LMFDB - Embedded newform 680.2.f.e.341.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(341,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, 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("680.341"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.f (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [30,0,0,-2,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			341.11
Character	$\chi$	$=$	680.341
Dual form			680.2.f.e.341.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.276941 - 1.38683i) q^{2} +2.54394i q^{3} +(-1.84661 + 0.768141i) q^{4} -1.00000i q^{5} +(3.52802 - 0.704520i) q^{6} +3.47689 q^{7} +(1.57668 + 2.34821i) q^{8} -3.47163 q^{9} +(-1.38683 + 0.276941i) q^{10} +0.0495512i q^{11} +(-1.95410 - 4.69766i) q^{12} +3.09291i q^{13} +(-0.962892 - 4.82186i) q^{14} +2.54394 q^{15} +(2.81992 - 2.83691i) q^{16} +1.00000 q^{17} +(0.961435 + 4.81457i) q^{18} -3.67080i q^{19} +(0.768141 + 1.84661i) q^{20} +8.84500i q^{21} +(0.0687192 - 0.0137227i) q^{22} +2.12995 q^{23} +(-5.97369 + 4.01099i) q^{24} -1.00000 q^{25} +(4.28935 - 0.856553i) q^{26} -1.19979i q^{27} +(-6.42045 + 2.67074i) q^{28} +7.05489i q^{29} +(-0.704520 - 3.52802i) q^{30} -2.99704 q^{31} +(-4.71527 - 3.12510i) q^{32} -0.126055 q^{33} +(-0.276941 - 1.38683i) q^{34} -3.47689i q^{35} +(6.41073 - 2.66670i) q^{36} +10.8445i q^{37} +(-5.09078 + 1.01659i) q^{38} -7.86818 q^{39} +(2.34821 - 1.57668i) q^{40} +9.08518 q^{41} +(12.2665 - 2.44954i) q^{42} +4.85028i q^{43} +(-0.0380623 - 0.0915016i) q^{44} +3.47163i q^{45} +(-0.589869 - 2.95388i) q^{46} +9.07941 q^{47} +(7.21692 + 7.17371i) q^{48} +5.08876 q^{49} +(0.276941 + 1.38683i) q^{50} +2.54394i q^{51} +(-2.37579 - 5.71139i) q^{52} -9.42277i q^{53} +(-1.66391 + 0.332271i) q^{54} +0.0495512 q^{55} +(5.48195 + 8.16445i) q^{56} +9.33829 q^{57} +(9.78395 - 1.95379i) q^{58} +8.60624i q^{59} +(-4.69766 + 1.95410i) q^{60} +10.1877i q^{61} +(0.830003 + 4.15639i) q^{62} -12.0705 q^{63} +(-3.02814 + 7.40475i) q^{64} +3.09291 q^{65} +(0.0349098 + 0.174817i) q^{66} -6.07949i q^{67} +(-1.84661 + 0.768141i) q^{68} +5.41845i q^{69} +(-4.82186 + 0.962892i) q^{70} -2.40305 q^{71} +(-5.47366 - 8.15210i) q^{72} +1.98250 q^{73} +(15.0395 - 3.00329i) q^{74} -2.54394i q^{75} +(2.81969 + 6.77853i) q^{76} +0.172284i q^{77} +(2.17902 + 10.9118i) q^{78} -7.95155 q^{79} +(-2.83691 - 2.81992i) q^{80} -7.36268 q^{81} +(-2.51606 - 12.5996i) q^{82} -16.7931i q^{83} +(-6.79420 - 16.3332i) q^{84} -1.00000i q^{85} +(6.72652 - 1.34324i) q^{86} -17.9472 q^{87} +(-0.116356 + 0.0781265i) q^{88} -0.333460 q^{89} +(4.81457 - 0.961435i) q^{90} +10.7537i q^{91} +(-3.93317 + 1.63610i) q^{92} -7.62429i q^{93} +(-2.51446 - 12.5916i) q^{94} -3.67080 q^{95} +(7.95007 - 11.9954i) q^{96} -9.92795 q^{97} +(-1.40929 - 7.05726i) q^{98} -0.172023i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 2 q^{4} - 8 q^{6} + 12 q^{7} + 6 q^{8} - 36 q^{9} + 2 q^{10} + 8 q^{12} - 10 q^{14} - 14 q^{15} - 2 q^{16} + 30 q^{17} + 6 q^{18} + 4 q^{20} - 6 q^{22} + 12 q^{23} - 46 q^{24} - 30 q^{25} + 4 q^{26}+ \cdots - 16 q^{98}+O(q^{100}) $ 30 * q - 2 * q^4 - 8 * q^6 + 12 * q^7 + 6 * q^8 - 36 * q^9 + 2 * q^10 + 8 * q^12 - 10 * q^14 - 14 * q^15 - 2 * q^16 + 30 * q^17 + 6 * q^18 + 4 * q^20 - 6 * q^22 + 12 * q^23 - 46 * q^24 - 30 * q^25 + 4 * q^26 + 22 * q^28 + 6 * q^30 - 26 * q^31 - 10 * q^32 + 12 * q^33 + 32 * q^36 + 6 * q^38 + 2 * q^39 + 4 * q^40 - 20 * q^41 + 48 * q^42 + 22 * q^44 + 38 * q^46 - 22 * q^47 + 24 * q^48 + 30 * q^49 + 48 * q^52 - 66 * q^54 + 32 * q^55 - 6 * q^56 - 26 * q^57 - 32 * q^58 - 14 * q^60 - 46 * q^62 - 4 * q^63 - 50 * q^64 + 6 * q^65 - 44 * q^66 - 2 * q^68 - 2 * q^70 + 58 * q^71 - 14 * q^72 - 18 * q^73 + 56 * q^74 - 6 * q^76 + 12 * q^78 - 60 * q^79 - 42 * q^81 - 24 * q^82 + 72 * q^84 + 48 * q^86 + 6 * q^87 + 18 * q^88 + 6 * q^89 - 14 * q^90 + 74 * q^92 - 16 * q^94 - 30 * q^95 + 22 * q^96 + 38 * q^97 - 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$1$	$1$	$-1$	$1$

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 $

$2$	−0.276941	−	1.38683i	−0.195827	−	0.980639i
$2$	−0.276941	−	1.38683i	−0.195827	−	0.980639i
$3$			2.54394i			1.46874i	0.678747	+	0.734372i	$0.262523\pi$
$3$			2.54394i			1.46874i	−0.678747	+	0.734372i	$0.737477\pi$
$4$	−1.84661	+	0.768141i	−0.923304	+	0.384070i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	3.52802	−	0.704520i	1.44031	−	0.287619i
$7$	3.47689			1.31414			0.657070	−	0.753829i	$-0.271795\pi$
$7$	3.47689			1.31414			0.657070	+	0.753829i	$0.271795\pi$
$8$	1.57668	+	2.34821i	0.557442	+	0.830216i
$9$	−3.47163			−1.15721
$10$	−1.38683	+	0.276941i	−0.438555	+	0.0875763i
$11$			0.0495512i			0.0149402i	0.999972	+	0.00747012i	$0.00237784\pi$
$11$			0.0495512i			0.0149402i	−0.999972	+	0.00747012i	$0.997622\pi$
$12$	−1.95410	−	4.69766i	−0.564101	−	1.35610i
$13$			3.09291i			0.857819i	0.903347	+	0.428910i	$0.141102\pi$
$13$			3.09291i			0.857819i	−0.903347	+	0.428910i	$0.858898\pi$
$14$	−0.962892	−	4.82186i	−0.257344	−	1.28870i
$15$	2.54394			0.656842
$16$	2.81992	−	2.83691i	0.704980	−	0.709227i
$17$	1.00000			0.242536
$17$	1.00000			0.242536
$18$	0.961435	+	4.81457i	0.226612	+	1.13480i
$19$		−	3.67080i		−	0.842139i	−0.907028	−	0.421070i	$-0.861655\pi$
$19$		−	3.67080i		−	0.842139i	0.907028	−	0.421070i	$-0.138345\pi$
$20$	0.768141	+	1.84661i	0.171761	+	0.412914i
$21$			8.84500i			1.93014i
$22$	0.0687192	−	0.0137227i	0.0146510	−	0.00292570i
$23$	2.12995			0.444124			0.222062	−	0.975033i	$-0.428721\pi$
$23$	2.12995			0.444124			0.222062	+	0.975033i	$0.428721\pi$
$24$	−5.97369	+	4.01099i	−1.21938	+	0.818739i
$25$	−1.00000			−0.200000
$26$	4.28935	−	0.856553i	0.841211	−	0.167984i
$27$		−	1.19979i		−	0.230900i
$28$	−6.42045	+	2.67074i	−1.21335	+	0.504722i
$29$			7.05489i			1.31006i	0.755603	+	0.655030i	$0.227344\pi$
$29$			7.05489i			1.31006i	−0.755603	+	0.655030i	$0.772656\pi$
$30$	−0.704520	−	3.52802i	−0.128627	−	0.644125i
$31$	−2.99704			−0.538285			−0.269142	−	0.963100i	$-0.586740\pi$
$31$	−2.99704			−0.538285			−0.269142	+	0.963100i	$0.586740\pi$
$32$	−4.71527	−	3.12510i	−0.833549	−	0.552445i
$33$	−0.126055			−0.0219434
$34$	−0.276941	−	1.38683i	−0.0474949	−	0.237840i
$35$		−	3.47689i		−	0.587702i
$36$	6.41073	−	2.66670i	1.06846	−	0.444450i
$37$			10.8445i			1.78283i	0.453190	+	0.891414i	$0.350286\pi$
$37$			10.8445i			1.78283i	−0.453190	+	0.891414i	$0.649714\pi$
$38$	−5.09078	+	1.01659i	−0.825834	+	0.164913i
$39$	−7.86818			−1.25992
$40$	2.34821	−	1.57668i	0.371284	−	0.249295i
$41$	9.08518			1.41887			0.709433	−	0.704772i	$-0.248951\pi$
$41$	9.08518			1.41887			0.709433	+	0.704772i	$0.248951\pi$
$42$	12.2665	−	2.44954i	1.89277	−	0.377972i
$43$			4.85028i			0.739660i	0.929099	+	0.369830i	$0.120584\pi$
$43$			4.85028i			0.739660i	−0.929099	+	0.369830i	$0.879416\pi$
$44$	−0.0380623	−	0.0915016i	−0.00573810	−	0.0137944i
$45$			3.47163i			0.517520i
$46$	−0.589869	−	2.95388i	−0.0869714	−	0.435525i
$47$	9.07941			1.32437			0.662184	−	0.749341i	$-0.269630\pi$
$47$	9.07941			1.32437			0.662184	+	0.749341i	$0.269630\pi$
$48$	7.21692	+	7.17371i	1.04167	+	1.03544i
$49$	5.08876			0.726966
$50$	0.276941	+	1.38683i	0.0391653	+	0.196128i
$51$			2.54394i			0.356223i
$52$	−2.37579	−	5.71139i	−0.329463	−	0.792028i
$53$		−	9.42277i		−	1.29432i	−0.762355	−	0.647159i	$-0.775957\pi$
$53$		−	9.42277i		−	1.29432i	0.762355	−	0.647159i	$-0.224043\pi$
$54$	−1.66391	+	0.332271i	−0.226430	+	0.0452164i
$55$	0.0495512			0.00668148
$56$	5.48195	+	8.16445i	0.732557	+	1.09102i
$57$	9.33829			1.23689
$58$	9.78395	−	1.95379i	1.28470	−	0.256545i
$59$			8.60624i			1.12044i	0.828345	+	0.560219i	$0.189283\pi$
$59$			8.60624i			1.12044i	−0.828345	+	0.560219i	$0.810717\pi$
$60$	−4.69766	+	1.95410i	−0.606465	+	0.252274i
$61$			10.1877i			1.30440i	0.758047	+	0.652200i	$0.226154\pi$
$61$			10.1877i			1.30440i	−0.758047	+	0.652200i	$0.773846\pi$
$62$	0.830003	+	4.15639i	0.105410	+	0.527863i
$63$	−12.0705			−1.52074
$64$	−3.02814	+	7.40475i	−0.378518	+	0.925594i
$65$	3.09291			0.383628
$66$	0.0349098	+	0.174817i	0.00429710	+	0.0215185i
$67$		−	6.07949i		−	0.742727i	−0.928487	−	0.371364i	$-0.878890\pi$
$67$		−	6.07949i		−	0.742727i	0.928487	−	0.371364i	$-0.121110\pi$
$68$	−1.84661	+	0.768141i	−0.223934	+	0.0931507i
$69$			5.41845i			0.652305i
$70$	−4.82186	+	0.962892i	−0.576323	+	0.115088i
$71$	−2.40305			−0.285189			−0.142595	−	0.989781i	$-0.545545\pi$
$71$	−2.40305			−0.285189			−0.142595	+	0.989781i	$0.545545\pi$
$72$	−5.47366	−	8.15210i	−0.645077	−	0.960734i
$73$	1.98250			0.232035			0.116017	−	0.993247i	$-0.462987\pi$
$73$	1.98250			0.232035			0.116017	+	0.993247i	$0.462987\pi$
$74$	15.0395	−	3.00329i	1.74831	−	0.349125i
$75$		−	2.54394i		−	0.293749i
$76$	2.81969	+	6.77853i	0.323441	+	0.777550i
$77$			0.172284i			0.0196336i
$78$	2.17902	+	10.9118i	0.246725	+	1.23552i
$79$	−7.95155			−0.894619			−0.447310	−	0.894379i	$-0.647618\pi$
$79$	−7.95155			−0.894619			−0.447310	+	0.894379i	$0.647618\pi$
$80$	−2.83691	−	2.81992i	−0.317176	−	0.315277i
$81$	−7.36268			−0.818076
$82$	−2.51606	−	12.5996i	−0.277852	−	1.39140i
$83$		−	16.7931i		−	1.84328i	−0.388046	−	0.921640i	$-0.626850\pi$
$83$		−	16.7931i		−	1.84328i	0.388046	−	0.921640i	$-0.373150\pi$
$84$	−6.79420	−	16.3332i	−0.741308	−	1.78210i
$85$		−	1.00000i		−	0.108465i
$86$	6.72652	−	1.34324i	0.725339	−	0.144845i
$87$	−17.9472			−1.92414
$88$	−0.116356	+	0.0781265i	−0.0124036	+	0.00832831i
$89$	−0.333460			−0.0353467			−0.0176733	−	0.999844i	$-0.505626\pi$
$89$	−0.333460			−0.0353467			−0.0176733	+	0.999844i	$0.505626\pi$
$90$	4.81457	−	0.961435i	0.507500	−	0.101344i
$91$			10.7537i			1.12730i
$92$	−3.93317	+	1.63610i	−0.410062	+	0.170575i
$93$		−	7.62429i		−	0.790602i
$94$	−2.51446	−	12.5916i	−0.259347	−	1.29873i
$95$	−3.67080			−0.376616
$96$	7.95007	−	11.9954i	0.811400	−	1.22427i
$97$	−9.92795			−1.00803			−0.504015	−	0.863695i	$-0.668144\pi$
$97$	−9.92795			−1.00803			−0.504015	+	0.863695i	$0.668144\pi$
$98$	−1.40929	−	7.05726i	−0.142359	−	0.712891i
$99$		−	0.172023i		−	0.0172890i
$100$	1.84661	−	0.768141i	0.184661	−	0.0768141i
$101$		−	14.7864i		−	1.47130i	−0.677361	−	0.735651i	$-0.736876\pi$
$101$		−	14.7864i		−	1.47130i	0.677361	−	0.735651i	$-0.263124\pi$
$102$	3.52802	−	0.704520i	0.349326	−	0.0697579i
$103$	−1.03107			−0.101594			−0.0507970	−	0.998709i	$-0.516176\pi$
$103$	−1.03107			−0.101594			−0.0507970	+	0.998709i	$0.516176\pi$
$104$	−7.26279	+	4.87654i	−0.712175	+	0.478184i
$105$	8.84500			0.863183
$106$	−13.0678	+	2.60955i	−1.26926	+	0.253462i
$107$		−	16.1005i		−	1.55650i	−0.627956	−	0.778249i	$-0.716108\pi$
$107$		−	16.1005i		−	1.55650i	0.627956	−	0.778249i	$-0.283892\pi$
$108$	0.921610	+	2.21555i	0.0886819	+	0.213191i
$109$			0.149174i			0.0142883i	0.999974	+	0.00714413i	$0.00227407\pi$
$109$			0.149174i			0.0142883i	−0.999974	+	0.00714413i	$0.997726\pi$
$110$	−0.0137227	−	0.0687192i	−0.00130841	−	0.00655212i
$111$	−27.5878			−2.61852
$112$	9.80455	−	9.86362i	0.926443	−	0.932024i
$113$	5.25333			0.494192			0.247096	−	0.968991i	$-0.420524\pi$
$113$	5.25333			0.494192			0.247096	+	0.968991i	$0.420524\pi$
$114$	−2.58615	−	12.9506i	−0.242215	−	1.21294i
$115$		−	2.12995i		−	0.198618i
$116$	−5.41915	−	13.0276i	−0.503155	−	1.20958i
$117$		−	10.7374i		−	0.992676i
$118$	11.9354	−	2.38342i	1.09874	−	0.219411i
$119$	3.47689			0.318726
$120$	4.01099	+	5.97369i	0.366151	+	0.545321i
$121$	10.9975			0.999777
$122$	14.1286	−	2.82138i	1.27914	−	0.255436i
$123$			23.1121i			2.08395i
$124$	5.53436	−	2.30215i	0.497000	−	0.206739i
$125$			1.00000i			0.0894427i
$126$	3.34280	+	16.7397i	0.297801	+	1.49129i
$127$	−5.46250			−0.484718			−0.242359	−	0.970187i	$-0.577921\pi$
$127$	−5.46250			−0.484718			−0.242359	+	0.970187i	$0.577921\pi$
$128$	11.1078	+	2.14885i	0.981797	+	0.189933i
$129$	−12.3388			−1.08637
$130$	−0.856553	−	4.28935i	−0.0751247	−	0.376201i
$131$		−	3.58169i		−	0.312934i	−0.987683	−	0.156467i	$-0.949990\pi$
$131$		−	3.58169i		−	0.312934i	0.987683	−	0.156467i	$-0.0500105\pi$
$132$	0.232775	−	0.0968281i	0.0202604	−	0.00842781i
$133$		−	12.7630i		−	1.10669i
$134$	−8.43123	+	1.68366i	−0.728347	+	0.145446i
$135$	−1.19979			−0.103262
$136$	1.57668	+	2.34821i	0.135199	+	0.201357i
$137$	−12.4319			−1.06213			−0.531066	−	0.847330i	$-0.678208\pi$
$137$	−12.4319			−1.06213			−0.531066	+	0.847330i	$0.678208\pi$
$138$	7.51448	−	1.50059i	0.639675	−	0.127739i
$139$		−	6.99701i		−	0.593479i	−0.954958	−	0.296740i	$-0.904101\pi$
$139$		−	6.99701i		−	0.593479i	0.954958	−	0.296740i	$-0.0958993\pi$
$140$	2.67074	+	6.42045i	0.225719	+	0.542627i
$141$			23.0975i			1.94516i
$142$	0.665502	+	3.33263i	0.0558477	+	0.279668i
$143$	−0.153257			−0.0128160
$144$	−9.78971	+	9.84869i	−0.815809	+	0.820724i
$145$	7.05489			0.585877
$146$	−0.549036	−	2.74940i	−0.0454386	−	0.227542i
$147$			12.9455i			1.06773i
$148$	−8.33011	−	20.0256i	−0.684731	−	1.64609i
$149$			4.44164i			0.363873i	0.983310	+	0.181937i	$0.0582366\pi$
$149$			4.44164i			0.363873i	−0.983310	+	0.181937i	$0.941763\pi$
$150$	−3.52802	+	0.704520i	−0.288061	+	0.0575238i
$151$	0.686658			0.0558794			0.0279397	−	0.999610i	$-0.491105\pi$
$151$	0.686658			0.0558794			0.0279397	+	0.999610i	$0.491105\pi$
$152$	8.61979	−	5.78769i	0.699157	−	0.469443i
$153$	−3.47163			−0.280664
$154$	0.238929	−	0.0477125i	0.0192535	−	0.00384478i
$155$			2.99704i			0.240728i
$156$	14.5294	−	6.04387i	1.16329	−	0.483897i
$157$			2.08771i			0.166617i	0.996524	+	0.0833086i	$0.0265487\pi$
$157$			2.08771i			0.166617i	−0.996524	+	0.0833086i	$0.973451\pi$
$158$	2.20211	+	11.0275i	0.175190	+	0.877298i
$159$	23.9710			1.90102
$160$	−3.12510	+	4.71527i	−0.247061	+	0.372775i
$161$	7.40559			0.583642
$162$	2.03903	+	10.2108i	0.160201	+	0.802237i
$163$		−	2.98957i		−	0.234161i	−0.993122	−	0.117081i	$-0.962646\pi$
$163$		−	2.98957i		−	0.234161i	0.993122	−	0.117081i	$-0.0373536\pi$
$164$	−16.7768	+	6.97870i	−1.31005	+	0.544945i
$165$			0.126055i			0.00981339i
$166$	−23.2892	+	4.65069i	−1.80759	+	0.360963i
$167$	17.4326			1.34897			0.674486	−	0.738287i	$-0.264365\pi$
$167$	17.4326			1.34897			0.674486	+	0.738287i	$0.264365\pi$
$168$	−20.7699	+	13.9458i	−1.60243	+	1.07594i
$169$	3.43390			0.264146
$170$	−1.38683	+	0.276941i	−0.106365	+	0.0212404i
$171$			12.7436i			0.974531i
$172$	−3.72569	−	8.95656i	−0.284082	−	0.682931i
$173$		−	24.9345i		−	1.89574i	−0.318663	−	0.947868i	$-0.603234\pi$
$173$		−	24.9345i		−	1.89574i	0.318663	−	0.947868i	$-0.396766\pi$
$174$	4.97031	+	24.8898i	0.376799	+	1.88689i
$175$	−3.47689			−0.262828
$176$	0.140572	+	0.139730i	0.0105960	+	0.0105326i
$177$	−21.8938			−1.64564
$178$	0.0923486	+	0.462453i	0.00692182	+	0.0346623i
$179$			1.09781i			0.0820539i	0.999158	+	0.0410269i	$0.0130629\pi$
$179$			1.09781i			0.0820539i	−0.999158	+	0.0410269i	$0.986937\pi$
$180$	−2.66670	−	6.41073i	−0.198764	−	0.477828i
$181$			11.0311i			0.819936i	0.912100	+	0.409968i	$0.134460\pi$
$181$			11.0311i			0.819936i	−0.912100	+	0.409968i	$0.865540\pi$
$182$	14.9136	−	2.97814i	1.10547	−	0.220754i
$183$	−25.9168			−1.91583
$184$	3.35825	+	5.00155i	0.247573	+	0.368719i
$185$	10.8445			0.797305
$186$	−10.5736	+	2.11148i	−0.775295	+	0.154821i
$187$			0.0495512i			0.00362354i
$188$	−16.7661	+	6.97426i	−1.22279	+	0.508651i
$189$		−	4.17155i		−	0.303435i
$190$	1.01659	+	5.09078i	0.0737514	+	0.369324i
$191$	−9.04760			−0.654662			−0.327331	−	0.944910i	$-0.606149\pi$
$191$	−9.04760			−0.654662			−0.327331	+	0.944910i	$0.606149\pi$
$192$	−18.8372	−	7.70341i	−1.35946	−	0.555946i
$193$	−0.0620567			−0.00446694			−0.00223347	−	0.999998i	$-0.500711\pi$
$193$	−0.0620567			−0.00446694			−0.00223347	+	0.999998i	$0.500711\pi$
$194$	2.74945	+	13.7684i	0.197399	+	0.988514i
$195$			7.86818i			0.563452i
$196$	−9.39695	+	3.90889i	−0.671211	+	0.279206i
$197$		−	20.2289i		−	1.44125i	−0.693324	−	0.720626i	$-0.743854\pi$
$197$		−	20.2289i		−	1.44125i	0.693324	−	0.720626i	$-0.256146\pi$
$198$	−0.238567	+	0.0476402i	−0.0169543	+	0.00338565i
$199$	21.4606			1.52130			0.760650	−	0.649163i	$-0.224881\pi$
$199$	21.4606			1.52130			0.760650	+	0.649163i	$0.224881\pi$
$200$	−1.57668	−	2.34821i	−0.111488	−	0.166043i
$201$	15.4658			1.09088
$202$	−20.5063	+	4.09496i	−1.44282	+	0.288120i
$203$			24.5291i			1.72160i
$204$	−1.95410	−	4.69766i	−0.136815	−	0.328902i
$205$		−	9.08518i		−	0.634537i
$206$	0.285544	+	1.42992i	0.0198948	+	0.0996271i
$207$	−7.39438			−0.513945
$208$	8.77431	+	8.72176i	0.608389	+	0.604745i
$209$	0.181892			0.0125818
$210$	−2.44954	−	12.2665i	−0.169034	−	0.846471i
$211$		−	21.0339i		−	1.44804i	−0.689781	−	0.724018i	$-0.742293\pi$
$211$		−	21.0339i		−	1.44804i	0.689781	−	0.724018i	$-0.257707\pi$
$212$	7.23801	+	17.4002i	0.497109	+	1.19505i
$213$		−	6.11321i		−	0.418870i
$214$	−22.3287	+	4.45889i	−1.52636	+	0.304804i
$215$	4.85028			0.330786
$216$	2.81736	−	1.89169i	0.191697	−	0.128713i
$217$	−10.4204			−0.707382
$218$	0.206879	−	0.0413123i	0.0140116	−	0.00279802i
$219$			5.04337i			0.340799i
$220$	−0.0915016	+	0.0380623i	−0.00616904	+	0.00256616i
$221$			3.09291i			0.208052i
$222$	7.64018	+	38.2596i	0.512775	+	2.56782i
$223$	−24.2053			−1.62091			−0.810455	−	0.585801i	$-0.800780\pi$
$223$	−24.2053			−1.62091			−0.810455	+	0.585801i	$0.800780\pi$
$224$	−16.3945	−	10.8656i	−1.09540	−	0.725991i
$225$	3.47163			0.231442
$226$	−1.45486	−	7.28549i	−0.0967760	−	0.484624i
$227$		−	4.24180i		−	0.281538i	−0.990042	−	0.140769i	$-0.955042\pi$
$227$		−	4.24180i		−	0.281538i	0.990042	−	0.140769i	$-0.0449576\pi$
$228$	−17.2442	+	7.17312i	−1.14202	+	0.475051i
$229$			11.6096i			0.767185i	0.923502	+	0.383593i	$0.125313\pi$
$229$			11.6096i			0.767185i	−0.923502	+	0.383593i	$0.874687\pi$
$230$	−2.95388	+	0.589869i	−0.194773	+	0.0388948i
$231$	−0.438280			−0.0288367
$232$	−16.5663	+	11.1233i	−1.08763	+	0.730282i
$233$	12.0080			0.786671			0.393336	−	0.919395i	$-0.371321\pi$
$233$	12.0080			0.786671			0.393336	+	0.919395i	$0.371321\pi$
$234$	−14.8910	+	2.97363i	−0.973457	+	0.194392i
$235$		−	9.07941i		−	0.592276i
$236$	−6.61080	−	15.8923i	−0.430327	−	1.03450i
$237$		−	20.2283i		−	1.31397i
$238$	−0.962892	−	4.82186i	−0.0624150	−	0.312555i
$239$	2.79213			0.180608			0.0903040	−	0.995914i	$-0.471216\pi$
$239$	2.79213			0.180608			0.0903040	+	0.995914i	$0.471216\pi$
$240$	7.17371	−	7.21692i	0.463061	−	0.465850i
$241$	−28.3488			−1.82610			−0.913052	−	0.407844i	$-0.866281\pi$
$241$	−28.3488			−1.82610			−0.913052	+	0.407844i	$0.866281\pi$
$242$	−3.04567	−	15.2518i	−0.195783	−	0.980420i
$243$		−	22.3296i		−	1.43244i
$244$	−7.82557	−	18.8127i	−0.500981	−	1.20436i
$245$		−	5.08876i		−	0.325109i
$246$	32.0527	−	6.40069i	2.04360	−	0.408093i
$247$	11.3535			0.722403
$248$	−4.72538	−	7.03767i	−0.300062	−	0.446893i
$249$	42.7206			2.70731
$250$	1.38683	−	0.276941i	0.0877110	−	0.0175153i
$251$		−	12.7763i		−	0.806435i	−0.915104	−	0.403217i	$-0.867892\pi$
$251$		−	12.7763i		−	0.806435i	0.915104	−	0.403217i	$-0.132108\pi$
$252$	22.2894	−	9.27182i	1.40410	−	0.584069i
$253$			0.105541i			0.00663533i
$254$	1.51279	+	7.57557i	0.0949208	+	0.475334i
$255$	2.54394			0.159308
$256$	−0.0961003	−	15.9997i	−0.00600627	−	0.999982i
$257$	23.1774			1.44577			0.722883	−	0.690971i	$-0.242817\pi$
$257$	23.1774			1.44577			0.722883	+	0.690971i	$0.242817\pi$
$258$	3.41712	+	17.1119i	0.212740	+	1.06534i
$259$			37.7052i			2.34289i
$260$	−5.71139	+	2.37579i	−0.354206	+	0.147340i
$261$		−	24.4920i		−	1.51601i
$262$	−4.96721	+	0.991916i	−0.306875	+	0.0612808i
$263$	18.3942			1.13424			0.567119	−	0.823636i	$-0.308058\pi$
$263$	18.3942			1.13424			0.567119	+	0.823636i	$0.308058\pi$
$264$	−0.198749	−	0.296004i	−0.0122322	−	0.0182178i
$265$	−9.42277			−0.578836
$266$	−17.7001	+	3.53458i	−1.08526	+	0.216719i
$267$		−	0.848302i		−	0.0519152i
$268$	4.66990	+	11.2264i	0.285259	+	0.685763i
$269$			29.1389i			1.77663i	0.459234	+	0.888315i	$0.348124\pi$
$269$			29.1389i			1.77663i	−0.459234	+	0.888315i	$0.651876\pi$
$270$	0.332271	+	1.66391i	0.0202214	+	0.101262i
$271$	−23.0152			−1.39808			−0.699038	−	0.715084i	$-0.746388\pi$
$271$	−23.0152			−1.39808			−0.699038	+	0.715084i	$0.746388\pi$
$272$	2.81992	−	2.83691i	0.170983	−	0.172013i
$273$	−27.3568			−1.65571
$274$	3.44291	+	17.2410i	0.207994	+	1.04157i
$275$		−	0.0495512i		−	0.00298805i
$276$	−4.16213	−	10.0058i	−0.250531	−	0.602276i
$277$			3.36682i			0.202292i	0.994872	+	0.101146i	$0.0322510\pi$
$277$			3.36682i			0.202292i	−0.994872	+	0.101146i	$0.967749\pi$
$278$	−9.70369	+	1.93776i	−0.581988	+	0.116219i
$279$	10.4046			0.622908
$280$	8.16445	−	5.48195i	0.487919	−	0.327609i
$281$	15.3021			0.912848			0.456424	−	0.889762i	$-0.349130\pi$
$281$	15.3021			0.912848			0.456424	+	0.889762i	$0.349130\pi$
$282$	32.0323	−	6.39663i	1.90750	−	0.380914i
$283$		−	11.1133i		−	0.660617i	−0.943873	−	0.330309i	$-0.892847\pi$
$283$		−	11.1133i		−	0.660617i	0.943873	−	0.330309i	$-0.107153\pi$
$284$	4.43749	−	1.84588i	0.263317	−	0.109533i
$285$		−	9.33829i		−	0.553153i
$286$	0.0424432	+	0.212542i	0.00250972	+	0.0125679i
$287$	31.5882			1.86459
$288$	16.3697	+	10.8492i	0.964591	+	0.639295i
$289$	1.00000			0.0588235
$290$	−1.95379	−	9.78395i	−0.114730	−	0.574533i
$291$		−	25.2561i		−	1.48054i
$292$	−3.66091	+	1.52284i	−0.214238	+	0.0891176i
$293$			18.3388i			1.07136i	0.844420	+	0.535682i	$0.179946\pi$
$293$			18.3388i			1.07136i	−0.844420	+	0.535682i	$0.820054\pi$
$294$	17.9532	−	3.58514i	1.04705	−	0.209089i
$295$	8.60624			0.501075
$296$	−25.4652	+	17.0984i	−1.48013	+	0.993822i
$297$	0.0594512			0.00344971
$298$	6.15981	−	1.23007i	0.356828	−	0.0712561i
$299$			6.58773i			0.380978i
$300$	1.95410	+	4.69766i	0.112820	+	0.271219i
$301$			16.8639i			0.972018i
$302$	−0.190163	−	0.952279i	−0.0109427	−	0.0547975i
$303$	37.6157			2.16097
$304$	−10.4137	−	10.3514i	−0.597268	−	0.593691i
$305$	10.1877			0.583345
$306$	0.961435	+	4.81457i	0.0549616	+	0.275230i
$307$			5.84542i			0.333616i	0.985989	+	0.166808i	$0.0533460\pi$
$307$			5.84542i			0.333616i	−0.985989	+	0.166808i	$0.946654\pi$
$308$	−0.132338	−	0.318141i	−0.00754068	−	0.0181278i
$309$		−	2.62297i		−	0.149216i
$310$	4.15639	−	0.830003i	0.236067	−	0.0471410i
$311$	−22.2459			−1.26145			−0.630726	−	0.776006i	$-0.717243\pi$
$311$	−22.2459			−1.26145			−0.630726	+	0.776006i	$0.717243\pi$
$312$	−12.4056	−	18.4761i	−0.702330	−	1.04600i
$313$	5.55110			0.313767			0.156883	−	0.987617i	$-0.449855\pi$
$313$	5.55110			0.313767			0.156883	+	0.987617i	$0.449855\pi$
$314$	2.89530	−	0.578171i	0.163391	−	0.0326281i
$315$			12.0705i			0.680094i
$316$	14.6834	−	6.10791i	0.826005	−	0.343597i
$317$			28.0476i			1.57531i	0.616115	+	0.787656i	$0.288706\pi$
$317$			28.0476i			1.57531i	−0.616115	+	0.787656i	$0.711294\pi$
$318$	−6.63853	−	33.2437i	−0.372271	−	1.86421i
$319$	−0.349578			−0.0195726
$320$	7.40475	+	3.02814i	0.413938	+	0.169278i
$321$	40.9588			2.28610
$322$	−2.05091	−	10.2703i	−0.114293	−	0.572342i
$323$		−	3.67080i		−	0.204249i
$324$	13.5960	−	5.65558i	0.755333	−	0.314199i
$325$		−	3.09291i		−	0.171564i
$326$	−4.14603	+	0.827933i	−0.229627	+	0.0458550i
$327$	−0.379489			−0.0209858
$328$	14.3244	+	21.3339i	0.790935	+	1.17797i
$329$	31.5681			1.74041
$330$	0.174817	−	0.0349098i	0.00962338	−	0.00192172i
$331$		−	21.6959i		−	1.19251i	−0.802794	−	0.596257i	$-0.796654\pi$
$331$		−	21.6959i		−	1.19251i	0.802794	−	0.596257i	$-0.203346\pi$
$332$	12.8994	+	31.0102i	0.707949	+	1.70191i
$333$		−	37.6481i		−	2.06310i
$334$	−4.82779	−	24.1761i	−0.264165	−	1.32285i
$335$	−6.07949			−0.332158
$336$	25.0924	+	24.9422i	1.36891	+	1.36071i
$337$	21.9155			1.19381			0.596907	−	0.802310i	$-0.296396\pi$
$337$	21.9155			1.19381			0.596907	+	0.802310i	$0.296396\pi$
$338$	−0.950987	−	4.76225i	−0.0517269	−	0.259032i
$339$			13.3642i			0.725842i
$340$	0.768141	+	1.84661i	0.0416583	+	0.100146i
$341$		−	0.148507i		−	0.00804210i
$342$	17.6733	−	3.52923i	0.955663	−	0.190839i
$343$	−6.64516			−0.358805
$344$	−11.3894	+	7.64735i	−0.614078	+	0.412317i
$345$	5.41845			0.291720
$346$	−34.5800	+	6.90538i	−1.85903	+	0.371236i
$347$		−	11.3501i		−	0.609305i	−0.952464	−	0.304653i	$-0.901460\pi$
$347$		−	11.3501i		−	0.609305i	0.952464	−	0.304653i	$-0.0985404\pi$
$348$	33.1415	−	13.7860i	1.77657	−	0.739006i
$349$		−	9.14942i		−	0.489757i	−0.969554	−	0.244879i	$-0.921252\pi$
$349$		−	9.14942i		−	0.489757i	0.969554	−	0.244879i	$-0.0787481\pi$
$350$	0.962892	+	4.82186i	0.0514688	+	0.257739i
$351$	3.71085			0.198071
$352$	0.154852	−	0.233647i	0.00825367	−	0.0124534i
$353$	−31.9513			−1.70060			−0.850299	−	0.526300i	$-0.823579\pi$
$353$	−31.9513			−1.70060			−0.850299	+	0.526300i	$0.823579\pi$
$354$	6.06327	+	30.3630i	0.322259	+	1.61377i
$355$			2.40305i			0.127541i
$356$	0.615769	−	0.256144i	0.0326357	−	0.0135756i
$357$			8.84500i			0.468127i
$358$	1.52247	−	0.304027i	0.0804652	−	0.0160683i
$359$	−14.1811			−0.748448			−0.374224	−	0.927338i	$-0.622091\pi$
$359$	−14.1811			−0.748448			−0.374224	+	0.927338i	$0.622091\pi$
$360$	−8.15210	+	5.47366i	−0.429653	+	0.288487i
$361$	5.52523			0.290802
$362$	15.2983	−	3.05496i	0.804061	−	0.160565i
$363$			27.9771i			1.46842i
$364$	−8.26036	−	19.8579i	−0.432961	−	1.04084i
$365$		−	1.98250i		−	0.103769i
$366$	7.17743	+	35.9423i	0.375170	+	1.87874i
$367$	20.4219			1.06601			0.533007	−	0.846111i	$-0.321062\pi$
$367$	20.4219			1.06601			0.533007	+	0.846111i	$0.321062\pi$
$368$	6.00628	−	6.04246i	0.313099	−	0.314985i
$369$	−31.5404			−1.64193
$370$	−3.00329	−	15.0395i	−0.156133	−	0.781868i
$371$		−	32.7619i		−	1.70092i
$372$	5.85653	+	14.0791i	0.303647	+	0.729966i
$373$			4.62610i			0.239531i	0.992802	+	0.119765i	$0.0382142\pi$
$373$			4.62610i			0.239531i	−0.992802	+	0.119765i	$0.961786\pi$
$374$	0.0687192	−	0.0137227i	0.00355338	−	0.000709586i
$375$	−2.54394			−0.131368
$376$	14.3154	+	21.3203i	0.738258	+	1.09951i
$377$	−21.8202			−1.12380
$378$	−5.78524	+	1.15527i	−0.297560	+	0.0594207i
$379$		−	29.3258i		−	1.50637i	−0.657811	−	0.753183i	$-0.728517\pi$
$379$		−	29.3258i		−	1.50637i	0.657811	−	0.753183i	$-0.271483\pi$
$380$	6.77853	−	2.81969i	0.347731	−	0.144647i
$381$		−	13.8963i		−	0.711927i
$382$	2.50565	+	12.5475i	0.128200	+	0.641986i
$383$	−16.0020			−0.817665			−0.408832	−	0.912610i	$-0.634064\pi$
$383$	−16.0020			−0.817665			−0.408832	+	0.912610i	$0.634064\pi$
$384$	−5.46654	+	28.2575i	−0.278963	+	1.44201i
$385$	0.172284			0.00878041
$386$	0.0171860	+	0.0860623i	0.000874746	+	0.00438046i
$387$		−	16.8384i		−	0.855942i
$388$	18.3330	−	7.62606i	0.930719	−	0.387155i
$389$		−	4.89231i		−	0.248050i	−0.992279	−	0.124025i	$-0.960420\pi$
$389$		−	4.89231i		−	0.248050i	0.992279	−	0.124025i	$-0.0395803\pi$
$390$	10.9118	−	2.17902i	0.552543	−	0.110339i
$391$	2.12995			0.107716
$392$	8.02337	+	11.9495i	0.405241	+	0.603539i
$393$	9.11161			0.459620
$394$	−28.0541	+	5.60222i	−1.41335	+	0.282236i
$395$			7.95155i			0.400086i
$396$	0.132138	+	0.317660i	0.00664019	+	0.0159630i
$397$		−	31.4976i		−	1.58082i	−0.612579	−	0.790409i	$-0.709868\pi$
$397$		−	31.4976i		−	1.58082i	0.612579	−	0.790409i	$-0.290132\pi$
$398$	−5.94330	−	29.7622i	−0.297911	−	1.49184i
$399$	32.4682			1.62544
$400$	−2.81992	+	2.83691i	−0.140996	+	0.141845i
$401$	−37.2953			−1.86244			−0.931219	−	0.364459i	$-0.881254\pi$
$401$	−37.2953			−1.86244			−0.931219	+	0.364459i	$0.881254\pi$
$402$	−4.28312	−	21.4485i	−0.213623	−	1.06976i
$403$		−	9.26958i		−	0.461751i
$404$	11.3580	+	27.3047i	0.565083	+	1.35846i
$405$			7.36268i			0.365855i
$406$	34.0177	−	6.79310i	1.68827	−	0.337136i
$407$	−0.537359			−0.0266359
$408$	−5.97369	+	4.01099i	−0.295742	+	0.198573i
$409$	−8.52412			−0.421490			−0.210745	−	0.977541i	$-0.567589\pi$
$409$	−8.52412			−0.421490			−0.210745	+	0.977541i	$0.567589\pi$
$410$	−12.5996	+	2.51606i	−0.622251	+	0.124259i
$411$		−	31.6261i		−	1.56000i
$412$	1.90398	−	0.792005i	0.0938022	−	0.0390193i
$413$			29.9229i			1.47241i
$414$	2.04780	+	10.2548i	0.100644	+	0.503994i
$415$	−16.7931			−0.824340
$416$	9.66566	−	14.5839i	0.473898	−	0.715035i
$417$	17.8000			0.871669
$418$	−0.0503734	−	0.252254i	−0.00246384	−	0.0123382i
$419$		−	6.51140i		−	0.318103i	−0.987270	−	0.159051i	$-0.949156\pi$
$419$		−	6.51140i		−	0.318103i	0.987270	−	0.159051i	$-0.0508435\pi$
$420$	−16.3332	+	6.79420i	−0.796981	+	0.331523i
$421$		−	13.1406i		−	0.640432i	−0.947345	−	0.320216i	$-0.896245\pi$
$421$		−	13.1406i		−	0.640432i	0.947345	−	0.320216i	$-0.103755\pi$
$422$	−29.1705	+	5.82515i	−1.42000	+	0.283564i
$423$	−31.5203			−1.53257
$424$	22.1266	−	14.8567i	1.07456	−	0.721506i
$425$	−1.00000			−0.0485071
$426$	−8.47800	+	1.69300i	−0.410760	+	0.0820260i
$427$			35.4215i			1.71416i
$428$	12.3675	+	29.7314i	0.597804	+	1.43712i
$429$		−	0.389878i		−	0.0188235i
$430$	−1.34324	−	6.72652i	−0.0647767	−	0.324382i
$431$	18.3569			0.884222			0.442111	−	0.896960i	$-0.354230\pi$
$431$	18.3569			0.884222			0.442111	+	0.896960i	$0.354230\pi$
$432$	−3.40370	−	3.38332i	−0.163761	−	0.162780i
$433$	−38.4016			−1.84546			−0.922732	−	0.385442i	$-0.874049\pi$
$433$	−38.4016			−1.84546			−0.922732	+	0.385442i	$0.874049\pi$
$434$	2.88583	+	14.4513i	0.138524	+	0.693686i
$435$			17.9472i			0.860503i
$436$	−0.114587	−	0.275466i	−0.00548770	−	0.0131924i
$437$		−	7.81860i		−	0.374014i
$438$	6.99431	−	1.39671i	0.334201	−	0.0667376i
$439$	5.90611			0.281883			0.140942	−	0.990018i	$-0.454987\pi$
$439$	5.90611			0.281883			0.140942	+	0.990018i	$0.454987\pi$
$440$	0.0781265	+	0.116356i	0.00372454	+	0.00554707i
$441$	−17.6663			−0.841252
$442$	4.28935	−	0.856553i	0.204024	−	0.0407421i
$443$			0.324084i			0.0153977i	0.999970	+	0.00769884i	$0.00245064\pi$
$443$			0.324084i			0.0153977i	−0.999970	+	0.00769884i	$0.997549\pi$
$444$	50.9438	−	21.1913i	2.41769	−	1.00569i
$445$			0.333460i			0.0158075i
$446$	6.70344	+	33.5687i	0.317417	+	1.58953i
$447$	−11.2993			−0.534437
$448$	−10.5285	+	25.7455i	−0.497426	+	1.21636i
$449$	25.0272			1.18111			0.590553	−	0.806999i	$-0.298910\pi$
$449$	25.0272			1.18111			0.590553	+	0.806999i	$0.298910\pi$
$450$	−0.961435	−	4.81457i	−0.0453225	−	0.226961i
$451$			0.450182i			0.0211982i
$452$	−9.70085	+	4.03530i	−0.456289	+	0.189804i
$453$			1.74682i			0.0820726i
$454$	−5.88267	+	1.17473i	−0.276087	+	0.0551327i
$455$	10.7537			0.504142
$456$	14.7235	+	21.9282i	0.689492	+	1.02688i
$457$	−5.47744			−0.256224			−0.128112	−	0.991760i	$-0.540892\pi$
$457$	−5.47744			−0.256224			−0.128112	+	0.991760i	$0.540892\pi$
$458$	16.1006	−	3.21518i	0.752331	−	0.150235i
$459$		−	1.19979i		−	0.0560015i
$460$	1.63610	+	3.93317i	0.0762834	+	0.183385i
$461$			18.3173i			0.853123i	0.904459	+	0.426562i	$0.140275\pi$
$461$			18.3173i			0.853123i	−0.904459	+	0.426562i	$0.859725\pi$
$462$	0.121378	+	0.607821i	0.00564700	+	0.0282784i
$463$	33.5012			1.55693			0.778467	−	0.627685i	$-0.215997\pi$
$463$	33.5012			1.55693			0.778467	+	0.627685i	$0.215997\pi$
$464$	20.0141	+	19.8942i	0.929131	+	0.923567i
$465$	−7.62429			−0.353568
$466$	−3.32551	−	16.6531i	−0.154051	−	0.771440i
$467$		−	38.7933i		−	1.79514i	−0.440873	−	0.897570i	$-0.645331\pi$
$467$		−	38.7933i		−	1.79514i	0.440873	−	0.897570i	$-0.354669\pi$
$468$	8.24786	+	19.8278i	0.381257	+	0.916542i
$469$		−	21.1377i		−	0.976048i
$470$	−12.5916	+	2.51446i	−0.580808	+	0.115983i
$471$	−5.31100			−0.244718
$472$	−20.2092	+	13.5693i	−0.930205	+	0.624578i
$473$	−0.240337			−0.0110507
$474$	−28.0532	+	5.60203i	−1.28853	+	0.257310i
$475$			3.67080i			0.168428i
$476$	−6.42045	+	2.67074i	−0.294281	+	0.122413i
$477$			32.7124i			1.49780i
$478$	−0.773255	−	3.87222i	−0.0353678	−	0.177111i
$479$	−14.5481			−0.664719			−0.332360	−	0.943153i	$-0.607845\pi$
$479$	−14.5481			−0.664719			−0.332360	+	0.943153i	$0.607845\pi$
$480$	−11.9954	−	7.95007i	−0.547510	−	0.362869i
$481$	−33.5411			−1.52934
$482$	7.85092	+	39.3150i	0.357600	+	1.79075i
$483$			18.8394i			0.857221i
$484$	−20.3082	+	8.44766i	−0.923098	+	0.383985i
$485$			9.92795i			0.450805i
$486$	−30.9674	+	6.18397i	−1.40471	+	0.280511i
$487$	23.0726			1.04552			0.522760	−	0.852480i	$-0.324902\pi$
$487$	23.0726			1.04552			0.522760	+	0.852480i	$0.324902\pi$
$488$	−23.9228	+	16.0627i	−1.08293	+	0.727126i
$489$	7.60528			0.343923
$490$	−7.05726	+	1.40929i	−0.318815	+	0.0636650i
$491$			5.11448i			0.230813i	0.993318	+	0.115407i	$0.0368171\pi$
$491$			5.11448i			0.230813i	−0.993318	+	0.115407i	$0.963183\pi$
$492$	−17.7534	−	42.6791i	−0.800384	−	1.92412i
$493$			7.05489i			0.317736i
$494$	−3.14423	−	15.7453i	−0.141466	−	0.708416i
$495$	−0.172023			−0.00773187
$496$	−8.45142	+	8.50233i	−0.379480	+	0.381766i
$497$	−8.35514			−0.374779
$498$	−11.8311	−	59.2463i	−0.530163	−	2.65489i
$499$		−	36.2614i		−	1.62328i	−0.584155	−	0.811642i	$-0.698574\pi$
$499$		−	36.2614i		−	1.62328i	0.584155	−	0.811642i	$-0.301426\pi$
$500$	−0.768141	−	1.84661i	−0.0343523	−	0.0825828i
$501$			44.3474i			1.98130i
$502$	−17.7186	+	3.53828i	−0.790821	+	0.157921i
$503$	−20.7090			−0.923367			−0.461684	−	0.887045i	$-0.652754\pi$
$503$	−20.7090			−0.923367			−0.461684	+	0.887045i	$0.652754\pi$
$504$	−19.0313	−	28.3439i	−0.847722	−	1.26254i
$505$	−14.7864			−0.657986
$506$	0.146368	−	0.0292287i	0.00650686	−	0.00129937i
$507$			8.73564i			0.387963i
$508$	10.0871	−	4.19597i	0.447542	−	0.186166i
$509$			10.6238i			0.470894i	0.971887	+	0.235447i	$0.0756554\pi$
$509$			10.6238i			0.470894i	−0.971887	+	0.235447i	$0.924345\pi$
$510$	−0.704520	−	3.52802i	−0.0311967	−	0.156223i
$511$	6.89295			0.304926
$512$	−22.1623	+	4.56425i	−0.979445	+	0.201713i
$513$	−4.40420			−0.194450
$514$	−6.41876	−	32.1431i	−0.283119	−	1.41777i
$515$			1.03107i			0.0454343i
$516$	22.7849	−	9.47794i	1.00305	−	0.417243i
$517$			0.449896i			0.0197864i
$518$	52.2908	−	10.4421i	2.29752	−	0.458800i
$519$	63.4319			2.78435
$520$	4.87654	+	7.26279i	0.213850	+	0.318494i
$521$	−31.0802			−1.36165			−0.680825	−	0.732446i	$-0.738379\pi$
$521$	−31.0802			−1.36165			−0.680825	+	0.732446i	$0.738379\pi$
$522$	−33.9662	+	6.78282i	−1.48666	+	0.296876i
$523$			4.19120i			0.183269i	0.995793	+	0.0916343i	$0.0292091\pi$
$523$			4.19120i			0.183269i	−0.995793	+	0.0916343i	$0.970791\pi$
$524$	2.75124	+	6.61398i	0.120189	+	0.288933i
$525$		−	8.84500i		−	0.386027i
$526$	−5.09411	−	25.5097i	−0.222114	−	1.11228i
$527$	−2.99704			−0.130553
$528$	−0.355466	+	0.357607i	−0.0154697	+	0.0155629i
$529$	−18.4633			−0.802754
$530$	2.60955	+	13.0678i	0.113352	+	0.567629i
$531$		−	29.8777i		−	1.29658i
$532$	9.80375	+	23.5682i	0.425046	+	1.02181i
$533$			28.0997i			1.21713i
$534$	−1.17645	+	0.234929i	−0.0509101	+	0.0101664i
$535$	−16.1005			−0.696087
$536$	14.2759	−	9.58542i	0.616624	−	0.414027i
$537$	−2.79275			−0.120516
$538$	40.4108	−	8.06975i	1.74223	−	0.347912i
$539$			0.252154i			0.0108611i
$540$	2.21555	−	0.921610i	0.0953419	−	0.0396598i
$541$			27.2765i			1.17271i	0.810055	+	0.586353i	$0.199437\pi$
$541$			27.2765i			1.17271i	−0.810055	+	0.586353i	$0.800563\pi$
$542$	6.37386	+	31.9183i	0.273781	+	1.37101i
$543$	−28.0625			−1.20428
$544$	−4.71527	−	3.12510i	−0.202165	−	0.133988i
$545$	0.149174			0.00638991
$546$	7.57621	+	37.9393i	0.324232	+	1.62365i
$547$			16.4229i			0.702194i	0.936339	+	0.351097i	$0.114191\pi$
$547$			16.4229i			0.702194i	−0.936339	+	0.351097i	$0.885809\pi$
$548$	22.9569	−	9.54948i	0.980671	−	0.407933i
$549$		−	35.3678i		−	1.50946i
$550$	−0.0687192	+	0.0137227i	−0.00293020	+	0.000585140i
$551$	25.8971			1.10325
$552$	−12.7236	+	8.54318i	−0.541554	+	0.363622i
$553$	−27.6467			−1.17566
$554$	4.66921	−	0.932408i	0.198376	−	0.0396142i
$555$			27.5878i			1.17104i
$556$	5.37469	+	12.9207i	0.227938	+	0.547961i
$557$			9.18864i			0.389335i	0.980869	+	0.194668i	$0.0623628\pi$
$557$			9.18864i			0.389335i	−0.980869	+	0.194668i	$0.937637\pi$
$558$	−2.88146	−	14.4295i	−0.121982	−	0.610848i
$559$	−15.0015			−0.634495
$560$	−9.86362	−	9.80455i	−0.416814	−	0.414318i
$561$	−0.126055			−0.00532206
$562$	−4.23778	−	21.2215i	−0.178760	−	0.895174i
$563$			45.4813i			1.91681i	0.285416	+	0.958404i	$0.407868\pi$
$563$			45.4813i			1.91681i	−0.285416	+	0.958404i	$0.592132\pi$
$564$	−17.7421	−	42.6520i	−0.747077	−	1.79597i
$565$		−	5.25333i		−	0.221009i
$566$	−15.4123	+	3.07772i	−0.647827	+	0.129366i
$567$	−25.5992			−1.07507
$568$	−3.78885	−	5.64285i	−0.158976	−	0.236769i
$569$	−19.7054			−0.826094			−0.413047	−	0.910710i	$-0.635535\pi$
$569$	−19.7054			−0.826094			−0.413047	+	0.910710i	$0.635535\pi$
$570$	−12.9506	+	2.58615i	−0.542443	+	0.108322i
$571$			6.15498i			0.257578i	0.991672	+	0.128789i	$0.0411090\pi$
$571$			6.15498i			0.257578i	−0.991672	+	0.128789i	$0.958891\pi$
$572$	0.283006	−	0.117723i	0.0118331	−	0.00492226i
$573$		−	23.0166i		−	0.961531i
$574$	−8.74805	−	43.8075i	−0.365137	−	1.82849i
$575$	−2.12995			−0.0888249
$576$	10.5126	−	25.7065i	0.438024	−	1.07111i
$577$	−36.2206			−1.50788			−0.753941	−	0.656942i	$-0.771850\pi$
$577$	−36.2206			−1.50788			−0.753941	+	0.656942i	$0.771850\pi$
$578$	−0.276941	−	1.38683i	−0.0115192	−	0.0576846i
$579$		−	0.157869i		−	0.00656079i
$580$	−13.0276	+	5.41915i	−0.540942	+	0.225018i
$581$		−	58.3877i		−	2.42233i
$582$	−35.0260	+	6.99444i	−1.45187	+	0.289929i
$583$	0.466910			0.0193374
$584$	3.12578	+	4.65533i	0.129346	+	0.192639i
$585$	−10.7374			−0.443938
$586$	25.4328	−	5.07876i	1.05062	−	0.209802i
$587$		−	14.8348i		−	0.612299i	−0.951983	−	0.306150i	$-0.900959\pi$
$587$		−	14.8348i		−	0.612299i	0.951983	−	0.306150i	$-0.0990408\pi$
$588$	−9.94397	−	23.9053i	−0.410082	−	0.985837i
$589$			11.0015i			0.453310i
$590$	−2.38342	−	11.9354i	−0.0981238	−	0.491373i
$591$	51.4612			2.11683
$592$	30.7649	+	30.5807i	1.26443	+	1.25686i
$593$	10.2911			0.422604			0.211302	−	0.977421i	$-0.432230\pi$
$593$	10.2911			0.422604			0.211302	+	0.977421i	$0.432230\pi$
$594$	−0.0164644	−	0.0824488i	−0.000675544	−	0.00338292i
$595$		−	3.47689i		−	0.142539i
$596$	−3.41180	−	8.20196i	−0.139753	−	0.335966i
$597$			54.5944i			2.23440i
$598$	9.13608	−	1.82441i	0.373602	−	0.0746057i
$599$	−31.9007			−1.30343			−0.651714	−	0.758465i	$-0.725950\pi$
$599$	−31.9007			−1.30343			−0.651714	+	0.758465i	$0.725950\pi$
$600$	5.97369	−	4.01099i	0.243875	−	0.163748i
$601$	−24.9428			−1.01744			−0.508719	−	0.860933i	$-0.669881\pi$
$601$	−24.9428			−1.01744			−0.508719	+	0.860933i	$0.669881\pi$
$602$	23.3874	−	4.67029i	0.953198	−	0.190347i
$603$			21.1057i			0.859491i
$604$	−1.26799	+	0.527450i	−0.0515937	+	0.0214616i
$605$		−	10.9975i		−	0.447114i
$606$	−10.4173	−	52.1667i	−0.423175	−	2.11913i
$607$	34.7077			1.40874			0.704371	−	0.709833i	$-0.251229\pi$
$607$	34.7077			1.40874			0.704371	+	0.709833i	$0.251229\pi$
$608$	−11.4716	+	17.3088i	−0.465236	+	0.701964i
$609$	−62.4005			−2.52860
$610$	−2.82138	−	14.1286i	−0.114234	−	0.572051i
$611$			28.0818i			1.13607i
$612$	6.41073	−	2.66670i	0.259139	−	0.107795i
$613$			20.6531i			0.834169i	0.908868	+	0.417084i	$0.136948\pi$
$613$			20.6531i			0.834169i	−0.908868	+	0.417084i	$0.863052\pi$
$614$	8.10662	−	1.61884i	0.327157	−	0.0653309i
$615$	23.1121			0.931972
$616$	−0.404558	+	0.271637i	−0.0163001	+	0.0109446i
$617$	43.7406			1.76093			0.880466	−	0.474110i	$-0.157230\pi$
$617$	43.7406			1.76093			0.880466	+	0.474110i	$0.157230\pi$
$618$	−3.63762	+	0.726408i	−0.146327	+	0.0292204i
$619$			11.8613i			0.476746i	0.971174	+	0.238373i	$0.0766140\pi$
$619$			11.8613i			0.476746i	−0.971174	+	0.238373i	$0.923386\pi$
$620$	−2.30215	−	5.53436i	−0.0924565	−	0.222265i
$621$		−	2.55549i		−	0.102548i
$622$	6.16080	+	30.8514i	0.247026	+	1.23703i
$623$	−1.15940			−0.0464505
$624$	−22.1876	+	22.3213i	−0.888216	+	0.893567i
$625$	1.00000			0.0400000
$626$	−1.53733	−	7.69845i	−0.0614439	−	0.307692i
$627$			0.462723i			0.0184794i
$628$	−1.60365	−	3.85518i	−0.0639927	−	0.153838i
$629$			10.8445i			0.432399i
$630$	16.7397	−	3.34280i	0.666926	−	0.133180i
$631$	41.3244			1.64510			0.822550	−	0.568693i	$-0.192551\pi$
$631$	41.3244			1.64510			0.822550	+	0.568693i	$0.192551\pi$
$632$	−12.5371	−	18.6719i	−0.498698	−	0.742727i
$633$	53.5091			2.12679
$634$	38.8974	−	7.76753i	1.54481	−	0.308488i
$635$			5.46250i			0.216773i
$636$	−44.2650	+	18.4131i	−1.75522	+	0.730126i
$637$			15.7391i			0.623605i
$638$	0.0968125	+	0.484807i	0.00383284	+	0.0191937i
$639$	8.34249			0.330024
$640$	2.14885	−	11.1078i	0.0849407	−	0.439073i
$641$	29.9682			1.18367			0.591836	−	0.806059i	$-0.298403\pi$
$641$	29.9682			1.18367			0.591836	+	0.806059i	$0.298403\pi$
$642$	−11.3432	−	56.8030i	−0.447679	−	2.24183i
$643$			46.1363i			1.81944i	0.415225	+	0.909719i	$0.363703\pi$
$643$			46.1363i			1.81944i	−0.415225	+	0.909719i	$0.636297\pi$
$644$	−13.6752	+	5.68853i	−0.538879	+	0.224160i
$645$			12.3388i			0.485840i
$646$	−5.09078	+	1.01659i	−0.200294	+	0.0399973i
$647$	3.56455			0.140137			0.0700685	−	0.997542i	$-0.477678\pi$
$647$	3.56455			0.140137			0.0700685	+	0.997542i	$0.477678\pi$
$648$	−11.6086	−	17.2891i	−0.456030	−	0.679180i
$649$	−0.426449			−0.0167396
$650$	−4.28935	+	0.856553i	−0.168242	+	0.0335968i
$651$		−	26.5088i		−	1.03896i
$652$	2.29641	+	5.52056i	0.0899343	+	0.216202i
$653$		−	34.1304i		−	1.33563i	−0.744328	−	0.667814i	$-0.767230\pi$
$653$		−	34.1304i		−	1.33563i	0.744328	−	0.667814i	$-0.232770\pi$
$654$	0.105096	+	0.526288i	0.00410958	+	0.0205795i
$655$	−3.58169			−0.139948
$656$	25.6195	−	25.7738i	1.00027	−	1.00630i
$657$	−6.88252			−0.268513
$658$	−8.74249	−	43.7797i	−0.340818	−	1.70671i
$659$		−	2.35872i		−	0.0918829i	−0.998944	−	0.0459414i	$-0.985371\pi$
$659$		−	2.35872i		−	0.0918829i	0.998944	−	0.0459414i	$-0.0146288\pi$
$660$	−0.0968281	−	0.232775i	−0.00376903	−	0.00906074i
$661$			24.8235i			0.965523i	0.875752	+	0.482762i	$0.160366\pi$
$661$			24.8235i			0.965523i	−0.875752	+	0.482762i	$0.839634\pi$
$662$	−30.0886	+	6.00848i	−1.16943	+	0.233526i
$663$	−7.86818			−0.305575
$664$	39.4336	−	26.4774i	1.53032	−	1.02752i
$665$	−12.7630			−0.494927
$666$	−52.2116	+	10.4263i	−2.02316	+	0.404011i
$667$			15.0265i			0.581830i
$668$	−32.1911	+	13.3907i	−1.24551	+	0.518100i
$669$		−	61.5769i		−	2.38070i
$670$	1.68366	+	8.43123i	0.0650453	+	0.325727i
$671$	−0.504812			−0.0194880
$672$	27.6415	−	41.7065i	1.06629	−	1.60886i
$673$	16.5114			0.636469			0.318235	−	0.948012i	$-0.396910\pi$
$673$	16.5114			0.636469			0.318235	+	0.948012i	$0.396910\pi$
$674$	−6.06930	−	30.3931i	−0.233781	−	1.17070i
$675$			1.19979i			0.0461800i
$676$	−6.34107	+	2.63772i	−0.243887	+	0.101451i
$677$			13.3983i			0.514940i	0.966286	+	0.257470i	$0.0828889\pi$
$677$			13.3983i			0.514940i	−0.966286	+	0.257470i	$0.917111\pi$
$678$	18.5339	−	3.70108i	0.711788	−	0.142139i
$679$	−34.5184			−1.32469
$680$	2.34821	−	1.57668i	0.0900496	−	0.0604630i
$681$	10.7909			0.413508
$682$	−0.205954	+	0.0411276i	−0.00788640	+	0.00157486i
$683$			11.7014i			0.447741i	0.974619	+	0.223871i	$0.0718693\pi$
$683$			11.7014i			0.447741i	−0.974619	+	0.223871i	$0.928131\pi$
$684$	−9.78891	−	23.5325i	−0.374288	−	0.899788i
$685$			12.4319i			0.475000i
$686$	1.84032	+	9.21572i	0.0702636	+	0.351858i
$687$	−29.5342			−1.12680
$688$	13.7598	+	13.6774i	0.524587	+	0.521446i
$689$	29.1438			1.11029
$690$	−1.50059	−	7.51448i	−0.0571265	−	0.286072i
$691$		−	18.1348i		−	0.689881i	−0.938624	−	0.344941i	$-0.887899\pi$
$691$		−	18.1348i		−	0.689881i	0.938624	−	0.344941i	$-0.112101\pi$
$692$	19.1532	+	46.0443i	0.728096	+	1.75034i
$693$		−	0.598106i		−	0.0227202i
$694$	−15.7407	+	3.14330i	−0.597508	+	0.119318i
$695$	−6.99701			−0.265412
$696$	−28.2971	−	42.1438i	−1.07260	−	1.59746i
$697$	9.08518			0.344126
$698$	−12.6887	+	2.53385i	−0.480275	+	0.0959075i
$699$			30.5477i			1.15542i
$700$	6.42045	−	2.67074i	0.242670	−	0.100944i
$701$		−	49.0724i		−	1.85344i	−0.375752	−	0.926720i	$-0.622615\pi$
$701$		−	49.0724i		−	1.85344i	0.375752	−	0.926720i	$-0.377385\pi$
$702$	−1.02769	−	5.14633i	−0.0387875	−	0.194236i
$703$	39.8080			1.50139
$704$	−0.366914	−	0.150048i	−0.0138286	−	0.00565515i
$705$	23.0975			0.869901
$706$	8.84862	+	44.3111i	0.333022	+	1.66767i
$707$		−	51.4107i		−	1.93350i
$708$	40.4292	−	16.8175i	1.51942	−	0.632040i
$709$			18.2457i			0.685232i	0.939475	+	0.342616i	$0.111313\pi$
$709$			18.2457i			0.685232i	−0.939475	+	0.342616i	$0.888687\pi$
$710$	3.33263	−	0.665502i	0.125071	−	0.0249758i
$711$	27.6048			1.03526
$712$	−0.525760	−	0.783032i	−0.0197037	−	0.0293454i
$713$	−6.38354			−0.239065
$714$	12.2665	−	2.44954i	0.459063	−	0.0916717i
$715$			0.153257i			0.00573150i
$716$	−0.843269	−	2.02722i	−0.0315145	−	0.0757607i
$717$			7.10301i			0.265267i
$718$	3.92731	+	19.6668i	0.146566	+	0.733957i
$719$	−13.0206			−0.485587			−0.242794	−	0.970078i	$-0.578064\pi$
$719$	−13.0206			−0.485587			−0.242794	+	0.970078i	$0.578064\pi$
$720$	9.84869	+	9.78971i	0.367039	+	0.364841i
$721$	−3.58491			−0.133509
$722$	−1.53016	−	7.66257i	−0.0569467	−	0.285171i
$723$		−	72.1175i		−	2.68208i
$724$	−8.47344	−	20.3701i	−0.314913	−	0.757050i
$725$		−	7.05489i		−	0.262012i
$726$	38.7995	−	7.74799i	1.43999	−	0.287555i
$727$	−29.7634			−1.10387			−0.551933	−	0.833889i	$-0.686109\pi$
$727$	−29.7634			−1.10387			−0.551933	+	0.833889i	$0.686109\pi$
$728$	−25.2519	+	16.9552i	−0.935899	+	0.628401i
$729$	34.7171			1.28582
$730$	−2.74940	+	0.549036i	−0.101760	+	0.0203207i
$731$			4.85028i			0.179394i
$732$	47.8583	−	19.9078i	1.76889	−	0.735813i
$733$		−	51.5972i		−	1.90578i	−0.303309	−	0.952892i	$-0.598091\pi$
$733$		−	51.5972i		−	1.90578i	0.303309	−	0.952892i	$-0.401909\pi$
$734$	−5.65565	−	28.3217i	−0.208754	−	1.04537i
$735$	12.9455			0.477502
$736$	−10.0433	−	6.65630i	−0.370200	−	0.245354i
$737$	0.301246			0.0110965
$738$	8.73481	+	43.7412i	0.321533	+	1.61014i
$739$			11.7777i			0.433248i	0.976255	+	0.216624i	$0.0695046\pi$
$739$			11.7777i			0.433248i	−0.976255	+	0.216624i	$0.930495\pi$
$740$	−20.0256	+	8.33011i	−0.736154	+	0.306221i
$741$			28.8825i			1.06103i
$742$	−45.4353	+	9.07311i	−1.66798	+	0.333085i
$743$	2.78439			0.102149			0.0510746	−	0.998695i	$-0.483735\pi$
$743$	2.78439			0.102149			0.0510746	+	0.998695i	$0.483735\pi$
$744$	17.9034	−	12.0211i	0.656371	−	0.440715i
$745$	4.44164			0.162729
$746$	6.41563	−	1.28116i	0.234893	−	0.0469065i
$747$			58.2993i			2.13306i
$748$	−0.0380623	−	0.0915016i	−0.00139169	−	0.00334563i
$749$		−	55.9798i		−	2.04546i
$750$	0.704520	+	3.52802i	0.0257254	+	0.128825i
$751$	2.03962			0.0744269			0.0372135	−	0.999307i	$-0.488152\pi$
$751$	2.03962			0.0744269			0.0372135	+	0.999307i	$0.488152\pi$
$752$	25.6032	−	25.7575i	0.933653	−	0.939278i
$753$	32.5022			1.18445
$754$	6.04289	+	30.2609i	0.220069	+	1.10204i
$755$		−	0.686658i		−	0.0249900i
$756$	3.20433	+	7.70321i	0.116541	+	0.280163i
$757$		−	16.9050i		−	0.614423i	−0.951641	−	0.307211i	$-0.900604\pi$
$757$		−	16.9050i		−	0.614423i	0.951641	−	0.307211i	$-0.0993959\pi$
$758$	−40.6700	+	8.12151i	−1.47720	+	0.294987i
$759$	−0.268491			−0.00974560
$760$	−5.78769	−	8.61979i	−0.209941	−	0.312673i
$761$	−10.9356			−0.396415			−0.198207	−	0.980160i	$-0.563512\pi$
$761$	−10.9356			−0.396415			−0.198207	+	0.980160i	$0.563512\pi$
$762$	−19.2718	+	3.84844i	−0.698143	+	0.139414i
$763$			0.518661i			0.0187768i
$764$	16.7074	−	6.94983i	0.604452	−	0.251436i
$765$			3.47163i			0.125517i
$766$	4.43161	+	22.1921i	0.160121	+	0.801833i
$767$	−26.6183			−0.961132
$768$	40.7023	−	0.244473i	1.46872	−	0.00882168i
$769$	−25.1767			−0.907896			−0.453948	−	0.891028i	$-0.649985\pi$
$769$	−25.1767			−0.907896			−0.453948	+	0.891028i	$0.649985\pi$
$770$	−0.0477125	−	0.238929i	−0.00171944	−	0.00861041i
$771$			58.9619i			2.12346i
$772$	0.114594	−	0.0476683i	0.00412434	−	0.00171562i
$773$			0.737635i			0.0265309i	0.999912	+	0.0132654i	$0.00422264\pi$
$773$			0.737635i			0.0265309i	−0.999912	+	0.0132654i	$0.995777\pi$
$774$	−23.3520	+	4.66323i	−0.839369	+	0.167616i
$775$	2.99704			0.107657
$776$	−15.6532	−	23.3129i	−0.561918	−	0.836883i
$777$	−95.9197			−3.44110
$778$	−6.78481	+	1.35488i	−0.243247	+	0.0485748i
$779$		−	33.3499i		−	1.19488i
$780$	−6.04387	−	14.5294i	−0.216405	−	0.520237i
$781$		−	0.119074i		−	0.00426080i
$782$	−0.589869	−	2.95388i	−0.0210937	−	0.105630i
$783$	8.46441			0.302493
$784$	14.3499	−	14.4364i	0.512497	−	0.515584i
$785$	2.08771			0.0745135
$786$	−2.52338	−	12.6363i	−0.0900058	−	0.450721i
$787$		−	4.23088i		−	0.150815i	−0.997153	−	0.0754073i	$-0.975974\pi$
$787$		−	4.23088i		−	0.150815i	0.997153	−	0.0754073i	$-0.0240257\pi$
$788$	15.5387	+	37.3549i	0.553542	+	1.33071i
$789$			46.7938i			1.66590i
$790$	11.0275	−	2.20211i	0.392340	−	0.0783475i
$791$	18.2653			0.649438
$792$	0.403946	−	0.271226i	0.0143536	−	0.00963760i
$793$	−31.5096			−1.11894
$794$	−43.6819	+	8.72296i	−1.55021	+	0.309566i
$795$		−	23.9710i		−	0.850162i
$796$	−39.6292	+	16.4847i	−1.40462	+	0.584286i
$797$			23.9029i			0.846685i	0.905970	+	0.423343i	$0.139143\pi$
$797$			23.9029i			0.846685i	−0.905970	+	0.423343i	$0.860857\pi$
$798$	−8.99177	−	45.0280i	−0.318305	−	1.59397i
$799$	9.07941			0.321206
$800$	4.71527	+	3.12510i	0.166710	+	0.110489i
$801$	1.15765			0.0409035
$802$	10.3286	+	51.7223i	0.364715	+	1.82638i
$803$			0.0982355i			0.00346665i
$804$	−28.5593	+	11.8799i	−1.00721	+	0.418973i
$805$		−	7.40559i		−	0.261013i
$806$	−12.8554	+	2.56712i	−0.452811	+	0.0904231i
$807$	−74.1276			−2.60942
$808$	34.7215	−	23.3135i	1.22150	−	0.820165i
$809$	37.3225			1.31219			0.656094	−	0.754679i	$-0.272207\pi$
$809$	37.3225			1.31219			0.656094	+	0.754679i	$0.272207\pi$
$810$	10.2108	−	2.03903i	0.358771	−	0.0716441i
$811$			0.102705i			0.00360647i	0.999998	+	0.00180323i	$0.000573987\pi$
$811$			0.102705i			0.00360647i	−0.999998	+	0.00180323i	$0.999426\pi$
$812$	−18.8418	−	45.2956i	−0.661217	−	1.58956i
$813$		−	58.5494i		−	2.05342i
$814$	0.148816	+	0.745226i	0.00521601	+	0.0261202i
$815$	−2.98957			−0.104720
$816$	7.21692	+	7.17371i	0.252643	+	0.251130i
$817$	17.8044			0.622897
$818$	2.36067	+	11.8215i	0.0825390	+	0.413330i
$819$		−	37.3329i		−	1.30452i
$820$	6.97870	+	16.7768i	0.243707	+	0.585870i
$821$			10.3664i			0.361789i	0.983502	+	0.180895i	$0.0578993\pi$
$821$			10.3664i			0.361789i	−0.983502	+	0.180895i	$0.942101\pi$
$822$	−43.8601	+	8.75855i	−1.52980	+	0.305490i
$823$	39.1878			1.36600			0.683001	−	0.730417i	$-0.260674\pi$
$823$	39.1878			1.36600			0.683001	+	0.730417i	$0.260674\pi$
$824$	−1.62567	−	2.42116i	−0.0566328	−	0.0843450i
$825$	0.126055			0.00438868
$826$	41.4981	−	8.28688i	1.44390	−	0.288337i
$827$		−	34.6513i		−	1.20494i	−0.798140	−	0.602472i	$-0.794182\pi$
$827$		−	34.6513i		−	1.20494i	0.798140	−	0.602472i	$-0.205818\pi$
$828$	13.6545	−	5.67992i	0.474527	−	0.197391i
$829$			24.2955i			0.843819i	0.906638	+	0.421909i	$0.138640\pi$
$829$			24.2955i			0.843819i	−0.906638	+	0.421909i	$0.861360\pi$
$830$	4.65069	+	23.2892i	0.161428	+	0.808379i
$831$	−8.56498			−0.297116
$832$	−22.9022	−	9.36577i	−0.793992	−	0.324700i
$833$	5.08876			0.176315
$834$	−4.92954	−	24.6856i	−0.170696	−	0.854792i
$835$		−	17.4326i		−	0.603279i
$836$	−0.335884	+	0.139719i	−0.0116168	+	0.00483228i
$837$			3.59583i			0.124290i
$838$	−9.03022	+	1.80327i	−0.311944	+	0.0622930i
$839$	27.7302			0.957351			0.478676	−	0.877992i	$-0.341117\pi$
$839$	27.7302			0.957351			0.478676	+	0.877992i	$0.341117\pi$
$840$	13.9458	+	20.7699i	0.481174	+	0.716629i
$841$	−20.7715			−0.716259
$842$	−18.2238	+	3.63916i	−0.628032	+	0.125414i
$843$			38.9277i			1.34074i
$844$	16.1570	+	38.8414i	0.556147	+	1.33698i
$845$		−	3.43390i		−	0.118130i
$846$	8.72926	+	43.7134i	0.300118	+	1.50290i
$847$	38.2373			1.31385
$848$	−26.7315	−	26.5715i	−0.917965	−	0.912468i
$849$	28.2716			0.970278
$850$	0.276941	+	1.38683i	0.00949899	+	0.0475680i
$851$			23.0982i			0.791797i
$852$	4.69581	+	11.2887i	0.160876	+	0.386745i
$853$			16.5528i			0.566757i	0.959008	+	0.283378i	$0.0914552\pi$
$853$			16.5528i			0.566757i	−0.959008	+	0.283378i	$0.908545\pi$
$854$	49.1236	−	9.80964i	1.68098	−	0.335679i
$855$	12.7436			0.435824
$856$	37.8074	−	25.3854i	1.29223	−	0.867656i
$857$	−19.8119			−0.676763			−0.338381	−	0.941009i	$-0.609879\pi$
$857$	−19.8119			−0.676763			−0.338381	+	0.941009i	$0.609879\pi$
$858$	−0.540695	+	0.107973i	−0.0184590	+	0.00368614i
$859$			55.9853i			1.91019i	0.296293	+	0.955097i	$0.404249\pi$
$859$			55.9853i			1.91019i	−0.296293	+	0.955097i	$0.595751\pi$
$860$	−8.95656	+	3.72569i	−0.305416	+	0.127045i
$861$			80.3584i			2.73861i
$862$	−5.08378	−	25.4580i	−0.173154	−	0.867102i
$863$	6.92444			0.235711			0.117855	−	0.993031i	$-0.462398\pi$
$863$	6.92444			0.235711			0.117855	+	0.993031i	$0.462398\pi$
$864$	−3.74947	+	5.65734i	−0.127560	+	0.192467i
$865$	−24.9345			−0.847799
$866$	10.6350	+	53.2566i	0.361391	+	1.80973i
$867$			2.54394i			0.0863967i
$868$	19.2424	−	8.00432i	0.653128	−	0.271684i
$869$		−	0.394009i		−	0.0133658i
$870$	24.8898	−	4.97031i	0.843843	−	0.168509i
$871$	18.8033			0.637126
$872$	−0.350291	+	0.235200i	−0.0118624	+	0.00796488i
$873$	34.4661			1.16650
$874$	−10.8431	+	2.16529i	−0.366773	+	0.0732420i
$875$			3.47689i			0.117540i
$876$	−3.87402	−	9.31313i	−0.130891	−	0.314661i
$877$		−	16.7774i		−	0.566532i	−0.959041	−	0.283266i	$-0.908582\pi$
$877$		−	16.7774i		−	0.566532i	0.959041	−	0.283266i	$-0.0914180\pi$
$878$	−1.63564	−	8.19079i	−0.0552003	−	0.276426i
$879$	−46.6528			−1.57356
$880$	0.139730	−	0.140572i	0.00471031	−	0.00473869i
$881$	−14.6295			−0.492882			−0.246441	−	0.969158i	$-0.579261\pi$
$881$	−14.6295			−0.492882			−0.246441	+	0.969158i	$0.579261\pi$
$882$	4.89251	+	24.5002i	0.164740	+	0.824964i
$883$			43.2649i			1.45598i	0.685588	+	0.727989i	$0.259545\pi$
$883$			43.2649i			1.45598i	−0.685588	+	0.727989i	$0.740455\pi$
$884$	−2.37579	−	5.71139i	−0.0799065	−	0.192095i
$885$			21.8938i			0.735950i
$886$	0.449450	−	0.0897520i	0.0150996	−	0.00301528i
$887$	−25.3231			−0.850265			−0.425133	−	0.905131i	$-0.639773\pi$
$887$	−25.3231			−0.850265			−0.425133	+	0.905131i	$0.639773\pi$
$888$	−43.4972	−	64.7818i	−1.45967	−	2.17394i
$889$	−18.9925			−0.636988
$890$	0.462453	−	0.0923486i	0.0155015	−	0.00309553i
$891$		−	0.364830i		−	0.0122223i
$892$	44.6978	−	18.5931i	1.49659	−	0.622543i
$893$		−	33.3287i		−	1.11530i
$894$	3.12922	+	15.6702i	0.104657	+	0.524089i
$895$	1.09781			0.0366956
$896$	38.6205	+	7.47131i	1.29022	+	0.249599i
$897$	−16.7588			−0.559560
$898$	−6.93105	−	34.7085i	−0.231292	−	1.15824i
$899$		−	21.1438i		−	0.705185i
$900$	−6.41073	+	2.66670i	−0.213691	+	0.0888899i
$901$		−	9.42277i		−	0.313918i
$902$	0.624326	−	0.124674i	0.0207878	−	0.00415118i
$903$	−42.9007			−1.42765
$904$	8.28284	+	12.3359i	0.275483	+	0.410286i
$905$	11.0311			0.366687
$906$	2.42254	−	0.483764i	0.0804835	−	0.0160720i
$907$		−	11.0579i		−	0.367171i	−0.983004	−	0.183585i	$-0.941230\pi$
$907$		−	11.0579i		−	0.367171i	0.983004	−	0.183585i	$-0.0587704\pi$
$908$	3.25830	+	7.83295i	0.108131	+	0.259946i
$909$			51.3329i			1.70260i
$910$	−2.97814	−	14.9136i	−0.0987244	−	0.494381i
$911$	2.88016			0.0954239			0.0477119	−	0.998861i	$-0.484807\pi$
$911$	2.88016			0.0954239			0.0477119	+	0.998861i	$0.484807\pi$
$912$	26.3332	−	26.4919i	0.871981	−	0.877234i
$913$	0.832117			0.0275391
$914$	1.51693	+	7.59629i	0.0501755	+	0.251263i
$915$			25.9168i			0.856785i
$916$	−8.91782	−	21.4384i	−0.294653	−	0.708345i
$917$		−	12.4532i		−	0.411239i
$918$	−1.66391	+	0.332271i	−0.0549173	+	0.0109666i
$919$	20.4953			0.676077			0.338038	−	0.941132i	$-0.390237\pi$
$919$	20.4953			0.676077			0.338038	+	0.941132i	$0.390237\pi$
$920$	5.00155	−	3.35825i	0.164896	−	0.110718i
$921$	−14.8704			−0.489996
$922$	25.4031	−	5.07281i	0.836605	−	0.167064i
$923$		−	7.43242i		−	0.244641i
$924$	0.809332	−	0.336661i	0.0266251	−	0.0110753i
$925$		−	10.8445i		−	0.356565i
$926$	−9.27786	−	46.4606i	−0.304889	−	1.52679i
$927$	3.57948			0.117566
$928$	22.0473	−	33.2657i	0.723736	−	1.09200i
$929$	−37.8844			−1.24295			−0.621473	−	0.783436i	$-0.713465\pi$
$929$	−37.8844			−1.24295			−0.621473	+	0.783436i	$0.713465\pi$
$930$	2.11148	+	10.5736i	0.0692381	+	0.346723i
$931$		−	18.6798i		−	0.612207i
$932$	−22.1741	+	9.22384i	−0.726337	+	0.302137i
$933$		−	56.5923i		−	1.85275i
$934$	−53.7998	+	10.7434i	−1.76038	+	0.351536i
$935$	0.0495512			0.00162050
$936$	25.2137	−	16.9295i	0.824136	−	0.553359i
$937$	52.0078			1.69902			0.849511	−	0.527571i	$-0.176897\pi$
$937$	52.0078			1.69902			0.849511	+	0.527571i	$0.176897\pi$
$938$	−29.3144	+	5.85389i	−0.957151	+	0.191136i
$939$			14.1217i			0.460843i
$940$	6.97426	+	16.7661i	0.227475	+	0.546850i
$941$			36.8805i			1.20227i	0.799148	+	0.601135i	$0.205284\pi$
$941$			36.8805i			1.20227i	−0.799148	+	0.601135i	$0.794716\pi$
$942$	1.47083	+	7.36547i	0.0479223	+	0.239980i
$943$	19.3509			0.630153
$944$	24.4151	+	24.2689i	0.794644	+	0.789886i
$945$	−4.17155			−0.135700
$946$	0.0665591	+	0.333307i	0.00216402	+	0.0108367i
$947$		−	24.3236i		−	0.790411i	−0.918593	−	0.395205i	$-0.870673\pi$
$947$		−	24.3236i		−	0.790411i	0.918593	−	0.395205i	$-0.129327\pi$
$948$	15.5381	+	37.3537i	0.504656	+	1.21319i
$949$			6.13171i			0.199044i
$950$	5.09078	−	1.01659i	0.165167	−	0.0329827i
$951$	−71.3515			−2.31373
$952$	5.48195	+	8.16445i	0.177671	+	0.264611i
$953$	−48.7836			−1.58026			−0.790128	−	0.612942i	$-0.789986\pi$
$953$	−48.7836			−1.58026			−0.790128	+	0.612942i	$0.789986\pi$
$954$	45.3666	−	9.05938i	1.46880	−	0.293308i
$955$			9.04760i			0.292774i
$956$	−5.15597	+	2.14475i	−0.166756	+	0.0693661i
$957$		−	0.889306i		−	0.0287472i
$958$	4.02896	+	20.1758i	0.130170	+	0.651849i
$959$	−43.2245			−1.39579
$960$	−7.70341	+	18.8372i	−0.248626	+	0.607969i
$961$	−22.0177			−0.710250
$962$	9.28890	+	46.5159i	0.299486	+	1.49973i
$963$			55.8951i			1.80119i
$964$	52.3490	−	21.7758i	1.68605	−	0.701352i
$965$			0.0620567i			0.00199768i
$966$	26.1270	−	5.21739i	0.840624	−	0.167867i
$967$	−21.4544			−0.689925			−0.344963	−	0.938616i	$-0.612108\pi$
$967$	−21.4544			−0.689925			−0.344963	+	0.938616i	$0.612108\pi$
$968$	17.3396	+	25.8245i	0.557317	+	0.830031i
$969$	9.33829			0.299989
$970$	13.7684	−	2.74945i	0.442077	−	0.0882796i
$971$			44.6617i			1.43326i	0.697453	+	0.716631i	$0.254317\pi$
$971$			44.6617i			1.43326i	−0.697453	+	0.716631i	$0.745683\pi$
$972$	17.1523	+	41.2340i	0.550159	+	1.32258i
$973$		−	24.3278i		−	0.779915i
$974$	−6.38975	−	31.9979i	−0.204741	−	1.02528i
$975$	7.86818			0.251983
$976$	28.9015	+	28.7285i	0.925115	+	0.919575i
$977$	43.8003			1.40129			0.700647	−	0.713508i	$-0.252895\pi$
$977$	43.8003			1.40129			0.700647	+	0.713508i	$0.252895\pi$
$978$	−2.10621	−	10.5472i	−0.0673492	−	0.337264i
$979$		−	0.0165233i		−	0.000528088i
$980$	3.90889	+	9.39695i	0.124865	+	0.300175i
$981$		−	0.517876i		−	0.0165345i
$982$	7.09293	−	1.41641i	0.226345	−	0.0451994i
$983$	−30.8726			−0.984683			−0.492342	−	0.870402i	$-0.663859\pi$
$983$	−30.8726			−0.984683			−0.492342	+	0.870402i	$0.663859\pi$
$984$	−54.2721	+	36.4405i	−1.73013	+	1.16168i
$985$	−20.2289			−0.644548
$986$	9.78395	−	1.95379i	0.311585	−	0.0622212i
$987$			80.3074i			2.55621i
$988$	−20.9654	+	8.72105i	−0.666998	+	0.277454i
$989$			10.3308i			0.328501i
$990$	0.0476402	+	0.238567i	0.00151411	+	0.00758217i
$991$	−14.5878			−0.463397			−0.231698	−	0.972788i	$-0.574428\pi$
$991$	−14.5878			−0.463397			−0.231698	+	0.972788i	$0.574428\pi$
$992$	14.1319	+	9.36606i	0.448687	+	0.297373i
$993$	55.1930			1.75150
$994$	2.31388	+	11.5872i	0.0733917	+	0.367523i
$995$		−	21.4606i		−	0.680346i
$996$	−78.8881	+	32.8154i	−2.49967	+	1.03980i
$997$		−	7.64012i		−	0.241965i	−0.992655	−	0.120983i	$-0.961395\pi$
$997$		−	7.64012i		−	0.241965i	0.992655	−	0.120983i	$-0.0386045\pi$
$998$	−50.2885	+	10.0423i	−1.59186	+	0.317882i
$999$	13.0112			0.411655

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.f.e.341.11	✓	30
4.3	odd	2		2720.2.f.e.1361.4		30
8.3	odd	2		2720.2.f.e.1361.27		30
8.5	even	2	inner	680.2.f.e.341.12	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.f.e.341.11	✓	30	1.1	even	1	trivial
680.2.f.e.341.12	yes	30	8.5	even	2	inner
2720.2.f.e.1361.4		30	4.3	odd	2
2720.2.f.e.1361.27		30	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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.276941 - 1.38683i) q^{2} +2.54394i q^{3} +(-1.84661 + 0.768141i) q^{4} -1.00000i q^{5} +(3.52802 - 0.704520i) q^{6} +3.47689 q^{7} +(1.57668 + 2.34821i) q^{8} -3.47163 q^{9} +(-1.38683 + 0.276941i) q^{10} +0.0495512i q^{11} +(-1.95410 - 4.69766i) q^{12} +3.09291i q^{13} +(-0.962892 - 4.82186i) q^{14} +2.54394 q^{15} +(2.81992 - 2.83691i) q^{16} +1.00000 q^{17} +(0.961435 + 4.81457i) q^{18} -3.67080i q^{19} +(0.768141 + 1.84661i) q^{20} +8.84500i q^{21} +(0.0687192 - 0.0137227i) q^{22} +2.12995 q^{23} +(-5.97369 + 4.01099i) q^{24} -1.00000 q^{25} +(4.28935 - 0.856553i) q^{26} -1.19979i q^{27} +(-6.42045 + 2.67074i) q^{28} +7.05489i q^{29} +(-0.704520 - 3.52802i) q^{30} -2.99704 q^{31} +(-4.71527 - 3.12510i) q^{32} -0.126055 q^{33} +(-0.276941 - 1.38683i) q^{34} -3.47689i q^{35} +(6.41073 - 2.66670i) q^{36} +10.8445i q^{37} +(-5.09078 + 1.01659i) q^{38} -7.86818 q^{39} +(2.34821 - 1.57668i) q^{40} +9.08518 q^{41} +(12.2665 - 2.44954i) q^{42} +4.85028i q^{43} +(-0.0380623 - 0.0915016i) q^{44} +3.47163i q^{45} +(-0.589869 - 2.95388i) q^{46} +9.07941 q^{47} +(7.21692 + 7.17371i) q^{48} +5.08876 q^{49} +(0.276941 + 1.38683i) q^{50} +2.54394i q^{51} +(-2.37579 - 5.71139i) q^{52} -9.42277i q^{53} +(-1.66391 + 0.332271i) q^{54} +0.0495512 q^{55} +(5.48195 + 8.16445i) q^{56} +9.33829 q^{57} +(9.78395 - 1.95379i) q^{58} +8.60624i q^{59} +(-4.69766 + 1.95410i) q^{60} +10.1877i q^{61} +(0.830003 + 4.15639i) q^{62} -12.0705 q^{63} +(-3.02814 + 7.40475i) q^{64} +3.09291 q^{65} +(0.0349098 + 0.174817i) q^{66} -6.07949i q^{67} +(-1.84661 + 0.768141i) q^{68} +5.41845i q^{69} +(-4.82186 + 0.962892i) q^{70} -2.40305 q^{71} +(-5.47366 - 8.15210i) q^{72} +1.98250 q^{73} +(15.0395 - 3.00329i) q^{74} -2.54394i q^{75} +(2.81969 + 6.77853i) q^{76} +0.172284i q^{77} +(2.17902 + 10.9118i) q^{78} -7.95155 q^{79} +(-2.83691 - 2.81992i) q^{80} -7.36268 q^{81} +(-2.51606 - 12.5996i) q^{82} -16.7931i q^{83} +(-6.79420 - 16.3332i) q^{84} -1.00000i q^{85} +(6.72652 - 1.34324i) q^{86} -17.9472 q^{87} +(-0.116356 + 0.0781265i) q^{88} -0.333460 q^{89} +(4.81457 - 0.961435i) q^{90} +10.7537i q^{91} +(-3.93317 + 1.63610i) q^{92} -7.62429i q^{93} +(-2.51446 - 12.5916i) q^{94} -3.67080 q^{95} +(7.95007 - 11.9954i) q^{96} -9.92795 q^{97} +(-1.40929 - 7.05726i) q^{98} -0.172023i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 2 q^{4} - 8 q^{6} + 12 q^{7} + 6 q^{8} - 36 q^{9} + 2 q^{10} + 8 q^{12} - 10 q^{14} - 14 q^{15} - 2 q^{16} + 30 q^{17} + 6 q^{18} + 4 q^{20} - 6 q^{22} + 12 q^{23} - 46 q^{24} - 30 q^{25} + 4 q^{26}+ \cdots - 16 q^{98}+O(q^{100}) \) 30 * q - 2 * q^4 - 8 * q^6 + 12 * q^7 + 6 * q^8 - 36 * q^9 + 2 * q^10 + 8 * q^12 - 10 * q^14 - 14 * q^15 - 2 * q^16 + 30 * q^17 + 6 * q^18 + 4 * q^20 - 6 * q^22 + 12 * q^23 - 46 * q^24 - 30 * q^25 + 4 * q^26 + 22 * q^28 + 6 * q^30 - 26 * q^31 - 10 * q^32 + 12 * q^33 + 32 * q^36 + 6 * q^38 + 2 * q^39 + 4 * q^40 - 20 * q^41 + 48 * q^42 + 22 * q^44 + 38 * q^46 - 22 * q^47 + 24 * q^48 + 30 * q^49 + 48 * q^52 - 66 * q^54 + 32 * q^55 - 6 * q^56 - 26 * q^57 - 32 * q^58 - 14 * q^60 - 46 * q^62 - 4 * q^63 - 50 * q^64 + 6 * q^65 - 44 * q^66 - 2 * q^68 - 2 * q^70 + 58 * q^71 - 14 * q^72 - 18 * q^73 + 56 * q^74 - 6 * q^76 + 12 * q^78 - 60 * q^79 - 42 * q^81 - 24 * q^82 + 72 * q^84 + 48 * q^86 + 6 * q^87 + 18 * q^88 + 6 * q^89 - 14 * q^90 + 74 * q^92 - 16 * q^94 - 30 * q^95 + 22 * q^96 + 38 * q^97 - 16 * q^98

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