$	−17.1708	+	7.69972i	−0.766371	+	0.343655i
$503$	−30.2823			−1.35022			−0.675112	−	0.737716i	$-0.735905\pi$
$503$	−30.2823			−1.35022			−0.675112	+	0.737716i	$0.735905\pi$
$504$	−20.2831	−	30.1855i	−0.903480	−	1.34457i
$505$		0			0
$506$	−23.8622	+	10.7003i	−1.06081	+	0.475686i
$507$	−4.23139	−	8.78397i	−0.187923	−	0.390110i
$508$	−4.38701	−	3.90802i	−0.194642	−	0.173391i
$509$	−8.84197			−0.391913			−0.195957	−	0.980613i	$-0.562781\pi$
$509$	−8.84197			−0.391913			−0.195957	+	0.980613i	$0.562781\pi$
$510$		0			0
$511$			41.2987i			1.82695i
$512$	13.7344	+	17.9824i	0.606980	+	0.794717i
$513$	30.6734	+	6.98979i	1.35427	+	0.308607i
$514$	38.9880	−	17.4830i	1.71969	−	0.771142i
$515$		0			0
$516$	5.00676	+	1.43323i	0.220410	+	0.0630946i
$517$		−	9.97804i		−	0.438834i
$518$	−3.38930	−	7.55832i	−0.148917	−	0.332094i
$519$	−6.02368	−	12.5046i	−0.264410	−	0.548890i
$520$		0			0
$521$		−	38.6076i		−	1.69143i	−0.533634	−	0.845716i	$-0.679174\pi$
$521$		−	38.6076i		−	1.69143i	0.533634	−	0.845716i	$-0.320826\pi$
$522$	3.01245	+	0.773789i	0.131852	+	0.0338678i
$523$	13.8674			0.606381			0.303191	−	0.952930i	$-0.401948\pi$
$523$	13.8674			0.606381			0.303191	+	0.952930i	$0.401948\pi$
$524$	11.7628	+	10.4785i	0.513860	+	0.457756i
$525$		0			0
$526$	8.63841	+	19.2641i	0.376653	+	0.839956i
$527$	−0.547333			−0.0238422
$528$	9.06566	+	14.3236i	0.394532	+	0.623354i
$529$	34.1206			1.48350
$530$		0			0
$531$	−3.83521	−	3.05702i	−0.166434	−	0.132663i
$532$	−38.7516	−	34.5206i	−1.68009	−	1.49666i
$533$	−12.7380			−0.551746
$534$	14.5338	+	12.2502i	0.628940	+	0.530117i
$535$		0			0
$536$	26.9050	+	8.50522i	1.16212	+	0.367370i
$537$	36.6734	−	17.6662i	1.58258	−	0.762355i
$538$	2.80674	+	6.25919i	0.121007	+	0.269853i
$539$			27.8169i			1.19816i
$540$		0			0
$541$			5.19654i			0.223417i	0.993741	+	0.111708i	$0.0356323\pi$
$541$			5.19654i			0.223417i	−0.993741	+	0.111708i	$0.964368\pi$
$542$	−19.2016	+	8.61036i	−0.824778	+	0.369846i
$543$	−15.4797	+	7.45684i	−0.664298	+	0.320004i
$544$	3.37083	+	5.66317i	0.144523	+	0.242806i
$545$		0			0
$546$	−18.3690	+	21.7933i	−0.786122	+	0.932668i
$547$	13.1393			0.561796			0.280898	−	0.959738i	$-0.409368\pi$
$547$	13.1393			0.561796			0.280898	+	0.959738i	$0.409368\pi$
$548$	3.75337	+	3.34357i	0.160336	+	0.142830i
$549$	−25.6494	−	20.4450i	−1.09469	−	0.872572i
$550$		0			0
$551$	4.43846			0.189085
$552$	−5.26691	−	36.6491i	−0.224174	−	1.55989i
$553$	−15.4797			−0.658264
$554$	25.3995	−	11.3896i	1.07912	−	0.483898i
$555$		0			0
$556$	−3.42526	+	3.84508i	−0.145264	+	0.163068i
$557$	0.506781			0.0214730			0.0107365	−	0.999942i	$-0.496582\pi$
$557$	0.506781			0.0214730			0.0107365	+	0.999942i	$0.496582\pi$
$558$	0.495880	−	1.93052i	0.0209923	−	0.0817254i
$559$		−	4.08156i		−	0.172632i
$560$		0			0
$561$	2.14271	+	4.44807i	0.0904654	+	0.187798i
$562$	2.96584	−	1.32994i	0.125106	−	0.0561001i
$563$			13.0410i			0.549612i	0.961500	+	0.274806i	$0.0886136\pi$
$563$			13.0410i			0.549612i	−0.961500	+	0.274806i	$0.911386\pi$
$564$	13.5815	+	3.88784i	0.571884	+	0.163707i
$565$		0			0
$566$	−12.5059	−	27.8888i	−0.525660	−	1.17225i
$567$	37.6021	−	8.60079i	1.57914	−	0.361199i
$568$	31.3807	+	9.92011i	1.31671	+	0.416239i
$569$			30.7683i			1.28988i	0.764235	+	0.644938i	$0.223117\pi$
$569$			30.7683i			1.28988i	−0.764235	+	0.644938i	$0.776883\pi$
$570$		0			0
$571$	27.6769			1.15824			0.579120	−	0.815242i	$-0.303396\pi$
$571$	27.6769			1.15824			0.579120	+	0.815242i	$0.303396\pi$
$572$	8.83701	−	9.92011i	0.369494	−	0.414781i
$573$	16.9028	+	35.0887i	0.706126	+	1.46585i
$574$	−11.6359	−	25.9488i	−0.485674	−	1.08308i
$575$		0			0
$576$	−23.0287	+	6.75859i	−0.959530	+	0.281608i
$577$	33.4626			1.39307			0.696533	−	0.717525i	$-0.254725\pi$
$577$	33.4626			1.39307			0.696533	+	0.717525i	$0.254725\pi$
$578$	−9.05159	−	20.1855i	−0.376496	−	0.839608i
$579$	−9.85889	−	20.4661i	−0.409721	−	0.850543i
$580$		0			0
$581$	23.3623			0.969230
$582$	27.0195	−	32.0564i	1.12000	−	1.32878i
$583$			2.46327i			0.102018i
$584$	25.9870	+	8.21503i	1.07535	+	0.339940i
$585$		0			0
$586$	3.47188	+	7.74248i	0.143422	+	0.319839i
$587$		−	28.7031i		−	1.18471i	−0.805679	−	0.592353i	$-0.798199\pi$
$587$		−	28.7031i		−	1.18471i	0.805679	−	0.592353i	$-0.201801\pi$
$588$	−37.8627	−	10.8386i	−1.56143	−	0.446975i
$589$		−	2.84437i		−	0.117200i
$590$		0			0
$591$	18.2500	+	37.8853i	0.750704	+	1.55839i
$592$	−5.43022	+	0.629215i	−0.223181	+	0.0258606i
$593$		−	44.2574i		−	1.81744i	−0.417411	−	0.908718i	$-0.637062\pi$
$593$		−	44.2574i		−	1.81744i	0.417411	−	0.908718i	$-0.362938\pi$
$594$	−17.6302	+	3.52773i	−0.723377	+	0.144744i
$595$		0			0
$596$	−21.4482	+	24.0770i	−0.878553	+	0.986231i
$597$	−2.83701	+	1.36664i	−0.116111	+	0.0559328i
$598$	−26.4779	+	11.8732i	−1.08276	+	0.485531i
$599$	−24.1359			−0.986166			−0.493083	−	0.869982i	$-0.664130\pi$
$599$	−24.1359			−0.986166			−0.493083	+	0.869982i	$0.664130\pi$
$600$		0			0
$601$	19.7669			0.806308			0.403154	−	0.915132i	$-0.367914\pi$
$601$	19.7669			0.806308			0.403154	+	0.915132i	$0.367914\pi$
$602$	8.31459	−	3.72842i	0.338877	−	0.151959i
$603$	−18.6550	+	23.4037i	−0.759689	+	0.953074i
$604$	−26.6521	−	23.7422i	−1.08446	−	0.966056i
$605$		0			0
$606$	8.46512	−	10.0432i	0.343872	−	0.407975i
$607$			7.68877i			0.312078i	0.987751	+	0.156039i	$0.0498725\pi$
$607$			7.68877i			0.312078i	−0.987751	+	0.156039i	$0.950127\pi$
$608$	−29.4302	+	17.5174i	−1.19355	+	0.710426i
$609$	4.90284	−	2.36178i	0.198673	−	0.0957043i
$610$		0			0
$611$		−	11.0718i		−	0.447916i
$612$	−6.88932	+	1.18339i	−0.278484	+	0.0478355i
$613$		−	26.6091i		−	1.07473i	−0.843349	−	0.537366i	$-0.819419\pi$
$613$		−	26.6091i		−	1.07473i	0.843349	−	0.537366i	$-0.180581\pi$
$614$	−2.88344	−	6.43024i	−0.116366	−	0.259503i
$615$		0			0
$616$	28.2807	+	8.94014i	1.13946	+	0.360208i
$617$		−	25.0592i		−	1.00885i	−0.863456	−	0.504423i	$-0.831705\pi$
$617$		−	25.0592i		−	1.00885i	0.863456	−	0.504423i	$-0.168295\pi$
$618$	−24.5186	−	20.6661i	−0.986284	−	0.831314i
$619$	−20.1498			−0.809889			−0.404944	−	0.914341i	$-0.632709\pi$
$619$	−20.1498			−0.809889			−0.404944	+	0.914341i	$0.632709\pi$
$620$		0			0
$621$	38.2900	+	8.72542i	1.53652	+	0.350139i
$622$	−6.41638	−	14.3089i	−0.257273	−	0.573734i
$623$	33.2583			1.33247
$624$	10.0594	+	15.8937i	0.402698	+	0.636256i
$625$		0			0
$626$	6.51460	+	14.5279i	0.260376	+	0.580653i
$627$	−23.1156	+	11.1352i	−0.923149	+	0.444697i
$628$	34.6971	+	30.9088i	1.38457	+	1.23340i
$629$	−1.59218			−0.0634845
$630$		0			0
$631$		−	27.8036i		−	1.10684i	−0.832902	−	0.553421i	$-0.813322\pi$
$631$		−	27.8036i		−	1.10684i	0.832902	−	0.553421i	$-0.186678\pi$
$632$	−3.07918	+	9.74051i	−0.122483	+	0.387457i
$633$	−0.797690	−	1.65593i	−0.0317053	−	0.0658173i
$634$	15.7455	+	35.1134i	0.625336	+	1.39453i
$635$		0			0
$636$	−3.35284	−	0.959785i	−0.132949	−	0.0380580i
$637$			30.8661i			1.22296i
$638$	−2.31459	+	1.03791i	−0.0916354	+	0.0410911i
$639$	−21.7583	+	27.2971i	−0.860746	+	1.07986i
$640$		0			0
$641$			36.3093i			1.43413i	0.697006	+	0.717065i	$0.254515\pi$
$641$			36.3093i			1.43413i	−0.697006	+	0.717065i	$0.745485\pi$
$642$	16.5309	+	13.9335i	0.652423	+	0.549911i
$643$	−32.8571			−1.29576			−0.647878	−	0.761744i	$-0.724344\pi$
$643$	−32.8571			−1.29576			−0.647878	+	0.761744i	$0.724344\pi$
$644$	−48.3740	−	43.0924i	−1.90620	−	1.69808i
$645$		0			0
$646$	−9.10212	+	4.08156i	−0.358118	+	0.160587i
$647$	17.1329			0.673563			0.336781	−	0.941583i	$-0.390662\pi$
$647$	17.1329			0.673563			0.336781	+	0.941583i	$0.390662\pi$
$648$	2.06771	−	25.3717i	0.0812273	−	0.996696i
$649$	4.00000			0.157014
$650$		0			0
$651$	−1.51354	−	3.14197i	−0.0593203	−	0.123143i
$652$	9.27186	−	10.4083i	0.363114	−	0.407619i
$653$	−27.7583			−1.08627			−0.543134	−	0.839646i	$-0.682762\pi$
$653$	−27.7583			−1.08627			−0.543134	+	0.839646i	$0.682762\pi$
$654$	1.46123	+	1.23163i	0.0571386	+	0.0481607i
$655$		0			0
$656$	−18.6427	+	2.16018i	−0.727875	+	0.0843409i
$657$	−18.0185	+	22.6052i	−0.702968	+	0.881913i
$658$	22.5544	−	10.1138i	0.879263	−	0.394278i
$659$			15.3389i			0.597519i	0.954328	+	0.298760i	$0.0965729\pi$
$659$			15.3389i			0.597519i	−0.954328	+	0.298760i	$0.903427\pi$
$660$		0			0
$661$			38.9369i			1.51447i	0.653141	+	0.757236i	$0.273451\pi$
$661$			38.9369i			1.51447i	−0.653141	+	0.757236i	$0.726549\pi$
$662$	10.6005	+	23.6398i	0.412002	+	0.918787i
$663$	2.37759	+	4.93564i	0.0923378	+	0.191685i
$664$	4.64716	−	14.7006i	0.180345	−	0.570492i
$665$		0			0
$666$	1.44251	−	5.61585i	0.0558960	−	0.217610i
$667$	5.54057			0.214532
$668$	13.2174	−	14.8374i	0.511398	−	0.574076i
$669$	−8.15407	+	3.92796i	−0.315255	+	0.151864i
$670$		0			0
$671$	26.7516			1.03273
$672$	−23.1881	+	35.0106i	−0.894499	+	1.35056i
$673$	6.78966			0.261722			0.130861	−	0.991401i	$-0.458226\pi$
$673$	6.78966			0.261722			0.130861	+	0.991401i	$0.458226\pi$
$674$	1.47401	+	3.28711i	0.0567766	+	0.126615i
$675$		0			0
$676$	−7.48869	+	8.40653i	−0.288027	+	0.323328i
$677$	−40.6772			−1.56335			−0.781675	−	0.623685i	$-0.785635\pi$
$677$	−40.6772			−1.56335			−0.781675	+	0.623685i	$0.785635\pi$
$678$	−5.46246	−	4.60417i	−0.209784	−	0.176822i
$679$		−	73.3561i		−	2.81515i
$680$		0			0
$681$	21.6824	−	10.4448i	0.830870	−	0.400245i
$682$	0.665138	+	1.48329i	0.0254694	+	0.0567983i
$683$			8.14204i			0.311546i	0.987793	+	0.155773i	$0.0497869\pi$
$683$			8.14204i			0.311546i	−0.987793	+	0.155773i	$0.950213\pi$
$684$	−6.14979	−	35.8023i	−0.235143	−	1.36893i
$685$		0			0
$686$	−24.1633	+	10.8353i	−0.922559	+	0.413694i
$687$	−0.364069	+	0.175378i	−0.0138901	+	0.00669110i
$688$	−0.692172	−	5.97355i	−0.0263888	−	0.227739i
$689$			2.73328i			0.104130i
$690$		0			0
$691$	−2.10179			−0.0799560			−0.0399780	−	0.999201i	$-0.512729\pi$
$691$	−2.10179			−0.0799560			−0.0399780	+	0.999201i	$0.512729\pi$
$692$	−10.6607	+	11.9673i	−0.405258	+	0.454928i
$693$	−19.6089	+	24.6005i	−0.744880	+	0.934495i
$694$	−37.9030	+	16.9964i	−1.43878	+	0.645176i
$695$		0			0
$696$	−0.510879	−	3.55488i	−0.0193648	−	0.134747i
$697$	−5.46618			−0.207046
$698$	−30.3416	+	13.6058i	−1.14845	+	0.514986i
$699$	−13.4539	+	6.48098i	−0.508873	+	0.245133i
$700$		0			0
$701$	20.0135			0.755900			0.377950	−	0.925826i	$-0.376629\pi$
$701$	20.0135			0.755900			0.377950	+	0.925826i	$0.376629\pi$
$702$	−19.5628	+	3.91442i	−0.738349	+	0.147740i
$703$		−	8.27422i		−	0.312068i
$704$	11.2511	−	16.0171i	0.424040	−	0.603669i
$705$		0			0
$706$	40.0902	−	17.9772i	1.50881	−	0.676581i
$707$		−	22.9822i		−	0.864334i
$708$	−1.55856	+	5.44455i	−0.0585742	+	0.204619i
$709$			15.3500i			0.576480i	0.957558	+	0.288240i	$0.0930701\pi$
$709$			15.3500i			0.576480i	−0.957558	+	0.288240i	$0.906930\pi$
$710$		0			0
$711$	−8.47294	−	6.75373i	−0.317760	−	0.253285i
$712$	6.61566	−	20.9276i	0.247932	−	0.784295i
$713$		−	3.55066i		−	0.132973i
$714$	−7.88256	+	9.35200i	−0.294998	+	0.349990i
$715$		0			0
$716$	−35.0977	−	31.2656i	−1.31166	−	1.16845i
$717$	15.1156	+	31.3786i	0.564504	+	1.17186i
$718$	−6.59533	−	14.7080i	−0.246136	−	0.548896i
$719$	−5.77864			−0.215507			−0.107754	−	0.994178i	$-0.534366\pi$
$719$	−5.77864			−0.215507			−0.107754	+	0.994178i	$0.534366\pi$
$720$		0			0
$721$	−56.1070			−2.08953
$722$	−10.2167	−	22.7838i	−0.380226	−	0.847926i
$723$	6.85856	+	14.2377i	0.255073	+	0.529507i
$724$	14.8146	+	13.1971i	0.550579	+	0.490466i
$725$		0			0
$726$	−7.91457	+	9.38998i	−0.293737	+	0.348495i
$727$		−	25.0657i		−	0.929636i	−0.885406	−	0.464818i	$-0.846120\pi$
$727$		−	25.0657i		−	0.929636i	0.885406	−	0.464818i	$-0.153880\pi$
$728$	31.3807	+	9.92011i	1.16305	+	0.367664i
$729$	24.3343	+	11.6979i	0.901271	+	0.433257i
$730$		0			0
$731$		−	1.75149i		−	0.0647813i
$732$	−10.4235	+	36.4126i	−0.385262	+	1.34585i
$733$		−	14.9596i		−	0.552546i	−0.961079	−	0.276273i	$-0.910901\pi$
$733$		−	14.9596i		−	0.552546i	0.961079	−	0.276273i	$-0.0890994\pi$
$734$	−27.1256	+	12.1636i	−1.00122	+	0.448968i
$735$		0			0
$736$	−36.7380	+	21.8672i	−1.35418	+	0.806036i
$737$		−	24.4094i		−	0.899130i
$738$	4.95232	−	19.2800i	0.182297	−	0.709706i
$739$	9.76476			0.359202			0.179601	−	0.983739i	$-0.442519\pi$
$739$	9.76476			0.359202			0.179601	+	0.983739i	$0.442519\pi$
$740$		0			0
$741$	−25.6494	+	12.3558i	−0.942256	+	0.453901i
$742$	−5.56798	+	2.49679i	−0.204407	+	0.0916600i
$743$	−13.6457			−0.500613			−0.250307	−	0.968167i	$-0.580531\pi$
$743$	−13.6457			−0.500613			−0.250307	+	0.968167i	$0.580531\pi$
$744$	−2.27813	+	0.327395i	−0.0835204	+	0.0120029i
$745$		0			0
$746$	13.3521	−	5.98734i	0.488855	−	0.219212i
$747$	12.7875	+	10.1929i	0.467871	+	0.372937i
$748$	3.79216	−	4.25694i	0.138655	−	0.155649i
$749$	37.8284			1.38222
$750$		0			0
$751$		−	36.7841i		−	1.34227i	−0.741335	−	0.671135i	$-0.765807\pi$
$751$		−	36.7841i		−	1.34227i	0.741335	−	0.671135i	$-0.234193\pi$
$752$	−1.87761	−	16.2040i	−0.0684693	−	0.590901i
$753$	−20.7639	+	10.0023i	−0.756677	+	0.364504i
$754$	−2.56830	+	1.15168i	−0.0935319	+	0.0419415i
$755$		0			0
$756$	−25.8443	−	36.2757i	−0.939947	−	1.31934i
$757$		−	10.1994i		−	0.370702i	−0.982672	−	0.185351i	$-0.940658\pi$
$757$		−	10.1994i		−	0.370702i	0.982672	−	0.185351i	$-0.0593422\pi$
$758$	10.1461	+	22.6263i	0.368522	+	0.821824i
$759$	−28.8555	+	13.9002i	−1.04739	+	0.504545i
$760$		0			0
$761$		−	28.0668i		−	1.01742i	−0.860938	−	0.508710i	$-0.830123\pi$
$761$		−	28.0668i		−	1.01742i	0.860938	−	0.508710i	$-0.169877\pi$
$762$	−5.50197	−	4.63747i	−0.199315	−	0.167998i
$763$	3.34379			0.121053
$764$	29.9146	−	33.5810i	1.08227	−	1.21492i
$765$		0			0
$766$	−14.3124	−	31.9175i	−0.517129	−	1.15323i
$767$	4.43846			0.160263
$768$	17.4177	+	21.5551i	0.628507	+	0.777804i
$769$	16.3302			0.588883			0.294442	−	0.955669i	$-0.404866\pi$
$769$	16.3302			0.588883			0.294442	+	0.955669i	$0.404866\pi$
$770$		0			0
$771$	47.1464	−	22.7112i	1.69794	−	0.817925i
$772$	−17.4482	+	19.5867i	−0.627975	+	0.704941i
$773$	42.5099			1.52897			0.764487	−	0.644639i	$-0.222992\pi$
$773$	42.5099			1.52897			0.764487	+	0.644639i	$0.222992\pi$
$774$	6.17775	+	1.58684i	0.222055	+	0.0570377i
$775$		0			0
$776$	−46.1588	−	14.5918i	−1.65701	−	0.523814i
$777$	−4.40286	−	9.13993i	−0.157952	−	0.327893i
$778$	14.0213	+	31.2684i	0.502689	+	1.12103i
$779$		−	28.4065i		−	1.01777i
$780$		0			0
$781$		−	28.4700i		−	1.01874i
$782$	−11.3623	+	5.09506i	−0.406314	+	0.182199i
$783$	3.71405	+	0.846347i	0.132729	+	0.0302460i
$784$	5.23442	+	45.1738i	0.186944	+	1.61335i
$785$		0			0
$786$	14.7523	+	12.4343i	0.526197	+	0.443518i
$787$	−27.9997			−0.998083			−0.499042	−	0.866578i	$-0.666315\pi$
$787$	−27.9997			−0.998083			−0.499042	+	0.866578i	$0.666315\pi$
$788$	32.2987	−	36.2574i	1.15059	−	1.29162i
$789$	11.2217	+	23.2952i	0.399503	+	0.829331i
$790$		0			0
$791$	−12.5000			−0.444448
$792$	11.5792	+	17.2322i	0.411447	+	0.612321i
$793$	29.6839			1.05411
$794$	28.2414	−	12.6640i	1.00225	−	0.449429i
$795$		0			0
$796$	2.71511	+	2.41867i	0.0962345	+	0.0857274i
$797$	1.92561			0.0682086			0.0341043	−	0.999418i	$-0.489142\pi$
$797$	1.92561			0.0682086			0.0341043	+	0.999418i	$0.489142\pi$
$798$	−48.6003	−	40.9639i	−1.72043	−	1.45011i
$799$		−	4.75115i		−	0.168084i
$800$		0			0
$801$	18.2042	+	14.5105i	0.643215	+	0.512703i
$802$	27.6359	−	12.3925i	0.975859	−	0.437594i
$803$		−	23.5765i		−	0.831997i
$804$	33.2245	+	9.51084i	1.17174	+	0.335422i
$805$		0			0
$806$	0.738047	+	1.64588i	0.0259966	+	0.0579738i
$807$	3.64609	+	7.56894i	0.128349	+	0.266439i
$808$	−14.4614	−	4.57155i	−0.508750	−	0.160827i
$809$		−	30.3334i		−	1.06647i	−0.845968	−	0.533233i	$-0.820977\pi$
$809$		−	30.3334i		−	1.06647i	0.845968	−	0.533233i	$-0.179023\pi$
$810$		0			0
$811$	7.56798			0.265748			0.132874	−	0.991133i	$-0.457579\pi$
$811$	7.56798			0.265748			0.132874	+	0.991133i	$0.457579\pi$
$812$	−4.69217	−	4.17987i	−0.164663	−	0.146685i
$813$	−23.2196	+	11.1853i	−0.814345	+	0.392284i
$814$	1.93487	+	4.31488i	0.0678173	+	0.151236i
$815$		0			0
$816$	4.31671	+	6.82033i	0.151115	+	0.238759i
$817$	9.10212			0.318443
$818$	12.4672	+	27.8027i	0.435907	+	0.972097i
$819$	−21.7583	+	27.2971i	−0.760297	+	0.953836i
$820$		0			0
$821$	−28.8505			−1.00689			−0.503445	−	0.864027i	$-0.667934\pi$
$821$	−28.8505			−1.00689			−0.503445	+	0.864027i	$0.667934\pi$
$822$	4.70729	+	3.96765i	0.164186	+	0.138388i
$823$		−	15.3789i		−	0.536076i	−0.963408	−	0.268038i	$-0.913625\pi$
$823$		−	15.3789i		−	0.536076i	0.963408	−	0.268038i	$-0.0863752\pi$
$824$	−11.1606	+	35.3050i	−0.388800	+	1.22991i
$825$		0			0
$826$	4.05444	+	9.04162i	0.141072	+	0.314598i
$827$			48.0070i			1.66937i	0.550731	+	0.834683i	$0.314349\pi$
$827$			48.0070i			1.66937i	−0.550731	+	0.834683i	$0.685651\pi$
$828$	−7.67685	−	44.6924i	−0.266789	−	1.55317i
$829$		−	19.0600i		−	0.661982i	−0.943634	−	0.330991i	$-0.892617\pi$
$829$		−	19.0600i		−	0.661982i	0.943634	−	0.330991i	$-0.107383\pi$
$830$		0			0
$831$	30.7144	−	14.7956i	1.06547	−	0.513255i
$832$	12.4843	−	17.7729i	0.432816	−	0.616163i
$833$			13.2453i			0.458923i
$834$	−4.06460	+	4.82231i	−0.140746	+	0.166983i
$835$		0			0
$836$	22.1224	+	19.7070i	0.765119	+	0.681582i
$837$	0.542379	−	2.38013i	0.0187473	−	0.0822694i
$838$	−18.9107	+	8.47991i	−0.653258	+	0.292934i
$839$	56.8469			1.96257			0.981287	−	0.192552i	$-0.0616763\pi$
$839$	56.8469			1.96257			0.981287	+	0.192552i	$0.0616763\pi$
$840$		0			0
$841$	−28.4626			−0.981468
$842$	−24.6427	+	11.0503i	−0.849243	+	0.380817i
$843$	3.58645	−	1.72766i	0.123524	−	0.0595036i
$844$	−1.41175	+	1.58478i	−0.0485943	+	0.0545502i
$845$		0			0
$846$	16.7580	+	4.30451i	0.576151	+	0.147992i
$847$			21.4875i			0.738319i
$848$	0.463523	+	4.00027i	0.0159174	+	0.137370i
$849$	−16.2457	−	33.7246i	−0.557551	−	1.15742i
$850$		0			0
$851$		−	10.3288i		−	0.354067i
$852$	38.7516	+	11.0930i	1.32761	+	0.380041i
$853$		−	29.3057i		−	1.00341i	−0.865039	−	0.501704i	$-0.832707\pi$
$853$		−	29.3057i		−	1.00341i	0.865039	−	0.501704i	$-0.167293\pi$
$854$	27.1156	+	60.4694i	0.927878	+	2.06922i
$855$		0			0
$856$	7.52472	−	23.8033i	0.257190	−	0.813580i
$857$		−	30.9833i		−	1.05837i	−0.848507	−	0.529185i	$-0.822498\pi$
$857$		−	30.9833i		−	1.05837i	0.848507	−	0.529185i	$-0.177502\pi$
$858$	10.4865	−	12.4413i	0.358002	−	0.424739i
$859$	−1.13559			−0.0387457			−0.0193729	−	0.999812i	$-0.506167\pi$
$859$	−1.13559			−0.0387457			−0.0193729	+	0.999812i	$0.506167\pi$
$860$		0			0
$861$	−15.1156	−	31.3786i	−0.515139	−	1.06938i
$862$	−16.1174	−	35.9428i	−0.548962	−	1.22422i
$863$	12.8678			0.438024			0.219012	−	0.975722i	$-0.429717\pi$
$863$	12.8678			0.438024			0.219012	+	0.975722i	$0.429717\pi$
$864$	−27.9671	+	9.04647i	−0.951462	+	0.307767i
$865$		0			0
$866$	13.9309	+	31.0668i	0.473393	+	1.05569i
$867$	−11.7584	−	24.4094i	−0.399338	−	0.828988i
$868$	−2.67866	+	3.00696i	−0.0909195	+	0.102063i
$869$	8.83701			0.299775
$870$		0			0
$871$		−	27.0850i		−	0.917740i
$872$	0.665138	−	2.10406i	0.0225244	−	0.0712525i
$873$	32.0050	−	40.1520i	1.08320	−	1.35894i
$874$	−26.4779	−	59.0472i	−0.895628	−	1.99730i
$875$		0			0
$876$	32.0909	+	9.18634i	1.08425	+	0.310378i
$877$		−	35.8017i		−	1.20894i	−0.796629	−	0.604469i	$-0.793385\pi$
$877$		−	35.8017i		−	1.20894i	0.796629	−	0.604469i	$-0.206615\pi$
$878$	31.7763	−	14.2491i	1.07240	−	0.480884i
$879$	4.51014	+	9.36262i	0.152123	+	0.315793i
$880$		0			0
$881$			26.0081i			0.876234i	0.898918	+	0.438117i	$0.144354\pi$
$881$			26.0081i			0.876234i	−0.898918	+	0.438117i	$0.855646\pi$
$882$	−46.7181	−	12.0002i	−1.57308	−	0.404067i
$883$	−41.3226			−1.39062			−0.695308	−	0.718712i	$-0.744732\pi$
$883$	−41.3226			−1.39062			−0.695308	+	0.718712i	$0.744732\pi$
$884$	4.20784	−	4.72357i	0.141525	−	0.158871i
$885$		0			0
$886$	9.82151	−	4.40415i	0.329960	−	0.147960i
$887$	14.9286			0.501255			0.250627	−	0.968084i	$-0.419363\pi$
$887$	14.9286			0.501255			0.250627	+	0.968084i	$0.419363\pi$
$888$	−6.62705	+	0.952386i	−0.222389	+	0.0319600i
$889$	−12.5904			−0.422268
$890$		0			0
$891$	−21.4662	+	4.90999i	−0.719144	+	0.164491i
$892$	7.80371	+	6.95168i	0.261287	+	0.232760i
$893$	24.6907			0.826242
$894$	−25.4516	+	30.1961i	−0.851227	+	1.00991i
$895$		0			0
$896$	47.6094	+	9.19681i	1.59052	+	0.307244i
$897$	−32.0185	+	15.4239i	−1.06907	+	0.514988i
$898$	−14.5747	+	6.53559i	−0.486365	+	0.218096i
$899$		−	0.344406i		−	0.0114866i
$900$		0			0
$901$			1.17291i			0.0390753i
$902$	6.64269	+	14.8136i	0.221177	+	0.493238i
$903$	10.0544	−	4.84340i	0.334591	−	0.161178i
$904$	−2.48646	+	7.86553i	−0.0826984	+	0.261604i
$905$		0			0
$906$	−33.4258	−	28.1737i	−1.11050	−	0.936009i
$907$	39.4794			1.31089			0.655447	−	0.755241i	$-0.272480\pi$
$907$	39.4794			1.31089			0.655447	+	0.755241i	$0.272480\pi$
$908$	−20.7507	−	18.4851i	−0.688636	−	0.613450i
$909$	10.0270	−	12.5795i	0.332576	−	0.417235i
$910$		0			0
$911$	−47.8266			−1.58457			−0.792284	−	0.610153i	$-0.791108\pi$
$911$	−47.8266			−1.58457			−0.792284	+	0.610153i	$0.791108\pi$
$912$	−35.4437	+	22.4330i	−1.17366	+	0.742831i
$913$	−13.3370			−0.441390
$914$	−17.0740	−	38.0759i	−0.564757	−	1.25944i
$915$		0			0
$916$	0.348425	+	0.310383i	0.0115123	+	0.0102554i
$917$	33.7583			1.11480
$918$	−8.39483	+	1.67977i	−0.277071	+	0.0554405i
$919$			30.2025i			0.996290i	0.867094	+	0.498145i	$0.165985\pi$
$919$			30.2025i			0.996290i	−0.867094	+	0.498145i	$0.834015\pi$
$920$		0			0
$921$	−3.74573	−	7.77578i	−0.123426	−	0.256221i
$922$	16.7523	+	37.3586i	0.551708	+	1.23034i
$923$		−	31.5907i		−	1.03982i
$924$	34.9234	+	9.99718i	1.14890	+	0.328883i
$925$		0			0
$926$	29.1665	−	13.0788i	0.958472	−	0.429797i
$927$	−30.7106	−	24.4793i	−1.00867	−	0.804005i
$928$	−3.56351	+	2.12107i	−0.116978	+	0.0696276i
$929$		−	2.81266i		−	0.0922804i	−0.998935	−	0.0461402i	$-0.985308\pi$
$929$		−	2.81266i		−	0.0922804i	0.998935	−	0.0461402i	$-0.0146921\pi$
$930$		0			0
$931$	−68.8330			−2.25591
$932$	12.8758	+	11.4700i	0.421761	+	0.375712i
$933$	−8.33518	−	17.3031i	−0.272882	−	0.566477i
$934$	−17.5678	+	7.87774i	−0.574836	+	0.257767i
$935$		0			0
$936$	12.8484	+	19.1211i	0.419963	+	0.624994i
$937$	20.7171			0.676798			0.338399	−	0.941003i	$-0.390115\pi$
$937$	20.7171			0.676798			0.338399	+	0.941003i	$0.390115\pi$
$938$	55.1750	−	24.7415i	1.80153	−	0.807840i
$939$	8.46278	+	17.5679i	0.276172	+	0.573308i
$940$		0			0
$941$	41.0867			1.33939			0.669695	−	0.742636i	$-0.266425\pi$
$941$	41.0867			1.33939			0.669695	+	0.742636i	$0.266425\pi$
$942$	43.5154	+	36.6780i	1.41781	+	1.19503i
$943$		−	35.4602i		−	1.15474i
$944$	6.49588	−	0.752696i	0.211423	−	0.0244982i
$945$		0			0
$946$	−4.74661	+	2.12847i	−0.154326	+	0.0692026i
$947$			12.3990i			0.402913i	0.979497	+	0.201456i	$0.0645674\pi$
$947$			12.3990i			0.402913i	−0.979497	+	0.201456i	$0.935433\pi$
$948$	−3.44325	+	12.0284i	−0.111831	+	0.390664i
$949$		−	26.1608i		−	0.849217i
$950$		0			0
$951$	20.4542	+	42.4610i	0.663274	+	1.37689i
$952$	13.4662	+	4.25694i	0.436442	+	0.137968i
$953$			24.4649i			0.792496i	0.918144	+	0.396248i	$0.129688\pi$
$953$			24.4649i			0.792496i	−0.918144	+	0.396248i	$0.870312\pi$
$954$	−4.13702	−	1.06265i	−0.133941	−	0.0344045i
$955$		0			0
$956$	26.7516	−	30.0303i	0.865207	−	0.971250i
$957$	−2.79892	+	1.34829i	−0.0904762	+	0.0435840i
$958$	0.238070	+	0.530908i	0.00769168	+	0.0171529i
$959$	10.7719			0.347842
$960$		0			0
$961$	30.7793			0.992880
$962$	2.14697	+	4.78785i	0.0692209	+	0.154367i
$963$	20.7057	+	16.5044i	0.667232	+	0.531846i
$964$	12.1382	−	13.6260i	0.390947	−	0.438863i
$965$		0			0
$966$	−60.6682	−	51.1357i	−1.95197	−	1.64526i
$967$			3.64391i			0.117180i	0.998282	+	0.0585901i	$0.0186605\pi$
$967$			3.64391i			0.117180i	−0.998282	+	0.0585901i	$0.981340\pi$
$968$	13.5209	+	4.27423i	0.434577	+	0.137379i
$969$	−11.0068	+	5.30215i	−0.353588	+	0.170330i
$970$		0			0
$971$			27.1170i			0.870225i	0.900376	+	0.435113i	$0.143291\pi$
$971$			27.1170i			0.870225i	−0.900376	+	0.435113i	$0.856709\pi$
$972$	1.68089	−	31.1316i	0.0539145	−	0.998546i
$973$			11.0351i			0.353769i
$974$	41.5836	−	18.6469i	1.33242	−	0.597484i
$975$		0			0
$976$	43.4437	−	5.03395i	1.39060	−	0.161133i
$977$			41.8998i			1.34049i	0.742139	+	0.670246i	$0.233812\pi$
$977$			41.8998i			1.34049i	−0.742139	+	0.670246i	$0.766188\pi$
$978$	11.0025	−	13.0535i	0.351820	−	0.417406i
$979$	−18.9864			−0.606809
$980$		0			0
$981$	1.83025	+	1.45888i	0.0584355	+	0.0465786i
$982$	−18.2729	+	8.19393i	−0.583112	+	0.261479i
$983$	0.734322			0.0234212			0.0117106	−	0.999931i	$-0.496272\pi$
$983$	0.734322			0.0234212			0.0117106	+	0.999931i	$0.496272\pi$
$984$	−22.7516	+	3.26967i	−0.725293	+	0.104233i
$985$		0			0
$986$	−1.10212	+	0.494210i	−0.0350985	+	0.0157388i
$987$	27.2740	−	13.1384i	0.868141	−	0.418199i
$988$	24.5473	+	21.8672i	0.780955	+	0.695689i
$989$	11.3623			0.361299
$990$		0			0
$991$			25.5433i			0.811408i	0.914004	+	0.405704i	$0.132974\pi$
$991$			25.5433i			0.811408i	−0.914004	+	0.405704i	$0.867026\pi$
$992$	1.35928	+	2.28366i	0.0431572	+	0.0725064i
$993$	13.7706	+	28.5865i	0.436997	+	0.907165i
$994$	64.3537	−	28.8574i	2.04117	−	0.915302i
$995$		0			0
$996$	5.19661	−	18.1535i	0.164661	−	0.575215i
$997$		−	23.4092i		−	0.741378i	−0.928757	−	0.370689i	$-0.879122\pi$
$997$		−	23.4092i		−	0.741378i	0.928757	−	0.370689i	$-0.120878\pi$
$998$	8.44926	+	18.8423i	0.267457	+	0.596443i
$999$	1.57777	−	6.92377i	0.0499184	−	0.219058i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.b.f.251.3		8
3.2	odd	2		600.2.b.e.251.6		8
4.3	odd	2		2400.2.b.f.2351.6		8
5.2	odd	4		600.2.m.c.299.15		16
5.3	odd	4		600.2.m.c.299.2		16
5.4	even	2		120.2.b.a.11.6	yes	8
8.3	odd	2		600.2.b.e.251.5		8
8.5	even	2		2400.2.b.e.2351.6		8
12.11	even	2		2400.2.b.e.2351.5		8
15.2	even	4		600.2.m.d.299.2		16
15.8	even	4		600.2.m.d.299.15		16
15.14	odd	2		120.2.b.b.11.3	yes	8
20.3	even	4		2400.2.m.d.1199.4		16
20.7	even	4		2400.2.m.d.1199.13		16
20.19	odd	2		480.2.b.b.431.3		8
24.5	odd	2		2400.2.b.f.2351.5		8
24.11	even	2	inner	600.2.b.f.251.4		8
40.3	even	4		600.2.m.d.299.1		16
40.13	odd	4		2400.2.m.c.1199.4		16
40.19	odd	2		120.2.b.b.11.4	yes	8
40.27	even	4		600.2.m.d.299.16		16
40.29	even	2		480.2.b.a.431.3		8
40.37	odd	4		2400.2.m.c.1199.13		16
60.23	odd	4		2400.2.m.c.1199.14		16
60.47	odd	4		2400.2.m.c.1199.3		16
60.59	even	2		480.2.b.a.431.4		8
120.29	odd	2		480.2.b.b.431.4		8
120.53	even	4		2400.2.m.d.1199.14		16
120.59	even	2		120.2.b.a.11.5	✓	8
120.77	even	4		2400.2.m.d.1199.3		16
120.83	odd	4		600.2.m.c.299.16		16
120.107	odd	4		600.2.m.c.299.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
120.2.b.a.11.5	✓	8	120.59	even	2
120.2.b.a.11.6	yes	8	5.4	even	2
120.2.b.b.11.3	yes	8	15.14	odd	2
120.2.b.b.11.4	yes	8	40.19	odd	2
480.2.b.a.431.3		8	40.29	even	2
480.2.b.a.431.4		8	60.59	even	2
480.2.b.b.431.3		8	20.19	odd	2
480.2.b.b.431.4		8	120.29	odd	2
600.2.b.e.251.5		8	8.3	odd	2
600.2.b.e.251.6		8	3.2	odd	2
600.2.b.f.251.3		8	1.1	even	1	trivial
600.2.b.f.251.4		8	24.11	even	2	inner
600.2.m.c.299.1		16	120.107	odd	4
600.2.m.c.299.2		16	5.3	odd	4
600.2.m.c.299.15		16	5.2	odd	4
600.2.m.c.299.16		16	120.83	odd	4
600.2.m.d.299.1		16	40.3	even	4
600.2.m.d.299.2		16	15.2	even	4
600.2.m.d.299.15		16	15.8	even	4
600.2.m.d.299.16		16	40.27	even	4
2400.2.b.e.2351.5		8	12.11	even	2
2400.2.b.e.2351.6		8	8.5	even	2
2400.2.b.f.2351.5		8	24.5	odd	2
2400.2.b.f.2351.6		8	4.3	odd	2
2400.2.m.c.1199.3		16	60.47	odd	4
2400.2.m.c.1199.4		16	40.13	odd	4
2400.2.m.c.1199.13		16	40.37	odd	4
2400.2.m.c.1199.14		16	60.23	odd	4
2400.2.m.d.1199.3		16	120.77	even	4
2400.2.m.d.1199.4		16	20.3	even	4
2400.2.m.d.1199.13		16	20.7	even	4
2400.2.m.d.1199.14		16	120.53	even	4

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:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.578647 - 1.29041i) q^{2} +(-0.751690 - 1.56044i) q^{3} +(-1.33034 + 1.49339i) q^{4} +(-1.57865 + 1.87293i) q^{6} +4.28591i q^{7} +(2.69688 + 0.852541i) q^{8} +(-1.86993 + 2.34593i) q^{9} +O(q^{10})\)	\(q+(-0.578647 - 1.29041i) q^{2} +(-0.751690 - 1.56044i) q^{3} +(-1.33034 + 1.49339i) q^{4} +(-1.57865 + 1.87293i) q^{6} +4.28591i q^{7} +(2.69688 + 0.852541i) q^{8} +(-1.86993 + 2.34593i) q^{9} -2.44673i q^{11} +(3.33034 + 0.953342i) q^{12} -2.71493i q^{13} +(5.53060 - 2.48003i) q^{14} +(-0.460411 - 3.97341i) q^{16} -1.16504i q^{17} +(4.10924 + 1.05551i) q^{18} +6.05444 q^{19} +(6.68789 - 3.22167i) q^{21} +(-3.15729 + 1.41579i) q^{22} +7.55782 q^{23} +(-0.696882 - 4.84916i) q^{24} +(-3.50338 + 1.57098i) q^{26} +(5.06628 + 1.15449i) q^{27} +(-6.40052 - 5.70170i) q^{28} +0.733092 q^{29} -0.469799i q^{31} +(-4.86093 + 2.89332i) q^{32} +(-3.81797 + 1.83918i) q^{33} +(-1.50338 + 0.674144i) q^{34} +(-1.01575 - 5.91340i) q^{36} -1.36664i q^{37} +(-3.50338 - 7.81273i) q^{38} +(-4.23647 + 2.04078i) q^{39} -4.69186i q^{41} +(-8.02722 - 6.76594i) q^{42} +1.50338 q^{43} +(3.65391 + 3.25497i) q^{44} +(-4.37330 - 9.75271i) q^{46} +4.07812 q^{47} +(-5.85418 + 3.70522i) q^{48} -11.3690 q^{49} +(-1.81797 + 0.875746i) q^{51} +(4.05444 + 3.61177i) q^{52} -1.00676 q^{53} +(-1.44181 - 7.20563i) q^{54} +(-3.65391 + 11.5586i) q^{56} +(-4.55106 - 9.44757i) q^{57} +(-0.424201 - 0.945992i) q^{58} +1.63484i q^{59} +10.9336i q^{61} +(-0.606236 + 0.271848i) q^{62} +(-10.0544 - 8.01433i) q^{63} +(6.54635 + 4.59841i) q^{64} +(4.58256 + 3.86252i) q^{66} +9.97632 q^{67} +(1.73985 + 1.54989i) q^{68} +(-5.68113 - 11.7935i) q^{69} +11.6359 q^{71} +(-7.04297 + 4.73250i) q^{72} +9.63593 q^{73} +(-1.76353 + 0.790800i) q^{74} +(-8.05444 + 9.04162i) q^{76} +10.4865 q^{77} +(5.08487 + 4.28591i) q^{78} +3.61177i q^{79} +(-2.00676 - 8.77342i) q^{81} +(-6.05444 + 2.71493i) q^{82} -5.45095i q^{83} +(-4.08594 + 14.2735i) q^{84} +(-0.869925 - 1.93998i) q^{86} +(-0.551058 - 1.14394i) q^{87} +(2.08594 - 6.59854i) q^{88} -7.75993i q^{89} +11.6359 q^{91} +(-10.0544 + 11.2867i) q^{92} +(-0.733092 + 0.353143i) q^{93} +(-2.35979 - 5.26246i) q^{94} +(8.16876 + 5.41030i) q^{96} -17.1156 q^{97} +(6.57865 + 14.6707i) q^{98} +(5.73985 + 4.57520i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + q^{2} + q^{4} - 7 q^{6} + 7 q^{8}+O(q^{10}) \) 8 * q + q^2 + q^4 - 7 * q^6 + 7 * q^8	\( 8 q + q^{2} + q^{4} - 7 q^{6} + 7 q^{8} + 15 q^{12} + 6 q^{14} - 7 q^{16} - 11 q^{18} - 4 q^{19} + 4 q^{21} - 14 q^{22} - 4 q^{23} + 9 q^{24} - 16 q^{26} + 12 q^{27} + 2 q^{28} + 11 q^{32} + 4 q^{33} - 19 q^{36} - 16 q^{38} - 16 q^{39} - 38 q^{42} + 30 q^{44} - 8 q^{46} + 28 q^{47} - 21 q^{48} - 16 q^{49} + 20 q^{51} - 20 q^{52} + 16 q^{53} - 15 q^{54} - 30 q^{56} + 4 q^{57} + 2 q^{58} - 34 q^{62} - 28 q^{63} + 25 q^{64} + 18 q^{66} + 32 q^{67} - 16 q^{68} - 20 q^{69} + 24 q^{71} - 41 q^{72} + 8 q^{73} - 32 q^{74} - 12 q^{76} + 12 q^{78} + 8 q^{81} + 4 q^{82} - 2 q^{84} + 8 q^{86} + 36 q^{87} - 14 q^{88} + 24 q^{91} - 28 q^{92} - 40 q^{94} + 17 q^{96} - 8 q^{97} + 47 q^{98} + 16 q^{99}+O(q^{100}) \) 8 * q + q^2 + q^4 - 7 * q^6 + 7 * q^8 + 15 * q^12 + 6 * q^14 - 7 * q^16 - 11 * q^18 - 4 * q^19 + 4 * q^21 - 14 * q^22 - 4 * q^23 + 9 * q^24 - 16 * q^26 + 12 * q^27 + 2 * q^28 + 11 * q^32 + 4 * q^33 - 19 * q^36 - 16 * q^38 - 16 * q^39 - 38 * q^42 + 30 * q^44 - 8 * q^46 + 28 * q^47 - 21 * q^48 - 16 * q^49 + 20 * q^51 - 20 * q^52 + 16 * q^53 - 15 * q^54 - 30 * q^56 + 4 * q^57 + 2 * q^58 - 34 * q^62 - 28 * q^63 + 25 * q^64 + 18 * q^66 + 32 * q^67 - 16 * q^68 - 20 * q^69 + 24 * q^71 - 41 * q^72 + 8 * q^73 - 32 * q^74 - 12 * q^76 + 12 * q^78 + 8 * q^81 + 4 * q^82 - 2 * q^84 + 8 * q^86 + 36 * q^87 - 14 * q^88 + 24 * q^91 - 28 * q^92 - 40 * q^94 + 17 * q^96 - 8 * q^97 + 47 * q^98 + 16 * q^99

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