LMFDB - Embedded newform 760.2.f.b.381.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [760,2,Mod(381,760)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("760.381"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(760, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 760 = 2^{3} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	760.f (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [44] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.06863055362$
Analytic rank:	$0$
Dimension:	$44$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			381.9
Character	$\chi$	$=$	760.381
Dual form			760.2.f.b.381.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.01061 - 0.989281i) q^{2} -0.530865i q^{3} +(0.0426469 + 1.99955i) q^{4} +1.00000i q^{5} +(-0.525175 + 0.536495i) q^{6} +1.59876 q^{7} +(1.93501 - 2.06294i) q^{8} +2.71818 q^{9} +(0.989281 - 1.01061i) q^{10} +4.08419i q^{11} +(1.06149 - 0.0226397i) q^{12} +4.29317i q^{13} +(-1.61572 - 1.58162i) q^{14} +0.530865 q^{15} +(-3.99636 + 0.170549i) q^{16} -7.51422 q^{17} +(-2.74701 - 2.68905i) q^{18} +1.00000i q^{19} +(-1.99955 + 0.0426469i) q^{20} -0.848726i q^{21} +(4.04041 - 4.12750i) q^{22} -7.97383 q^{23} +(-1.09514 - 1.02723i) q^{24} -1.00000 q^{25} +(4.24715 - 4.33870i) q^{26} -3.03558i q^{27} +(0.0681821 + 3.19679i) q^{28} +5.77844i q^{29} +(-0.536495 - 0.525175i) q^{30} +3.57200 q^{31} +(4.20747 + 3.78117i) q^{32} +2.16815 q^{33} +(7.59391 + 7.43368i) q^{34} +1.59876i q^{35} +(0.115922 + 5.43513i) q^{36} +1.10308i q^{37} +(0.989281 - 1.01061i) q^{38} +2.27909 q^{39} +(2.06294 + 1.93501i) q^{40} +2.90996 q^{41} +(-0.839628 + 0.857727i) q^{42} -4.31616i q^{43} +(-8.16652 + 0.174178i) q^{44} +2.71818i q^{45} +(8.05839 + 7.88835i) q^{46} +6.15476 q^{47} +(0.0905383 + 2.12153i) q^{48} -4.44396 q^{49} +(1.01061 + 0.989281i) q^{50} +3.98904i q^{51} +(-8.58438 + 0.183090i) q^{52} +11.5004i q^{53} +(-3.00304 + 3.06778i) q^{54} -4.08419 q^{55} +(3.09362 - 3.29815i) q^{56} +0.530865 q^{57} +(5.71650 - 5.83973i) q^{58} +6.91548i q^{59} +(0.0226397 + 1.06149i) q^{60} +4.61636i q^{61} +(-3.60989 - 3.53371i) q^{62} +4.34572 q^{63} +(-0.511452 - 7.98363i) q^{64} -4.29317 q^{65} +(-2.19115 - 2.14491i) q^{66} -10.2207i q^{67} +(-0.320458 - 15.0250i) q^{68} +4.23303i q^{69} +(1.58162 - 1.61572i) q^{70} +11.3535 q^{71} +(5.25972 - 5.60745i) q^{72} +15.1543 q^{73} +(1.09126 - 1.11478i) q^{74} +0.530865i q^{75} +(-1.99955 + 0.0426469i) q^{76} +6.52964i q^{77} +(-2.30326 - 2.25466i) q^{78} -3.08138 q^{79} +(-0.170549 - 3.99636i) q^{80} +6.54306 q^{81} +(-2.94082 - 2.87877i) q^{82} -3.40976i q^{83} +(1.69707 - 0.0361955i) q^{84} -7.51422i q^{85} +(-4.26989 + 4.36193i) q^{86} +3.06757 q^{87} +(8.42544 + 7.90295i) q^{88} -13.5566 q^{89} +(2.68905 - 2.74701i) q^{90} +6.86375i q^{91} +(-0.340059 - 15.9440i) q^{92} -1.89625i q^{93} +(-6.22004 - 6.08879i) q^{94} -1.00000 q^{95} +(2.00729 - 2.23360i) q^{96} +3.07007 q^{97} +(4.49110 + 4.39633i) q^{98} +11.1016i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 2 q^{2} - 2 q^{4} - 6 q^{6} + 4 q^{7} + 8 q^{8} - 60 q^{9} + 4 q^{12} + 4 q^{14} - 6 q^{16} + 24 q^{17} - 14 q^{18} - 4 q^{20} - 4 q^{22} + 4 q^{23} + 2 q^{24} - 44 q^{25} + 18 q^{26} - 14 q^{28}+ \cdots + 78 q^{98}+O(q^{100}) $ 44 * q + 2 * q^2 - 2 * q^4 - 6 * q^6 + 4 * q^7 + 8 * q^8 - 60 * q^9 + 4 * q^12 + 4 * q^14 - 6 * q^16 + 24 * q^17 - 14 * q^18 - 4 * q^20 - 4 * q^22 + 4 * q^23 + 2 * q^24 - 44 * q^25 + 18 * q^26 - 14 * q^28 + 12 * q^32 + 40 * q^33 + 32 * q^34 - 28 * q^36 - 24 * q^39 + 6 * q^40 - 32 * q^41 + 46 * q^42 - 36 * q^44 - 16 * q^46 - 20 * q^47 + 64 * q^48 + 108 * q^49 - 2 * q^50 - 24 * q^52 - 26 * q^54 + 8 * q^55 + 60 * q^56 + 2 * q^58 - 14 * q^60 - 72 * q^62 + 20 * q^63 + 22 * q^64 + 12 * q^65 + 88 * q^66 - 62 * q^68 - 18 * q^70 - 8 * q^71 + 48 * q^72 - 88 * q^73 + 84 * q^74 - 4 * q^76 - 116 * q^78 + 40 * q^79 + 8 * q^80 + 116 * q^81 + 44 * q^82 - 108 * q^84 - 88 * q^86 + 48 * q^87 + 76 * q^88 - 64 * q^89 + 30 * q^90 - 62 * q^92 - 24 * q^94 - 44 * q^95 + 118 * q^96 + 116 * q^97 + 78 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/760\mathbb{Z}\right)^\times$.

$n$	$191$	$381$	$401$	$457$
$\chi(n)$	$1$	$-1$	$1$	$1$

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 $

$2$	−1.01061	−	0.989281i	−0.714606	−	0.699527i
$2$	−1.01061	−	0.989281i	−0.714606	−	0.699527i
$3$		−	0.530865i		−	0.306495i	−0.988188	−	0.153248i	$-0.951027\pi$
$3$		−	0.530865i		−	0.306495i	0.988188	−	0.153248i	$-0.0489732\pi$
$4$	0.0426469	+	1.99955i	0.0213234	+	0.999773i
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−0.525175	+	0.536495i	−0.214402	+	0.219023i
$7$	1.59876			0.604275			0.302137	−	0.953264i	$-0.402300\pi$
$7$	1.59876			0.604275			0.302137	+	0.953264i	$0.402300\pi$
$8$	1.93501	−	2.06294i	0.684130	−	0.729360i
$9$	2.71818			0.906061
$10$	0.989281	−	1.01061i	0.312838	−	0.319582i
$11$			4.08419i			1.23143i	0.787970	+	0.615714i	$0.211132\pi$
$11$			4.08419i			1.23143i	−0.787970	+	0.615714i	$0.788868\pi$
$12$	1.06149	−	0.0226397i	0.306425	−	0.00653553i
$13$			4.29317i			1.19071i	0.803463	+	0.595355i	$0.202989\pi$
$13$			4.29317i			1.19071i	−0.803463	+	0.595355i	$0.797011\pi$
$14$	−1.61572	−	1.58162i	−0.431818	−	0.422707i
$15$	0.530865			0.137069
$16$	−3.99636	+	0.170549i	−0.999091	+	0.0426372i
$17$	−7.51422			−1.82247			−0.911233	−	0.411891i	$-0.864869\pi$
$17$	−7.51422			−1.82247			−0.911233	+	0.411891i	$0.864869\pi$
$18$	−2.74701	−	2.68905i	−0.647476	−	0.633814i
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	−1.99955	+	0.0426469i	−0.447112	+	0.00953613i
$21$		−	0.848726i		−	0.185207i
$22$	4.04041	−	4.12750i	0.861418	−	0.879986i
$23$	−7.97383			−1.66266			−0.831329	−	0.555781i	$-0.812419\pi$
$23$	−7.97383			−1.66266			−0.831329	+	0.555781i	$0.812419\pi$
$24$	−1.09514	−	1.02723i	−0.223545	−	0.209683i
$25$	−1.00000			−0.200000
$26$	4.24715	−	4.33870i	0.832934	−	0.850889i
$27$		−	3.03558i		−	0.584198i
$28$	0.0681821	+	3.19679i	0.0128852	+	0.604137i
$29$			5.77844i			1.07303i	0.843891	+	0.536515i	$0.180260\pi$
$29$			5.77844i			1.07303i	−0.843891	+	0.536515i	$0.819740\pi$
$30$	−0.536495	−	0.525175i	−0.0979502	−	0.0958833i
$31$	3.57200			0.641551			0.320775	−	0.947155i	$-0.396057\pi$
$31$	3.57200			0.641551			0.320775	+	0.947155i	$0.396057\pi$
$32$	4.20747	+	3.78117i	0.743782	+	0.668422i
$33$	2.16815			0.377427
$34$	7.59391	+	7.43368i	1.30235	+	1.27486i
$35$			1.59876i			0.270240i
$36$	0.115922	+	5.43513i	0.0193203	+	0.905855i
$37$			1.10308i			0.181346i	0.995881	+	0.0906728i	$0.0289017\pi$
$37$			1.10308i			0.181346i	−0.995881	+	0.0906728i	$0.971098\pi$
$38$	0.989281	−	1.01061i	0.160483	−	0.163942i
$39$	2.27909			0.364947
$40$	2.06294	+	1.93501i	0.326180	+	0.305952i
$41$	2.90996			0.454459			0.227230	−	0.973841i	$-0.427033\pi$
$41$	2.90996			0.454459			0.227230	+	0.973841i	$0.427033\pi$
$42$	−0.839628	+	0.857727i	−0.129557	+	0.132350i
$43$		−	4.31616i		−	0.658208i	−0.944294	−	0.329104i	$-0.893253\pi$
$43$		−	4.31616i		−	0.658208i	0.944294	−	0.329104i	$-0.106747\pi$
$44$	−8.16652	+	0.174178i	−1.23115	+	0.0262583i
$45$			2.71818i			0.405203i
$46$	8.05839	+	7.88835i	1.18815	+	1.16307i
$47$	6.15476			0.897764			0.448882	−	0.893591i	$-0.351822\pi$
$47$	6.15476			0.897764			0.448882	+	0.893591i	$0.351822\pi$
$48$	0.0905383	+	2.12153i	0.0130681	+	0.306216i
$49$	−4.44396			−0.634852
$50$	1.01061	+	0.989281i	0.142921	+	0.139905i
$51$			3.98904i			0.558577i
$52$	−8.58438	+	0.183090i	−1.19044	+	0.0253900i
$53$			11.5004i			1.57971i	0.613296	+	0.789853i	$0.289843\pi$
$53$			11.5004i			1.57971i	−0.613296	+	0.789853i	$0.710157\pi$
$54$	−3.00304	+	3.06778i	−0.408663	+	0.417472i
$55$	−4.08419			−0.550712
$56$	3.09362	−	3.29815i	0.413403	−	0.440734i
$57$	0.530865			0.0703148
$58$	5.71650	−	5.83973i	0.750614	−	0.766794i
$59$			6.91548i			0.900319i	0.892948	+	0.450159i	$0.148633\pi$
$59$			6.91548i			0.900319i	−0.892948	+	0.450159i	$0.851367\pi$
$60$	0.0226397	+	1.06149i	0.00292278	+	0.137038i
$61$			4.61636i			0.591064i	0.955333	+	0.295532i	$0.0954969\pi$
$61$			4.61636i			0.591064i	−0.955333	+	0.295532i	$0.904503\pi$
$62$	−3.60989	−	3.53371i	−0.458456	−	0.448782i
$63$	4.34572			0.547510
$64$	−0.511452	−	7.98363i	−0.0639315	−	0.997954i
$65$	−4.29317			−0.532502
$66$	−2.19115	−	2.14491i	−0.269711	−	0.264020i
$67$		−	10.2207i		−	1.24866i	−0.781162	−	0.624328i	$-0.785373\pi$
$67$		−	10.2207i		−	1.24866i	0.781162	−	0.624328i	$-0.214627\pi$
$68$	−0.320458	−	15.0250i	−0.0388613	−	1.82205i
$69$			4.23303i			0.509596i
$70$	1.58162	−	1.61572i	0.189040	−	0.193115i
$71$	11.3535			1.34741			0.673704	−	0.739001i	$-0.264702\pi$
$71$	11.3535			1.34741			0.673704	+	0.739001i	$0.264702\pi$
$72$	5.25972	−	5.60745i	0.619864	−	0.660844i
$73$	15.1543			1.77368			0.886840	−	0.462078i	$-0.152896\pi$
$73$	15.1543			1.77368			0.886840	+	0.462078i	$0.152896\pi$
$74$	1.09126	−	1.11478i	0.126856	−	0.129591i
$75$			0.530865i			0.0612990i
$76$	−1.99955	+	0.0426469i	−0.229364	+	0.00489193i
$77$			6.52964i			0.744121i
$78$	−2.30326	−	2.25466i	−0.260793	−	0.255290i
$79$	−3.08138			−0.346683			−0.173341	−	0.984862i	$-0.555456\pi$
$79$	−3.08138			−0.346683			−0.173341	+	0.984862i	$0.555456\pi$
$80$	−0.170549	−	3.99636i	−0.0190679	−	0.446807i
$81$	6.54306			0.727007
$82$	−2.94082	−	2.87877i	−0.324759	−	0.317907i
$83$		−	3.40976i		−	0.374270i	−0.982334	−	0.187135i	$-0.940080\pi$
$83$		−	3.40976i		−	0.374270i	0.982334	−	0.187135i	$-0.0599202\pi$
$84$	1.69707	−	0.0361955i	0.185165	−	0.00394925i
$85$		−	7.51422i		−	0.815032i
$86$	−4.26989	+	4.36193i	−0.460434	+	0.470359i
$87$	3.06757			0.328878
$88$	8.42544	+	7.90295i	0.898155	+	0.842458i
$89$	−13.5566			−1.43699			−0.718497	−	0.695530i	$-0.755170\pi$
$89$	−13.5566			−1.43699			−0.718497	+	0.695530i	$0.755170\pi$
$90$	2.68905	−	2.74701i	0.283450	−	0.289560i
$91$			6.86375i			0.719516i
$92$	−0.340059	−	15.9440i	−0.0354536	−	1.66228i
$93$		−	1.89625i		−	0.196632i
$94$	−6.22004	−	6.08879i	−0.641548	−	0.628010i
$95$	−1.00000			−0.102598
$96$	2.00729	−	2.23360i	0.204868	−	0.227966i
$97$	3.07007			0.311718			0.155859	−	0.987779i	$-0.450185\pi$
$97$	3.07007			0.311718			0.155859	+	0.987779i	$0.450185\pi$
$98$	4.49110	+	4.39633i	0.453669	+	0.444096i
$99$			11.1016i			1.11575i
$100$	−0.0426469	−	1.99955i	−0.00426469	−	0.199955i
$101$		−	10.5727i		−	1.05202i	−0.850478	−	0.526010i	$-0.823687\pi$
$101$		−	10.5727i		−	1.05202i	0.850478	−	0.526010i	$-0.176313\pi$
$102$	3.94628	−	4.03134i	0.390740	−	0.399162i
$103$	10.5955			1.04401			0.522004	−	0.852943i	$-0.325185\pi$
$103$	10.5955			1.04401			0.522004	+	0.852943i	$0.325185\pi$
$104$	8.85655	+	8.30733i	0.868456	+	0.814601i
$105$	0.848726			0.0828272
$106$	11.3772	−	11.6224i	1.10505	−	1.12887i
$107$		−	2.02637i		−	0.195897i	−0.995191	−	0.0979484i	$-0.968772\pi$
$107$		−	2.02637i		−	0.195897i	0.995191	−	0.0979484i	$-0.0312280\pi$
$108$	6.06979	−	0.129458i	0.584065	−	0.0124571i
$109$			9.89833i			0.948088i	0.880501	+	0.474044i	$0.157206\pi$
$109$			9.89833i			0.948088i	−0.880501	+	0.474044i	$0.842794\pi$
$110$	4.12750	+	4.04041i	0.393542	+	0.385238i
$111$	0.585588			0.0555815
$112$	−6.38923	+	0.272667i	−0.603725	+	0.0257646i
$113$	−10.9289			−1.02811			−0.514054	−	0.857758i	$-0.671857\pi$
$113$	−10.9289			−1.02811			−0.514054	+	0.857758i	$0.671857\pi$
$114$	−0.536495	−	0.525175i	−0.0502474	−	0.0491871i
$115$		−	7.97383i		−	0.743563i
$116$	−11.5543	+	0.246433i	−1.07279	+	0.0228807i
$117$			11.6696i			1.07886i
$118$	6.84135	−	6.98882i	0.629797	−	0.643373i
$119$	−12.0134			−1.10127
$120$	1.02723	−	1.09514i	0.0937729	−	0.0999724i
$121$	−5.68058			−0.516416
$122$	4.56688	−	4.66532i	0.413466	−	0.422378i
$123$		−	1.54480i		−	0.139290i
$124$	0.152335	+	7.14238i	0.0136801	+	0.641405i
$125$		−	1.00000i		−	0.0894427i
$126$	−4.39181	−	4.29914i	−0.391254	−	0.382998i
$127$	4.07012			0.361165			0.180583	−	0.983560i	$-0.442202\pi$
$127$	4.07012			0.361165			0.180583	+	0.983560i	$0.442202\pi$
$128$	−7.38118	+	8.57427i	−0.652410	+	0.757866i
$129$	−2.29130			−0.201737
$130$	4.33870	+	4.24715i	0.380529	+	0.372500i
$131$		−	17.8997i		−	1.56390i	−0.623338	−	0.781952i	$-0.714224\pi$
$131$		−	17.8997i		−	1.56390i	0.623338	−	0.781952i	$-0.285776\pi$
$132$	0.0924649	+	4.33532i	0.00804804	+	0.377341i
$133$			1.59876i			0.138630i
$134$	−10.1111	+	10.3291i	−0.873469	+	0.892297i
$135$	3.03558			0.261261
$136$	−14.5401	+	15.5014i	−1.24680	+	1.32923i
$137$	2.57962			0.220392			0.110196	−	0.993910i	$-0.464852\pi$
$137$	2.57962			0.220392			0.110196	+	0.993910i	$0.464852\pi$
$138$	4.18765	−	4.27792i	0.356477	−	0.364161i
$139$			13.5951i			1.15312i	0.817055	+	0.576560i	$0.195605\pi$
$139$			13.5951i			1.15312i	−0.817055	+	0.576560i	$0.804395\pi$
$140$	−3.19679	+	0.0681821i	−0.270178	+	0.00576244i
$141$		−	3.26735i		−	0.275160i
$142$	−11.4739	−	11.2318i	−0.962866	−	0.942548i
$143$	−17.5341			−1.46627
$144$	−10.8628	+	0.463583i	−0.905237	+	0.0386319i
$145$	−5.77844			−0.479874
$146$	−15.3150	−	14.9919i	−1.26748	−	1.24074i
$147$			2.35915i			0.194579i
$148$	−2.20566	+	0.0470430i	−0.181304	+	0.00386691i
$149$		−	1.38602i		−	0.113547i	−0.998387	−	0.0567735i	$-0.981919\pi$
$149$		−	1.38602i		−	0.113547i	0.998387	−	0.0567735i	$-0.0180813\pi$
$150$	0.525175	−	0.536495i	0.0428803	−	0.0438046i
$151$	17.6513			1.43644			0.718220	−	0.695816i	$-0.244957\pi$
$151$	17.6513			1.43644			0.718220	+	0.695816i	$0.244957\pi$
$152$	2.06294	+	1.93501i	0.167327	+	0.156950i
$153$	−20.4250			−1.65127
$154$	6.45964	−	6.59889i	0.520533	−	0.531753i
$155$			3.57200i			0.286910i
$156$	0.0971962	+	4.55715i	0.00778192	+	0.364864i
$157$			12.4964i			0.997325i	0.866796	+	0.498662i	$0.166175\pi$
$157$			12.4964i			0.997325i	−0.866796	+	0.498662i	$0.833825\pi$
$158$	3.11406	+	3.04835i	0.247742	+	0.242514i
$159$	6.10518			0.484172
$160$	−3.78117	+	4.20747i	−0.298928	+	0.332629i
$161$	−12.7482			−1.00470
$162$	−6.61245	−	6.47293i	−0.519523	−	0.508561i
$163$		−	10.6418i		−	0.833533i	−0.909013	−	0.416767i	$-0.863163\pi$
$163$		−	10.6418i		−	0.833533i	0.909013	−	0.416767i	$-0.136837\pi$
$164$	0.124101	+	5.81860i	0.00969064	+	0.454356i
$165$			2.16815i			0.168790i
$166$	−3.37321	+	3.44592i	−0.261812	+	0.267456i
$167$	9.32577			0.721650			0.360825	−	0.932634i	$-0.382495\pi$
$167$	9.32577			0.721650			0.360825	+	0.932634i	$0.382495\pi$
$168$	−1.75087	−	1.64230i	−0.135083	−	0.126706i
$169$	−5.43128			−0.417791
$170$	−7.43368	+	7.59391i	−0.570137	+	0.582427i
$171$			2.71818i			0.207865i
$172$	8.63035	−	0.184071i	0.658058	−	0.0140353i
$173$		−	14.2559i		−	1.08386i	−0.840424	−	0.541929i	$-0.817694\pi$
$173$		−	14.2559i		−	1.08386i	0.840424	−	0.541929i	$-0.182306\pi$
$174$	−3.10011	−	3.03469i	−0.235019	−	0.230059i
$175$	−1.59876			−0.120855
$176$	−0.696553	−	16.3219i	−0.0525046	−	1.23031i
$177$	3.67119			0.275943
$178$	13.7003	+	13.4113i	1.02688	+	1.00522i
$179$		−	15.8824i		−	1.18711i	−0.804794	−	0.593554i	$-0.797724\pi$
$179$		−	15.8824i		−	1.18711i	0.804794	−	0.593554i	$-0.202276\pi$
$180$	−5.43513	+	0.115922i	−0.405111	+	0.00864031i
$181$			9.70924i			0.721682i	0.932627	+	0.360841i	$0.117510\pi$
$181$			9.70924i			0.721682i	−0.932627	+	0.360841i	$0.882490\pi$
$182$	6.79017	−	6.93654i	0.503321	−	0.514171i
$183$	2.45066			0.181158
$184$	−15.4295	+	16.4495i	−1.13747	+	1.21268i
$185$	−1.10308			−0.0811002
$186$	−1.87593	+	1.91636i	−0.137550	+	0.140514i
$187$		−	30.6895i		−	2.24424i
$188$	0.262481	+	12.3067i	0.0191434	+	0.897560i
$189$		−	4.85317i		−	0.353016i
$190$	1.01061	+	0.989281i	0.0733170	+	0.0717700i
$191$	5.34269			0.386584			0.193292	−	0.981141i	$-0.438084\pi$
$191$	5.34269			0.386584			0.193292	+	0.981141i	$0.438084\pi$
$192$	−4.23823	+	0.271512i	−0.305868	+	0.0195947i
$193$	−6.68316			−0.481065			−0.240532	−	0.970641i	$-0.577322\pi$
$193$	−6.68316			−0.481065			−0.240532	+	0.970641i	$0.577322\pi$
$194$	−3.10263	−	3.03716i	−0.222756	−	0.218055i
$195$			2.27909i			0.163209i
$196$	−0.189521	−	8.88591i	−0.0135372	−	0.634708i
$197$		−	1.87200i		−	0.133374i	−0.997774	−	0.0666872i	$-0.978757\pi$
$197$		−	1.87200i		−	0.133374i	0.997774	−	0.0666872i	$-0.0212429\pi$
$198$	10.9826	−	11.2193i	0.780497	−	0.797321i
$199$	11.7535			0.833184			0.416592	−	0.909094i	$-0.363224\pi$
$199$	11.7535			0.833184			0.416592	+	0.909094i	$0.363224\pi$
$200$	−1.93501	+	2.06294i	−0.136826	+	0.145872i
$201$	−5.42580			−0.382707
$202$	−10.4593	+	10.6848i	−0.735917	+	0.751780i
$203$			9.23835i			0.648405i
$204$	−7.97626	+	0.170120i	−0.558450	+	0.0119108i
$205$			2.90996i			0.203240i
$206$	−10.7079	−	10.4819i	−0.746054	−	0.730312i
$207$	−21.6743			−1.50647
$208$	−0.732194	−	17.1571i	−0.0507685	−	1.18963i
$209$	−4.08419			−0.282509
$210$	−0.857727	−	0.839628i	−0.0591888	−	0.0579399i
$211$		−	16.3391i		−	1.12483i	−0.826856	−	0.562413i	$-0.809873\pi$
$211$		−	16.3391i		−	1.12483i	0.826856	−	0.562413i	$-0.190127\pi$
$212$	−22.9956	+	0.490458i	−1.57935	+	0.0336848i
$213$		−	6.02715i		−	0.412974i
$214$	−2.00465	+	2.04786i	−0.137035	+	0.139989i
$215$	4.31616			0.294360
$216$	−6.26223	−	5.87389i	−0.426091	−	0.399668i
$217$	5.71078			0.387673
$218$	9.79223	−	10.0033i	0.663214	−	0.677510i
$219$		−	8.04490i		−	0.543624i
$220$	−0.174178	−	8.16652i	−0.0117431	−	0.550586i
$221$		−	32.2598i		−	2.17003i
$222$	−0.591798	−	0.579310i	−0.0397189	−	0.0388808i
$223$	14.1309			0.946278			0.473139	−	0.880988i	$-0.343121\pi$
$223$	14.1309			0.946278			0.473139	+	0.880988i	$0.343121\pi$
$224$	6.72673	+	6.04518i	0.449449	+	0.403911i
$225$	−2.71818			−0.181212
$226$	11.0448	+	10.8118i	0.734692	+	0.719190i
$227$			14.1373i			0.938324i	0.883112	+	0.469162i	$0.155444\pi$
$227$			14.1373i			0.938324i	−0.883112	+	0.469162i	$0.844556\pi$
$228$	0.0226397	+	1.06149i	0.00149935	+	0.0702988i
$229$			13.1301i			0.867665i	0.900994	+	0.433832i	$0.142839\pi$
$229$			13.1301i			0.867665i	−0.900994	+	0.433832i	$0.857161\pi$
$230$	−7.88835	+	8.05839i	−0.520143	+	0.531355i
$231$	3.46636			0.228069
$232$	11.9206	+	11.1814i	0.782625	+	0.734092i
$233$	−16.8001			−1.10061			−0.550306	−	0.834963i	$-0.685489\pi$
$233$	−16.8001			−1.10061			−0.550306	+	0.834963i	$0.685489\pi$
$234$	11.5445	−	11.7934i	0.754689	−	0.770957i
$235$			6.15476i			0.401492i
$236$	−13.8278	+	0.294924i	−0.900114	+	0.0191979i
$237$			1.63580i			0.106257i
$238$	12.1408	+	11.8847i	0.786974	+	0.770369i
$239$	−12.7091			−0.822083			−0.411042	−	0.911617i	$-0.634835\pi$
$239$	−12.7091			−0.822083			−0.411042	+	0.911617i	$0.634835\pi$
$240$	−2.12153	+	0.0905383i	−0.136944	+	0.00584423i
$241$	−2.78627			−0.179479			−0.0897396	−	0.995965i	$-0.528603\pi$
$241$	−2.78627			−0.179479			−0.0897396	+	0.995965i	$0.528603\pi$
$242$	5.74082	+	5.61969i	0.369034	+	0.361247i
$243$		−	12.5802i		−	0.807022i
$244$	−9.23062	+	0.196873i	−0.590930	+	0.0126035i
$245$		−	4.44396i		−	0.283915i
$246$	−1.52824	+	1.56118i	−0.0974368	+	0.0995371i
$247$	−4.29317			−0.273168
$248$	6.91187	−	7.36883i	0.438904	−	0.467921i
$249$	−1.81012			−0.114712
$250$	−0.989281	+	1.01061i	−0.0625676	+	0.0639163i
$251$			19.1306i			1.20752i	0.797168	+	0.603758i	$0.206331\pi$
$251$			19.1306i			1.20752i	−0.797168	+	0.603758i	$0.793669\pi$
$252$	0.185331	+	8.68947i	0.0116748	+	0.547385i
$253$		−	32.5666i		−	2.04744i
$254$	−4.11329	−	4.02650i	−0.258091	−	0.252645i
$255$	−3.98904			−0.249803
$256$	15.9418	−	1.36315i	0.996364	−	0.0851968i
$257$	15.3571			0.957952			0.478976	−	0.877828i	$-0.341008\pi$
$257$	15.3571			0.957952			0.478976	+	0.877828i	$0.341008\pi$
$258$	2.31560	+	2.26674i	0.144163	+	0.141121i
$259$			1.76356i			0.109583i
$260$	−0.183090	−	8.58438i	−0.0113548	−	0.532381i
$261$			15.7069i			0.972231i
$262$	−17.7078	+	18.0895i	−1.09399	+	1.11758i
$263$	−30.6398			−1.88933			−0.944665	−	0.328037i	$-0.893613\pi$
$263$	−30.6398			−1.88933			−0.944665	+	0.328037i	$0.893613\pi$
$264$	4.19540	−	4.47277i	0.258209	−	0.275280i
$265$	−11.5004			−0.706466
$266$	1.58162	−	1.61572i	0.0969755	−	0.0990659i
$267$			7.19671i			0.440432i
$268$	20.4367	−	0.435880i	1.24837	−	0.0266256i
$269$			21.9765i			1.33993i	0.742394	+	0.669964i	$0.233690\pi$
$269$			21.9765i			1.33993i	−0.742394	+	0.669964i	$0.766310\pi$
$270$	−3.06778	−	3.00304i	−0.186699	−	0.182759i
$271$	2.44649			0.148614			0.0743069	−	0.997235i	$-0.476326\pi$
$271$	2.44649			0.148614			0.0743069	+	0.997235i	$0.476326\pi$
$272$	30.0296	−	1.28154i	1.82081	−	0.0777048i
$273$	3.64372			0.220528
$274$	−2.60698	−	2.55197i	−0.157494	−	0.154170i
$275$		−	4.08419i		−	0.246286i
$276$	−8.46413	+	0.180525i	−0.509481	+	0.0108663i
$277$		−	27.0414i		−	1.62476i	−0.583127	−	0.812381i	$-0.698171\pi$
$277$		−	27.0414i		−	1.62476i	0.583127	−	0.812381i	$-0.301829\pi$
$278$	13.4494	−	13.7393i	0.806639	−	0.824026i
$279$	9.70936			0.581284
$280$	3.29815	+	3.09362i	0.197102	+	0.184879i
$281$	15.9317			0.950404			0.475202	−	0.879877i	$-0.342375\pi$
$281$	15.9317			0.950404			0.475202	+	0.879877i	$0.342375\pi$
$282$	−3.23232	+	3.30200i	−0.192482	+	0.196631i
$283$			4.15406i			0.246933i	0.992349	+	0.123467i	$0.0394012\pi$
$283$			4.15406i			0.246933i	−0.992349	+	0.123467i	$0.960599\pi$
$284$	0.484190	+	22.7018i	0.0287314	+	1.34710i
$285$			0.530865i			0.0314457i
$286$	17.7201	+	17.3461i	1.04781	+	1.02570i
$287$	4.65233			0.274618
$288$	11.4367	+	10.2779i	0.673912	+	0.605631i
$289$	39.4635			2.32138
$290$	5.83973	+	5.71650i	0.342921	+	0.335685i
$291$		−	1.62979i		−	0.0955401i
$292$	0.646284	+	30.3017i	0.0378209	+	1.77328i
$293$			21.0272i			1.22842i	0.789141	+	0.614212i	$0.210526\pi$
$293$			21.0272i			1.22842i	−0.789141	+	0.614212i	$0.789474\pi$
$294$	2.33386	−	2.38417i	0.136113	−	0.139047i
$295$	−6.91548			−0.402635
$296$	2.27559	+	2.13448i	0.132266	+	0.124064i
$297$	12.3979			0.719398
$298$	−1.37116	+	1.40072i	−0.0794293	+	0.0811414i
$299$		−	34.2330i		−	1.97974i
$300$	−1.06149	+	0.0226397i	−0.0612851	+	0.00130711i
$301$		−	6.90050i		−	0.397738i
$302$	−17.8385	−	17.4621i	−1.02649	−	1.00483i
$303$	−5.61266			−0.322439
$304$	−0.170549	−	3.99636i	−0.00978164	−	0.229207i
$305$	−4.61636			−0.264332
$306$	20.6416	+	20.2061i	1.18000	+	1.15511i
$307$			16.6865i			0.952348i	0.879351	+	0.476174i	$0.157977\pi$
$307$			16.6865i			0.952348i	−0.879351	+	0.476174i	$0.842023\pi$
$308$	−13.0563	+	0.278469i	−0.743952	+	0.0158672i
$309$		−	5.62479i		−	0.319983i
$310$	3.53371	−	3.60989i	0.200701	−	0.205028i
$311$	−9.12451			−0.517403			−0.258702	−	0.965957i	$-0.583295\pi$
$311$	−9.12451			−0.517403			−0.258702	+	0.965957i	$0.583295\pi$
$312$	4.41007	−	4.70163i	0.249671	−	0.266178i
$313$	−23.5688			−1.33219			−0.666093	−	0.745869i	$-0.732035\pi$
$313$	−23.5688			−1.33219			−0.666093	+	0.745869i	$0.732035\pi$
$314$	12.3625	−	12.6290i	0.697656	−	0.712694i
$315$			4.34572i			0.244854i
$316$	−0.131411	−	6.16137i	−0.00739247	−	0.346604i
$317$		−	13.6522i		−	0.766786i	−0.923585	−	0.383393i	$-0.874756\pi$
$317$		−	13.6522i		−	0.766786i	0.923585	−	0.383393i	$-0.125244\pi$
$318$	−6.16993	−	6.03974i	−0.345992	−	0.338692i
$319$	−23.6002			−1.32136
$320$	7.98363	−	0.511452i	0.446299	−	0.0285910i
$321$	−1.07573			−0.0600414
$322$	12.8834	+	12.6116i	0.717966	+	0.702816i
$323$		−	7.51422i		−	0.418102i
$324$	0.279041	+	13.0831i	0.0155023	+	0.726842i
$325$		−	4.29317i		−	0.238142i
$326$	−10.5278	+	10.7547i	−0.583079	+	0.595648i
$327$	5.25468			0.290584
$328$	5.63081	−	6.00308i	0.310909	−	0.331464i
$329$	9.83999			0.542496
$330$	2.14491	−	2.19115i	0.118073	−	0.120619i
$331$		−	22.6976i		−	1.24757i	−0.781595	−	0.623786i	$-0.785594\pi$
$331$		−	22.6976i		−	1.24757i	0.781595	−	0.623786i	$-0.214406\pi$
$332$	6.81797	−	0.145416i	0.374185	−	0.00798072i
$333$			2.99838i			0.164310i
$334$	−9.42467	−	9.22581i	−0.515695	−	0.504814i
$335$	10.2207			0.558416
$336$	0.144749	+	3.39182i	0.00789671	+	0.185039i
$337$	35.6697			1.94305			0.971527	−	0.236930i	$-0.0761413\pi$
$337$	35.6697			1.94305			0.971527	+	0.236930i	$0.0761413\pi$
$338$	5.48889	+	5.37307i	0.298556	+	0.292256i
$339$			5.80179i			0.315110i
$340$	15.0250	−	0.320458i	0.814846	−	0.0173793i
$341$			14.5887i			0.790024i
$342$	2.68905	−	2.74701i	0.145407	−	0.148541i
$343$	−18.2962			−0.987900
$344$	−8.90398	−	8.35182i	−0.480070	−	0.450300i
$345$	−4.23303			−0.227898
$346$	−14.1031	+	14.4071i	−0.758188	+	0.774531i
$347$		−	6.33393i		−	0.340023i	−0.985442	−	0.170012i	$-0.945619\pi$
$347$		−	6.33393i		−	0.340023i	0.985442	−	0.170012i	$-0.0543805\pi$
$348$	0.130822	+	6.13375i	0.00701282	+	0.328804i
$349$		−	17.8252i		−	0.954159i	−0.878860	−	0.477079i	$-0.841695\pi$
$349$		−	17.8252i		−	0.954159i	0.878860	−	0.477079i	$-0.158305\pi$
$350$	1.61572	+	1.58162i	0.0863637	+	0.0845413i
$351$	13.0323			0.695611
$352$	−15.4430	+	17.1841i	−0.823114	+	0.915914i
$353$	27.7834			1.47876			0.739381	−	0.673287i	$-0.235118\pi$
$353$	27.7834			1.47876			0.739381	+	0.673287i	$0.235118\pi$
$354$	−3.71012	−	3.63183i	−0.197191	−	0.193030i
$355$			11.3535i			0.602579i
$356$	−0.578145	−	27.1070i	−0.0306416	−	1.43667i
$357$			6.37752i			0.337534i
$358$	−15.7122	+	16.0509i	−0.830414	+	0.848314i
$359$	9.93716			0.524463			0.262232	−	0.965005i	$-0.415542\pi$
$359$	9.93716			0.524463			0.262232	+	0.965005i	$0.415542\pi$
$360$	5.60745	+	5.25972i	0.295539	+	0.277211i
$361$	−1.00000			−0.0526316
$362$	9.60516	−	9.81221i	0.504836	−	0.515718i
$363$			3.01562i			0.158279i
$364$	−13.7244	+	0.292717i	−0.719352	+	0.0153426i
$365$			15.1543i			0.793213i
$366$	−2.47665	−	2.42439i	−0.129457	−	0.126725i
$367$	−6.50515			−0.339566			−0.169783	−	0.985481i	$-0.554307\pi$
$367$	−6.50515			−0.339566			−0.169783	+	0.985481i	$0.554307\pi$
$368$	31.8663	−	1.35993i	1.66115	−	0.0708910i
$369$	7.90980			0.411768
$370$	1.11478	+	1.09126i	0.0579547	+	0.0567318i
$371$			18.3864i			0.954576i
$372$	3.79164	−	0.0808692i	0.196587	−	0.00419287i
$373$			18.1569i			0.940129i	0.882632	+	0.470065i	$0.155769\pi$
$373$			18.1569i			0.940129i	−0.882632	+	0.470065i	$0.844231\pi$
$374$	−30.3605	+	31.0150i	−1.56990	+	1.60375i
$375$	−0.530865			−0.0274138
$376$	11.9095	−	12.6969i	0.614188	−	0.654793i
$377$	−24.8078			−1.27767
$378$	−4.80115	+	4.90464i	−0.246944	+	0.252267i
$379$		−	30.5842i		−	1.57101i	−0.618858	−	0.785503i	$-0.712404\pi$
$379$		−	30.5842i		−	1.57101i	0.618858	−	0.785503i	$-0.287596\pi$
$380$	−0.0426469	−	1.99955i	−0.00218774	−	0.102575i
$381$		−	2.16069i		−	0.110695i
$382$	−5.39935	−	5.28542i	−0.276255	−	0.270426i
$383$	32.9375			1.68303			0.841514	−	0.540236i	$-0.181665\pi$
$383$	32.9375			1.68303			0.841514	+	0.540236i	$0.181665\pi$
$384$	4.55178	+	3.91841i	0.232282	+	0.199961i
$385$	−6.52964			−0.332781
$386$	6.75404	+	6.61153i	0.343772	+	0.336518i
$387$		−	11.7321i		−	0.596376i
$388$	0.130929	+	6.13874i	0.00664691	+	0.311647i
$389$		−	13.4993i		−	0.684444i	−0.939619	−	0.342222i	$-0.888821\pi$
$389$		−	13.4993i		−	0.684444i	0.939619	−	0.342222i	$-0.111179\pi$
$390$	2.25466	−	2.30326i	0.114169	−	0.116630i
$391$	59.9171			3.03014
$392$	−8.59913	+	9.16764i	−0.434322	+	0.463036i
$393$	−9.50233			−0.479329
$394$	−1.85193	+	1.89185i	−0.0932990	+	0.0953101i
$395$		−	3.08138i		−	0.155041i
$396$	−22.1981	+	0.473447i	−1.11550	+	0.0237916i
$397$			29.6811i			1.48965i	0.667259	+	0.744826i	$0.267467\pi$
$397$			29.6811i			1.48965i	−0.667259	+	0.744826i	$0.732533\pi$
$398$	−11.8782	−	11.6275i	−0.595398	−	0.582835i
$399$	0.848726			0.0424894
$400$	3.99636	−	0.170549i	0.199818	−	0.00852744i
$401$	5.56949			0.278127			0.139064	−	0.990283i	$-0.455591\pi$
$401$	5.56949			0.278127			0.139064	+	0.990283i	$0.455591\pi$
$402$	5.48335	+	5.36764i	0.273485	+	0.267714i
$403$			15.3352i			0.763901i
$404$	21.1405	−	0.450892i	1.05178	−	0.0224327i
$405$			6.54306i			0.325127i
$406$	9.13932	−	9.33633i	0.453577	−	0.463354i
$407$	−4.50519			−0.223314
$408$	8.22915	+	7.71884i	0.407404	+	0.382139i
$409$	−29.9040			−1.47866			−0.739330	−	0.673343i	$-0.764858\pi$
$409$	−29.9040			−1.47866			−0.739330	+	0.673343i	$0.764858\pi$
$410$	2.87877	−	2.94082i	0.142172	−	0.145237i
$411$		−	1.36943i		−	0.0675491i
$412$	0.451866	+	21.1862i	0.0222618	+	1.04377i
$413$			11.0562i			0.544040i
$414$	21.9042	+	21.4420i	1.07653	+	1.05382i
$415$	3.40976			0.167379
$416$	−16.2332	+	18.0634i	−0.795897	+	0.885629i
$417$	7.21715			0.353425
$418$	4.12750	+	4.04041i	0.201883	+	0.197623i
$419$			0.927860i			0.0453289i	0.999743	+	0.0226645i	$0.00721494\pi$
$419$			0.927860i			0.0453289i	−0.999743	+	0.0226645i	$0.992785\pi$
$420$	0.0361955	+	1.69707i	0.00176616	+	0.0828083i
$421$		−	36.2436i		−	1.76641i	−0.468990	−	0.883204i	$-0.655382\pi$
$421$		−	36.2436i		−	1.76641i	0.468990	−	0.883204i	$-0.344618\pi$
$422$	−16.1639	+	16.5123i	−0.786847	+	0.803808i
$423$	16.7298			0.813429
$424$	23.7247	+	22.2535i	1.15217	+	1.08072i
$425$	7.51422			0.364493
$426$	−5.96255	+	6.09107i	−0.288886	+	0.295114i
$427$			7.38045i			0.357165i
$428$	4.05182	−	0.0864185i	0.195852	−	0.00417719i
$429$			9.30824i			0.449406i
$430$	−4.36193	−	4.26989i	−0.210351	−	0.205912i
$431$	14.2580			0.686785			0.343392	−	0.939192i	$-0.388424\pi$
$431$	14.2580			0.686785			0.343392	+	0.939192i	$0.388424\pi$
$432$	0.517715	+	12.1313i	0.0249086	+	0.583667i
$433$	8.82519			0.424112			0.212056	−	0.977258i	$-0.431984\pi$
$433$	8.82519			0.424112			0.212056	+	0.977258i	$0.431984\pi$
$434$	−5.77134	−	5.64956i	−0.277033	−	0.271188i
$435$			3.06757i			0.147079i
$436$	−19.7922	+	0.422133i	−0.947873	+	0.0202165i
$437$		−	7.97383i		−	0.381440i
$438$	−7.95866	+	8.13022i	−0.380280	+	0.388477i
$439$	−20.6663			−0.986351			−0.493175	−	0.869930i	$-0.664164\pi$
$439$	−20.6663			−0.986351			−0.493175	+	0.869930i	$0.664164\pi$
$440$	−7.90295	+	8.42544i	−0.376758	+	0.401667i
$441$	−12.0795			−0.575215
$442$	−31.9140	+	32.6019i	−1.51799	+	1.55072i
$443$		−	11.4417i		−	0.543612i	−0.962352	−	0.271806i	$-0.912379\pi$
$443$		−	11.4417i		−	0.543612i	0.962352	−	0.271806i	$-0.0876209\pi$
$444$	0.0249735	+	1.17091i	0.00118519	+	0.0555689i
$445$		−	13.5566i		−	0.642643i
$446$	−14.2808	−	13.9795i	−0.676216	−	0.661947i
$447$	−0.735789			−0.0348016
$448$	−0.817690	−	12.7639i	−0.0386322	−	0.603038i
$449$	28.4103			1.34077			0.670383	−	0.742015i	$-0.266130\pi$
$449$	28.4103			1.34077			0.670383	+	0.742015i	$0.266130\pi$
$450$	2.74701	+	2.68905i	0.129495	+	0.126763i
$451$			11.8848i			0.559634i
$452$	−0.466085	−	21.8529i	−0.0219228	−	1.02787i
$453$		−	9.37045i		−	0.440262i
$454$	13.9857	−	14.2872i	0.656383	−	0.670532i
$455$	−6.86375			−0.321777
$456$	1.02723	−	1.09514i	0.0481045	−	0.0512848i
$457$	−35.1259			−1.64312			−0.821561	−	0.570121i	$-0.806896\pi$
$457$	−35.1259			−1.64312			−0.821561	+	0.570121i	$0.806896\pi$
$458$	12.9894	−	13.2694i	0.606955	−	0.620038i
$459$			22.8100i			1.06468i
$460$	15.9440	−	0.340059i	0.743394	−	0.0158553i
$461$		−	30.0315i		−	1.39871i	−0.714777	−	0.699353i	$-0.753472\pi$
$461$		−	30.0315i		−	1.39871i	0.714777	−	0.699353i	$-0.246528\pi$
$462$	−3.50312	−	3.42920i	−0.162980	−	0.159541i
$463$	−2.07091			−0.0962432			−0.0481216	−	0.998841i	$-0.515323\pi$
$463$	−2.07091			−0.0962432			−0.0481216	+	0.998841i	$0.515323\pi$
$464$	−0.985506	−	23.0928i	−0.0457510	−	1.07205i
$465$	1.89625			0.0879366
$466$	16.9783	+	16.6200i	0.786505	+	0.769909i
$467$		−	40.1423i		−	1.85756i	−0.370628	−	0.928781i	$-0.620858\pi$
$467$		−	40.1423i		−	1.85756i	0.370628	−	0.928781i	$-0.379142\pi$
$468$	−23.3339	+	0.497672i	−1.07861	+	0.0230049i
$469$		−	16.3404i		−	0.754531i
$470$	6.08879	−	6.22004i	0.280855	−	0.286909i
$471$	6.63393			0.305675
$472$	14.2662	+	13.3815i	0.656656	+	0.615935i
$473$	17.6280			0.810536
$474$	1.61826	−	1.65315i	0.0743293	−	0.0759316i
$475$		−	1.00000i		−	0.0458831i
$476$	−0.512336	−	24.0214i	−0.0234829	−	1.10102i
$477$			31.2603i			1.43131i
$478$	12.8439	+	12.5729i	0.587466	+	0.575070i
$479$	−26.0532			−1.19040			−0.595200	−	0.803577i	$-0.702927\pi$
$479$	−26.0532			−1.19040			−0.595200	+	0.803577i	$0.702927\pi$
$480$	2.23360	+	2.00729i	0.101949	+	0.0916198i
$481$	−4.73571			−0.215930
$482$	2.81582	+	2.75640i	0.128257	+	0.125551i
$483$			6.76759i			0.307936i
$484$	−0.242259	−	11.3586i	−0.0110118	−	0.516299i
$485$			3.07007i			0.139405i
$486$	−12.4454	+	12.7137i	−0.564534	+	0.576703i
$487$	−7.11676			−0.322491			−0.161245	−	0.986914i	$-0.551551\pi$
$487$	−7.11676			−0.322491			−0.161245	+	0.986914i	$0.551551\pi$
$488$	9.52328	+	8.93271i	0.431099	+	0.404365i
$489$	−5.64938			−0.255474
$490$	−4.39633	+	4.49110i	−0.198606	+	0.202887i
$491$			37.1832i			1.67805i	0.544090	+	0.839027i	$0.316875\pi$
$491$			37.1832i			1.67805i	−0.544090	+	0.839027i	$0.683125\pi$
$492$	3.08889	−	0.0658807i	0.139258	−	0.00297013i
$493$		−	43.4205i		−	1.95556i
$494$	4.33870	+	4.24715i	0.195207	+	0.191088i
$495$	−11.1016			−0.498978
$496$	−14.2750	+	0.609201i	−0.640967	+	0.0273539i
$497$	18.1515			0.814204
$498$	1.82932	+	1.79072i	0.0819738	+	0.0802441i
$499$			10.4518i			0.467888i	0.972250	+	0.233944i	$0.0751633\pi$
$499$			10.4518i			0.467888i	−0.972250	+	0.233944i	$0.924837\pi$
$500$	1.99955	−	0.0426469i	0.0894224	−	0.00190723i
$501$		−	4.95073i		−	0.221182i
$502$	18.9256	−	19.3335i	0.844690	−	0.862898i
$503$	−30.2318			−1.34797			−0.673985	−	0.738745i	$-0.735419\pi$
$503$	−30.2318			−1.34797			−0.673985	+	0.738745i	$0.735419\pi$
$504$	8.40903	−	8.96497i	0.374568	−	0.399331i
$505$	10.5727			0.470478
$506$	−32.2175	+	32.9120i	−1.43224	+	1.46312i
$507$			2.88328i			0.128051i
$508$	0.173578	+	8.13840i	0.00770128	+	0.361083i
$509$		−	12.5208i		−	0.554975i	−0.960729	−	0.277488i	$-0.910498\pi$
$509$		−	12.5208i		−	0.554975i	0.960729	−	0.277488i	$-0.0895017\pi$
$510$	4.03134	+	3.94628i	0.178511	+	0.174744i
$511$	24.2281			1.07179
$512$	−17.4594	−	14.3933i	−0.771605	−	0.636102i
$513$	3.03558			0.134024
$514$	−15.5200	−	15.1925i	−0.684558	−	0.670114i
$515$			10.5955i			0.466894i
$516$	−0.0977167	−	4.58155i	−0.00430174	−	0.201692i
$517$			25.1372i			1.10553i
$518$	1.74466	−	1.78227i	0.0766559	−	0.0783083i
$519$	−7.56797			−0.332197
$520$	−8.30733	+	8.85655i	−0.364301	+	0.388385i
$521$	15.0001			0.657168			0.328584	−	0.944475i	$-0.393429\pi$
$521$	15.0001			0.657168			0.328584	+	0.944475i	$0.393429\pi$
$522$	15.5385	−	15.8734i	0.680102	−	0.694762i
$523$			23.4506i			1.02543i	0.858560	+	0.512713i	$0.171359\pi$
$523$			23.4506i			1.02543i	−0.858560	+	0.512713i	$0.828641\pi$
$524$	35.7913	−	0.763366i	1.56355	−	0.0333478i
$525$			0.848726i			0.0370414i
$526$	30.9647	+	30.3113i	1.35013	+	1.32164i
$527$	−26.8408			−1.16920
$528$	−8.66472	+	0.369775i	−0.377084	+	0.0160924i
$529$	40.5819			1.76443
$530$	11.6224	+	11.3772i	0.504845	+	0.494192i
$531$			18.7975i			0.815743i
$532$	−3.19679	+	0.0681821i	−0.138599	+	0.00295607i
$533$			12.4929i			0.541129i
$534$	7.11957	−	7.27304i	0.308094	−	0.314735i
$535$	2.02637			0.0876077
$536$	−21.0847	−	19.7772i	−0.910719	−	0.854243i
$537$	−8.43142			−0.363843
$538$	21.7409	−	22.2095i	0.937316	−	0.957521i
$539$		−	18.1500i		−	0.781775i
$540$	0.129458	+	6.06979i	0.00557099	+	0.261202i
$541$			6.30059i			0.270884i	0.990785	+	0.135442i	$0.0432454\pi$
$541$			6.30059i			0.270884i	−0.990785	+	0.135442i	$0.956755\pi$
$542$	−2.47244	−	2.42027i	−0.106200	−	0.103959i
$543$	5.15429			0.221192
$544$	−31.6158	−	28.4125i	−1.35552	−	1.21818i
$545$	−9.89833			−0.423998
$546$	−3.68237	−	3.60466i	−0.157591	−	0.154265i
$547$		−	2.94592i		−	0.125958i	−0.998015	−	0.0629792i	$-0.979940\pi$
$547$		−	2.94592i		−	0.125958i	0.998015	−	0.0629792i	$-0.0200602\pi$
$548$	0.110013	+	5.15807i	0.00469952	+	0.220342i
$549$			12.5481i			0.535540i
$550$	−4.04041	+	4.12750i	−0.172284	+	0.175997i
$551$	−5.77844			−0.246170
$552$	8.73248	+	8.19096i	0.371679	+	0.348630i
$553$	−4.92639			−0.209492
$554$	−26.7516	+	27.3282i	−1.13657	+	1.16106i
$555$			0.585588i			0.0248568i
$556$	−27.1840	+	0.579788i	−1.15286	+	0.0245885i
$557$		−	1.01592i		−	0.0430460i	−0.999768	−	0.0215230i	$-0.993148\pi$
$557$		−	1.01592i		−	0.0430460i	0.999768	−	0.0215230i	$-0.00685151\pi$
$558$	−9.81233	−	9.60528i	−0.415389	−	0.406624i
$559$	18.5300			0.783735
$560$	−0.272667	−	6.38923i	−0.0115223	−	0.269994i
$561$	−16.2920			−0.687848
$562$	−16.1006	−	15.7609i	−0.679165	−	0.664834i
$563$		−	20.8276i		−	0.877781i	−0.898541	−	0.438890i	$-0.855372\pi$
$563$		−	20.8276i		−	0.877781i	0.898541	−	0.438890i	$-0.144628\pi$
$564$	6.53321	−	0.139342i	0.275098	−	0.00586736i
$565$		−	10.9289i		−	0.459784i
$566$	4.10953	−	4.19811i	0.172736	−	0.176460i
$567$	10.4608			0.439312
$568$	21.9691	−	23.4215i	0.921802	−	0.982745i
$569$	21.6656			0.908269			0.454135	−	0.890933i	$-0.349948\pi$
$569$	21.6656			0.908269			0.454135	+	0.890933i	$0.349948\pi$
$570$	0.525175	−	0.536495i	0.0219971	−	0.0224713i
$571$			11.1870i			0.468160i	0.972217	+	0.234080i	$0.0752078\pi$
$571$			11.1870i			0.468160i	−0.972217	+	0.234080i	$0.924792\pi$
$572$	−0.747774	−	35.0602i	−0.0312660	−	1.46594i
$573$		−	2.83625i		−	0.118486i
$574$	−4.70167	−	4.60246i	−0.196244	−	0.192103i
$575$	7.97383			0.332532
$576$	−1.39022	−	21.7010i	−0.0579259	−	0.904207i
$577$	−7.17954			−0.298888			−0.149444	−	0.988770i	$-0.547748\pi$
$577$	−7.17954			−0.298888			−0.149444	+	0.988770i	$0.547748\pi$
$578$	−39.8821	−	39.0405i	−1.65887	−	1.62387i
$579$			3.54786i			0.147444i
$580$	−0.246433	−	11.5543i	−0.0102326	−	0.479765i
$581$		−	5.45139i		−	0.226162i
$582$	−1.61232	+	1.64708i	−0.0668329	+	0.0682735i
$583$	−46.9699			−1.94530
$584$	29.3238	−	31.2625i	1.21343	−	1.29365i
$585$	−11.6696			−0.482479
$586$	20.8018	−	21.2502i	0.859316	−	0.877839i
$587$			21.8913i			0.903550i	0.892132	+	0.451775i	$0.149209\pi$
$587$			21.8913i			0.903550i	−0.892132	+	0.451775i	$0.850791\pi$
$588$	−4.71722	+	0.100610i	−0.194535	+	0.00414909i
$589$			3.57200i			0.147182i
$590$	6.98882	+	6.84135i	0.287725	+	0.281654i
$591$	−0.993778			−0.0408786
$592$	−0.188129	−	4.40831i	−0.00773206	−	0.181181i
$593$	−15.5372			−0.638036			−0.319018	−	0.947749i	$-0.603353\pi$
$593$	−15.5372			−0.638036			−0.319018	+	0.947749i	$0.603353\pi$
$594$	−12.5294	−	12.2650i	−0.514086	−	0.503239i
$595$		−	12.0134i		−	0.492503i
$596$	2.77141	−	0.0591094i	0.113521	−	0.00242121i
$597$		−	6.23953i		−	0.255367i
$598$	−33.8660	+	34.5960i	−1.38488	+	1.41474i
$599$	−33.3360			−1.36207			−0.681037	−	0.732249i	$-0.738471\pi$
$599$	−33.3360			−1.36207			−0.681037	+	0.732249i	$0.738471\pi$
$600$	1.09514	+	1.02723i	0.0447090	+	0.0419365i
$601$	0.180219			0.00735130			0.00367565	−	0.999993i	$-0.498830\pi$
$601$	0.180219			0.00735130			0.00367565	+	0.999993i	$0.498830\pi$
$602$	−6.82654	+	6.97369i	−0.278229	+	0.284226i
$603$		−	27.7817i		−	1.13136i
$604$	0.752772	+	35.2945i	0.0306299	+	1.43611i
$605$		−	5.68058i		−	0.230948i
$606$	5.67219	+	5.55250i	0.230417	+	0.225555i
$607$	−21.7657			−0.883441			−0.441720	−	0.897153i	$-0.645632\pi$
$607$	−21.7657			−0.883441			−0.441720	+	0.897153i	$0.645632\pi$
$608$	−3.78117	+	4.20747i	−0.153347	+	0.170635i
$609$	4.90432			0.198733
$610$	4.66532	+	4.56688i	0.188893	+	0.184907i
$611$			26.4234i			1.06898i
$612$	−0.871063	−	40.8408i	−0.0352107	−	1.65089i
$613$		−	0.0959402i		−	0.00387499i	−0.999998	−	0.00193749i	$-0.999383\pi$
$613$		−	0.0959402i		−	0.00387499i	0.999998	−	0.00193749i	$-0.000616724\pi$
$614$	16.5076	−	16.8635i	0.666194	−	0.680554i
$615$	1.54480			0.0622922
$616$	13.4703	+	12.6349i	0.542732	+	0.509076i
$617$	46.4973			1.87191			0.935956	−	0.352117i	$-0.114538\pi$
$617$	46.4973			1.87191			0.935956	+	0.352117i	$0.114538\pi$
$618$	−5.56450	+	5.68445i	−0.223837	+	0.228662i
$619$		−	6.37072i		−	0.256061i	−0.991770	−	0.128030i	$-0.959135\pi$
$619$		−	6.37072i		−	0.256061i	0.991770	−	0.128030i	$-0.0408655\pi$
$620$	−7.14238	+	0.152335i	−0.286845	+	0.00611791i
$621$			24.2052i			0.971322i
$622$	9.22128	+	9.02670i	0.369739	+	0.361938i
$623$	−21.6737			−0.868339
$624$	−9.10808	+	0.388696i	−0.364615	+	0.0155603i
$625$	1.00000			0.0400000
$626$	23.8187	+	23.3161i	0.951988	+	0.931900i
$627$			2.16815i			0.0865876i
$628$	−24.9872	+	0.532934i	−0.997098	+	0.0212664i
$629$		−	8.28880i		−	0.330496i
$630$	4.29914	−	4.39181i	0.171282	−	0.174974i
$631$	−28.9645			−1.15306			−0.576530	−	0.817076i	$-0.695594\pi$
$631$	−28.9645			−1.15306			−0.576530	+	0.817076i	$0.695594\pi$
$632$	−5.96252	+	6.35671i	−0.237176	+	0.252856i
$633$	−8.67383			−0.344754
$634$	−13.5059	+	13.7970i	−0.536387	+	0.547950i
$635$			4.07012i			0.161518i
$636$	0.260367	+	12.2076i	0.0103242	+	0.484062i
$637$		−	19.0787i		−	0.755925i
$638$	23.8505	+	23.3473i	0.944252	+	0.924327i
$639$	30.8608			1.22083
$640$	−8.57427	−	7.38118i	−0.338928	−	0.291767i
$641$	23.1989			0.916301			0.458151	−	0.888875i	$-0.348512\pi$
$641$	23.1989			0.916301			0.458151	+	0.888875i	$0.348512\pi$
$642$	1.08714	+	1.06420i	0.0429060	+	0.0420006i
$643$			2.62001i			0.103323i	0.998665	+	0.0516616i	$0.0164517\pi$
$643$			2.62001i			0.103323i	−0.998665	+	0.0516616i	$0.983548\pi$
$644$	−0.543673	−	25.4907i	−0.0214237	−	1.00447i
$645$		−	2.29130i		−	0.0902197i
$646$	−7.43368	+	7.59391i	−0.292474	+	0.298779i
$647$	−6.48788			−0.255065			−0.127532	−	0.991834i	$-0.540706\pi$
$647$	−6.48788			−0.255065			−0.127532	+	0.991834i	$0.540706\pi$
$648$	12.6609	−	13.4980i	0.497367	−	0.530250i
$649$	−28.2441			−1.10868
$650$	−4.24715	+	4.33870i	−0.166587	+	0.170178i
$651$		−	3.03165i		−	0.118820i
$652$	21.2788	−	0.453841i	0.833344	−	0.0177738i
$653$		−	26.3459i		−	1.03099i	−0.856891	−	0.515497i	$-0.827607\pi$
$653$		−	26.3459i		−	1.03099i	0.856891	−	0.515497i	$-0.172393\pi$
$654$	−5.31041	−	5.19835i	−0.207653	−	0.203272i
$655$	17.8997			0.699399
$656$	−11.6293	+	0.496290i	−0.454046	+	0.0193769i
$657$	41.1922			1.60706
$658$	−9.94435	−	9.73451i	−0.387671	−	0.379491i
$659$			17.9787i			0.700350i	0.936684	+	0.350175i	$0.113878\pi$
$659$			17.9787i			0.700350i	−0.936684	+	0.350175i	$0.886122\pi$
$660$	−4.33532	+	0.0924649i	−0.168752	+	0.00359919i
$661$		−	20.4574i		−	0.795700i	−0.917450	−	0.397850i	$-0.869756\pi$
$661$		−	20.4574i		−	0.795700i	0.917450	−	0.397850i	$-0.130244\pi$
$662$	−22.4543	+	22.9383i	−0.872710	+	0.891522i
$663$	−17.1256			−0.665103
$664$	−7.03414	−	6.59793i	−0.272977	−	0.256049i
$665$	−1.59876			−0.0619973
$666$	2.96624	−	3.03018i	0.114939	−	0.117417i
$667$		−	46.0763i		−	1.78408i
$668$	0.397715	+	18.6473i	0.0153881	+	0.721486i
$669$		−	7.50162i		−	0.290029i
$670$	−10.3291	−	10.1111i	−0.399047	−	0.390627i
$671$	−18.8541			−0.727853
$672$	3.20918	−	3.57099i	0.123797	−	0.137754i
$673$	−26.5170			−1.02215			−0.511077	−	0.859535i	$-0.670753\pi$
$673$	−26.5170			−1.02215			−0.511077	+	0.859535i	$0.670753\pi$
$674$	−36.0480	−	35.2874i	−1.38852	−	1.35922i
$675$			3.03558i			0.116840i
$676$	−0.231627	−	10.8601i	−0.00890874	−	0.417696i
$677$			24.0962i			0.926092i	0.886334	+	0.463046i	$0.153244\pi$
$677$			24.0962i			0.926092i	−0.886334	+	0.463046i	$0.846756\pi$
$678$	5.73960	−	5.86332i	0.220428	−	0.225180i
$679$	4.90831			0.188363
$680$	−15.5014	−	14.5401i	−0.594451	−	0.557588i
$681$	7.50498			0.287592
$682$	14.4323	−	14.7434i	0.552643	−	0.564556i
$683$			36.1606i			1.38365i	0.722066	+	0.691824i	$0.243193\pi$
$683$			36.1606i			1.38365i	−0.722066	+	0.691824i	$0.756807\pi$
$684$	−5.43513	+	0.115922i	−0.207817	+	0.00443239i
$685$			2.57962i			0.0985623i
$686$	18.4902	+	18.1000i	0.705959	+	0.691063i
$687$	6.97034			0.265935
$688$	0.736115	+	17.2489i	0.0280641	+	0.657609i
$689$	−49.3733			−1.88097
$690$	4.27792	+	4.18765i	0.162858	+	0.159421i
$691$			21.7649i			0.827976i	0.910282	+	0.413988i	$0.135864\pi$
$691$			21.7649i			0.827976i	−0.910282	+	0.413988i	$0.864136\pi$
$692$	28.5054	−	0.607970i	1.08361	−	0.0231116i
$693$			17.7487i			0.674219i
$694$	−6.26604	+	6.40111i	−0.237856	+	0.242983i
$695$	−13.5951			−0.515691
$696$	5.93579	−	6.32822i	0.224996	−	0.239871i
$697$	−21.8661			−0.828237
$698$	−17.6341	+	18.0142i	−0.667460	+	0.681848i
$699$			8.91860i			0.337332i
$700$	−0.0681821	−	3.19679i	−0.00257704	−	0.120827i
$701$			9.06451i			0.342362i	0.985240	+	0.171181i	$0.0547583\pi$
$701$			9.06451i			0.342362i	−0.985240	+	0.171181i	$0.945242\pi$
$702$	−13.1705	−	12.8926i	−0.497088	−	0.486599i
$703$	−1.10308			−0.0416035
$704$	32.6067	−	2.08887i	1.22891	−	0.0787271i
$705$	3.26735			0.123055
$706$	−28.0781	−	27.4856i	−1.05673	−	1.03443i
$707$		−	16.9032i		−	0.635709i
$708$	0.156565	+	7.34070i	0.00588406	+	0.275880i
$709$		−	21.2734i		−	0.798938i	−0.916747	−	0.399469i	$-0.869195\pi$
$709$		−	21.2734i		−	0.798938i	0.916747	−	0.399469i	$-0.130805\pi$
$710$	11.2318	−	11.4739i	0.421520	−	0.430607i
$711$	−8.37576			−0.314116
$712$	−26.2321	+	27.9664i	−0.983091	+	1.04809i
$713$	−28.4825			−1.06668
$714$	6.30915	−	6.44515i	0.236114	−	0.241204i
$715$		−	17.5341i		−	0.655738i
$716$	31.7576	−	0.677335i	1.18684	−	0.0253132i
$717$			6.74682i			0.251965i
$718$	−10.0426	−	9.83064i	−0.374785	−	0.366876i
$719$	38.8544			1.44902			0.724512	−	0.689262i	$-0.242065\pi$
$719$	38.8544			1.44902			0.724512	+	0.689262i	$0.242065\pi$
$720$	−0.463583	−	10.8628i	−0.0172767	−	0.404834i
$721$	16.9397			0.630867
$722$	1.01061	+	0.989281i	0.0376108	+	0.0368172i
$723$			1.47913i			0.0550095i
$724$	−19.4141	+	0.414069i	−0.721518	+	0.0153887i
$725$		−	5.77844i		−	0.214606i
$726$	2.98330	−	3.04760i	0.110720	−	0.113107i
$727$	22.3400			0.828546			0.414273	−	0.910153i	$-0.364036\pi$
$727$	22.3400			0.828546			0.414273	+	0.910153i	$0.364036\pi$
$728$	14.1595	+	13.2814i	0.524786	+	0.492243i
$729$	12.9508			0.479659
$730$	14.9919	−	15.3150i	0.554874	−	0.566835i
$731$			32.4326i			1.19956i
$732$	0.104513	+	4.90021i	0.00386292	+	0.181117i
$733$			7.54019i			0.278503i	0.990257	+	0.139252i	$0.0444697\pi$
$733$			7.54019i			0.278503i	−0.990257	+	0.139252i	$0.955530\pi$
$734$	6.57414	+	6.43542i	0.242656	+	0.237536i
$735$	−2.35915			−0.0870184
$736$	−33.5496	−	30.1504i	−1.23665	−	1.11136i
$737$	41.7432			1.53763
$738$	−7.99369	−	7.82501i	−0.294252	−	0.288043i
$739$		−	20.2897i		−	0.746369i	−0.927757	−	0.373184i	$-0.878266\pi$
$739$		−	20.2897i		−	0.746369i	0.927757	−	0.373184i	$-0.121734\pi$
$740$	−0.0470430	−	2.20566i	−0.00172933	−	0.0810817i
$741$			2.27909i			0.0837245i
$742$	18.1894	−	18.5814i	0.667752	−	0.682146i
$743$	−40.5952			−1.48929			−0.744647	−	0.667458i	$-0.767382\pi$
$743$	−40.5952			−1.48929			−0.744647	+	0.667458i	$0.767382\pi$
$744$	−3.91186	−	3.66927i	−0.143416	−	0.134522i
$745$	1.38602			0.0507798
$746$	17.9623	−	18.3495i	0.657646	−	0.671822i
$747$		−	9.26835i		−	0.339111i
$748$	61.3650	−	1.30881i	2.24373	−	0.0478549i
$749$		−	3.23968i		−	0.118376i
$750$	0.536495	+	0.525175i	0.0195900	+	0.0191767i
$751$	−41.1087			−1.50008			−0.750038	−	0.661394i	$-0.769965\pi$
$751$	−41.1087			−1.50008			−0.750038	+	0.661394i	$0.769965\pi$
$752$	−24.5967	+	1.04969i	−0.896948	+	0.0382781i
$753$	10.1558			0.370098
$754$	25.0709	+	24.5419i	0.913029	+	0.893764i
$755$			17.6513i			0.642396i
$756$	9.70413	−	0.206973i	0.352936	−	0.00752752i
$757$			23.1182i			0.840245i	0.907467	+	0.420123i	$0.138013\pi$
$757$			23.1182i			0.840245i	−0.907467	+	0.420123i	$0.861987\pi$
$758$	−30.2564	+	30.9086i	−1.09896	+	1.12265i
$759$	−17.2885			−0.627532
$760$	−1.93501	+	2.06294i	−0.0701903	+	0.0748307i
$761$	−19.5773			−0.709676			−0.354838	−	0.934928i	$-0.615464\pi$
$761$	−19.5773			−0.709676			−0.354838	+	0.934928i	$0.615464\pi$
$762$	−2.13753	+	2.18360i	−0.0774344	+	0.0791036i
$763$			15.8251i			0.572906i
$764$	0.227849	+	10.6830i	0.00824329	+	0.386496i
$765$		−	20.4250i		−	0.738468i
$766$	−33.2868	−	32.5844i	−1.20270	−	1.17732i
$767$	−29.6893			−1.07202
$768$	−0.723648	−	8.46296i	−0.0261124	−	0.305381i
$769$	37.2201			1.34219			0.671095	−	0.741371i	$-0.265824\pi$
$769$	37.2201			1.34219			0.671095	+	0.741371i	$0.265824\pi$
$770$	6.59889	+	6.45964i	0.237807	+	0.232789i
$771$		−	8.15257i		−	0.293608i
$772$	−0.285016	−	13.3633i	−0.0102580	−	0.480955i
$773$		−	7.99430i		−	0.287535i	−0.989611	−	0.143768i	$-0.954078\pi$
$773$		−	7.99430i		−	0.287535i	0.989611	−	0.143768i	$-0.0459218\pi$
$774$	−11.6063	+	11.8565i	−0.417181	+	0.426174i
$775$	−3.57200			−0.128310
$776$	5.94062	−	6.33337i	0.213256	−	0.227355i
$777$	0.936214			0.0335865
$778$	−13.3546	+	13.6425i	−0.478787	+	0.489108i
$779$			2.90996i			0.104260i
$780$	−4.55715	+	0.0971962i	−0.163172	+	0.00348018i
$781$			46.3696i			1.65924i
$782$	−60.5526	−	59.2748i	−2.16535	−	2.11966i
$783$	17.5409			0.626862
$784$	17.7597	−	0.757913i	0.634275	−	0.0270683i
$785$	−12.4964			−0.446017
$786$	9.60310	+	9.40047i	0.342531	+	0.335304i
$787$			34.8314i			1.24160i	0.783967	+	0.620802i	$0.213193\pi$
$787$			34.8314i			1.24160i	−0.783967	+	0.620802i	$0.786807\pi$
$788$	3.74314	−	0.0798349i	0.133344	−	0.00284400i
$789$			16.2656i			0.579070i
$790$	−3.04835	+	3.11406i	−0.108456	+	0.110793i
$791$	−17.4728			−0.621260
$792$	22.9019	+	21.4817i	0.813783	+	0.763318i
$793$	−19.8188			−0.703786
$794$	29.3629	−	29.9959i	1.04205	−	1.06451i
$795$			6.10518i			0.216528i
$796$	0.501250	+	23.5017i	0.0177663	+	0.832995i
$797$			10.7193i			0.379697i	0.981813	+	0.189849i	$0.0607998\pi$
$797$			10.7193i			0.379697i	−0.981813	+	0.189849i	$0.939200\pi$
$798$	−0.857727	−	0.839628i	−0.0303632	−	0.0297225i
$799$	−46.2482			−1.63615
$800$	−4.20747	−	3.78117i	−0.148756	−	0.133684i
$801$	−36.8492			−1.30200
$802$	−5.62856	−	5.50979i	−0.198751	−	0.194558i
$803$			61.8931i			2.18416i
$804$	−0.231394	−	10.8491i	−0.00816062	−	0.382620i
$805$		−	12.7482i		−	0.449316i
$806$	15.1708	−	15.4978i	0.534370	−	0.545888i
$807$	11.6665			0.410681
$808$	−21.8108	−	20.4583i	−0.767302	−	0.719719i
$809$	28.7727			1.01159			0.505797	−	0.862652i	$-0.331198\pi$
$809$	28.7727			1.01159			0.505797	+	0.862652i	$0.331198\pi$
$810$	6.47293	−	6.61245i	0.227435	−	0.232338i
$811$			17.7551i			0.623465i	0.950170	+	0.311733i	$0.100909\pi$
$811$			17.7551i			0.623465i	−0.950170	+	0.311733i	$0.899091\pi$
$812$	−18.4725	+	0.393987i	−0.648258	+	0.0138262i
$813$		−	1.29876i		−	0.0455494i
$814$	4.55297	+	4.45690i	0.159582	+	0.156214i
$815$	10.6418			0.372767
$816$	−0.680325	−	15.9416i	−0.0238161	−	0.558069i
$817$	4.31616			0.151003
$818$	30.2212	+	29.5835i	1.05666	+	1.03436i
$819$			18.6569i			0.651925i
$820$	−5.81860	+	0.124101i	−0.203194	+	0.00433378i
$821$		−	44.3665i		−	1.54840i	−0.632939	−	0.774202i	$-0.718152\pi$
$821$		−	44.3665i		−	1.54840i	0.632939	−	0.774202i	$-0.281848\pi$
$822$	−1.35475	+	1.38396i	−0.0472524	+	0.0482710i
$823$	52.3287			1.82406			0.912032	−	0.410118i	$-0.134513\pi$
$823$	52.3287			1.82406			0.912032	+	0.410118i	$0.134513\pi$
$824$	20.5025	−	21.8579i	0.714237	−	0.761457i
$825$	−2.16815			−0.0754854
$826$	10.9377	−	11.1734i	0.380571	−	0.388774i
$827$			36.8109i			1.28004i	0.768358	+	0.640021i	$0.221074\pi$
$827$			36.8109i			1.28004i	−0.768358	+	0.640021i	$0.778926\pi$
$828$	−0.924342	−	43.3388i	−0.0321231	−	1.50613i
$829$		−	6.63815i		−	0.230553i	−0.993333	−	0.115276i	$-0.963225\pi$
$829$		−	6.63815i		−	0.230553i	0.993333	−	0.115276i	$-0.0367753\pi$
$830$	−3.44592	−	3.37321i	−0.119610	−	0.117086i
$831$	−14.3553			−0.497981
$832$	34.2751	−	2.19575i	1.18827	−	0.0761239i
$833$	33.3929			1.15700
$834$	−7.29369	−	7.13979i	−0.252560	−	0.247231i
$835$			9.32577i			0.322732i
$836$	−0.174178	−	8.16652i	−0.00602406	−	0.282445i
$837$		−	10.8431i		−	0.374793i
$838$	0.917914	−	0.937701i	0.0317088	−	0.0323923i
$839$	34.1930			1.18047			0.590236	−	0.807231i	$-0.299035\pi$
$839$	34.1930			1.18047			0.590236	+	0.807231i	$0.299035\pi$
$840$	1.64230	−	1.75087i	0.0566646	−	0.0604108i
$841$	−4.39042			−0.151394
$842$	−35.8551	+	36.6280i	−1.23565	+	1.26229i
$843$		−	8.45757i		−	0.291294i
$844$	32.6707	−	0.696810i	1.12457	−	0.0239852i
$845$		−	5.43128i		−	0.186842i
$846$	−16.9072	−	16.5504i	−0.581281	−	0.569016i
$847$	−9.08188			−0.312057
$848$	−1.96138	−	45.9599i	−0.0673542	−	1.57827i
$849$	2.20524			0.0756838
$850$	−7.59391	−	7.43368i	−0.260469	−	0.254973i
$851$		−	8.79578i		−	0.301516i
$852$	12.0516	−	0.257039i	0.412880	−	0.00880602i
$853$			27.3027i			0.934826i	0.884039	+	0.467413i	$0.154814\pi$
$853$			27.3027i			0.934826i	−0.884039	+	0.467413i	$0.845186\pi$
$854$	7.30134	−	7.45873i	0.249847	−	0.255232i
$855$	−2.71818			−0.0929599
$856$	−4.18029	−	3.92106i	−0.142879	−	0.134019i
$857$	8.87790			0.303263			0.151632	−	0.988437i	$-0.451547\pi$
$857$	8.87790			0.303263			0.151632	+	0.988437i	$0.451547\pi$
$858$	9.20846	−	9.40696i	0.314372	−	0.321148i
$859$		−	36.8942i		−	1.25881i	−0.777076	−	0.629407i	$-0.783298\pi$
$859$		−	36.8942i		−	1.25881i	0.777076	−	0.629407i	$-0.216702\pi$
$860$	0.184071	+	8.63035i	0.00627676	+	0.294293i
$861$		−	2.46976i		−	0.0841691i
$862$	−14.4092	−	14.1052i	−0.490780	−	0.480425i
$863$	−25.5457			−0.869587			−0.434793	−	0.900530i	$-0.643179\pi$
$863$	−25.5457			−0.869587			−0.434793	+	0.900530i	$0.643179\pi$
$864$	11.4780	−	12.7721i	0.390491	−	0.434516i
$865$	14.2559			0.484716
$866$	−8.91879	−	8.73060i	−0.303073	−	0.296678i
$867$		−	20.9498i		−	0.711493i
$868$	0.243547	+	11.4190i	0.00826652	+	0.387585i
$869$		−	12.5849i		−	0.426915i
$870$	3.03469	−	3.10011i	0.102886	−	0.105103i
$871$	43.8791			1.48679
$872$	20.4197	+	19.1534i	0.691498	+	0.648616i
$873$	8.34501			0.282436
$874$	−7.88835	+	8.05839i	−0.266828	+	0.272579i
$875$		−	1.59876i		−	0.0540480i
$876$	16.0861	−	0.343090i	0.543500	−	0.0115919i
$877$			22.6731i			0.765615i	0.923828	+	0.382808i	$0.125043\pi$
$877$			22.6731i			0.765615i	−0.923828	+	0.382808i	$0.874957\pi$
$878$	20.8855	+	20.4448i	0.704852	+	0.689979i
$879$	11.1626			0.376506
$880$	16.3219	−	0.696553i	0.550211	−	0.0234808i
$881$	32.3070			1.08845			0.544225	−	0.838939i	$-0.316824\pi$
$881$	32.3070			1.08845			0.544225	+	0.838939i	$0.316824\pi$
$882$	12.2076	+	11.9500i	0.411052	+	0.402378i
$883$		−	23.7637i		−	0.799711i	−0.916578	−	0.399856i	$-0.869060\pi$
$883$		−	23.7637i		−	0.799711i	0.916578	−	0.399856i	$-0.130940\pi$
$884$	64.5050	−	1.37578i	2.16954	−	0.0462725i
$885$			3.67119i			0.123406i
$886$	−11.3191	+	11.5630i	−0.380271	+	0.388468i
$887$	−40.8668			−1.37217			−0.686087	−	0.727520i	$-0.740673\pi$
$887$	−40.8668			−1.37217			−0.686087	+	0.727520i	$0.740673\pi$
$888$	1.13312	−	1.20803i	0.0380250	−	0.0405389i
$889$	6.50715			0.218243
$890$	−13.4113	+	13.7003i	−0.449546	+	0.459237i
$891$			26.7231i			0.895257i
$892$	0.602640	+	28.2555i	0.0201779	+	0.946062i
$893$			6.15476i			0.205961i
$894$	0.743592	+	0.727902i	0.0248694	+	0.0243447i
$895$	15.8824			0.530891
$896$	−11.8007	+	13.7082i	−0.394235	+	0.457959i
$897$	−18.1731			−0.606782
$898$	−28.7116	−	28.1058i	−0.958120	−	0.937903i
$899$			20.6406i			0.688403i
$900$	−0.115922	−	5.43513i	−0.00386407	−	0.181171i
$901$		−	86.4168i		−	2.87896i
$902$	11.7574	−	12.0109i	0.391479	−	0.399918i
$903$	−3.66324			−0.121905
$904$	−21.1476	+	22.5458i	−0.703360	+	0.749861i
$905$	−9.70924			−0.322746
$906$	−9.27000	+	9.46982i	−0.307975	+	0.314614i
$907$			6.07897i			0.201849i	0.994894	+	0.100925i	$0.0321801\pi$
$907$			6.07897i			0.201849i	−0.994894	+	0.100925i	$0.967820\pi$
$908$	−28.2681	+	0.602910i	−0.938110	+	0.0200083i
$909$		−	28.7385i		−	0.953195i
$910$	6.93654	+	6.79017i	0.229944	+	0.225092i
$911$	36.8291			1.22020			0.610102	−	0.792323i	$-0.291129\pi$
$911$	36.8291			1.22020			0.610102	+	0.792323i	$0.291129\pi$
$912$	−2.12153	+	0.0905383i	−0.0702508	+	0.00299802i
$913$	13.9261			0.460887
$914$	35.4984	+	34.7494i	1.17418	+	1.14941i
$915$			2.45066i			0.0810164i
$916$	−26.2543	+	0.559960i	−0.867467	+	0.0185016i
$917$		−	28.6173i		−	0.945028i
$918$	22.5655	−	23.0520i	0.744774	−	0.760828i
$919$	21.5592			0.711171			0.355586	−	0.934644i	$-0.384281\pi$
$919$	21.5592			0.711171			0.355586	+	0.934644i	$0.384281\pi$
$920$	−16.4495	−	15.4295i	−0.542325	−	0.508694i
$921$	8.85827			0.291890
$922$	−29.7096	+	30.3500i	−0.978433	+	0.999524i
$923$			48.7423i			1.60437i
$924$	0.147829	+	6.93113i	0.00486322	+	0.228018i
$925$		−	1.10308i		−	0.0362691i
$926$	2.09287	+	2.04871i	0.0687759	+	0.0673247i
$927$	28.8006			0.945934
$928$	−21.8493	+	24.3126i	−0.717237	+	0.798101i
$929$	−36.9410			−1.21200			−0.605998	−	0.795466i	$-0.707226\pi$
$929$	−36.9410			−1.21200			−0.605998	+	0.795466i	$0.707226\pi$
$930$	−1.91636	−	1.87593i	−0.0628400	−	0.0615140i
$931$		−	4.44396i		−	0.145645i
$932$	−0.716473	−	33.5926i	−0.0234689	−	1.10036i
$933$			4.84388i			0.158582i
$934$	−39.7120	+	40.5680i	−1.29942	+	1.32743i
$935$	30.6895			1.00365
$936$	24.0737	+	22.5808i	0.786874	+	0.738078i
$937$	−55.5587			−1.81502			−0.907512	−	0.420026i	$-0.862021\pi$
$937$	−55.5587			−1.81502			−0.907512	+	0.420026i	$0.862021\pi$
$938$	−16.1653	+	16.5137i	−0.527815	+	0.539192i
$939$			12.5118i			0.408308i
$940$	−12.3067	+	0.262481i	−0.401401	+	0.00856120i
$941$		−	3.59643i		−	0.117240i	−0.998280	−	0.0586201i	$-0.981330\pi$
$941$		−	3.59643i		−	0.117240i	0.998280	−	0.0586201i	$-0.0186701\pi$
$942$	−6.70428	−	6.56282i	−0.218437	−	0.213828i
$943$	−23.2035			−0.755610
$944$	−1.17943	−	27.6368i	−0.0383870	−	0.899500i
$945$	4.85317			0.157874
$946$	−17.8149	−	17.4390i	−0.579214	−	0.566992i
$947$		−	29.4296i		−	0.956334i	−0.878269	−	0.478167i	$-0.841301\pi$
$947$		−	29.4296i		−	0.956334i	0.878269	−	0.478167i	$-0.158699\pi$
$948$	−3.27085	+	0.0697617i	−0.106232	+	0.00226576i
$949$			65.0600i			2.11194i
$950$	−0.989281	+	1.01061i	−0.0320965	+	0.0327884i
$951$	−7.24749			−0.235016
$952$	−23.2462	+	24.7830i	−0.753412	+	0.803222i
$953$	54.0253			1.75005			0.875026	−	0.484077i	$-0.160844\pi$
$953$	54.0253			1.75005			0.875026	+	0.484077i	$0.160844\pi$
$954$	30.9252	−	31.5918i	1.00124	−	1.02282i
$955$			5.34269i			0.172885i
$956$	−0.542003	−	25.4124i	−0.0175296	−	0.821897i
$957$			12.5285i			0.404990i
$958$	26.3295	+	25.7739i	0.850667	+	0.832717i
$959$	4.12420			0.133177
$960$	−0.271512	−	4.23823i	−0.00876302	−	0.136788i
$961$	−18.2408			−0.588413
$962$	4.78594	+	4.68495i	0.154305	+	0.151049i
$963$		−	5.50805i		−	0.177494i
$964$	−0.118826	−	5.57127i	−0.00382711	−	0.179438i
$965$		−	6.68316i		−	0.215139i
$966$	6.69505	−	6.83937i	0.215410	−	0.220053i
$967$	−4.11964			−0.132479			−0.0662394	−	0.997804i	$-0.521100\pi$
$967$	−4.11964			−0.132479			−0.0662394	+	0.997804i	$0.521100\pi$
$968$	−10.9920	+	11.7187i	−0.353296	+	0.376653i
$969$	−3.98904			−0.128146
$970$	3.03716	−	3.10263i	0.0975174	−	0.0996194i
$971$		−	22.6082i		−	0.725531i	−0.931881	−	0.362765i	$-0.881833\pi$
$971$		−	22.6082i		−	0.725531i	0.931881	−	0.362765i	$-0.118167\pi$
$972$	25.1547	−	0.536508i	0.806839	−	0.0172085i
$973$			21.7353i			0.696801i
$974$	7.19223	+	7.04047i	0.230454	+	0.225591i
$975$	−2.27909			−0.0729894
$976$	−0.787314	−	18.4486i	−0.0252013	−	0.590527i
$977$	33.7930			1.08113			0.540567	−	0.841301i	$-0.318210\pi$
$977$	33.7930			1.08113			0.540567	+	0.841301i	$0.318210\pi$
$978$	5.70930	+	5.58882i	0.182563	+	0.178711i
$979$		−	55.3676i		−	1.76956i
$980$	8.88591	−	0.189521i	0.283850	−	0.00605403i
$981$			26.9055i			0.859026i
$982$	36.7846	−	37.5775i	1.17384	−	1.19915i
$983$	54.5710			1.74054			0.870272	−	0.492572i	$-0.163943\pi$
$983$	54.5710			1.74054			0.870272	+	0.492572i	$0.163943\pi$
$984$	−3.18682	−	2.98920i	−0.101592	−	0.0952922i
$985$	1.87200			0.0596468
$986$	−42.9551	+	43.8810i	−1.36797	+	1.39746i
$987$		−	5.22371i		−	0.166272i
$988$	−0.183090	−	8.58438i	−0.00582487	−	0.273106i
$989$			34.4163i			1.09437i
$990$	11.2193	+	10.9826i	0.356573	+	0.349049i
$991$	33.8783			1.07618			0.538090	−	0.842888i	$-0.319146\pi$
$991$	33.8783			1.07618			0.538090	+	0.842888i	$0.319146\pi$
$992$	15.0291	+	13.5063i	0.477174	+	0.428827i
$993$	−12.0493			−0.382374
$994$	−18.3440	−	17.9569i	−0.581835	−	0.569558i
$995$			11.7535i			0.372611i
$996$	−0.0771961	−	3.61942i	−0.00244605	−	0.114686i
$997$		−	41.4264i		−	1.31199i	−0.754767	−	0.655993i	$-0.772250\pi$
$997$		−	41.4264i		−	1.31199i	0.754767	−	0.655993i	$-0.227750\pi$
$998$	10.3398	−	10.5627i	0.327300	−	0.334356i
$999$	3.34850			0.105942

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	760.2.f.b.381.9	✓	44
4.3	odd	2		3040.2.f.b.1521.25		44
8.3	odd	2		3040.2.f.b.1521.20		44
8.5	even	2	inner	760.2.f.b.381.10	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
760.2.f.b.381.9	✓	44	1.1	even	1	trivial
760.2.f.b.381.10	yes	44	8.5	even	2	inner
3040.2.f.b.1521.20		44	8.3	odd	2
3040.2.f.b.1521.25		44	4.3	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	760.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.01061 - 0.989281i) q^{2} -0.530865i q^{3} +(0.0426469 + 1.99955i) q^{4} +1.00000i q^{5} +(-0.525175 + 0.536495i) q^{6} +1.59876 q^{7} +(1.93501 - 2.06294i) q^{8} +2.71818 q^{9} +(0.989281 - 1.01061i) q^{10} +4.08419i q^{11} +(1.06149 - 0.0226397i) q^{12} +4.29317i q^{13} +(-1.61572 - 1.58162i) q^{14} +0.530865 q^{15} +(-3.99636 + 0.170549i) q^{16} -7.51422 q^{17} +(-2.74701 - 2.68905i) q^{18} +1.00000i q^{19} +(-1.99955 + 0.0426469i) q^{20} -0.848726i q^{21} +(4.04041 - 4.12750i) q^{22} -7.97383 q^{23} +(-1.09514 - 1.02723i) q^{24} -1.00000 q^{25} +(4.24715 - 4.33870i) q^{26} -3.03558i q^{27} +(0.0681821 + 3.19679i) q^{28} +5.77844i q^{29} +(-0.536495 - 0.525175i) q^{30} +3.57200 q^{31} +(4.20747 + 3.78117i) q^{32} +2.16815 q^{33} +(7.59391 + 7.43368i) q^{34} +1.59876i q^{35} +(0.115922 + 5.43513i) q^{36} +1.10308i q^{37} +(0.989281 - 1.01061i) q^{38} +2.27909 q^{39} +(2.06294 + 1.93501i) q^{40} +2.90996 q^{41} +(-0.839628 + 0.857727i) q^{42} -4.31616i q^{43} +(-8.16652 + 0.174178i) q^{44} +2.71818i q^{45} +(8.05839 + 7.88835i) q^{46} +6.15476 q^{47} +(0.0905383 + 2.12153i) q^{48} -4.44396 q^{49} +(1.01061 + 0.989281i) q^{50} +3.98904i q^{51} +(-8.58438 + 0.183090i) q^{52} +11.5004i q^{53} +(-3.00304 + 3.06778i) q^{54} -4.08419 q^{55} +(3.09362 - 3.29815i) q^{56} +0.530865 q^{57} +(5.71650 - 5.83973i) q^{58} +6.91548i q^{59} +(0.0226397 + 1.06149i) q^{60} +4.61636i q^{61} +(-3.60989 - 3.53371i) q^{62} +4.34572 q^{63} +(-0.511452 - 7.98363i) q^{64} -4.29317 q^{65} +(-2.19115 - 2.14491i) q^{66} -10.2207i q^{67} +(-0.320458 - 15.0250i) q^{68} +4.23303i q^{69} +(1.58162 - 1.61572i) q^{70} +11.3535 q^{71} +(5.25972 - 5.60745i) q^{72} +15.1543 q^{73} +(1.09126 - 1.11478i) q^{74} +0.530865i q^{75} +(-1.99955 + 0.0426469i) q^{76} +6.52964i q^{77} +(-2.30326 - 2.25466i) q^{78} -3.08138 q^{79} +(-0.170549 - 3.99636i) q^{80} +6.54306 q^{81} +(-2.94082 - 2.87877i) q^{82} -3.40976i q^{83} +(1.69707 - 0.0361955i) q^{84} -7.51422i q^{85} +(-4.26989 + 4.36193i) q^{86} +3.06757 q^{87} +(8.42544 + 7.90295i) q^{88} -13.5566 q^{89} +(2.68905 - 2.74701i) q^{90} +6.86375i q^{91} +(-0.340059 - 15.9440i) q^{92} -1.89625i q^{93} +(-6.22004 - 6.08879i) q^{94} -1.00000 q^{95} +(2.00729 - 2.23360i) q^{96} +3.07007 q^{97} +(4.49110 + 4.39633i) q^{98} +11.1016i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 2 q^{2} - 2 q^{4} - 6 q^{6} + 4 q^{7} + 8 q^{8} - 60 q^{9} + 4 q^{12} + 4 q^{14} - 6 q^{16} + 24 q^{17} - 14 q^{18} - 4 q^{20} - 4 q^{22} + 4 q^{23} + 2 q^{24} - 44 q^{25} + 18 q^{26} - 14 q^{28}+ \cdots + 78 q^{98}+O(q^{100}) \) 44 * q + 2 * q^2 - 2 * q^4 - 6 * q^6 + 4 * q^7 + 8 * q^8 - 60 * q^9 + 4 * q^12 + 4 * q^14 - 6 * q^16 + 24 * q^17 - 14 * q^18 - 4 * q^20 - 4 * q^22 + 4 * q^23 + 2 * q^24 - 44 * q^25 + 18 * q^26 - 14 * q^28 + 12 * q^32 + 40 * q^33 + 32 * q^34 - 28 * q^36 - 24 * q^39 + 6 * q^40 - 32 * q^41 + 46 * q^42 - 36 * q^44 - 16 * q^46 - 20 * q^47 + 64 * q^48 + 108 * q^49 - 2 * q^50 - 24 * q^52 - 26 * q^54 + 8 * q^55 + 60 * q^56 + 2 * q^58 - 14 * q^60 - 72 * q^62 + 20 * q^63 + 22 * q^64 + 12 * q^65 + 88 * q^66 - 62 * q^68 - 18 * q^70 - 8 * q^71 + 48 * q^72 - 88 * q^73 + 84 * q^74 - 4 * q^76 - 116 * q^78 + 40 * q^79 + 8 * q^80 + 116 * q^81 + 44 * q^82 - 108 * q^84 - 88 * q^86 + 48 * q^87 + 76 * q^88 - 64 * q^89 + 30 * q^90 - 62 * q^92 - 24 * q^94 - 44 * q^95 + 118 * q^96 + 116 * q^97 + 78 * q^98

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