LMFDB - Embedded newform 760.2.f.b.381.13

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)

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")

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);

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			381.13
Character	$\chi$	$=$	760.381
Dual form			760.2.f.b.381.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.750213 - 1.19882i) q^{2} +1.80124i q^{3} +(-0.874362 + 1.79875i) q^{4} -1.00000i q^{5} +(2.15937 - 1.35131i) q^{6} +4.97691 q^{7} +(2.81234 - 0.301237i) q^{8} -0.244448 q^{9} +(-1.19882 + 0.750213i) q^{10} +5.55944i q^{11} +(-3.23997 - 1.57493i) q^{12} -5.33303i q^{13} +(-3.73374 - 5.96645i) q^{14} +1.80124 q^{15} +(-2.47098 - 3.14551i) q^{16} -0.586816 q^{17} +(0.183388 + 0.293051i) q^{18} -1.00000i q^{19} +(1.79875 + 0.874362i) q^{20} +8.96459i q^{21} +(6.66479 - 4.17076i) q^{22} +1.77875 q^{23} +(0.542599 + 5.06569i) q^{24} -1.00000 q^{25} +(-6.39337 + 4.00091i) q^{26} +4.96340i q^{27} +(-4.35162 + 8.95221i) q^{28} -7.19616i q^{29} +(-1.35131 - 2.15937i) q^{30} -2.10284 q^{31} +(-1.91715 + 5.32208i) q^{32} -10.0139 q^{33} +(0.440237 + 0.703489i) q^{34} -4.97691i q^{35} +(0.213736 - 0.439701i) q^{36} +3.39104i q^{37} +(-1.19882 + 0.750213i) q^{38} +9.60604 q^{39} +(-0.301237 - 2.81234i) q^{40} +5.88614 q^{41} +(10.7470 - 6.72535i) q^{42} +2.50471i q^{43} +(-10.0000 - 4.86096i) q^{44} +0.244448i q^{45} +(-1.33444 - 2.13241i) q^{46} +6.94927 q^{47} +(5.66581 - 4.45082i) q^{48} +17.7697 q^{49} +(0.750213 + 1.19882i) q^{50} -1.05699i q^{51} +(9.59277 + 4.66300i) q^{52} +11.8871i q^{53} +(5.95024 - 3.72360i) q^{54} +5.55944 q^{55} +(13.9968 - 1.49923i) q^{56} +1.80124 q^{57} +(-8.62694 + 5.39865i) q^{58} +5.63624i q^{59} +(-1.57493 + 3.23997i) q^{60} -2.34909i q^{61} +(1.57758 + 2.52094i) q^{62} -1.21660 q^{63} +(7.81851 - 1.69436i) q^{64} -5.33303 q^{65} +(7.51252 + 12.0049i) q^{66} -12.1321i q^{67} +(0.513089 - 1.05553i) q^{68} +3.20394i q^{69} +(-5.96645 + 3.73374i) q^{70} -6.57777 q^{71} +(-0.687472 + 0.0736369i) q^{72} -1.31957 q^{73} +(4.06526 - 2.54400i) q^{74} -1.80124i q^{75} +(1.79875 + 0.874362i) q^{76} +27.6689i q^{77} +(-7.20657 - 11.5160i) q^{78} -0.202718 q^{79} +(-3.14551 + 2.47098i) q^{80} -9.67359 q^{81} +(-4.41586 - 7.05645i) q^{82} +8.37708i q^{83} +(-16.1250 - 7.83830i) q^{84} +0.586816i q^{85} +(3.00271 - 1.87906i) q^{86} +12.9620 q^{87} +(1.67471 + 15.6350i) q^{88} -12.2197 q^{89} +(0.293051 - 0.183388i) q^{90} -26.5420i q^{91} +(-1.55527 + 3.19952i) q^{92} -3.78771i q^{93} +(-5.21343 - 8.33096i) q^{94} -1.00000 q^{95} +(-9.58632 - 3.45324i) q^{96} +12.2726 q^{97} +(-13.3310 - 21.3027i) q^{98} -1.35900i 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 $

$2$	−0.750213	−	1.19882i	−0.530481	−	0.847697i
$2$	−0.750213	−	1.19882i	−0.530481	−	0.847697i
$3$			1.80124i			1.03994i	0.854183	+	0.519972i	$0.174058\pi$
$3$			1.80124i			1.03994i	−0.854183	+	0.519972i	$0.825942\pi$
$4$	−0.874362	+	1.79875i	−0.437181	+	0.899374i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	2.15937	−	1.35131i	0.881557	−	0.551670i
$7$	4.97691			1.88110			0.940548	−	0.339660i	$-0.110312\pi$
$7$	4.97691			1.88110			0.940548	+	0.339660i	$0.110312\pi$
$8$	2.81234	−	0.301237i	0.994312	−	0.106503i
$9$	−0.244448			−0.0814828
$10$	−1.19882	+	0.750213i	−0.379102	+	0.237238i
$11$			5.55944i			1.67623i	0.545490	+	0.838117i	$0.316343\pi$
$11$			5.55944i			1.67623i	−0.545490	+	0.838117i	$0.683657\pi$
$12$	−3.23997	−	1.57493i	−0.935298	−	0.454643i
$13$		−	5.33303i		−	1.47912i	−0.673093	−	0.739558i	$-0.735035\pi$
$13$		−	5.33303i		−	1.47912i	0.673093	−	0.739558i	$-0.264965\pi$
$14$	−3.73374	−	5.96645i	−0.997885	−	1.59460i
$15$	1.80124			0.465077
$16$	−2.47098	−	3.14551i	−0.617746	−	0.786378i
$17$	−0.586816			−0.142324			−0.0711619	−	0.997465i	$-0.522671\pi$
$17$	−0.586816			−0.142324			−0.0711619	+	0.997465i	$0.522671\pi$
$18$	0.183388	+	0.293051i	0.0432250	+	0.0690727i
$19$		−	1.00000i		−	0.229416i
$19$		−	1.00000i		−	0.229416i
$20$	1.79875	+	0.874362i	0.402212	+	0.195513i
$21$			8.96459i			1.95623i
$22$	6.66479	−	4.17076i	1.42094	−	0.889210i
$23$	1.77875			0.370895			0.185447	−	0.982654i	$-0.440627\pi$
$23$	1.77875			0.370895			0.185447	+	0.982654i	$0.440627\pi$
$24$	0.542599	+	5.06569i	0.110757	+	1.03403i
$25$	−1.00000			−0.200000
$26$	−6.39337	+	4.00091i	−1.25384	+	0.784642i
$27$			4.96340i			0.955206i
$28$	−4.35162	+	8.95221i	−0.822379	+	1.69181i
$29$		−	7.19616i		−	1.33629i	−0.744030	−	0.668147i	$-0.767088\pi$
$29$		−	7.19616i		−	1.33629i	0.744030	−	0.668147i	$-0.232912\pi$
$30$	−1.35131	−	2.15937i	−0.246714	−	0.394244i
$31$	−2.10284			−0.377681			−0.188841	−	0.982008i	$-0.560473\pi$
$31$	−2.10284			−0.377681			−0.188841	+	0.982008i	$0.560473\pi$
$32$	−1.91715	+	5.32208i	−0.338908	+	0.940820i
$33$	−10.0139			−1.74319
$34$	0.440237	+	0.703489i	0.0755000	+	0.120647i
$35$		−	4.97691i		−	0.841252i
$36$	0.213736	−	0.439701i	0.0356227	−	0.0732834i
$37$			3.39104i			0.557483i	0.960366	+	0.278742i	$0.0899173\pi$
$37$			3.39104i			0.557483i	−0.960366	+	0.278742i	$0.910083\pi$
$38$	−1.19882	+	0.750213i	−0.194475	+	0.121701i
$39$	9.60604			1.53820
$40$	−0.301237	−	2.81234i	−0.0476298	−	0.444670i
$41$	5.88614			0.919261			0.459631	−	0.888110i	$-0.347982\pi$
$41$	5.88614			0.919261			0.459631	+	0.888110i	$0.347982\pi$
$42$	10.7470	−	6.72535i	1.65829	−	1.03774i
$43$			2.50471i			0.381964i	0.981594	+	0.190982i	$0.0611673\pi$
$43$			2.50471i			0.381964i	−0.981594	+	0.190982i	$0.938833\pi$
$44$	−10.0000	−	4.86096i	−1.50756	−	0.732817i
$45$			0.244448i			0.0364402i
$46$	−1.33444	−	2.13241i	−0.196752	−	0.314406i
$47$	6.94927			1.01366			0.506828	−	0.862047i	$-0.330818\pi$
$47$	6.94927			1.01366			0.506828	+	0.862047i	$0.330818\pi$
$48$	5.66581	−	4.45082i	0.817789	−	0.642421i
$49$	17.7697			2.53852
$50$	0.750213	+	1.19882i	0.106096	+	0.169539i
$51$		−	1.05699i		−	0.148009i
$52$	9.59277	+	4.66300i	1.33028	+	0.646641i
$53$			11.8871i			1.63282i	0.577475	+	0.816409i	$0.304038\pi$
$53$			11.8871i			1.63282i	−0.577475	+	0.816409i	$0.695962\pi$
$54$	5.95024	−	3.72360i	0.809725	−	0.506718i
$55$	5.55944			0.749635
$56$	13.9968	−	1.49923i	1.87040	−	0.200343i
$57$	1.80124			0.238579
$58$	−8.62694	+	5.39865i	−1.13277	+	0.708878i
$59$			5.63624i			0.733776i	0.930265	+	0.366888i	$0.119577\pi$
$59$			5.63624i			0.733776i	−0.930265	+	0.366888i	$0.880423\pi$
$60$	−1.57493	+	3.23997i	−0.203323	+	0.418278i
$61$		−	2.34909i		−	0.300770i	−0.988628	−	0.150385i	$-0.951949\pi$
$61$		−	2.34909i		−	0.300770i	0.988628	−	0.150385i	$-0.0480513\pi$
$62$	1.57758	+	2.52094i	0.200352	+	0.320159i
$63$	−1.21660			−0.153277
$64$	7.81851	−	1.69436i	0.977314	−	0.211795i
$65$	−5.33303			−0.661481
$66$	7.51252	+	12.0049i	0.924728	+	1.47770i
$67$		−	12.1321i		−	1.48217i	−0.671412	−	0.741084i	$-0.734312\pi$
$67$		−	12.1321i		−	1.48217i	0.671412	−	0.741084i	$-0.265688\pi$
$68$	0.513089	−	1.05553i	0.0622212	−	0.128002i
$69$			3.20394i			0.385710i
$70$	−5.96645	+	3.73374i	−0.713127	+	0.446268i
$71$	−6.57777			−0.780638			−0.390319	−	0.920680i	$-0.627635\pi$
$71$	−6.57777			−0.780638			−0.390319	+	0.920680i	$0.627635\pi$
$72$	−0.687472	+	0.0736369i	−0.0810193	+	0.00867819i
$73$	−1.31957			−0.154444			−0.0772222	−	0.997014i	$-0.524605\pi$
$73$	−1.31957			−0.154444			−0.0772222	+	0.997014i	$0.524605\pi$
$74$	4.06526	−	2.54400i	0.472577	−	0.295734i
$75$		−	1.80124i		−	0.207989i
$76$	1.79875	+	0.874362i	0.206330	+	0.100296i
$77$			27.6689i			3.15316i
$78$	−7.20657	−	11.5160i	−0.815984	−	1.30393i
$79$	−0.202718			−0.0228076			−0.0114038	−	0.999935i	$-0.503630\pi$
$79$	−0.202718			−0.0228076			−0.0114038	+	0.999935i	$0.503630\pi$
$80$	−3.14551	+	2.47098i	−0.351679	+	0.276264i
$81$	−9.67359			−1.07484
$82$	−4.41586	−	7.05645i	−0.487650	−	0.779255i
$83$			8.37708i			0.919504i	0.888047	+	0.459752i	$0.152062\pi$
$83$			8.37708i			0.919504i	−0.888047	+	0.459752i	$0.847938\pi$
$84$	−16.1250	−	7.83830i	−1.75939	−	0.855228i
$85$			0.586816i			0.0636491i
$86$	3.00271	−	1.87906i	0.323790	−	0.202625i
$87$	12.9620			1.38967
$88$	1.67471	+	15.6350i	0.178525	+	1.66670i
$89$	−12.2197			−1.29528			−0.647641	−	0.761946i	$-0.724244\pi$
$89$	−12.2197			−1.29528			−0.647641	+	0.761946i	$0.724244\pi$
$90$	0.293051	−	0.183388i	0.0308902	−	0.0193308i
$91$		−	26.5420i		−	2.78236i
$92$	−1.55527	+	3.19952i	−0.162148	+	0.333573i
$93$		−	3.78771i		−	0.392767i
$94$	−5.21343	−	8.33096i	−0.537725	−	0.859273i
$95$	−1.00000			−0.102598
$96$	−9.58632	−	3.45324i	−0.978399	−	0.352445i
$97$	12.2726			1.24609			0.623045	−	0.782186i	$-0.285895\pi$
$97$	12.2726			1.24609			0.623045	+	0.782186i	$0.285895\pi$
$98$	−13.3310	−	21.3027i	−1.34664	−	2.15190i
$99$		−	1.35900i		−	0.136584i
$100$	0.874362	−	1.79875i	0.0874362	−	0.179875i
$101$			16.5155i			1.64336i	0.569952	+	0.821678i	$0.306962\pi$
$101$			16.5155i			1.64336i	−0.569952	+	0.821678i	$0.693038\pi$
$102$	−1.26715	+	0.792970i	−0.125467	+	0.0785157i
$103$	8.19759			0.807733			0.403866	−	0.914818i	$-0.367666\pi$
$103$	8.19759			0.807733			0.403866	+	0.914818i	$0.367666\pi$
$104$	−1.60651	−	14.9983i	−0.157531	−	1.47070i
$105$	8.96459			0.874855
$106$	14.2505	−	8.91785i	1.38413	−	0.866178i
$107$			1.39487i			0.134847i	0.997724	+	0.0674234i	$0.0214778\pi$
$107$			1.39487i			0.134847i	−0.997724	+	0.0674234i	$0.978522\pi$
$108$	−8.92790	−	4.33980i	−0.859087	−	0.417598i
$109$		−	16.0569i		−	1.53797i	−0.639266	−	0.768986i	$-0.720762\pi$
$109$		−	16.0569i		−	1.53797i	0.639266	−	0.768986i	$-0.279238\pi$
$110$	−4.17076	−	6.66479i	−0.397667	−	0.635463i
$111$	−6.10806			−0.579751
$112$	−12.2979	−	15.6549i	−1.16204	−	1.47925i
$113$	−9.35758			−0.880287			−0.440143	−	0.897928i	$-0.645072\pi$
$113$	−9.35758			−0.880287			−0.440143	+	0.897928i	$0.645072\pi$
$114$	−1.35131	−	2.15937i	−0.126562	−	0.202243i
$115$		−	1.77875i		−	0.165869i
$116$	12.9441	+	6.29205i	1.20183	+	0.584202i
$117$			1.30365i			0.120522i
$118$	6.75687	−	4.22838i	0.622020	−	0.389254i
$119$	−2.92053			−0.267725
$120$	5.06569	−	0.542599i	0.462432	−	0.0495323i
$121$	−19.9074			−1.80976
$122$	−2.81614	+	1.76232i	−0.254962	+	0.159553i
$123$			10.6023i			0.955980i
$124$	1.83864	−	3.78248i	0.165115	−	0.339676i
$125$			1.00000i			0.0894427i
$126$	0.912707	+	1.45849i	0.0813104	+	0.129932i
$127$	−13.4310			−1.19181			−0.595904	−	0.803056i	$-0.703206\pi$
$127$	−13.4310			−1.19181			−0.595904	+	0.803056i	$0.703206\pi$
$128$	−7.89679	−	8.10189i	−0.697984	−	0.716113i
$129$	−4.51157			−0.397221
$130$	4.00091	+	6.39337i	0.350903	+	0.560735i
$131$		−	15.7227i		−	1.37370i	−0.726800	−	0.686850i	$-0.758993\pi$
$131$		−	15.7227i		−	1.37370i	0.726800	−	0.686850i	$-0.241007\pi$
$132$	8.75573	−	18.0124i	0.762089	−	1.56778i
$133$		−	4.97691i		−	0.431553i
$134$	−14.5442	+	9.10163i	−1.25643	+	0.786261i
$135$	4.96340			0.427181
$136$	−1.65033	+	0.176771i	−0.141514	+	0.0151580i
$137$	−19.2732			−1.64662			−0.823311	−	0.567591i	$-0.807876\pi$
$137$	−19.2732			−1.64662			−0.823311	+	0.567591i	$0.807876\pi$
$138$	3.84097	−	2.40364i	0.326965	−	0.204611i
$139$		−	10.5025i		−	0.890814i	−0.895328	−	0.445407i	$-0.853059\pi$
$139$		−	10.5025i		−	0.890814i	0.895328	−	0.445407i	$-0.146941\pi$
$140$	8.95221	+	4.35162i	0.756600	+	0.367779i
$141$			12.5173i			1.05414i
$142$	4.93473	+	7.88560i	0.414113	+	0.661745i
$143$	29.6487			2.47934
$144$	0.604028	+	0.768915i	0.0503356	+	0.0640762i
$145$	−7.19616			−0.597609
$146$	0.989961	+	1.58194i	0.0819298	+	0.130922i
$147$			32.0074i			2.63992i
$148$	−6.09962	−	2.96499i	−0.501386	−	0.243721i
$149$		−	12.1933i		−	0.998914i	−0.866339	−	0.499457i	$-0.833533\pi$
$149$		−	12.1933i		−	0.998914i	0.866339	−	0.499457i	$-0.166467\pi$
$150$	−2.15937	+	1.35131i	−0.176311	+	0.110334i
$151$	−1.41469			−0.115126			−0.0575628	−	0.998342i	$-0.518333\pi$
$151$	−1.41469			−0.115126			−0.0575628	+	0.998342i	$0.518333\pi$
$152$	−0.301237	−	2.81234i	−0.0244335	−	0.228111i
$153$	0.143446			0.0115969
$154$	33.1701	−	20.7575i	2.67292	−	1.67269i
$155$			2.10284i			0.168904i
$156$	−8.39915	+	17.2788i	−0.672470	+	1.38341i
$157$			16.4141i			1.30999i	0.755634	+	0.654994i	$0.227329\pi$
$157$			16.4141i			1.30999i	−0.755634	+	0.654994i	$0.772671\pi$
$158$	0.152082	+	0.243024i	0.0120990	+	0.0193339i
$159$	−21.4114			−1.69804
$160$	5.32208	+	1.91715i	0.420747	+	0.151564i
$161$	8.85268			0.697689
$162$	7.25725	+	11.5969i	0.570183	+	0.911142i
$163$			8.77560i			0.687358i	0.939087	+	0.343679i	$0.111673\pi$
$163$			8.77560i			0.687358i	−0.939087	+	0.343679i	$0.888327\pi$
$164$	−5.14662	+	10.5877i	−0.401883	+	0.826759i
$165$			10.0139i			0.779578i
$166$	10.0426	−	6.28459i	0.779460	−	0.487779i
$167$	−4.19020			−0.324247			−0.162124	−	0.986770i	$-0.551834\pi$
$167$	−4.19020			−0.324247			−0.162124	+	0.986770i	$0.551834\pi$
$168$	2.70047	+	25.2115i	0.208346	+	1.94511i
$169$	−15.4412			−1.18778
$170$	0.703489	−	0.440237i	0.0539552	−	0.0337646i
$171$			0.244448i			0.0186934i
$172$	−4.50534	−	2.19002i	−0.343529	−	0.166987i
$173$			7.51333i			0.571228i	0.958345	+	0.285614i	$0.0921976\pi$
$173$			7.51333i			0.571228i	−0.958345	+	0.285614i	$0.907802\pi$
$174$	−9.72424	−	15.5391i	−0.737193	−	1.17802i
$175$	−4.97691			−0.376219
$176$	17.4873	−	13.7373i	1.31815	−	1.03549i
$177$	−10.1522			−0.763086
$178$	9.16735	+	14.6492i	0.687122	+	1.09801i
$179$			0.224608i			0.0167880i	0.999965	+	0.00839401i	$0.00267193\pi$
$179$			0.224608i			0.0167880i	−0.999965	+	0.00839401i	$0.997328\pi$
$180$	−0.439701	−	0.213736i	−0.0327734	−	0.0159310i
$181$		−	12.2976i		−	0.914072i	−0.889448	−	0.457036i	$-0.848911\pi$
$181$		−	12.2976i		−	0.914072i	0.889448	−	0.457036i	$-0.151089\pi$
$182$	−31.8192	+	19.9122i	−2.35860	+	1.47599i
$183$	4.23126			0.312784
$184$	5.00244	−	0.535825i	0.368785	−	0.0395015i
$185$	3.39104			0.249314
$186$	−4.54080	+	2.84159i	−0.332947	+	0.208355i
$187$		−	3.26237i		−	0.238568i
$188$	−6.07618	+	12.5000i	−0.443151	+	0.911655i
$189$			24.7024i			1.79684i
$190$	0.750213	+	1.19882i	0.0544262	+	0.0869719i
$191$	−9.08176			−0.657133			−0.328567	−	0.944481i	$-0.606566\pi$
$191$	−9.08176			−0.657133			−0.328567	+	0.944481i	$0.606566\pi$
$192$	3.05194	+	14.0830i	0.220255	+	1.01635i
$193$	20.0382			1.44238			0.721190	−	0.692738i	$-0.243596\pi$
$193$	20.0382			1.44238			0.721190	+	0.692738i	$0.243596\pi$
$194$	−9.20703	−	14.7126i	−0.661026	−	1.05631i
$195$		−	9.60604i		−	0.687903i
$196$	−15.5371	+	31.9632i	−1.10979	+	2.28308i
$197$		−	9.75114i		−	0.694740i	−0.937728	−	0.347370i	$-0.887075\pi$
$197$		−	9.75114i		−	0.694740i	0.937728	−	0.347370i	$-0.112925\pi$
$198$	−1.62920	+	1.01954i	−0.115782	+	0.0724552i
$199$	0.526183			0.0373001			0.0186501	−	0.999826i	$-0.494063\pi$
$199$	0.526183			0.0373001			0.0186501	+	0.999826i	$0.494063\pi$
$200$	−2.81234	+	0.301237i	−0.198862	+	0.0213007i
$201$	21.8527			1.54137
$202$	19.7992	−	12.3902i	1.39307	−	0.871768i
$203$		−	35.8147i		−	2.51370i
$204$	1.90126	+	0.924194i	0.133115	+	0.0647065i
$205$		−	5.88614i		−	0.411106i
$206$	−6.14994	−	9.82747i	−0.428486	−	0.684713i
$207$	−0.434812			−0.0302215
$208$	−16.7751	+	13.1778i	−1.16314	+	0.913718i
$209$	5.55944			0.384554
$210$	−6.72535	−	10.7470i	−0.464093	−	0.741612i
$211$		−	9.28274i		−	0.639050i	−0.947578	−	0.319525i	$-0.896477\pi$
$211$		−	9.28274i		−	0.639050i	0.947578	−	0.319525i	$-0.103523\pi$
$212$	−21.3819	−	10.3936i	−1.46851	−	0.713836i
$213$		−	11.8481i		−	0.811820i
$214$	1.67220	−	1.04645i	0.114309	−	0.0715336i
$215$	2.50471			0.170820
$216$	1.49516	+	13.9588i	0.101733	+	0.949773i
$217$	−10.4656			−0.710455
$218$	−19.2494	+	12.0461i	−1.30373	+	0.815864i
$219$		−	2.37686i		−	0.160614i
$220$	−4.86096	+	10.0000i	−0.327726	+	0.674202i
$221$			3.12951i			0.210513i
$222$	4.58234	+	7.32249i	0.307547	+	0.491453i
$223$	−21.3597			−1.43035			−0.715175	−	0.698946i	$-0.753653\pi$
$223$	−21.3597			−1.43035			−0.715175	+	0.698946i	$0.753653\pi$
$224$	−9.54150	+	26.4875i	−0.637519	+	1.76977i
$225$	0.244448			0.0162966
$226$	7.02017	+	11.2181i	0.466975	+	0.746217i
$227$		−	16.4852i		−	1.09416i	−0.837080	−	0.547080i	$-0.815739\pi$
$227$		−	16.4852i		−	1.09416i	0.837080	−	0.547080i	$-0.184261\pi$
$228$	−1.57493	+	3.23997i	−0.104302	+	0.214572i
$229$			1.52550i			0.100808i	0.998729	+	0.0504038i	$0.0160508\pi$
$229$			1.52550i			0.100808i	−0.998729	+	0.0504038i	$0.983949\pi$
$230$	−2.13241	+	1.33444i	−0.140607	+	0.0879903i
$231$	−49.8381			−3.27911
$232$	−2.16775	−	20.2381i	−0.142320	−	1.32869i
$233$	18.5252			1.21363			0.606814	−	0.794844i	$-0.292447\pi$
$233$	18.5252			1.21363			0.606814	+	0.794844i	$0.292447\pi$
$234$	1.56285	−	0.978015i	0.102167	−	0.0639348i
$235$		−	6.94927i		−	0.453321i
$236$	−10.1382	−	4.92811i	−0.659939	−	0.320793i
$237$		−	0.365143i		−	0.0237186i
$238$	2.19102	+	3.50121i	0.142023	+	0.226949i
$239$	−21.9308			−1.41859			−0.709294	−	0.704913i	$-0.750986\pi$
$239$	−21.9308			−1.41859			−0.709294	+	0.704913i	$0.750986\pi$
$240$	−4.45082	−	5.66581i	−0.287299	−	0.365726i
$241$	20.9234			1.34780			0.673898	−	0.738824i	$-0.264619\pi$
$241$	20.9234			1.34780			0.673898	+	0.738824i	$0.264619\pi$
$242$	14.9348	+	23.8654i	0.960043	+	1.53413i
$243$		−	2.53422i		−	0.162570i
$244$	4.22542	+	2.05395i	0.270505	+	0.131491i
$245$		−	17.7697i		−	1.13526i
$246$	12.7103	−	7.95400i	0.810381	−	0.507129i
$247$	−5.33303			−0.339332
$248$	−5.91390	+	0.633453i	−0.375533	+	0.0402243i
$249$	−15.0891			−0.956232
$250$	1.19882	−	0.750213i	0.0758203	−	0.0474476i
$251$			19.5825i			1.23603i	0.786165	+	0.618017i	$0.212064\pi$
$251$			19.5825i			1.23603i	−0.786165	+	0.618017i	$0.787936\pi$
$252$	1.06375	−	2.18835i	0.0670097	−	0.137853i
$253$			9.88884i			0.621706i
$254$	10.0761	+	16.1014i	0.632231	+	1.01029i
$255$	−1.05699			−0.0661915
$256$	−3.78848	+	15.5450i	−0.236780	+	0.971563i
$257$	5.40454			0.337126			0.168563	−	0.985691i	$-0.446087\pi$
$257$	5.40454			0.337126			0.168563	+	0.985691i	$0.446087\pi$
$258$	3.38464	+	5.40858i	0.210718	+	0.336723i
$259$			16.8769i			1.04868i
$260$	4.66300	−	9.59277i	0.289187	−	0.594918i
$261$			1.75909i			0.108885i
$262$	−18.8488	+	11.7954i	−1.16448	+	0.728721i
$263$	24.3152			1.49934			0.749670	−	0.661812i	$-0.230212\pi$
$263$	24.3152			1.49934			0.749670	+	0.661812i	$0.230212\pi$
$264$	−28.1624	+	3.01654i	−1.73327	+	0.185655i
$265$	11.8871			0.730218
$266$	−5.96645	+	3.73374i	−0.365826	+	0.228931i
$267$		−	22.0105i		−	1.34702i
$268$	21.8225	+	10.6078i	1.33302	+	0.647975i
$269$		−	6.48637i		−	0.395481i	−0.980254	−	0.197740i	$-0.936640\pi$
$269$		−	6.48637i		−	0.395481i	0.980254	−	0.197740i	$-0.0633603\pi$
$270$	−3.72360	−	5.95024i	−0.226611	−	0.362120i
$271$	1.48004			0.0899058			0.0449529	−	0.998989i	$-0.485686\pi$
$271$	1.48004			0.0899058			0.0449529	+	0.998989i	$0.485686\pi$
$272$	1.45001	+	1.84584i	0.0879199	+	0.111920i
$273$	47.8084			2.89350
$274$	14.4590	+	23.1052i	0.873501	+	1.39584i
$275$		−	5.55944i		−	0.335247i
$276$	−5.76309	−	2.80141i	−0.346897	−	0.168625i
$277$		−	6.27850i		−	0.377238i	−0.982050	−	0.188619i	$-0.939599\pi$
$277$		−	6.27850i		−	0.377238i	0.982050	−	0.188619i	$-0.0604012\pi$
$278$	−12.5907	+	7.87914i	−0.755141	+	0.472560i
$279$	0.514035			0.0307745
$280$	−1.49923	−	13.9968i	−0.0895962	−	0.836467i
$281$	−11.5011			−0.686101			−0.343050	−	0.939317i	$-0.611460\pi$
$281$	−11.5011			−0.686101			−0.343050	+	0.939317i	$0.611460\pi$
$282$	15.0060	−	9.39062i	0.893596	−	0.559203i
$283$			11.5769i			0.688173i	0.938938	+	0.344086i	$0.111811\pi$
$283$			11.5769i			0.688173i	−0.938938	+	0.344086i	$0.888189\pi$
$284$	5.75135	−	11.8318i	0.341280	−	0.702085i
$285$		−	1.80124i		−	0.106696i
$286$	−22.2428	−	35.5435i	−1.31524	−	2.10173i
$287$	29.2948			1.72922
$288$	0.468645	−	1.30097i	0.0276152	−	0.0766606i
$289$	−16.6556			−0.979744
$290$	5.39865	+	8.62694i	0.317020	+	0.506591i
$291$			22.1058i			1.29586i
$292$	1.15378	−	2.37358i	0.0675201	−	0.138903i
$293$		−	4.64456i		−	0.271338i	−0.990754	−	0.135669i	$-0.956682\pi$
$293$		−	4.64456i		−	0.271338i	0.990754	−	0.135669i	$-0.0433184\pi$
$294$	38.3712	−	24.0123i	2.23785	−	1.40043i
$295$	5.63624			0.328155
$296$	1.02151	+	9.53675i	0.0593738	+	0.554312i
$297$	−27.5937			−1.60115
$298$	−14.6176	+	9.14757i	−0.846776	+	0.529904i
$299$		−	9.48612i		−	0.548596i
$300$	3.23997	+	1.57493i	0.187060	+	0.0909287i
$301$			12.4657i			0.718512i
$302$	1.06132	+	1.69596i	0.0610718	+	0.0975916i
$303$	−29.7483			−1.70900
$304$	−3.14551	+	2.47098i	−0.180407	+	0.141721i
$305$	−2.34909			−0.134508
$306$	−0.107615	−	0.171967i	−0.00615195	−	0.00983069i
$307$		−	18.8691i		−	1.07692i	−0.842652	−	0.538458i	$-0.819007\pi$
$307$		−	18.8691i		−	1.07692i	0.842652	−	0.538458i	$-0.180993\pi$
$308$	−49.7693	−	24.1926i	−2.83587	−	1.37850i
$309$			14.7658i			0.839996i
$310$	2.52094	−	1.57758i	0.143180	−	0.0896003i
$311$	−8.72224			−0.494593			−0.247296	−	0.968940i	$-0.579542\pi$
$311$	−8.72224			−0.494593			−0.247296	+	0.968940i	$0.579542\pi$
$312$	27.0154	−	2.89369i	1.52945	−	0.163823i
$313$	−11.2913			−0.638224			−0.319112	−	0.947717i	$-0.603385\pi$
$313$	−11.2913			−0.638224			−0.319112	+	0.947717i	$0.603385\pi$
$314$	19.6776	−	12.3141i	1.11047	−	0.694923i
$315$			1.21660i			0.0685475i
$316$	0.177249	−	0.364639i	0.00997104	−	0.0205125i
$317$		−	25.4356i		−	1.42861i	−0.699837	−	0.714303i	$-0.746744\pi$
$317$		−	25.4356i		−	1.42861i	0.699837	−	0.714303i	$-0.253256\pi$
$318$	16.0631	+	25.6686i	0.900776	+	1.43942i
$319$	40.0066			2.23994
$320$	−1.69436	−	7.81851i	−0.0947177	−	0.437068i
$321$	−2.51248			−0.140233
$322$	−6.64139	−	10.6128i	−0.370110	−	0.591429i
$323$			0.586816i			0.0326513i
$324$	8.45821	−	17.4003i	0.469901	−	0.966686i
$325$			5.33303i			0.295823i
$326$	10.5204	−	6.58357i	0.582671	−	0.364630i
$327$	28.9222			1.59940
$328$	16.5538	−	1.77312i	0.914033	−	0.0979044i
$329$	34.5859			1.90678
$330$	12.0049	−	7.51252i	0.660846	−	0.413551i
$331$		−	8.44784i		−	0.464335i	−0.972676	−	0.232168i	$-0.925418\pi$
$331$		−	8.44784i		−	0.464335i	0.972676	−	0.232168i	$-0.0745818\pi$
$332$	−15.0682	−	7.32459i	−0.826977	−	0.401989i
$333$		−	0.828933i		−	0.0454253i
$334$	3.14354	+	5.02332i	0.172007	+	0.274864i
$335$	−12.1321			−0.662846
$336$	28.1982	−	22.1514i	1.53834	−	1.20846i
$337$	−25.5142			−1.38985			−0.694925	−	0.719083i	$-0.744562\pi$
$337$	−25.5142			−1.38985			−0.694925	+	0.719083i	$0.744562\pi$
$338$	11.5842	+	18.5113i	0.630096	+	1.00688i
$339$		−	16.8552i		−	0.915449i
$340$	−1.05553	−	0.513089i	−0.0572443	−	0.0278262i
$341$		−	11.6906i		−	0.633082i
$342$	0.293051	−	0.183388i	0.0158464	−	0.00991650i
$343$	53.5997			2.89411
$344$	0.754511	+	7.04409i	0.0406805	+	0.379792i
$345$	3.20394			0.172495
$346$	9.00717	−	5.63660i	0.484229	−	0.303025i
$347$		−	1.27204i		−	0.0682866i	−0.999417	−	0.0341433i	$-0.989130\pi$
$347$		−	1.27204i		−	0.0682866i	0.999417	−	0.0341433i	$-0.0108703\pi$
$348$	−11.3335	+	23.3153i	−0.607537	+	1.24983i
$349$		−	27.9794i		−	1.49770i	−0.662737	−	0.748852i	$-0.730605\pi$
$349$		−	27.9794i		−	1.49770i	0.662737	−	0.748852i	$-0.269395\pi$
$350$	3.73374	+	5.96645i	0.199577	+	0.318920i
$351$	26.4699			1.41286
$352$	−29.5878	−	10.6583i	−1.57703	−	0.568089i
$353$	−23.9987			−1.27732			−0.638661	−	0.769488i	$-0.720511\pi$
$353$	−23.9987			−1.27732			−0.638661	+	0.769488i	$0.720511\pi$
$354$	7.61631	+	12.1707i	0.404802	+	0.646866i
$355$			6.57777i			0.349112i
$356$	10.6844	−	21.9801i	0.566272	−	1.16494i
$357$		−	5.26057i		−	0.278419i
$358$	0.269266	−	0.168504i	0.0142312	−	0.00890572i
$359$	31.9623			1.68691			0.843453	−	0.537203i	$-0.180519\pi$
$359$	31.9623			1.68691			0.843453	+	0.537203i	$0.180519\pi$
$360$	0.0736369	+	0.687472i	0.00388100	+	0.0362329i
$361$	−1.00000			−0.0526316
$362$	−14.7426	+	9.22580i	−0.774856	+	0.484897i
$363$		−	35.8579i		−	1.88205i
$364$	47.7424	+	23.2073i	2.50238	+	1.21639i
$365$			1.31957i			0.0690697i
$366$	−3.17435	−	5.07254i	−0.165926	−	0.265146i
$367$	−26.9571			−1.40715			−0.703575	−	0.710621i	$-0.748414\pi$
$367$	−26.9571			−1.40715			−0.703575	+	0.710621i	$0.748414\pi$
$368$	−4.39526	−	5.59507i	−0.229119	−	0.291663i
$369$	−1.43886			−0.0749039
$370$	−2.54400	−	4.06526i	−0.132256	−	0.211343i
$371$			59.1610i			3.07149i
$372$	6.81313	+	3.31183i	0.353244	+	0.171710i
$373$		−	22.9560i		−	1.18862i	−0.804236	−	0.594310i	$-0.797425\pi$
$373$		−	22.9560i		−	1.18862i	0.804236	−	0.594310i	$-0.202575\pi$
$374$	−3.91101	+	2.44747i	−0.202233	+	0.126556i
$375$	−1.80124			−0.0930154
$376$	19.5437	−	2.09338i	1.00789	−	0.107958i
$377$	−38.3773			−1.97653
$378$	29.6138	−	18.5321i	1.52317	−	0.953186i
$379$			7.27783i			0.373837i	0.982375	+	0.186918i	$0.0598500\pi$
$379$			7.27783i			0.373837i	−0.982375	+	0.186918i	$0.940150\pi$
$380$	0.874362	−	1.79875i	0.0448538	−	0.0922738i
$381$		−	24.1924i		−	1.23941i
$382$	6.81325	+	10.8874i	0.348596	+	0.557050i
$383$	−10.4151			−0.532187			−0.266093	−	0.963947i	$-0.585733\pi$
$383$	−10.4151			−0.532187			−0.266093	+	0.963947i	$0.585733\pi$
$384$	14.5934	−	14.2240i	0.744717	−	0.725864i
$385$	27.6689			1.41014
$386$	−15.0329	−	24.0223i	−0.765154	−	1.22270i
$387$		−	0.612272i		−	0.0311235i
$388$	−10.7307	+	22.0752i	−0.544766	+	1.12070i
$389$		−	19.5711i		−	0.992295i	−0.868238	−	0.496147i	$-0.834748\pi$
$389$		−	19.5711i		−	0.992295i	0.868238	−	0.496147i	$-0.165252\pi$
$390$	−11.5160	+	7.20657i	−0.583133	+	0.364919i
$391$	−1.04380			−0.0527871
$392$	49.9744	−	5.35288i	2.52409	−	0.270361i
$393$	28.3203			1.42857
$394$	−11.6899	+	7.31543i	−0.588929	+	0.368546i
$395$			0.202718i			0.0101999i
$396$	2.44449	+	1.18825i	0.122840	+	0.0597120i
$397$		−	0.419562i		−	0.0210572i	−0.999945	−	0.0105286i	$-0.996649\pi$
$397$		−	0.419562i		−	0.0210572i	0.999945	−	0.0105286i	$-0.00335142\pi$
$398$	−0.394749	−	0.630802i	−0.0197870	−	0.0316192i
$399$	8.96459			0.448791
$400$	2.47098	+	3.14551i	0.123549	+	0.157276i
$401$	−13.9622			−0.697237			−0.348619	−	0.937265i	$-0.613349\pi$
$401$	−13.9622			−0.697237			−0.348619	+	0.937265i	$0.613349\pi$
$402$	−16.3942	−	26.1976i	−0.817668	−	1.30662i
$403$			11.2145i			0.558634i
$404$	−29.7072	−	14.4405i	−1.47799	−	0.718444i
$405$			9.67359i			0.480685i
$406$	−42.9355	+	26.8686i	−2.13085	+	1.33347i
$407$	−18.8523			−0.934472
$408$	−0.318406	−	2.97262i	−0.0157634	−	0.147167i
$409$	−2.89534			−0.143166			−0.0715828	−	0.997435i	$-0.522805\pi$
$409$	−2.89534			−0.143166			−0.0715828	+	0.997435i	$0.522805\pi$
$410$	−7.05645	+	4.41586i	−0.348493	+	0.218084i
$411$		−	34.7156i		−	1.71239i
$412$	−7.16766	+	14.7454i	−0.353125	+	0.726453i
$413$			28.0511i			1.38030i
$414$	0.326201	+	0.521263i	0.0160319	+	0.0256187i
$415$	8.37708			0.411214
$416$	28.3828	+	10.2242i	1.39158	+	0.501284i
$417$	18.9176			0.926397
$418$	−4.17076	−	6.66479i	−0.203999	−	0.325986i
$419$		−	16.6884i		−	0.815284i	−0.913142	−	0.407642i	$-0.866351\pi$
$419$		−	16.6884i		−	0.815284i	0.913142	−	0.407642i	$-0.133649\pi$
$420$	−7.83830	+	16.1250i	−0.382470	+	0.786821i
$421$			25.5257i			1.24405i	0.782998	+	0.622024i	$0.213689\pi$
$421$			25.5257i			1.24405i	−0.782998	+	0.622024i	$0.786311\pi$
$422$	−11.1284	+	6.96403i	−0.541721	+	0.339004i
$423$	−1.69874			−0.0825955
$424$	3.58083	+	33.4305i	0.173901	+	1.62353i
$425$	0.586816			0.0284647
$426$	−14.2038	+	8.88861i	−0.688177	+	0.430655i
$427$		−	11.6912i		−	0.565777i
$428$	−2.50901	−	1.21962i	−0.121278	−	0.0589524i
$429$			53.4042i			2.57838i
$430$	−1.87906	−	3.00271i	−0.0906165	−	0.144803i
$431$	−12.6662			−0.610107			−0.305054	−	0.952335i	$-0.598674\pi$
$431$	−12.6662			−0.610107			−0.305054	+	0.952335i	$0.598674\pi$
$432$	15.6124	−	12.2645i	0.751153	−	0.590075i
$433$	−6.03137			−0.289849			−0.144925	−	0.989443i	$-0.546294\pi$
$433$	−6.03137			−0.289849			−0.144925	+	0.989443i	$0.546294\pi$
$434$	7.85146	+	12.5465i	0.376882	+	0.602250i
$435$		−	12.9620i		−	0.621479i
$436$	28.8823	+	14.0395i	1.38321	+	0.672371i
$437$		−	1.77875i		−	0.0850891i
$438$	−2.84944	+	1.78315i	−0.136152	+	0.0852023i
$439$	−21.4871			−1.02552			−0.512762	−	0.858531i	$-0.671378\pi$
$439$	−21.4871			−1.02552			−0.512762	+	0.858531i	$0.671378\pi$
$440$	15.6350	−	1.67471i	0.745371	−	0.0798386i
$441$	−4.34377			−0.206846
$442$	3.75173	−	2.34780i	0.178452	−	0.111673i
$443$		−	23.6389i		−	1.12312i	−0.827436	−	0.561560i	$-0.810201\pi$
$443$		−	23.6389i		−	1.12312i	0.827436	−	0.561560i	$-0.189799\pi$
$444$	5.34065	−	10.9869i	0.253456	−	0.521413i
$445$			12.2197i			0.579268i
$446$	16.0243	+	25.6065i	0.758773	+	1.21250i
$447$	21.9630			1.03881
$448$	38.9121	−	8.43269i	1.83842	−	0.398407i
$449$	10.5806			0.499329			0.249665	−	0.968332i	$-0.419680\pi$
$449$	10.5806			0.499329			0.249665	+	0.968332i	$0.419680\pi$
$450$	−0.183388	−	0.293051i	−0.00864500	−	0.0138145i
$451$			32.7237i			1.54090i
$452$	8.18191	−	16.8319i	0.384844	−	0.791707i
$453$		−	2.54818i		−	0.119724i
$454$	−19.7629	+	12.3674i	−0.927517	+	0.580431i
$455$	−26.5420			−1.24431
$456$	5.06569	−	0.542599i	0.237222	−	0.0254095i
$457$	−9.95196			−0.465533			−0.232767	−	0.972533i	$-0.574778\pi$
$457$	−9.95196			−0.465533			−0.232767	+	0.972533i	$0.574778\pi$
$458$	1.82880	−	1.14445i	0.0854543	−	0.0534765i
$459$		−	2.91260i		−	0.135949i
$460$	3.19952	+	1.55527i	0.149178	+	0.0725148i
$461$		−	17.7564i		−	0.826998i	−0.910505	−	0.413499i	$-0.864307\pi$
$461$		−	17.7564i		−	0.826998i	0.910505	−	0.413499i	$-0.135693\pi$
$462$	37.3892	+	59.7472i	1.73950	+	2.77969i
$463$	−7.30430			−0.339460			−0.169730	−	0.985491i	$-0.554290\pi$
$463$	−7.30430			−0.339460			−0.169730	+	0.985491i	$0.554290\pi$
$464$	−22.6356	+	17.7816i	−1.05083	+	0.825490i
$465$	−3.78771			−0.175651
$466$	−13.8979	−	22.2085i	−0.643806	−	1.02879i
$467$			36.1163i			1.67126i	0.549292	+	0.835631i	$0.314898\pi$
$467$			36.1163i			1.67126i	−0.549292	+	0.835631i	$0.685102\pi$
$468$	−2.34494	−	1.13986i	−0.108395	−	0.0526901i
$469$		−	60.3803i		−	2.78810i
$470$	−8.33096	+	5.21343i	−0.384279	+	0.240478i
$471$	−29.5656			−1.36231
$472$	1.69784	+	15.8510i	0.0781496	+	0.729603i
$473$	−13.9248			−0.640262
$474$	−0.437743	+	0.273935i	−0.0201062	+	0.0125823i
$475$			1.00000i			0.0458831i
$476$	2.55360	−	5.25330i	0.117044	−	0.240785i
$477$		−	2.90578i		−	0.133046i
$478$	16.4528	+	26.2912i	0.752533	+	1.20253i
$479$	−3.43156			−0.156792			−0.0783961	−	0.996922i	$-0.524980\pi$
$479$	−3.43156			−0.156792			−0.0783961	+	0.996922i	$0.524980\pi$
$480$	−3.45324	+	9.58632i	−0.157618	+	0.437553i
$481$	18.0845			0.824582
$482$	−15.6970	−	25.0835i	−0.714980	−	1.14252i
$483$			15.9458i			0.725557i
$484$	17.4062	−	35.8083i	0.791193	−	1.62765i
$485$		−	12.2726i		−	0.557268i
$486$	−3.03809	+	1.90120i	−0.137810	+	0.0862404i
$487$	39.1218			1.77278			0.886390	−	0.462939i	$-0.153205\pi$
$487$	39.1218			1.77278			0.886390	+	0.462939i	$0.153205\pi$
$488$	−0.707632	−	6.60643i	−0.0320330	−	0.299059i
$489$	−15.8069			−0.714814
$490$	−21.3027	+	13.3310i	−0.962359	+	0.602235i
$491$			3.47805i			0.156962i	0.996916	+	0.0784812i	$0.0250071\pi$
$491$			3.47805i			0.156962i	−0.996916	+	0.0784812i	$0.974993\pi$
$492$	−19.0709	−	9.27027i	−0.859783	−	0.417936i
$493$			4.22282i			0.190186i
$494$	4.00091	+	6.39337i	0.180009	+	0.287651i
$495$	−1.35900			−0.0610823
$496$	5.19608	+	6.61450i	0.233311	+	0.297000i
$497$	−32.7370			−1.46846
$498$	11.3200	+	18.0892i	0.507262	+	0.810595i
$499$		−	22.2374i		−	0.995484i	−0.867325	−	0.497742i	$-0.834163\pi$
$499$		−	22.2374i		−	0.995484i	0.867325	−	0.497742i	$-0.165837\pi$
$500$	−1.79875	−	0.874362i	−0.0804424	−	0.0391026i
$501$		−	7.54754i		−	0.337199i
$502$	23.4759	−	14.6910i	1.04778	−	0.655692i
$503$	11.2855			0.503196			0.251598	−	0.967832i	$-0.419044\pi$
$503$	11.2855			0.503196			0.251598	+	0.967832i	$0.419044\pi$
$504$	−3.42149	+	0.366484i	−0.152405	+	0.0163245i
$505$	16.5155			0.734931
$506$	11.8550	−	7.41874i	0.527019	−	0.329803i
$507$		−	27.8132i		−	1.23523i
$508$	11.7435	−	24.1590i	0.521036	−	1.07188i
$509$		−	29.6354i		−	1.31356i	−0.754080	−	0.656782i	$-0.771917\pi$
$509$		−	29.6354i		−	1.31356i	0.754080	−	0.656782i	$-0.228083\pi$
$510$	0.792970	+	1.26715i	0.0351133	+	0.0561103i
$511$	−6.56741			−0.290525
$512$	21.4779	−	7.12035i	0.949199	−	0.314678i
$513$	4.96340			0.219139
$514$	−4.05456	−	6.47910i	−0.178839	−	0.285781i
$515$		−	8.19759i		−	0.361229i
$516$	3.94474	−	8.11517i	0.173658	−	0.357250i
$517$			38.6341i			1.69912i
$518$	20.2325	−	12.6613i	0.888963	−	0.556304i
$519$	−13.5333			−0.594045
$520$	−14.9983	+	1.60651i	−0.657719	+	0.0704499i
$521$	−13.2542			−0.580679			−0.290339	−	0.956924i	$-0.593768\pi$
$521$	−13.2542			−0.580679			−0.290339	+	0.956924i	$0.593768\pi$
$522$	2.10884	−	1.31969i	0.0923014	−	0.0577613i
$523$		−	6.95400i		−	0.304077i	−0.988375	−	0.152039i	$-0.951416\pi$
$523$		−	6.95400i		−	0.304077i	0.988375	−	0.152039i	$-0.0485838\pi$
$524$	28.2812	+	13.7473i	1.23547	+	0.600555i
$525$		−	8.96459i		−	0.391247i
$526$	−18.2416	−	29.1497i	−0.795371	−	1.27099i
$527$	1.23398			0.0537530
$528$	24.7441	+	31.4987i	1.07685	+	1.37080i
$529$	−19.8361			−0.862437
$530$	−8.91785	−	14.2505i	−0.387366	−	0.619004i
$531$		−	1.37777i		−	0.0597901i
$532$	8.95221	+	4.35162i	0.388128	+	0.188667i
$533$		−	31.3910i		−	1.35969i
$534$	−26.3867	+	16.5126i	−1.14187	+	0.714568i
$535$	1.39487			0.0603053
$536$	−3.65463	−	34.1195i	−0.157856	−	1.47374i
$537$	−0.404573			−0.0174586
$538$	−7.77602	+	4.86616i	−0.335248	+	0.209795i
$539$			98.7894i			4.25516i
$540$	−4.33980	+	8.92790i	−0.186755	+	0.384196i
$541$			24.3877i			1.04851i	0.851561	+	0.524255i	$0.175656\pi$
$541$			24.3877i			1.04851i	−0.851561	+	0.524255i	$0.824344\pi$
$542$	−1.11034	−	1.77430i	−0.0476933	−	0.0762129i
$543$	22.1508			0.950583
$544$	1.12502	−	3.12308i	0.0482346	−	0.133901i
$545$	−16.0569			−0.687802
$546$	−35.8665	−	57.3139i	−1.53494	−	2.45281i
$547$			23.4628i			1.00320i	0.865100	+	0.501599i	$0.167255\pi$
$547$			23.4628i			1.00320i	−0.865100	+	0.501599i	$0.832745\pi$
$548$	16.8518	−	34.6676i	0.719871	−	1.48093i
$549$			0.574231i			0.0245076i
$550$	−6.66479	+	4.17076i	−0.284188	+	0.177842i
$551$	−7.19616			−0.306567
$552$	0.965146	+	9.01058i	0.0410794	+	0.383516i
$553$	−1.00891			−0.0429033
$554$	−7.52682	+	4.71021i	−0.319784	+	0.200118i
$555$			6.10806i			0.259273i
$556$	18.8914	+	9.18302i	0.801175	+	0.389447i
$557$		−	9.51132i		−	0.403007i	−0.979488	−	0.201504i	$-0.935417\pi$
$557$		−	9.51132i		−	0.403007i	0.979488	−	0.201504i	$-0.0645828\pi$
$558$	−0.385636	−	0.616238i	−0.0163253	−	0.0260874i
$559$	13.3577			0.564970
$560$	−15.6549	+	12.2979i	−0.661542	+	0.519680i
$561$	5.87629			0.248097
$562$	8.62831	+	13.7879i	0.363963	+	0.581606i
$563$			14.9643i			0.630668i	0.948981	+	0.315334i	$0.102117\pi$
$563$			14.9643i			0.630668i	−0.948981	+	0.315334i	$0.897883\pi$
$564$	−22.5154	−	10.9446i	−0.948070	−	0.460852i
$565$			9.35758i			0.393676i
$566$	13.8786	−	8.68511i	0.583362	−	0.365062i
$567$	−48.1446			−2.02188
$568$	−18.4989	+	1.98147i	−0.776198	+	0.0831406i
$569$	0.281236			0.0117900			0.00589501	−	0.999983i	$-0.498124\pi$
$569$	0.281236			0.0117900			0.00589501	+	0.999983i	$0.498124\pi$
$570$	−2.15937	+	1.35131i	−0.0904459	+	0.0566001i
$571$		−	4.96274i		−	0.207684i	−0.994594	−	0.103842i	$-0.966886\pi$
$571$		−	4.96274i		−	0.207684i	0.994594	−	0.103842i	$-0.0331137\pi$
$572$	−25.9236	+	53.3304i	−1.08392	+	2.22986i
$573$		−	16.3584i		−	0.683382i
$574$	−21.9774	−	35.1194i	−0.917317	−	1.46585i
$575$	−1.77875			−0.0741789
$576$	−1.91122	+	0.414184i	−0.0796342	+	0.0172577i
$577$	3.65475			0.152149			0.0760747	−	0.997102i	$-0.475761\pi$
$577$	3.65475			0.152149			0.0760747	+	0.997102i	$0.475761\pi$
$578$	12.4953	+	19.9672i	0.519735	+	0.830526i
$579$			36.0935i			1.49999i
$580$	6.29205	−	12.9441i	0.261263	−	0.537473i
$581$			41.6920i			1.72968i
$582$	26.5009	−	16.5840i	1.09850	−	0.687430i
$583$	−66.0855			−2.73698
$584$	−3.71109	+	0.397504i	−0.153566	+	0.0164489i
$585$	1.30365			0.0538993
$586$	−5.56802	+	3.48441i	−0.230013	+	0.143940i
$587$			36.7537i			1.51699i	0.651680	+	0.758494i	$0.274065\pi$
$587$			36.7537i			1.51699i	−0.651680	+	0.758494i	$0.725935\pi$
$588$	−57.5732	−	27.9860i	−2.37428	−	1.15412i
$589$			2.10284i			0.0866460i
$590$	−4.22838	−	6.75687i	−0.174080	−	0.278176i
$591$	17.5641			0.722490
$592$	10.6665	−	8.37920i	0.438392	−	0.344383i
$593$	44.9393			1.84543			0.922717	−	0.385478i	$-0.125963\pi$
$593$	44.9393			1.84543			0.922717	+	0.385478i	$0.125963\pi$
$594$	20.7011	+	33.0800i	0.849378	+	1.35729i
$595$			2.92053i			0.119730i
$596$	21.9327	+	10.6614i	0.898397	+	0.436706i
$597$			0.947780i			0.0387900i
$598$	−11.3722	+	7.11661i	−0.465043	+	0.291020i
$599$	−22.3983			−0.915168			−0.457584	−	0.889166i	$-0.651285\pi$
$599$	−22.3983			−0.915168			−0.457584	+	0.889166i	$0.651285\pi$
$600$	−0.542599	−	5.06569i	−0.0221515	−	0.206806i
$601$	−18.3927			−0.750252			−0.375126	−	0.926974i	$-0.622401\pi$
$601$	−18.3927			−0.750252			−0.375126	+	0.926974i	$0.622401\pi$
$602$	14.9442	−	9.35194i	0.609081	−	0.381157i
$603$			2.96566i			0.120771i
$604$	1.23695	−	2.54466i	0.0503307	−	0.103541i
$605$			19.9074i			0.809350i
$606$	22.3176	+	35.6630i	0.906590	+	1.44871i
$607$	23.4700			0.952617			0.476309	−	0.879278i	$-0.341975\pi$
$607$	23.4700			0.952617			0.476309	+	0.879278i	$0.341975\pi$
$608$	5.32208	+	1.91715i	0.215839	+	0.0777508i
$609$	64.5107			2.61410
$610$	1.76232	+	2.81614i	0.0713541	+	0.114022i
$611$		−	37.0607i		−	1.49931i
$612$	−0.125424	+	0.258023i	−0.00506996	+	0.0104300i
$613$			1.30553i			0.0527297i	0.999652	+	0.0263649i	$0.00839317\pi$
$613$			1.30553i			0.0527297i	−0.999652	+	0.0263649i	$0.991607\pi$
$614$	−22.6208	+	14.1558i	−0.912899	+	0.571283i
$615$	10.6023			0.427527
$616$	8.33488	+	77.8142i	0.335822	+	3.13522i
$617$	−8.36103			−0.336602			−0.168301	−	0.985736i	$-0.553828\pi$
$617$	−8.36103			−0.336602			−0.168301	+	0.985736i	$0.553828\pi$
$618$	17.7016	−	11.0775i	0.712063	−	0.445602i
$619$			31.8606i			1.28059i	0.768130	+	0.640293i	$0.221187\pi$
$619$			31.8606i			1.28059i	−0.768130	+	0.640293i	$0.778813\pi$
$620$	−3.78248	−	1.83864i	−0.151908	−	0.0738416i
$621$			8.82863i			0.354281i
$622$	6.54354	+	10.4564i	0.262372	+	0.419265i
$623$	−60.8162			−2.43655
$624$	−23.7364	−	30.2159i	−0.950215	−	1.20960i
$625$	1.00000			0.0400000
$626$	8.47090	+	13.5363i	0.338565	+	0.541020i
$627$			10.0139i			0.399915i
$628$	−29.5248	−	14.3519i	−1.17817	−	0.572701i
$629$		−	1.98991i		−	0.0793431i
$630$	1.45849	−	0.912707i	0.0581075	−	0.0363631i
$631$	−19.6579			−0.782567			−0.391284	−	0.920270i	$-0.627969\pi$
$631$	−19.6579			−0.782567			−0.391284	+	0.920270i	$0.627969\pi$
$632$	−0.570113	+	0.0610662i	−0.0226779	+	0.00242908i
$633$	16.7204			0.664576
$634$	−30.4928	+	19.0821i	−1.21102	+	0.757847i
$635$			13.4310i			0.532993i
$636$	18.7213	−	38.5138i	0.742349	−	1.52717i
$637$		−	94.7662i		−	3.75477i
$638$	−30.0135	−	47.9609i	−1.18824	−	1.89879i
$639$	1.60793			0.0636085
$640$	−8.10189	+	7.89679i	−0.320255	+	0.312148i
$641$	−15.7895			−0.623648			−0.311824	−	0.950140i	$-0.600940\pi$
$641$	−15.7895			−0.623648			−0.311824	+	0.950140i	$0.600940\pi$
$642$	1.88490	+	3.01203i	0.0743909	+	0.118875i
$643$			26.9723i			1.06368i	0.846844	+	0.531841i	$0.178500\pi$
$643$			26.9723i			1.06368i	−0.846844	+	0.531841i	$0.821500\pi$
$644$	−7.74044	+	15.9237i	−0.305016	+	0.627483i
$645$			4.51157i			0.177643i
$646$	0.703489	−	0.440237i	0.0276784	−	0.0173209i
$647$	−0.997247			−0.0392058			−0.0196029	−	0.999808i	$-0.506240\pi$
$647$	−0.997247			−0.0392058			−0.0196029	+	0.999808i	$0.506240\pi$
$648$	−27.2054	+	2.91404i	−1.06873	+	0.114474i
$649$	−31.3343			−1.22998
$650$	6.39337	−	4.00091i	0.250768	−	0.156928i
$651$		−	18.8511i		−	0.738833i
$652$	−15.7851	−	7.67305i	−0.618192	−	0.300500i
$653$		−	19.4317i		−	0.760419i	−0.924900	−	0.380210i	$-0.875852\pi$
$653$		−	19.4317i		−	0.760419i	0.924900	−	0.380210i	$-0.124148\pi$
$654$	−21.6978	−	34.6727i	−0.848452	−	1.35581i
$655$	−15.7227			−0.614337
$656$	−14.5446	−	18.5149i	−0.567870	−	0.722887i
$657$	0.322568			0.0125846
$658$	−25.9468	−	41.4625i	−1.01151	−	1.61638i
$659$			4.99649i			0.194636i	0.995253	+	0.0973179i	$0.0310263\pi$
$659$			4.99649i			0.194636i	−0.995253	+	0.0973179i	$0.968974\pi$
$660$	−18.0124	−	8.75573i	−0.701132	−	0.340816i
$661$			30.5171i			1.18698i	0.804843	+	0.593488i	$0.202250\pi$
$661$			30.5171i			1.18698i	−0.804843	+	0.593488i	$0.797750\pi$
$662$	−10.1275	+	6.33768i	−0.393616	+	0.246321i
$663$	−5.63698			−0.218922
$664$	2.52349	+	23.5592i	0.0979302	+	0.914274i
$665$	−4.97691			−0.192996
$666$	−0.993746	+	0.621876i	−0.0385069	+	0.0240972i
$667$		−	12.8002i		−	0.495624i
$668$	3.66375	−	7.53711i	0.141755	−	0.291620i
$669$		−	38.4738i		−	1.48748i
$670$	9.10163	+	14.5442i	0.351627	+	0.561892i
$671$	13.0596			0.504161
$672$	−47.7103	−	17.1865i	−1.84046	−	0.662983i
$673$	23.2380			0.895760			0.447880	−	0.894094i	$-0.352179\pi$
$673$	23.2380			0.895760			0.447880	+	0.894094i	$0.352179\pi$
$674$	19.1411	+	30.5871i	0.737288	+	1.17817i
$675$		−	4.96340i		−	0.191041i
$676$	13.5012	−	27.7748i	0.519276	−	1.06826i
$677$			15.6525i			0.601576i	0.953691	+	0.300788i	$0.0972496\pi$
$677$			15.6525i			0.601576i	−0.953691	+	0.300788i	$0.902750\pi$
$678$	−20.2064	+	12.6450i	−0.776023	+	0.485628i
$679$	61.0795			2.34401
$680$	0.176771	+	1.65033i	0.00677884	+	0.0632871i
$681$	29.6937			1.13787
$682$	−14.0150	+	8.77044i	−0.536662	+	0.335838i
$683$			13.5590i			0.518819i	0.965767	+	0.259410i	$0.0835280\pi$
$683$			13.5590i			0.518819i	−0.965767	+	0.259410i	$0.916472\pi$
$684$	−0.439701	−	0.213736i	−0.0168124	−	0.00817241i
$685$			19.2732i			0.736392i
$686$	−40.2112	−	64.2567i	−1.53527	−	2.45333i
$687$	−2.74778			−0.104834
$688$	7.87859	−	6.18909i	0.300368	−	0.235957i
$689$	63.3942			2.41513
$690$	−2.40364	−	3.84097i	−0.0915050	−	0.146223i
$691$		−	7.61615i		−	0.289732i	−0.989451	−	0.144866i	$-0.953725\pi$
$691$		−	7.61615i		−	0.289732i	0.989451	−	0.144866i	$-0.0462751\pi$
$692$	−13.5146	−	6.56937i	−0.513748	−	0.249730i
$693$		−	6.76360i		−	0.256928i
$694$	−1.52495	+	0.954300i	−0.0578864	+	0.0362247i
$695$	−10.5025			−0.398384
$696$	36.4535	−	3.90463i	1.38177	−	0.148005i
$697$	−3.45408			−0.130833
$698$	−33.5424	+	20.9905i	−1.26960	+	0.794503i
$699$			33.3683i			1.26211i
$700$	4.35162	−	8.95221i	0.164476	−	0.338362i
$701$			4.07911i			0.154066i	0.997029	+	0.0770330i	$0.0245447\pi$
$701$			4.07911i			0.154066i	−0.997029	+	0.0770330i	$0.975455\pi$
$702$	−19.8581	−	31.7328i	−0.749495	−	1.19768i
$703$	3.39104			0.127895
$704$	9.41970	+	43.4665i	0.355018	+	1.63821i
$705$	12.5173			0.471428
$706$	18.0041	+	28.7702i	0.677594	+	1.08278i
$707$			82.1963i			3.09131i
$708$	8.87669	−	18.2612i	0.333606	−	0.686299i
$709$			26.3975i			0.991378i	0.868500	+	0.495689i	$0.165084\pi$
$709$			26.3975i			0.991378i	−0.868500	+	0.495689i	$0.834916\pi$
$710$	7.88560	−	4.93473i	0.295941	−	0.185197i
$711$	0.0495541			0.00185842
$712$	−34.3659	+	3.68102i	−1.28791	+	0.137952i
$713$	−3.74042			−0.140080
$714$	−6.30650	+	3.94654i	−0.236015	+	0.147696i
$715$		−	29.6487i		−	1.10880i
$716$	−0.404014	−	0.196389i	−0.0150987	−	0.00733940i
$717$		−	39.5026i		−	1.47525i
$718$	−23.9785	−	38.3172i	−0.894871	−	1.42999i
$719$	10.7686			0.401601			0.200800	−	0.979632i	$-0.435646\pi$
$719$	10.7686			0.401601			0.200800	+	0.979632i	$0.435646\pi$
$720$	0.768915	−	0.604028i	0.0286558	−	0.0225108i
$721$	40.7987			1.51942
$722$	0.750213	+	1.19882i	0.0279200	+	0.0446156i
$723$			37.6880i			1.40163i
$724$	22.1202	+	10.7525i	0.822092	+	0.399615i
$725$			7.19616i			0.267259i
$726$	−42.9873	+	26.9010i	−1.59541	+	0.998390i
$727$	26.0101			0.964661			0.482331	−	0.875989i	$-0.339790\pi$
$727$	26.0101			0.964661			0.482331	+	0.875989i	$0.339790\pi$
$728$	−7.99544	−	74.6452i	−0.296331	−	2.76654i
$729$	−24.4560			−0.905779
$730$	1.58194	−	0.989961i	0.0585501	−	0.0366401i
$731$		−	1.46980i		−	0.0543626i
$732$	−3.69965	+	7.61097i	−0.136743	+	0.281309i
$733$			4.15957i			0.153637i	0.997045	+	0.0768186i	$0.0244762\pi$
$733$			4.15957i			0.153637i	−0.997045	+	0.0768186i	$0.975524\pi$
$734$	20.2236	+	32.3169i	0.746466	+	1.19284i
$735$	32.0074			1.18061
$736$	−3.41013	+	9.46664i	−0.125699	+	0.348945i
$737$	67.4475			2.48446
$738$	1.07945	+	1.72494i	0.0397351	+	0.0634958i
$739$		−	46.7464i		−	1.71959i	−0.510636	−	0.859797i	$-0.670590\pi$
$739$		−	46.7464i		−	1.71959i	0.510636	−	0.859797i	$-0.329410\pi$
$740$	−2.96499	+	6.09962i	−0.108995	+	0.224227i
$741$		−	9.60604i		−	0.352887i
$742$	70.9237	−	44.3834i	2.60369	−	1.62936i
$743$	−32.7727			−1.20231			−0.601156	−	0.799131i	$-0.705293\pi$
$743$	−32.7727			−1.20231			−0.601156	+	0.799131i	$0.705293\pi$
$744$	−1.14100	−	10.6523i	−0.0418310	−	0.390533i
$745$	−12.1933			−0.446728
$746$	−27.5203	+	17.2219i	−1.00759	+	0.630539i
$747$		−	2.04776i		−	0.0749237i
$748$	5.86817	+	2.85249i	0.214562	+	0.104297i
$749$			6.94213i			0.253660i
$750$	1.35131	+	2.15937i	0.0493429	+	0.0788489i
$751$	30.7417			1.12178			0.560891	−	0.827890i	$-0.310459\pi$
$751$	30.7417			1.12178			0.560891	+	0.827890i	$0.310459\pi$
$752$	−17.1715	−	21.8590i	−0.626182	−	0.797116i
$753$	−35.2726			−1.28541
$754$	28.7912	+	46.0077i	1.04851	+	1.67550i
$755$			1.41469i			0.0514857i
$756$	−44.4334	−	21.5988i	−1.61603	−	0.785542i
$757$		−	49.5932i		−	1.80249i	−0.433306	−	0.901247i	$-0.642653\pi$
$757$		−	49.5932i		−	1.80249i	0.433306	−	0.901247i	$-0.357347\pi$
$758$	8.72484	−	5.45992i	0.316900	−	0.198313i
$759$	−17.8121			−0.646539
$760$	−2.81234	+	0.301237i	−0.102014	+	0.0109270i
$761$	13.2743			0.481193			0.240597	−	0.970625i	$-0.422657\pi$
$761$	13.2743			0.481193			0.240597	+	0.970625i	$0.422657\pi$
$762$	−29.0024	+	18.1494i	−1.05065	+	0.657485i
$763$		−	79.9138i		−	2.89307i
$764$	7.94074	−	16.3358i	0.287286	−	0.591008i
$765$		−	0.143446i		−	0.00518631i
$766$	7.81354	+	12.4859i	0.282315	+	0.451133i
$767$	30.0582			1.08534
$768$	−28.0002	−	6.82394i	−1.01037	−	0.246238i
$769$	−41.9713			−1.51352			−0.756762	−	0.653690i	$-0.773220\pi$
$769$	−41.9713			−1.51352			−0.756762	+	0.653690i	$0.773220\pi$
$770$	−20.7575	−	33.1701i	−0.748049	−	1.19537i
$771$			9.73485i			0.350592i
$772$	−17.5206	+	36.0436i	−0.630581	+	1.29724i
$773$		−	5.38445i		−	0.193665i	−0.995301	−	0.0968327i	$-0.969129\pi$
$773$		−	5.38445i		−	0.193665i	0.995301	−	0.0968327i	$-0.0308712\pi$
$774$	−0.734006	+	0.459334i	−0.0263833	+	0.0165104i
$775$	2.10284			0.0755362
$776$	34.5146	−	3.69695i	1.23900	−	0.132713i
$777$	−30.3993			−1.09057
$778$	−23.4623	+	14.6825i	−0.841165	+	0.526393i
$779$		−	5.88614i		−	0.210893i
$780$	17.2788	+	8.39915i	0.618682	+	0.300738i
$781$		−	36.5687i		−	1.30853i
$782$	0.783070	+	1.25133i	0.0280025	+	0.0447475i
$783$	35.7174			1.27644
$784$	−43.9086	−	55.8947i	−1.56816	−	1.99624i
$785$	16.4141			0.585844
$786$	−21.2462	−	33.9511i	−0.757829	−	1.21099i
$787$			8.87276i			0.316280i	0.987417	+	0.158140i	$0.0505497\pi$
$787$			8.87276i			0.316280i	−0.987417	+	0.158140i	$0.949450\pi$
$788$	17.5398	+	8.52602i	0.624831	+	0.303727i
$789$			43.7974i			1.55923i
$790$	0.243024	−	0.152082i	0.00864639	−	0.00541083i
$791$	−46.5719			−1.65590
$792$	−0.409380	−	3.82196i	−0.0145467	−	0.135807i
$793$	−12.5278			−0.444874
$794$	−0.502981	+	0.314761i	−0.0178501	+	0.0111704i
$795$			21.4114i			0.759386i
$796$	−0.460074	+	0.946471i	−0.0163069	+	0.0335468i
$797$		−	37.5180i		−	1.32896i	−0.747307	−	0.664479i	$-0.768654\pi$
$797$		−	37.5180i		−	1.32896i	0.747307	−	0.664479i	$-0.231346\pi$
$798$	−6.72535	−	10.7470i	−0.238075	−	0.380439i
$799$	−4.07794			−0.144267
$800$	1.91715	−	5.32208i	0.0677816	−	0.188164i
$801$	2.98708			0.105543
$802$	10.4746	+	16.7382i	0.369871	+	0.591046i
$803$		−	7.33609i		−	0.258885i
$804$	−19.1072	+	39.3075i	−0.673858	+	1.38627i
$805$		−	8.85268i		−	0.312016i
$806$	13.4442	−	8.41326i	0.473552	−	0.296344i
$807$	11.6835			0.411278
$808$	4.97509	+	46.4473i	0.175023	+	1.63401i
$809$	11.8562			0.416842			0.208421	−	0.978039i	$-0.433168\pi$
$809$	11.8562			0.416842			0.208421	+	0.978039i	$0.433168\pi$
$810$	11.5969	−	7.25725i	0.407475	−	0.254994i
$811$			28.7564i			1.00977i	0.863186	+	0.504886i	$0.168466\pi$
$811$			28.7564i			1.00977i	−0.863186	+	0.504886i	$0.831534\pi$
$812$	64.4215	+	31.3150i	2.26075	+	1.09894i
$813$			2.66589i			0.0934969i
$814$	14.1432	+	22.6006i	0.495719	+	0.792150i
$815$	8.77560			0.307396
$816$	−3.32478	+	2.61181i	−0.116391	+	0.0914318i
$817$	2.50471			0.0876286
$818$	2.17212	+	3.47101i	0.0759466	+	0.121361i
$819$			6.48815i			0.226714i
$820$	10.5877	+	5.14662i	0.369738	+	0.179728i
$821$		−	25.0626i		−	0.874690i	−0.899294	−	0.437345i	$-0.855919\pi$
$821$		−	25.0626i		−	0.874690i	0.899294	−	0.437345i	$-0.144081\pi$
$822$	−41.6179	+	26.0441i	−1.45159	+	0.908392i
$823$	54.6661			1.90554			0.952769	−	0.303695i	$-0.0982202\pi$
$823$	54.6661			1.90554			0.952769	+	0.303695i	$0.0982202\pi$
$824$	23.0544	−	2.46942i	0.803139	−	0.0860262i
$825$	10.0139			0.348638
$826$	33.6283	−	21.0443i	1.17008	−	0.732224i
$827$			0.0672364i			0.00233804i	0.999999	+	0.00116902i	$0.000372110\pi$
$827$			0.0672364i			0.00233804i	−0.999999	+	0.00116902i	$0.999628\pi$
$828$	0.380183	−	0.782117i	0.0132123	−	0.0271804i
$829$			25.7086i			0.892897i	0.894809	+	0.446449i	$0.147311\pi$
$829$			25.7086i			0.892897i	−0.894809	+	0.446449i	$0.852689\pi$
$830$	−6.28459	−	10.0426i	−0.218141	−	0.348585i
$831$	11.3090			0.392307
$832$	−9.03608	−	41.6964i	−0.313270	−	1.44556i
$833$	−10.4275			−0.361292
$834$	−14.1922	−	22.6788i	−0.491435	−	0.785304i
$835$			4.19020i			0.145008i
$836$	−4.86096	+	10.0000i	−0.168120	+	0.345858i
$837$		−	10.4372i		−	0.360763i
$838$	−20.0065	+	12.5199i	−0.691114	+	0.432492i
$839$	−39.1907			−1.35301			−0.676507	−	0.736436i	$-0.736507\pi$
$839$	−39.1907			−1.35301			−0.676507	+	0.736436i	$0.736507\pi$
$840$	25.2115	−	2.70047i	0.869879	−	0.0931750i
$841$	−22.7847			−0.785680
$842$	30.6009	−	19.1497i	1.05458	−	0.659943i
$843$		−	20.7163i		−	0.713506i
$844$	16.6973	+	8.11647i	0.574745	+	0.279380i
$845$			15.4412i			0.531193i
$846$	1.27442	+	2.03649i	0.0438153	+	0.0700159i
$847$	−99.0773			−3.40433
$848$	37.3910	−	29.3728i	1.28401	−	1.00867i
$849$	−20.8526			−0.715661
$850$	−0.440237	−	0.703489i	−0.0151000	−	0.0241295i
$851$			6.03180i			0.206768i
$852$	21.3118	+	10.3595i	0.730129	+	0.354912i
$853$			33.9517i			1.16249i	0.813730	+	0.581243i	$0.197433\pi$
$853$			33.9517i			1.16249i	−0.813730	+	0.581243i	$0.802567\pi$
$854$	−14.0157	+	8.77089i	−0.479608	+	0.300134i
$855$	0.244448			0.00835995
$856$	0.420185	+	3.92284i	0.0143616	+	0.134080i
$857$	−32.7122			−1.11743			−0.558714	−	0.829360i	$-0.688705\pi$
$857$	−32.7122			−1.11743			−0.558714	+	0.829360i	$0.688705\pi$
$858$	64.0223	−	40.0645i	2.18568	−	1.36778i
$859$		−	13.1984i		−	0.450324i	−0.974321	−	0.225162i	$-0.927709\pi$
$859$		−	13.1984i		−	0.450324i	0.974321	−	0.225162i	$-0.0722911\pi$
$860$	−2.19002	+	4.50534i	−0.0746791	+	0.153631i
$861$			52.7669i			1.79829i
$862$	9.50231	+	15.1845i	0.323650	+	0.517186i
$863$	50.0256			1.70289			0.851445	−	0.524444i	$-0.175727\pi$
$863$	50.0256			1.70289			0.851445	+	0.524444i	$0.175727\pi$
$864$	−26.4156	−	9.51559i	−0.898677	−	0.323727i
$865$	7.51333			0.255461
$866$	4.52481	+	7.23056i	0.153759	+	0.245704i
$867$		−	30.0007i		−	1.01888i
$868$	9.15076	−	18.8251i	0.310597	−	0.638964i
$869$		−	1.12700i		−	0.0382308i
$870$	−15.5391	+	9.72424i	−0.526826	+	0.329683i
$871$	−64.7007			−2.19230
$872$	−4.83693	−	45.1574i	−0.163799	−	1.52922i
$873$	−3.00001			−0.101535
$874$	−2.13241	+	1.33444i	−0.0721298	+	0.0451381i
$875$			4.97691i			0.168250i
$876$	4.27538	+	2.07824i	0.144452	+	0.0702171i
$877$			43.3237i			1.46294i	0.681875	+	0.731468i	$0.261165\pi$
$877$			43.3237i			1.46294i	−0.681875	+	0.731468i	$0.738835\pi$
$878$	16.1199	+	25.7593i	0.544020	+	0.869333i
$879$	8.36595			0.282177
$880$	−13.7373	−	17.4873i	−0.463084	−	0.589496i
$881$	36.6786			1.23573			0.617867	−	0.786282i	$-0.287997\pi$
$881$	36.6786			1.23573			0.617867	+	0.786282i	$0.287997\pi$
$882$	3.25875	+	5.20741i	0.109728	+	0.175343i
$883$			31.5830i			1.06285i	0.847104	+	0.531427i	$0.178344\pi$
$883$			31.5830i			1.06285i	−0.847104	+	0.531427i	$0.821656\pi$
$884$	−5.62919	−	2.73632i	−0.189330	−	0.0920324i
$885$			10.1522i			0.341262i
$886$	−28.3390	+	17.7342i	−0.952066	+	0.595793i
$887$	−14.6563			−0.492110			−0.246055	−	0.969256i	$-0.579134\pi$
$887$	−14.6563			−0.492110			−0.246055	+	0.969256i	$0.579134\pi$
$888$	−17.1779	+	1.83997i	−0.576454	+	0.0617454i
$889$	−66.8449			−2.24191
$890$	14.6492	−	9.16735i	0.491044	−	0.307290i
$891$		−	53.7797i		−	1.80169i
$892$	18.6761	−	38.4207i	0.625321	−	1.28642i
$893$		−	6.94927i		−	0.232549i
$894$	−16.4769	−	26.3298i	−0.551071	−	0.880600i
$895$	0.224608			0.00750783
$896$	−39.3017	−	40.3224i	−1.31298	−	1.34708i
$897$	17.0867			0.570509
$898$	−7.93770	−	12.6843i	−0.264885	−	0.423280i
$899$			15.1324i			0.504693i
$900$	−0.213736	+	0.439701i	−0.00712454	+	0.0146567i
$901$		−	6.97553i		−	0.232389i
$902$	39.2299	−	24.5497i	1.30621	−	0.817416i
$903$	−22.4537			−0.747212
$904$	−26.3167	+	2.81885i	−0.875280	+	0.0937535i
$905$	−12.2976			−0.408785
$906$	−3.05482	+	1.91168i	−0.101490	+	0.0635113i
$907$		−	3.17938i		−	0.105570i	−0.998606	−	0.0527848i	$-0.983190\pi$
$907$		−	3.17938i		−	0.105570i	0.998606	−	0.0527848i	$-0.0168097\pi$
$908$	29.6527	+	14.4140i	0.984059	+	0.478346i
$909$		−	4.03719i		−	0.133905i
$910$	19.9122	+	31.8192i	0.660082	+	1.05480i
$911$	48.2520			1.59866			0.799331	−	0.600891i	$-0.205188\pi$
$911$	48.2520			1.59866			0.799331	+	0.600891i	$0.205188\pi$
$912$	−4.45082	−	5.66581i	−0.147381	−	0.187614i
$913$	−46.5718			−1.54130
$914$	7.46609	+	11.9307i	0.246956	+	0.394631i
$915$		−	4.23126i		−	0.139881i
$916$	−2.74398	−	1.33384i	−0.0906637	−	0.0440712i
$917$		−	78.2506i		−	2.58406i
$918$	−3.49170	+	2.18507i	−0.115243	+	0.0721180i
$919$	11.6699			0.384953			0.192477	−	0.981302i	$-0.438348\pi$
$919$	11.6699			0.384953			0.192477	+	0.981302i	$0.438348\pi$
$920$	−0.535825	−	5.00244i	−0.0176656	−	0.164926i
$921$	33.9877			1.11993
$922$	−21.2868	+	13.3211i	−0.701044	+	0.438706i
$923$			35.0795i			1.15465i
$924$	43.5765	−	89.6462i	1.43356	−	2.94914i
$925$		−	3.39104i		−	0.111497i
$926$	5.47978	+	8.75658i	0.180077	+	0.287759i
$927$	−2.00389			−0.0658163
$928$	38.2985	+	13.7961i	1.25721	+	0.452880i
$929$	23.1765			0.760395			0.380197	−	0.924905i	$-0.375856\pi$
$929$	23.1765			0.760395			0.380197	+	0.924905i	$0.375856\pi$
$930$	2.84159	+	4.54080i	0.0931793	+	0.148899i
$931$		−	17.7697i		−	0.582378i
$932$	−16.1978	+	33.3222i	−0.530575	+	1.09151i
$933$		−	15.7108i		−	0.514349i
$934$	43.2971	−	27.0949i	1.41672	−	0.886572i
$935$	−3.26237			−0.106691
$936$	0.392708	+	3.66631i	0.0128360	+	0.119837i
$937$	41.2136			1.34639			0.673194	−	0.739466i	$-0.264922\pi$
$937$	41.2136			1.34639			0.673194	+	0.739466i	$0.264922\pi$
$938$	−72.3854	+	45.2980i	−2.36347	+	1.47903i
$939$		−	20.3383i		−	0.663717i
$940$	12.5000	+	6.07618i	0.407705	+	0.198183i
$941$			33.3470i			1.08708i	0.839383	+	0.543540i	$0.182916\pi$
$941$			33.3470i			1.08708i	−0.839383	+	0.543540i	$0.817084\pi$
$942$	22.1805	+	35.4440i	0.722681	+	1.15483i
$943$	10.4700			0.340949
$944$	17.7289	−	13.9271i	0.577025	−	0.453287i
$945$	24.7024			0.803569
$946$	10.4465	+	16.6934i	0.339646	+	0.542748i
$947$		−	9.76298i		−	0.317254i	−0.987339	−	0.158627i	$-0.949293\pi$
$947$		−	9.76298i		−	0.317254i	0.987339	−	0.158627i	$-0.0507068\pi$
$948$	0.656800	+	0.319267i	0.0213319	+	0.0103693i
$949$			7.03733i			0.228441i
$950$	1.19882	−	0.750213i	0.0388950	−	0.0243401i
$951$	45.8155			1.48567
$952$	−8.21353	+	0.879772i	−0.266202	+	0.0285136i
$953$	−16.5110			−0.534842			−0.267421	−	0.963580i	$-0.586171\pi$
$953$	−16.5110			−0.534842			−0.267421	+	0.963580i	$0.586171\pi$
$954$	−3.48352	+	2.17995i	−0.112783	+	0.0705786i
$955$			9.08176i			0.293879i
$956$	19.1755	−	39.4480i	0.620179	−	1.27584i
$957$			72.0613i			2.32941i
$958$	2.57440	+	4.11384i	0.0831752	+	0.132912i
$959$	−95.9211			−3.09745
$960$	14.0830	−	3.05194i	0.454526	−	0.0985011i
$961$	−26.5781			−0.857357
$962$	−13.5672	−	21.6802i	−0.437425	−	0.698996i
$963$		−	0.340973i		−	0.0109877i
$964$	−18.2946	+	37.6360i	−0.589231	+	1.21217i
$965$		−	20.0382i		−	0.645052i
$966$	19.1162	−	11.9627i	0.615053	−	0.384894i
$967$	−4.50738			−0.144948			−0.0724738	−	0.997370i	$-0.523089\pi$
$967$	−4.50738			−0.144948			−0.0724738	+	0.997370i	$0.523089\pi$
$968$	−55.9863	+	5.99684i	−1.79947	+	0.192746i
$969$	−1.05699			−0.0339555
$970$	−14.7126	+	9.20703i	−0.472395	+	0.295620i
$971$			39.1846i			1.25749i	0.777611	+	0.628746i	$0.216432\pi$
$971$			39.1846i			1.25749i	−0.777611	+	0.628746i	$0.783568\pi$
$972$	4.55842	+	2.21582i	0.146211	+	0.0710726i
$973$		−	52.2703i		−	1.67571i
$974$	−29.3497	−	46.9002i	−0.940425	−	1.50278i
$975$	−9.60604			−0.307639
$976$	−7.38908	+	5.80456i	−0.236519	+	0.185799i
$977$	44.1693			1.41310			0.706551	−	0.707662i	$-0.250250\pi$
$977$	44.1693			1.41310			0.706551	+	0.707662i	$0.250250\pi$
$978$	11.8586	+	18.9497i	0.379195	+	0.605945i
$979$		−	67.9345i		−	2.17120i
$980$	31.9632	+	15.5371i	1.02103	+	0.496315i
$981$			3.92508i			0.125318i
$982$	4.16958	−	2.60928i	0.133057	−	0.0832655i
$983$	24.5139			0.781873			0.390936	−	0.920418i	$-0.372151\pi$
$983$	24.5139			0.781873			0.390936	+	0.920418i	$0.372151\pi$
$984$	3.19381	+	29.8174i	0.101815	+	0.950543i
$985$	−9.75114			−0.310697
$986$	5.06242	−	3.16801i	0.161220	−	0.100890i
$987$			62.2974i			1.98295i
$988$	4.66300	−	9.59277i	0.148350	−	0.305187i
$989$			4.45524i			0.141669i
$990$	1.01954	+	1.62920i	0.0324030	+	0.0517793i
$991$	12.4774			0.396357			0.198179	−	0.980166i	$-0.436497\pi$
$991$	12.4774			0.396357			0.198179	+	0.980166i	$0.436497\pi$
$992$	4.03146	−	11.1915i	0.127999	−	0.355330i
$993$	15.2165			0.482882
$994$	24.5597	+	39.2459i	0.778987	+	1.24481i
$995$		−	0.526183i		−	0.0166811i
$996$	13.1933	−	27.1414i	0.418046	−	0.860010i
$997$			55.2170i			1.74874i	0.485261	+	0.874369i	$0.338725\pi$
$997$			55.2170i			1.74874i	−0.485261	+	0.874369i	$0.661275\pi$
$998$	−26.6588	+	16.6828i	−0.843869	+	0.528085i
$999$	−16.8311			−0.532511

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	760.2.f.b.381.13	✓	44
4.3	odd	2		3040.2.f.b.1521.12		44
8.3	odd	2		3040.2.f.b.1521.33		44
8.5	even	2	inner	760.2.f.b.381.14	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
760.2.f.b.381.13	✓	44	1.1	even	1	trivial
760.2.f.b.381.14	yes	44	8.5	even	2	inner
3040.2.f.b.1521.12		44	4.3	odd	2
3040.2.f.b.1521.33		44	8.3	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+(-0.750213 - 1.19882i) q^{2} +1.80124i q^{3} +(-0.874362 + 1.79875i) q^{4} -1.00000i q^{5} +(2.15937 - 1.35131i) q^{6} +4.97691 q^{7} +(2.81234 - 0.301237i) q^{8} -0.244448 q^{9} +(-1.19882 + 0.750213i) q^{10} +5.55944i q^{11} +(-3.23997 - 1.57493i) q^{12} -5.33303i q^{13} +(-3.73374 - 5.96645i) q^{14} +1.80124 q^{15} +(-2.47098 - 3.14551i) q^{16} -0.586816 q^{17} +(0.183388 + 0.293051i) q^{18} -1.00000i q^{19} +(1.79875 + 0.874362i) q^{20} +8.96459i q^{21} +(6.66479 - 4.17076i) q^{22} +1.77875 q^{23} +(0.542599 + 5.06569i) q^{24} -1.00000 q^{25} +(-6.39337 + 4.00091i) q^{26} +4.96340i q^{27} +(-4.35162 + 8.95221i) q^{28} -7.19616i q^{29} +(-1.35131 - 2.15937i) q^{30} -2.10284 q^{31} +(-1.91715 + 5.32208i) q^{32} -10.0139 q^{33} +(0.440237 + 0.703489i) q^{34} -4.97691i q^{35} +(0.213736 - 0.439701i) q^{36} +3.39104i q^{37} +(-1.19882 + 0.750213i) q^{38} +9.60604 q^{39} +(-0.301237 - 2.81234i) q^{40} +5.88614 q^{41} +(10.7470 - 6.72535i) q^{42} +2.50471i q^{43} +(-10.0000 - 4.86096i) q^{44} +0.244448i q^{45} +(-1.33444 - 2.13241i) q^{46} +6.94927 q^{47} +(5.66581 - 4.45082i) q^{48} +17.7697 q^{49} +(0.750213 + 1.19882i) q^{50} -1.05699i q^{51} +(9.59277 + 4.66300i) q^{52} +11.8871i q^{53} +(5.95024 - 3.72360i) q^{54} +5.55944 q^{55} +(13.9968 - 1.49923i) q^{56} +1.80124 q^{57} +(-8.62694 + 5.39865i) q^{58} +5.63624i q^{59} +(-1.57493 + 3.23997i) q^{60} -2.34909i q^{61} +(1.57758 + 2.52094i) q^{62} -1.21660 q^{63} +(7.81851 - 1.69436i) q^{64} -5.33303 q^{65} +(7.51252 + 12.0049i) q^{66} -12.1321i q^{67} +(0.513089 - 1.05553i) q^{68} +3.20394i q^{69} +(-5.96645 + 3.73374i) q^{70} -6.57777 q^{71} +(-0.687472 + 0.0736369i) q^{72} -1.31957 q^{73} +(4.06526 - 2.54400i) q^{74} -1.80124i q^{75} +(1.79875 + 0.874362i) q^{76} +27.6689i q^{77} +(-7.20657 - 11.5160i) q^{78} -0.202718 q^{79} +(-3.14551 + 2.47098i) q^{80} -9.67359 q^{81} +(-4.41586 - 7.05645i) q^{82} +8.37708i q^{83} +(-16.1250 - 7.83830i) q^{84} +0.586816i q^{85} +(3.00271 - 1.87906i) q^{86} +12.9620 q^{87} +(1.67471 + 15.6350i) q^{88} -12.2197 q^{89} +(0.293051 - 0.183388i) q^{90} -26.5420i q^{91} +(-1.55527 + 3.19952i) q^{92} -3.78771i q^{93} +(-5.21343 - 8.33096i) q^{94} -1.00000 q^{95} +(-9.58632 - 3.45324i) q^{96} +12.2726 q^{97} +(-13.3310 - 21.3027i) q^{98} -1.35900i 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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