LMFDB - Embedded newform 668.2.b.b.667.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [668,2,Mod(667,668)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(668, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("668.667");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 668 = 2^{2} \cdot 167 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	668.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.33400685502$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			667.7
Character	$\chi$	$=$	668.667
Dual form			668.2.b.b.667.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37670 + 0.323577i) q^{2} +0.453678i q^{3} +(1.79060 - 0.890936i) q^{4} -4.09468i q^{5} +(-0.146800 - 0.624578i) q^{6} -3.11488i q^{7} +(-2.17682 + 1.80595i) q^{8} +2.79418 q^{9} +O(q^{10})$	\(q+(-1.37670 + 0.323577i) q^{2} +0.453678i q^{3} +(1.79060 - 0.890936i) q^{4} -4.09468i q^{5} +(-0.146800 - 0.624578i) q^{6} -3.11488i q^{7} +(-2.17682 + 1.80595i) q^{8} +2.79418 q^{9} +(1.32494 + 5.63714i) q^{10} -5.38294i q^{11} +(0.404198 + 0.812354i) q^{12} +3.33978i q^{13} +(1.00790 + 4.28825i) q^{14} +1.85767 q^{15} +(2.41247 - 3.19061i) q^{16} +3.84512i q^{17} +(-3.84674 + 0.904131i) q^{18} -4.72052i q^{19} +(-3.64809 - 7.33191i) q^{20} +1.41315 q^{21} +(1.74180 + 7.41068i) q^{22} -7.33522 q^{23} +(-0.819318 - 0.987577i) q^{24} -11.7664 q^{25} +(-1.08067 - 4.59786i) q^{26} +2.62869i q^{27} +(-2.77516 - 5.57749i) q^{28} +1.81805 q^{29} +(-2.55744 + 0.601098i) q^{30} +6.72408i q^{31} +(-2.28883 + 5.17313i) q^{32} +2.44212 q^{33} +(-1.24419 - 5.29357i) q^{34} -12.7544 q^{35} +(5.00324 - 2.48943i) q^{36} +6.28125i q^{37} +(1.52745 + 6.49873i) q^{38} -1.51518 q^{39} +(7.39476 + 8.91339i) q^{40} -5.90120i q^{41} +(-1.94548 + 0.457263i) q^{42} +9.23290 q^{43} +(-4.79585 - 9.63867i) q^{44} -11.4413i q^{45} +(10.0984 - 2.37351i) q^{46} -3.82414i q^{47} +(1.44751 + 1.09448i) q^{48} -2.70246 q^{49} +(16.1988 - 3.80733i) q^{50} -1.74445 q^{51} +(2.97553 + 5.98019i) q^{52} +0.840714i q^{53} +(-0.850584 - 3.61891i) q^{54} -22.0414 q^{55} +(5.62530 + 6.78054i) q^{56} +2.14160 q^{57} +(-2.50290 + 0.588279i) q^{58} -5.09391 q^{59} +(3.32633 - 1.65506i) q^{60} +3.73897 q^{61} +(-2.17576 - 9.25704i) q^{62} -8.70352i q^{63} +(1.47712 - 7.86245i) q^{64} +13.6753 q^{65} +(-3.36206 + 0.790214i) q^{66} +3.33280 q^{67} +(3.42576 + 6.88506i) q^{68} -3.32783i q^{69} +(17.5590 - 4.12704i) q^{70} +2.45201 q^{71} +(-6.08243 + 5.04613i) q^{72} -5.62294i q^{73} +(-2.03247 - 8.64738i) q^{74} -5.33815i q^{75} +(-4.20568 - 8.45255i) q^{76} -16.7672 q^{77} +(2.08595 - 0.490279i) q^{78} -14.8272 q^{79} +(-13.0645 - 9.87827i) q^{80} +7.18995 q^{81} +(1.90949 + 8.12417i) q^{82} +15.5714 q^{83} +(2.53038 - 1.25903i) q^{84} +15.7445 q^{85} +(-12.7109 + 2.98755i) q^{86} +0.824808i q^{87} +(9.72129 + 11.7177i) q^{88} -2.19382 q^{89} +(3.70213 + 15.7511i) q^{90} +10.4030 q^{91} +(-13.1344 + 6.53521i) q^{92} -3.05057 q^{93} +(1.23740 + 5.26469i) q^{94} -19.3290 q^{95} +(-2.34693 - 1.03839i) q^{96} +10.1378 q^{97} +(3.72047 - 0.874454i) q^{98} -15.0409i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 2 q^{2} + 2 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) $ 60 * q - 2 * q^2 + 2 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9	$ 60 q - 2 q^{2} + 2 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9} + 18 q^{12} + 10 q^{14} + 10 q^{16} - 20 q^{18} + 20 q^{22} + 10 q^{24} - 188 q^{25} + 4 q^{29} + 18 q^{32} + 8 q^{33} + 30 q^{36} - 36 q^{38} + 14 q^{42} + 28 q^{44} - 28 q^{48} + 72 q^{49} - 40 q^{50} - 74 q^{54} + 50 q^{56} + 8 q^{57} - 22 q^{58} + 36 q^{61} + 104 q^{62} + 8 q^{64} + 24 q^{65} + 24 q^{66} + 90 q^{72} - 36 q^{76} - 84 q^{81} - 110 q^{84} - 16 q^{85} - 20 q^{88} + 28 q^{89} + 72 q^{93} + 90 q^{94} + 2 q^{96} - 4 q^{97} - 114 q^{98}+O(q^{100}) $ 60 * q - 2 * q^2 + 2 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9 + 18 * q^12 + 10 * q^14 + 10 * q^16 - 20 * q^18 + 20 * q^22 + 10 * q^24 - 188 * q^25 + 4 * q^29 + 18 * q^32 + 8 * q^33 + 30 * q^36 - 36 * q^38 + 14 * q^42 + 28 * q^44 - 28 * q^48 + 72 * q^49 - 40 * q^50 - 74 * q^54 + 50 * q^56 + 8 * q^57 - 22 * q^58 + 36 * q^61 + 104 * q^62 + 8 * q^64 + 24 * q^65 + 24 * q^66 + 90 * q^72 - 36 * q^76 - 84 * q^81 - 110 * q^84 - 16 * q^85 - 20 * q^88 + 28 * q^89 + 72 * q^93 + 90 * q^94 + 2 * q^96 - 4 * q^97 - 114 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/668\mathbb{Z}\right)^\times$.

$n$	$5$	$335$
$\chi(n)$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.37670	+	0.323577i	−0.973473	+	0.228804i
$2$	−1.37670	+	0.323577i	−0.973473	+	0.228804i
$3$			0.453678i			0.261931i	0.991387	+	0.130966i	$0.0418077\pi$
$3$			0.453678i			0.261931i	−0.991387	+	0.130966i	$0.958192\pi$
$4$	1.79060	−	0.890936i	0.895298	−	0.445468i
$5$		−	4.09468i		−	1.83120i	−0.402095	−	0.915598i	$-0.631718\pi$
$5$		−	4.09468i		−	1.83120i	0.402095	−	0.915598i	$-0.368282\pi$
$6$	−0.146800	−	0.624578i	−0.0599308	−	0.254983i
$7$		−	3.11488i		−	1.17731i	−0.808383	−	0.588656i	$-0.799657\pi$
$7$		−	3.11488i		−	1.17731i	0.808383	−	0.588656i	$-0.200343\pi$
$8$	−2.17682	+	1.80595i	−0.769623	+	0.638498i
$9$	2.79418			0.931392
$10$	1.32494	+	5.63714i	0.418984	+	1.78262i
$11$		−	5.38294i		−	1.62302i	−0.584341	−	0.811509i	$-0.698647\pi$
$11$		−	5.38294i		−	1.62302i	0.584341	−	0.811509i	$-0.301353\pi$
$12$	0.404198	+	0.812354i	0.116682	+	0.234506i
$13$			3.33978i			0.926287i	0.886283	+	0.463144i	$0.153279\pi$
$13$			3.33978i			0.926287i	−0.886283	+	0.463144i	$0.846721\pi$
$14$	1.00790	+	4.28825i	0.269373	+	1.14608i
$15$	1.85767			0.479647
$16$	2.41247	−	3.19061i	0.603117	−	0.797653i
$17$			3.84512i			0.932579i	0.884632	+	0.466289i	$0.154409\pi$
$17$			3.84512i			0.932579i	−0.884632	+	0.466289i	$0.845591\pi$
$18$	−3.84674	+	0.904131i	−0.906685	+	0.213106i
$19$		−	4.72052i		−	1.08296i	−0.840713	−	0.541481i	$-0.817864\pi$
$19$		−	4.72052i		−	1.08296i	0.840713	−	0.541481i	$-0.182136\pi$
$20$	−3.64809	−	7.33191i	−0.815739	−	1.63947i
$21$	1.41315			0.308375
$22$	1.74180	+	7.41068i	0.371352	+	1.57996i
$23$	−7.33522			−1.52950			−0.764749	−	0.644328i	$-0.777137\pi$
$23$	−7.33522			−1.52950			−0.764749	+	0.644328i	$0.777137\pi$
$24$	−0.819318	−	0.987577i	−0.167243	−	0.201588i
$25$	−11.7664			−2.35328
$26$	−1.08067	−	4.59786i	−0.211938	−	0.901715i
$27$			2.62869i			0.505892i
$28$	−2.77516	−	5.57749i	−0.524455	−	1.05405i
$29$	1.81805			0.337603			0.168802	−	0.985650i	$-0.446010\pi$
$29$	1.81805			0.337603			0.168802	+	0.985650i	$0.446010\pi$
$30$	−2.55744	+	0.601098i	−0.466923	+	0.109745i
$31$			6.72408i			1.20768i	0.797105	+	0.603841i	$0.206364\pi$
$31$			6.72408i			1.20768i	−0.797105	+	0.603841i	$0.793636\pi$
$32$	−2.28883	+	5.17313i	−0.404612	+	0.914489i
$33$	2.44212			0.425119
$34$	−1.24419	−	5.29357i	−0.213377	−	0.907840i
$35$	−12.7544			−2.15589
$36$	5.00324	−	2.48943i	0.833873	−	0.414905i
$37$			6.28125i			1.03263i	0.856399	+	0.516315i	$0.172697\pi$
$37$			6.28125i			1.03263i	−0.856399	+	0.516315i	$0.827303\pi$
$38$	1.52745	+	6.49873i	0.247785	+	1.05423i
$39$	−1.51518			−0.242624
$40$	7.39476	+	8.91339i	1.16921	+	1.40933i
$41$		−	5.90120i		−	0.921612i	−0.887501	−	0.460806i	$-0.847560\pi$
$41$		−	5.90120i		−	0.921612i	0.887501	−	0.460806i	$-0.152440\pi$
$42$	−1.94548	+	0.457263i	−0.300195	+	0.0705573i
$43$	9.23290			1.40800			0.704002	−	0.710198i	$-0.251395\pi$
$43$	9.23290			1.40800			0.704002	+	0.710198i	$0.251395\pi$
$44$	−4.79585	−	9.63867i	−0.723002	−	1.45308i
$45$		−	11.4413i		−	1.70556i
$46$	10.0984	−	2.37351i	1.48892	−	0.349955i
$47$		−	3.82414i		−	0.557808i	−0.960319	−	0.278904i	$-0.910029\pi$
$47$		−	3.82414i		−	0.557808i	0.960319	−	0.278904i	$-0.0899711\pi$
$48$	1.44751	+	1.09448i	0.208930	+	0.157975i
$49$	−2.70246			−0.386066
$50$	16.1988	−	3.80733i	2.29085	−	0.538438i
$51$	−1.74445			−0.244271
$52$	2.97553	+	5.98019i	0.412631	+	0.829303i
$53$			0.840714i			0.115481i	0.998332	+	0.0577405i	$0.0183896\pi$
$53$			0.840714i			0.115481i	−0.998332	+	0.0577405i	$0.981610\pi$
$54$	−0.850584	−	3.61891i	−0.115750	−	0.492472i
$55$	−22.0414			−2.97206
$56$	5.62530	+	6.78054i	0.751712	+	0.906088i
$57$	2.14160			0.283661
$58$	−2.50290	+	0.588279i	−0.328647	+	0.0772448i
$59$	−5.09391			−0.663171			−0.331585	−	0.943425i	$-0.607584\pi$
$59$	−5.09391			−0.663171			−0.331585	+	0.943425i	$0.607584\pi$
$60$	3.32633	−	1.65506i	0.429427	−	0.213667i
$61$	3.73897			0.478726			0.239363	−	0.970930i	$-0.423061\pi$
$61$	3.73897			0.478726			0.239363	+	0.970930i	$0.423061\pi$
$62$	−2.17576	−	9.25704i	−0.276322	−	1.17564i
$63$		−	8.70352i		−	1.09654i
$64$	1.47712	−	7.86245i	0.184640	−	0.982806i
$65$	13.6753			1.69621
$66$	−3.36206	+	0.790214i	−0.413841	+	0.0972686i
$67$	3.33280			0.407166			0.203583	−	0.979058i	$-0.434741\pi$
$67$	3.33280			0.407166			0.203583	+	0.979058i	$0.434741\pi$
$68$	3.42576	+	6.88506i	0.415434	+	0.834936i
$69$		−	3.32783i		−	0.400623i
$70$	17.5590	−	4.12704i	2.09870	−	0.493275i
$71$	2.45201			0.291001			0.145500	−	0.989358i	$-0.453521\pi$
$71$	2.45201			0.291001			0.145500	+	0.989358i	$0.453521\pi$
$72$	−6.08243	+	5.04613i	−0.716821	+	0.594692i
$73$		−	5.62294i		−	0.658115i	−0.944310	−	0.329058i	$-0.893269\pi$
$73$		−	5.62294i		−	0.658115i	0.944310	−	0.329058i	$-0.106731\pi$
$74$	−2.03247	−	8.64738i	−0.236270	−	1.00524i
$75$		−	5.33815i		−	0.616397i
$76$	−4.20568	−	8.45255i	−0.482425	−	0.969574i
$77$	−16.7672			−1.91080
$78$	2.08595	−	0.490279i	0.236187	−	0.0555131i
$79$	−14.8272			−1.66819			−0.834097	−	0.551618i	$-0.814010\pi$
$79$	−14.8272			−1.66819			−0.834097	+	0.551618i	$0.814010\pi$
$80$	−13.0645	−	9.87827i	−1.46066	−	1.10442i
$81$	7.18995			0.798883
$82$	1.90949	+	8.12417i	0.210868	+	0.897164i
$83$	15.5714			1.70919			0.854594	−	0.519297i	$-0.173806\pi$
$83$	15.5714			1.70919			0.854594	+	0.519297i	$0.173806\pi$
$84$	2.53038	−	1.25903i	0.276087	−	0.137371i
$85$	15.7445			1.70773
$86$	−12.7109	+	2.98755i	−1.37065	+	0.322156i
$87$			0.824808i			0.0884287i
$88$	9.72129	+	11.7177i	1.03629	+	1.24911i
$89$	−2.19382			−0.232545			−0.116272	−	0.993217i	$-0.537095\pi$
$89$	−2.19382			−0.232545			−0.116272	+	0.993217i	$0.537095\pi$
$90$	3.70213	+	15.7511i	0.390238	+	1.66032i
$91$	10.4030			1.09053
$92$	−13.1344	+	6.53521i	−1.36936	+	0.681342i
$93$	−3.05057			−0.316329
$94$	1.23740	+	5.26469i	0.127628	+	0.543011i
$95$	−19.3290			−1.98312
$96$	−2.34693	−	1.03839i	−0.239533	−	0.105980i
$97$	10.1378			1.02934			0.514671	−	0.857388i	$-0.327914\pi$
$97$	10.1378			1.02934			0.514671	+	0.857388i	$0.327914\pi$
$98$	3.72047	−	0.874454i	0.375824	−	0.0883332i
$99$		−	15.0409i		−	1.51167i
$100$	−21.0688	+	10.4831i	−2.10688	+	1.04831i
$101$		−	14.3606i		−	1.42894i	−0.699667	−	0.714469i	$-0.746668\pi$
$101$		−	14.3606i		−	1.42894i	0.699667	−	0.714469i	$-0.253332\pi$
$102$	2.40158	−	0.564463i	0.237792	−	0.0558902i
$103$	−4.96770			−0.489482			−0.244741	−	0.969588i	$-0.578703\pi$
$103$	−4.96770			−0.489482			−0.244741	+	0.969588i	$0.578703\pi$
$104$	−6.03145	−	7.27011i	−0.591433	−	0.712892i
$105$		−	5.78640i		−	0.564695i
$106$	−0.272036	−	1.15741i	−0.0264224	−	0.112418i
$107$		−	7.45661i		−	0.720858i	−0.932787	−	0.360429i	$-0.882630\pi$
$107$		−	7.45661i		−	0.720858i	0.932787	−	0.360429i	$-0.117370\pi$
$108$	2.34199	+	4.70692i	0.225359	+	0.452924i
$109$			13.6126i			1.30385i	0.758284	+	0.651924i	$0.226038\pi$
$109$			13.6126i			1.30385i	−0.758284	+	0.651924i	$0.773962\pi$
$110$	30.3444	−	7.13209i	2.89322	−	0.680018i
$111$	−2.84966			−0.270478
$112$	−9.93836	−	7.51454i	−0.939087	−	0.710057i
$113$		−	19.4327i		−	1.82807i	−0.405635	−	0.914035i	$-0.632949\pi$
$113$		−	19.4327i		−	1.82807i	0.405635	−	0.914035i	$-0.367051\pi$
$114$	−2.94833	+	0.692972i	−0.276137	+	0.0649027i
$115$			30.0353i			2.80081i
$116$	3.25539	−	1.61976i	0.302255	−	0.150391i
$117$			9.33192i			0.862737i
$118$	7.01278	−	1.64827i	0.645579	−	0.151736i
$119$	11.9771			1.09794
$120$	−4.04381	+	3.35484i	−0.369148	+	0.306254i
$121$	−17.9760			−1.63418
$122$	−5.14744	+	1.20985i	−0.466027	+	0.109534i
$123$	2.67724			0.241399
$124$	5.99073	+	12.0401i	0.537983	+	1.08123i
$125$			27.7062i			2.47811i
$126$	2.81626	+	11.9821i	0.250892	+	1.06745i
$127$		−	0.831973i		−	0.0738256i	−0.999318	−	0.0369128i	$-0.988248\pi$
$127$		−	0.831973i		−	0.0738256i	0.999318	−	0.0369128i	$-0.0117524\pi$
$128$	0.510555	+	11.3022i	0.0451272	+	0.998981i
$129$			4.18876i			0.368800i
$130$	−18.8268	+	4.42502i	−1.65122	+	0.388100i
$131$	−6.33941			−0.553877			−0.276938	−	0.960888i	$-0.589320\pi$
$131$	−6.33941			−0.553877			−0.276938	+	0.960888i	$0.589320\pi$
$132$	4.37285	−	2.17577i	0.380608	−	0.189377i
$133$	−14.7038			−1.27499
$134$	−4.58826	+	1.07842i	−0.396365	+	0.0931610i
$135$	10.7636			0.926387
$136$	−6.94408	−	8.37015i	−0.595450	−	0.717734i
$137$	−4.76576			−0.407166			−0.203583	−	0.979058i	$-0.565259\pi$
$137$	−4.76576			−0.407166			−0.203583	+	0.979058i	$0.565259\pi$
$138$	1.07681	+	4.58141i	0.0916640	+	0.389996i
$139$	5.37145			0.455600			0.227800	−	0.973708i	$-0.426847\pi$
$139$	5.37145			0.455600			0.227800	+	0.973708i	$0.426847\pi$
$140$	−22.8380	+	11.3634i	−1.93016	+	0.960380i
$141$	1.73493			0.146107
$142$	−3.37568	+	0.793415i	−0.283281	+	0.0665819i
$143$	17.9778			1.50338
$144$	6.74086	−	8.91513i	0.561738	−	0.742928i
$145$		−	7.44432i		−	0.618217i
$146$	1.81945	+	7.74109i	0.150579	+	0.640657i
$147$		−	1.22605i		−	0.101123i
$148$	5.59619	+	11.2472i	0.460004	+	0.924512i
$149$			8.09028i			0.662781i	0.943494	+	0.331391i	$0.107518\pi$
$149$			8.09028i			0.662781i	−0.943494	+	0.331391i	$0.892482\pi$
$150$	1.72730	+	7.34902i	0.141034	+	0.600045i
$151$	1.84094			0.149814			0.0749070	−	0.997191i	$-0.476134\pi$
$151$	1.84094			0.149814			0.0749070	+	0.997191i	$0.476134\pi$
$152$	8.52500	+	10.2757i	0.691469	+	0.833473i
$153$			10.7439i			0.868596i
$154$	23.0834	−	5.42548i	1.86011	−	0.437197i
$155$	27.5330			2.21150
$156$	−2.71308	+	1.34993i	−0.217220	+	0.108081i
$157$	−19.9586			−1.59287			−0.796435	−	0.604725i	$-0.793283\pi$
$157$	−19.9586			−1.59287			−0.796435	+	0.604725i	$0.793283\pi$
$158$	20.4126	−	4.79775i	1.62394	−	0.381688i
$159$	−0.381413			−0.0302481
$160$	21.1823	+	9.37202i	1.67461	+	0.740923i
$161$			22.8483i			1.80070i
$162$	−9.89839	+	2.32650i	−0.777691	+	0.182787i
$163$	3.00661			0.235496			0.117748	−	0.993044i	$-0.462433\pi$
$163$	3.00661			0.235496			0.117748	+	0.993044i	$0.462433\pi$
$164$	−5.25759	−	10.5667i	−0.410549	−	0.825118i
$165$		−	9.99970i		−	0.778475i
$166$	−21.4372	+	5.03856i	−1.66385	+	0.391068i
$167$	10.4620	−	7.58598i	0.809572	−	0.587021i
$167$	10.4620	−	7.58598i	0.809572	−	0.587021i
$168$	−3.07618	+	2.55207i	−0.237333	+	0.196897i
$169$	1.84589			0.141992
$170$	−21.6755	+	5.09457i	−1.66243	+	0.390736i
$171$		−	13.1900i		−	1.00866i
$172$	16.5324	−	8.22592i	1.26058	−	0.627220i
$173$	16.2563			1.23595			0.617973	−	0.786200i	$-0.287954\pi$
$173$	16.2563			1.23595			0.617973	+	0.786200i	$0.287954\pi$
$174$	−0.266889	−	1.13551i	−0.0202328	−	0.0860830i
$175$			36.6508i			2.77054i
$176$	−17.1749	−	12.9862i	−1.29460	−	0.978869i
$177$		−	2.31100i		−	0.173705i
$178$	3.02023	−	0.709871i	0.226376	−	0.0532071i
$179$			17.4585i			1.30491i	0.757829	+	0.652453i	$0.226260\pi$
$179$			17.4585i			1.30491i	−0.757829	+	0.652453i	$0.773740\pi$
$180$	−10.1934	−	20.4867i	−0.759773	−	1.52699i
$181$	9.39564			0.698372			0.349186	−	0.937053i	$-0.386458\pi$
$181$	9.39564			0.698372			0.349186	+	0.937053i	$0.386458\pi$
$182$	−14.3218	+	3.36617i	−1.06160	+	0.249517i
$183$			1.69629i			0.125393i
$184$	15.9675	−	13.2470i	1.17714	−	0.976582i
$185$	25.7197			1.89095
$186$	4.19971	−	0.987094i	0.307938	−	0.0723773i
$187$	20.6980			1.51359
$188$	−3.40706	−	6.84749i	−0.248486	−	0.499404i
$189$	8.18805			0.595593
$190$	26.6102	−	6.25442i	1.93051	−	0.453744i
$191$			8.70813i			0.630098i	0.949075	+	0.315049i	$0.102021\pi$
$191$			8.70813i			0.630098i	−0.949075	+	0.315049i	$0.897979\pi$
$192$	3.56702	+	0.670138i	0.257428	+	0.0483631i
$193$			1.61820i			0.116481i	0.998303	+	0.0582404i	$0.0185490\pi$
$193$			1.61820i			0.116481i	−0.998303	+	0.0582404i	$0.981451\pi$
$194$	−13.9567	+	3.28037i	−1.00204	+	0.235517i
$195$			6.20419i			0.444291i
$196$	−4.83901	+	2.40772i	−0.345644	+	0.171980i
$197$		−	3.52496i		−	0.251143i	−0.992085	−	0.125572i	$-0.959924\pi$
$197$		−	3.52496i		−	0.251143i	0.992085	−	0.125572i	$-0.0400765\pi$
$198$	4.86688	+	20.7068i	0.345874	+	1.47156i
$199$		−	1.39751i		−	0.0990671i	−0.998772	−	0.0495335i	$-0.984227\pi$
$199$		−	1.39751i		−	0.0990671i	0.998772	−	0.0495335i	$-0.0157735\pi$
$200$	25.6133	−	21.2494i	1.81114	−	1.50256i
$201$			1.51202i			0.106650i
$202$	4.64678	+	19.7703i	0.326946	+	1.39103i
$203$		−	5.66300i		−	0.397464i
$204$	−3.12360	+	1.55419i	−0.218696	+	0.108815i
$205$	−24.1635			−1.68765
$206$	6.83902	−	1.60743i	0.476497	−	0.111995i
$207$	−20.4959			−1.42456
$208$	10.6559	+	8.05710i	0.738856	+	0.558659i
$209$	−25.4103			−1.75767
$210$	1.87235	+	7.96613i	0.129204	+	0.549715i
$211$		−	17.7954i		−	1.22508i	−0.790439	−	0.612541i	$-0.790147\pi$
$211$		−	17.7954i		−	1.22508i	0.790439	−	0.612541i	$-0.209853\pi$
$212$	0.749022	+	1.50538i	0.0514431	+	0.103390i
$213$			1.11242i			0.0762221i
$214$	2.41279	+	10.2655i	0.164935	+	0.701735i
$215$		−	37.8057i		−	2.57833i
$216$	−4.74727	−	5.72220i	−0.323011	−	0.389346i
$217$	20.9447			1.42182
$218$	−4.40472	−	18.7404i	−0.298325	−	1.26926i
$219$	2.55100			0.172381
$220$	−39.4672	+	19.6375i	−2.66088	+	1.32396i
$221$	−12.8418			−0.863836
$222$	3.92313	−	0.922086i	0.263303	−	0.0618863i
$223$			15.4864i			1.03705i	0.855063	+	0.518524i	$0.173518\pi$
$223$			15.4864i			1.03705i	−0.855063	+	0.518524i	$0.826482\pi$
$224$	16.1137	+	7.12942i	1.07664	+	0.476355i
$225$	−32.8774			−2.19182
$226$	6.28796	+	26.7529i	0.418269	+	1.77958i
$227$	−27.0115			−1.79282			−0.896408	−	0.443229i	$-0.853833\pi$
$227$	−27.0115			−1.79282			−0.896408	+	0.443229i	$0.853833\pi$
$228$	3.83473	−	1.90803i	0.253962	−	0.126362i
$229$	7.15359			0.472723			0.236361	−	0.971665i	$-0.424045\pi$
$229$	7.15359			0.472723			0.236361	+	0.971665i	$0.424045\pi$
$230$	−9.71875	−	41.3496i	−0.640835	−	2.72651i
$231$		−	7.60691i		−	0.500498i
$232$	−3.95757	+	3.28330i	−0.259827	+	0.215559i
$233$	4.64417			0.304249			0.152125	−	0.988361i	$-0.451388\pi$
$233$	4.64417			0.304249			0.152125	+	0.988361i	$0.451388\pi$
$234$	−3.01960	−	12.8472i	−0.197397	−	0.839851i
$235$	−15.6586			−1.02146
$236$	−9.12114	+	4.53835i	−0.593735	+	0.295421i
$237$		−	6.72679i		−	0.436952i
$238$	−16.4888	+	3.87551i	−1.06881	+	0.251212i
$239$			14.2655i			0.922757i	0.887203	+	0.461379i	$0.152645\pi$
$239$			14.2655i			0.922757i	−0.887203	+	0.461379i	$0.847355\pi$
$240$	4.48156	−	5.92709i	0.289283	−	0.382592i
$241$		−	19.8815i		−	1.28068i	−0.768092	−	0.640339i	$-0.778794\pi$
$241$		−	19.8815i		−	1.28068i	0.768092	−	0.640339i	$-0.221206\pi$
$242$	24.7476	−	5.81663i	1.59083	−	0.373907i
$243$			11.1480i			0.715144i
$244$	6.69499	−	3.33118i	0.428603	−	0.213257i
$245$			11.0657i			0.706962i
$246$	−3.68576	+	0.866295i	−0.234995	+	0.0552329i
$247$	15.7655			1.00313
$248$	−12.1433	−	14.6371i	−0.771102	−	0.929460i
$249$			7.06442i			0.447690i
$250$	−8.96508	−	38.1430i	−0.567001	−	2.41238i
$251$			2.53812i			0.160205i	0.996787	+	0.0801023i	$0.0255247\pi$
$251$			2.53812i			0.160205i	−0.996787	+	0.0801023i	$0.974475\pi$
$252$	−7.75427	−	15.5845i	−0.488473	−	0.981730i
$253$			39.4850i			2.48240i
$254$	0.269207	+	1.14538i	0.0168916	+	0.0718672i
$255$			7.14295i			0.447309i
$256$	−4.36001	−	15.3945i	−0.272500	−	0.962156i
$257$		−	2.73861i		−	0.170830i	−0.996345	−	0.0854150i	$-0.972778\pi$
$257$		−	2.73861i		−	0.170830i	0.996345	−	0.0854150i	$-0.0272216\pi$
$258$	−1.35539	−	5.76666i	−0.0843827	−	0.359017i
$259$	19.5653			1.21573
$260$	24.4870	−	12.1838i	1.51862	−	0.755609i
$261$	5.07995			0.314441
$262$	8.72745	−	2.05129i	0.539184	−	0.126729i
$263$		−	1.85563i		−	0.114423i	−0.998362	−	0.0572116i	$-0.981779\pi$
$263$		−	1.85563i		−	0.114423i	0.998362	−	0.0572116i	$-0.0182210\pi$
$264$	−5.31607	+	4.41034i	−0.327181	+	0.271437i
$265$	3.44245			0.211468
$266$	20.2428	−	4.75783i	1.24116	−	0.291721i
$267$		−	0.995289i		−	0.0609107i
$268$	5.96770	−	2.96931i	0.364535	−	0.181379i
$269$		−	11.9417i		−	0.728099i	−0.931380	−	0.364049i	$-0.881394\pi$
$269$		−	11.9417i		−	0.728099i	0.931380	−	0.364049i	$-0.118606\pi$
$270$	−14.8183	+	3.48287i	−0.901812	+	0.211961i
$271$	0.718269			0.0436317			0.0218159	−	0.999762i	$-0.493055\pi$
$271$	0.718269			0.0436317			0.0218159	+	0.999762i	$0.493055\pi$
$272$	12.2683	+	9.27623i	0.743874	+	0.562454i
$273$			4.71961i			0.285644i
$274$	6.56101	−	1.54209i	0.396365	−	0.0931611i
$275$			63.3377i			3.81941i
$276$	−2.96488	−	5.95879i	−0.178465	−	0.358677i
$277$		−	22.3508i		−	1.34293i	−0.741038	−	0.671464i	$-0.765666\pi$
$277$		−	22.3508i		−	1.34293i	0.741038	−	0.671464i	$-0.234334\pi$
$278$	−7.39487	+	1.73808i	−0.443515	+	0.104243i
$279$			18.7883i			1.12482i
$280$	27.7641	−	23.0338i	1.65922	−	1.37653i
$281$	18.0109			1.07444			0.537221	−	0.843441i	$-0.319474\pi$
$281$	18.0109			1.07444			0.537221	+	0.843441i	$0.319474\pi$
$282$	−2.38847	+	0.561383i	−0.142231	+	0.0334299i
$283$		−	11.6678i		−	0.693576i	−0.937943	−	0.346788i	$-0.887272\pi$
$283$		−	11.6678i		−	0.693576i	0.937943	−	0.346788i	$-0.112728\pi$
$284$	4.39057	−	2.18459i	0.260532	−	0.129631i
$285$		−	8.76915i		−	0.519440i
$286$	−24.7500	+	5.81721i	−1.46350	+	0.343979i
$287$	−18.3815			−1.08503
$288$	−6.39539	+	14.4546i	−0.376852	+	0.851747i
$289$	2.21505			0.130297
$290$	2.40881	+	10.2486i	0.141450	+	0.601817i
$291$			4.59932i			0.269617i
$292$	−5.00968	−	10.0684i	−0.293169	−	0.589209i
$293$	−15.2491			−0.890862			−0.445431	−	0.895316i	$-0.646949\pi$
$293$	−15.2491			−0.890862			−0.445431	+	0.895316i	$0.646949\pi$
$294$	0.396720	+	1.68790i	0.0231372	+	0.0984401i
$295$			20.8579i			1.21440i
$296$	−11.3436	−	13.6732i	−0.659333	−	0.794737i
$297$	14.1501			0.821071
$298$	−2.61783	−	11.1379i	−0.151647	−	0.645200i
$299$		−	24.4980i		−	1.41675i
$300$	−4.75595	−	9.55847i	−0.274585	−	0.551859i
$301$		−	28.7593i		−	1.65766i
$302$	−2.53443	+	0.595687i	−0.145840	+	0.0342780i
$303$	6.51511			0.374283
$304$	−15.0614	−	11.3881i	−0.863828	−	0.653152i
$305$		−	15.3099i		−	0.876642i
$306$	−3.47649	−	14.7912i	−0.198738	−	0.845555i
$307$	−4.33153			−0.247213			−0.123607	−	0.992331i	$-0.539446\pi$
$307$	−4.33153			−0.247213			−0.123607	+	0.992331i	$0.539446\pi$
$308$	−30.0233	+	14.9385i	−1.71073	+	0.851200i
$309$		−	2.25374i		−	0.128211i
$310$	−37.9046	+	8.90903i	−2.15284	+	0.505999i
$311$		−	9.61651i		−	0.545302i	−0.962113	−	0.272651i	$-0.912100\pi$
$311$		−	9.61651i		−	0.545302i	0.962113	−	0.272651i	$-0.0879005\pi$
$312$	3.29829	−	2.73634i	0.186729	−	0.154915i
$313$			22.1917i			1.25435i	0.778879	+	0.627174i	$0.215789\pi$
$313$			22.1917i			1.25435i	−0.778879	+	0.627174i	$0.784211\pi$
$314$	27.4770	−	6.45814i	1.55061	−	0.364454i
$315$	−35.6381			−2.00798
$316$	−26.5496	+	13.2101i	−1.49353	+	0.743127i
$317$	−1.13102			−0.0635243			−0.0317622	−	0.999495i	$-0.510112\pi$
$317$	−1.13102			−0.0635243			−0.0317622	+	0.999495i	$0.510112\pi$
$318$	0.525091	−	0.123417i	0.0294457	−	0.00692086i
$319$		−	9.78644i		−	0.547935i
$320$	−32.1942	−	6.04834i	−1.79971	−	0.338113i
$321$	3.38290			0.188815
$322$	−7.39318	−	31.4552i	−0.412006	−	1.75293i
$323$	18.1510			1.00995
$324$	12.8743	−	6.40578i	0.715239	−	0.355877i
$325$		−	39.2971i		−	2.17981i
$326$	−4.13919	+	0.972870i	−0.229249	+	0.0538823i
$327$	−6.17573			−0.341519
$328$	10.6572	+	12.8459i	0.588448	+	0.709294i
$329$	−11.9117			−0.656715
$330$	3.23567	+	13.7666i	0.178118	+	0.757825i
$331$	−1.45673			−0.0800693			−0.0400346	−	0.999198i	$-0.512747\pi$
$331$	−1.45673			−0.0800693			−0.0400346	+	0.999198i	$0.512747\pi$
$332$	27.8822	−	13.8732i	1.53023	−	0.761388i
$333$			17.5509i			0.961784i
$334$	−11.9483	+	13.8289i	−0.653783	+	0.756682i
$335$		−	13.6467i		−	0.745601i
$336$	3.40918	−	4.50882i	0.185986	−	0.245976i
$337$	21.8413			1.18977			0.594886	−	0.803810i	$-0.297197\pi$
$337$	21.8413			1.18977			0.594886	+	0.803810i	$0.297197\pi$
$338$	−2.54124	+	0.597288i	−0.138225	+	0.0324882i
$339$	8.81617			0.478829
$340$	28.1921	−	14.0274i	1.52893	−	0.760741i
$341$	36.1953			1.96009
$342$	4.26797	+	18.1586i	0.230785	+	0.981905i
$343$		−	13.3863i		−	0.722793i
$344$	−20.0984	+	16.6741i	−1.08363	+	0.899007i
$345$	−13.6264			−0.733619
$346$	−22.3800	+	5.26017i	−1.20316	+	0.282789i
$347$	21.1818			1.13710			0.568549	−	0.822649i	$-0.307505\pi$
$347$	21.1818			1.13710			0.568549	+	0.822649i	$0.307505\pi$
$348$	0.734851	+	1.47690i	0.0393922	+	0.0791701i
$349$		−	21.1916i		−	1.13436i	−0.823595	−	0.567179i	$-0.808035\pi$
$349$		−	21.1916i		−	1.13436i	0.823595	−	0.567179i	$-0.191965\pi$
$350$	−11.8594	−	50.4572i	−0.633910	−	2.69705i
$351$	−8.77924			−0.468601
$352$	27.8466	+	12.3206i	1.48423	+	0.656692i
$353$	−14.6305			−0.778703			−0.389352	−	0.921089i	$-0.627301\pi$
$353$	−14.6305			−0.778703			−0.389352	+	0.921089i	$0.627301\pi$
$354$	0.747785	+	3.18154i	0.0397443	+	0.169097i
$355$		−	10.0402i		−	0.532879i
$356$	−3.92825	+	1.95456i	−0.208197	+	0.103591i
$357$			5.43374i			0.287584i
$358$	−5.64916	−	24.0350i	−0.298567	−	1.27029i
$359$		−	11.8776i		−	0.626875i	−0.949609	−	0.313438i	$-0.898519\pi$
$359$		−	11.8776i		−	0.626875i	0.949609	−	0.313438i	$-0.101481\pi$
$360$	20.6623	+	24.9056i	1.08900	+	1.31264i
$361$	−3.28332			−0.172807
$362$	−12.9350	+	3.04021i	−0.679846	+	0.159790i
$363$		−	8.15533i		−	0.428044i
$364$	18.6276	−	9.26840i	0.976349	−	0.485796i
$365$	−23.0241			−1.20514
$366$	−0.548880	−	2.33528i	−0.0286904	−	0.122067i
$367$		−	3.30181i		−	0.172353i	−0.996280	−	0.0861765i	$-0.972535\pi$
$367$		−	3.30181i		−	0.172353i	0.996280	−	0.0861765i	$-0.0274649\pi$
$368$	−17.6960	+	23.4038i	−0.922466	+	1.22001i
$369$		−	16.4890i		−	0.858382i
$370$	−35.4082	+	8.32230i	−1.84079	+	0.432656i
$371$	2.61872			0.135957
$372$	−5.46234	+	2.71786i	−0.283209	+	0.140915i
$373$			4.52247i			0.234164i	0.993122	+	0.117082i	$0.0373541\pi$
$373$			4.52247i			0.234164i	−0.993122	+	0.117082i	$0.962646\pi$
$374$	−28.4950	+	6.69741i	−1.47344	+	0.346315i
$375$	−12.5697			−0.649095
$376$	6.90619	+	8.32448i	0.356159	+	0.429302i
$377$			6.07187i			0.312717i
$378$	−11.2725	+	2.64946i	−0.579793	+	0.136274i
$379$	30.3097			1.55691			0.778453	−	0.627703i	$-0.216005\pi$
$379$	30.3097			1.55691			0.778453	+	0.627703i	$0.216005\pi$
$380$	−34.6105	+	17.2209i	−1.77548	+	0.883414i
$381$	0.377448			0.0193372
$382$	−2.81775	−	11.9885i	−0.144169	−	0.613384i
$383$			10.6776i			0.545597i	0.962071	+	0.272799i	$0.0879493\pi$
$383$			10.6776i			0.545597i	−0.962071	+	0.272799i	$0.912051\pi$
$384$	−5.12755	+	0.231628i	−0.261664	+	0.0118202i
$385$			68.6562i			3.49905i
$386$	−0.523613	−	2.22778i	−0.0266512	−	0.113391i
$387$	25.7983			1.31140
$388$	18.1528	−	9.03217i	0.921568	−	0.458539i
$389$			32.8448i			1.66530i	0.553803	+	0.832648i	$0.313176\pi$
$389$			32.8448i			1.66530i	−0.553803	+	0.832648i	$0.686824\pi$
$390$	−2.00753	−	8.54129i	−0.101655	−	0.432505i
$391$		−	28.2048i		−	1.42638i
$392$	5.88278	−	4.88049i	0.297125	−	0.246502i
$393$		−	2.87605i		−	0.145078i
$394$	1.14060	+	4.85281i	0.0574624	+	0.244481i
$395$			60.7127i			3.05479i
$396$	−13.4005	−	26.9321i	−0.673398	−	1.35339i
$397$	25.3936			1.27447			0.637233	−	0.770671i	$-0.280079\pi$
$397$	25.3936			1.27447			0.637233	+	0.770671i	$0.280079\pi$
$398$	0.452203	+	1.92395i	0.0226669	+	0.0964391i
$399$		−	6.67081i		−	0.333958i
$400$	−28.3860	+	37.5420i	−1.41930	+	1.87710i
$401$			8.92239i			0.445563i	0.974868	+	0.222781i	$0.0715136\pi$
$401$			8.92239i			0.445563i	−0.974868	+	0.222781i	$0.928486\pi$
$402$	−0.489254	−	2.08159i	−0.0244018	−	0.103820i
$403$	−22.4569			−1.11866
$404$	−12.7944	−	25.7141i	−0.636546	−	1.27933i
$405$		−	29.4405i		−	1.46291i
$406$	1.83242	+	7.79624i	0.0909412	+	0.386921i
$407$	33.8116			1.67598
$408$	3.79735	−	3.15038i	0.187997	−	0.155967i
$409$	−8.02669			−0.396894			−0.198447	−	0.980112i	$-0.563590\pi$
$409$	−8.02669			−0.396894			−0.198447	+	0.980112i	$0.563590\pi$
$410$	33.2659	−	7.81875i	1.64288	−	0.386141i
$411$		−	2.16212i		−	0.106650i
$412$	−8.89514	+	4.42590i	−0.438232	+	0.218049i
$413$			15.8669i			0.780760i
$414$	28.2166	−	6.63200i	1.38677	−	0.325945i
$415$		−	63.7600i		−	3.12986i
$416$	−17.2771	−	7.64418i	−0.847079	−	0.374787i
$417$			2.43691i			0.119336i
$418$	34.9823	−	8.22218i	1.71104	−	0.402160i
$419$			14.4655i			0.706688i	0.935494	+	0.353344i	$0.114955\pi$
$419$			14.4655i			0.706688i	−0.935494	+	0.353344i	$0.885045\pi$
$420$	−5.15531	−	10.3611i	−0.251553	−	0.505570i
$421$	37.7405			1.83936			0.919679	−	0.392672i	$-0.128449\pi$
$421$	37.7405			1.83936			0.919679	+	0.392672i	$0.128449\pi$
$422$	5.75817	+	24.4988i	0.280303	+	1.19258i
$423$		−	10.6853i		−	0.519538i
$424$	−1.51828	−	1.83009i	−0.0737344	−	0.0888768i
$425$		−	45.2432i		−	2.19462i
$426$	−0.359955	−	1.53147i	−0.0174399	−	0.0742001i
$427$		−	11.6464i		−	0.563611i
$428$	−6.64336	−	13.3518i	−0.321119	−	0.645382i
$429$			8.15614i			0.393782i
$430$	12.2331	+	52.0471i	0.589931	+	2.50993i
$431$		−	31.2657i		−	1.50602i	−0.658011	−	0.753008i	$-0.728602\pi$
$431$		−	31.2657i		−	1.50602i	0.658011	−	0.753008i	$-0.271398\pi$
$432$	8.38713	+	6.34163i	0.403526	+	0.305112i
$433$	−12.0909			−0.581053			−0.290527	−	0.956867i	$-0.593831\pi$
$433$	−12.0909			−0.581053			−0.290527	+	0.956867i	$0.593831\pi$
$434$	−28.8345	+	6.77722i	−1.38410	+	0.325317i
$435$	3.37732			0.161930
$436$	12.1279	+	24.3746i	0.580823	+	1.16733i
$437$			34.6260i			1.65639i
$438$	−3.51196	+	0.825446i	−0.167808	+	0.0394414i
$439$	3.19059			0.152279			0.0761394	−	0.997097i	$-0.475741\pi$
$439$	3.19059			0.152279			0.0761394	+	0.997097i	$0.475741\pi$
$440$	47.9802	−	39.8056i	2.28737	−	1.89766i
$441$	−7.55115			−0.359578
$442$	17.6793	−	4.15533i	0.840921	−	0.197649i
$443$	23.0794			1.09654			0.548269	−	0.836302i	$-0.315287\pi$
$443$	23.0794			1.09654			0.548269	+	0.836302i	$0.315287\pi$
$444$	−5.10260	+	2.53887i	−0.242159	+	0.120489i
$445$			8.98300i			0.425835i
$446$	−5.01105	−	21.3201i	−0.237280	−	1.00954i
$447$	−3.67038			−0.173603
$448$	−24.4906	−	4.60106i	−1.15707	−	0.217379i
$449$	−36.5780			−1.72622			−0.863110	−	0.505015i	$-0.831487\pi$
$449$	−36.5780			−1.72622			−0.863110	+	0.505015i	$0.831487\pi$
$450$	45.2622	−	10.6384i	2.13368	−	0.501497i
$451$	−31.7658			−1.49579
$452$	−17.3132	−	34.7960i	−0.814347	−	1.63667i
$453$			0.835196i			0.0392409i
$454$	37.1867	−	8.74030i	1.74526	−	0.410203i
$455$		−	42.5969i		−	1.99697i
$456$	−4.66188	+	3.86761i	−0.218312	+	0.181117i
$457$			21.4628i			1.00399i	0.864872	+	0.501993i	$0.167400\pi$
$457$			21.4628i			1.00399i	−0.864872	+	0.501993i	$0.832600\pi$
$458$	−9.84834	+	2.31474i	−0.460182	+	0.108161i
$459$	−10.1076			−0.471784
$460$	26.7596	+	53.7812i	1.24767	+	2.50756i
$461$	32.0797			1.49410			0.747051	−	0.664767i	$-0.231469\pi$
$461$	32.0797			1.49410			0.747051	+	0.664767i	$0.231469\pi$
$462$	2.46142	+	10.4724i	0.114516	+	0.487221i
$463$	0.446652			0.0207577			0.0103788	−	0.999946i	$-0.496696\pi$
$463$	0.446652			0.0207577			0.0103788	+	0.999946i	$0.496696\pi$
$464$	4.38598	−	5.80068i	0.203614	−	0.269290i
$465$			12.4911i			0.579261i
$466$	−6.39361	+	1.50275i	−0.296178	+	0.0696133i
$467$			9.56798i			0.442753i	0.975188	+	0.221377i	$0.0710550\pi$
$467$			9.56798i			0.442753i	−0.975188	+	0.221377i	$0.928945\pi$
$468$	8.31415	+	16.7097i	0.384322	+	0.772406i
$469$		−	10.3813i		−	0.479362i
$470$	21.5572	−	5.06677i	0.994359	−	0.233713i
$471$		−	9.05478i		−	0.417222i
$472$	11.0885	−	9.19933i	0.510392	−	0.423433i
$473$		−	49.7001i		−	2.28521i
$474$	2.17663	+	9.26076i	0.0999761	+	0.425361i
$475$			55.5435i			2.54851i
$476$	21.4461	−	10.6708i	0.982981	−	0.489096i
$477$			2.34910i			0.107558i
$478$	−4.61598	−	19.6393i	−0.211130	−	0.898279i
$479$	23.0966			1.05531			0.527655	−	0.849459i	$-0.323071\pi$
$479$	23.0966			1.05531			0.527655	+	0.849459i	$0.323071\pi$
$480$	−4.25188	+	9.60994i	−0.194071	+	0.438632i
$481$	−20.9780			−0.956513
$482$	6.43319	+	27.3708i	0.293024	+	1.24671i
$483$	−10.3658			−0.471659
$484$	−32.1878	+	16.0155i	−1.46308	+	0.727977i
$485$		−	41.5112i		−	1.88493i
$486$	−3.60723	−	15.3474i	−0.163627	−	0.696173i
$487$	13.0232			0.590138			0.295069	−	0.955476i	$-0.404657\pi$
$487$	13.0232			0.590138			0.295069	+	0.955476i	$0.404657\pi$
$488$	−8.13908	+	6.75238i	−0.368439	+	0.305666i
$489$			1.36403i			0.0616837i
$490$	−3.58061	−	15.2341i	−0.161755	−	0.688208i
$491$			28.0726i			1.26690i	0.773784	+	0.633450i	$0.218362\pi$
$491$			28.0726i			1.26690i	−0.773784	+	0.633450i	$0.781638\pi$
$492$	4.79386	−	2.38525i	0.216124	−	0.107535i
$493$			6.99061i			0.314841i
$494$	−21.7043	+	5.10135i	−0.976523	+	0.229521i
$495$	−61.5876			−2.76815
$496$	21.4539	+	16.2216i	0.963311	+	0.728373i
$497$		−	7.63772i		−	0.342599i
$498$	−2.28588	−	9.72558i	−0.102433	−	0.435814i
$499$	34.9449			1.56435			0.782173	−	0.623061i	$-0.214111\pi$
$499$	34.9449			1.56435			0.782173	+	0.623061i	$0.214111\pi$
$500$	24.6844	+	49.6105i	1.10392	+	2.21865i
$501$	3.44159	+	4.74637i	0.153759	+	0.212052i
$502$	−0.821277	−	3.49422i	−0.0366554	−	0.155955i
$503$			39.3978i			1.75666i	0.478055	+	0.878330i	$0.341342\pi$
$503$			39.3978i			1.75666i	−0.478055	+	0.878330i	$0.658658\pi$
$504$	15.7181	+	18.9460i	0.700139	+	0.843923i
$505$	−58.8022			−2.61666
$506$	−12.7764	−	54.3590i	−0.567982	−	2.41655i
$507$			0.837440i			0.0371920i
$508$	−0.741234	−	1.48973i	−0.0328870	−	0.0660959i
$509$	22.9249			1.01613			0.508065	−	0.861319i	$-0.330361\pi$
$509$	22.9249			1.01613			0.508065	+	0.861319i	$0.330361\pi$
$510$	−2.31129	−	9.83368i	−0.102346	−	0.435443i
$511$	−17.5148			−0.774808
$512$	10.9837	+	19.7828i	0.485416	+	0.874283i
$513$	12.4088			0.547861
$514$	0.886152	+	3.77024i	0.0390865	+	0.166298i
$515$			20.3411i			0.896337i
$516$	3.73192	+	7.50038i	0.164289	+	0.330186i
$517$	−20.5851			−0.905332
$518$	−26.9355	+	6.33089i	−1.18348	+	0.278163i
$519$			7.37514i			0.323733i
$520$	−29.7687	+	24.6969i	−1.30545	+	1.08303i
$521$		−	12.7235i		−	0.557427i	−0.960374	−	0.278714i	$-0.910092\pi$
$521$		−	12.7235i		−	0.557427i	0.960374	−	0.278714i	$-0.0899080\pi$
$522$	−6.99355	+	1.64375i	−0.306099	+	0.0719451i
$523$		−	5.77389i		−	0.252475i	−0.992000	−	0.126237i	$-0.959710\pi$
$523$		−	5.77389i		−	0.252475i	0.992000	−	0.126237i	$-0.0402901\pi$
$524$	−11.3513	+	5.64801i	−0.495885	+	0.246734i
$525$	−16.6277			−0.725692
$526$	0.600440	+	2.55464i	0.0261804	+	0.111388i
$527$	−25.8549			−1.12626
$528$	5.89154	−	7.79186i	0.256396	−	0.339097i
$529$	30.8054			1.33936
$530$	−4.73922	+	1.11390i	−0.205858	+	0.0483847i
$531$	−14.2333			−0.617672
$532$	−26.3286	+	13.1002i	−1.14149	+	0.567965i
$533$	19.7087			0.853678
$534$	0.322053	+	1.37021i	0.0139366	+	0.0592949i
$535$	−30.5324			−1.32003
$536$	−7.25492	+	6.01885i	−0.313365	+	0.259975i
$537$	−7.92052			−0.341796
$538$	3.86406	+	16.4401i	0.166592	+	0.708784i
$539$			14.5472i			0.626591i
$540$	19.2733	−	9.58971i	0.829392	−	0.412676i
$541$		−	27.2450i		−	1.17135i	−0.810544	−	0.585677i	$-0.800829\pi$
$541$		−	27.2450i		−	1.17135i	0.810544	−	0.585677i	$-0.199171\pi$
$542$	−0.988840	+	0.232415i	−0.0424743	+	0.00998309i
$543$			4.26259i			0.182925i
$544$	−19.8913	−	8.80083i	−0.852833	−	0.377332i
$545$	55.7391			2.38760
$546$	−1.52716	−	6.49748i	−0.0653563	−	0.278066i
$547$	−17.5974			−0.752409			−0.376204	−	0.926537i	$-0.622771\pi$
$547$	−17.5974			−0.752409			−0.376204	+	0.926537i	$0.622771\pi$
$548$	−8.53355	+	4.24598i	−0.364535	+	0.181379i
$549$	10.4473			0.445882
$550$	−20.4946	−	87.1969i	−0.873894	−	3.71809i
$551$		−	8.58213i		−	0.365611i
$552$	6.00987	+	7.24409i	0.255797	+	0.308329i
$553$			46.1850i			1.96399i
$554$	7.23219	+	30.7703i	0.307266	+	1.30730i
$555$			11.6685i			0.495298i
$556$	9.61810	−	4.78562i	0.407898	−	0.202955i
$557$	−7.25790			−0.307527			−0.153764	−	0.988108i	$-0.549139\pi$
$557$	−7.25790			−0.307527			−0.153764	+	0.988108i	$0.549139\pi$
$558$	−6.07946	−	25.8658i	−0.257364	−	1.09499i
$559$			30.8358i			1.30422i
$560$	−30.7696	+	40.6944i	−1.30025	+	1.71965i
$561$			9.39025i			0.396457i
$562$	−24.7956	+	5.82792i	−1.04594	+	0.245836i
$563$			43.0684i			1.81512i	0.419925	+	0.907559i	$0.362056\pi$
$563$			43.0684i			1.81512i	−0.419925	+	0.907559i	$0.637944\pi$
$564$	3.10655	−	1.54571i	0.130810	−	0.0650861i
$565$	−79.5705			−3.34755
$566$	3.77542	+	16.0630i	0.158693	+	0.675178i
$567$		−	22.3958i		−	0.940536i
$568$	−5.33760	+	4.42820i	−0.223961	+	0.185803i
$569$			9.58999i			0.402033i	0.979588	+	0.201017i	$0.0644246\pi$
$569$			9.58999i			0.402033i	−0.979588	+	0.201017i	$0.935575\pi$
$570$	2.83750	+	12.0725i	0.118850	+	0.505660i
$571$	27.2143			1.13888			0.569442	−	0.822032i	$-0.307159\pi$
$571$	27.2143			1.13888			0.569442	+	0.822032i	$0.307159\pi$
$572$	32.1910	−	16.0171i	1.34597	−	0.669708i
$573$	−3.95069			−0.165042
$574$	25.3058	−	5.94783i	1.05624	−	0.248258i
$575$	86.3090			3.59933
$576$	4.12734	−	21.9691i	0.171973	−	0.915378i
$577$	−43.1867			−1.79789			−0.898944	−	0.438065i	$-0.855664\pi$
$577$	−43.1867			−1.79789			−0.898944	+	0.438065i	$0.855664\pi$
$578$	−3.04945	+	0.716738i	−0.126840	+	0.0298124i
$579$	−0.734143			−0.0305099
$580$	−6.63241	−	13.3298i	−0.275396	−	0.553489i
$581$		−	48.5031i		−	2.01225i
$582$	−1.48823	−	6.33187i	−0.0616892	−	0.262464i
$583$	4.52551			0.187428
$584$	10.1547	+	12.2402i	0.420205	+	0.506501i
$585$	38.2112			1.57984
$586$	20.9934	−	4.93426i	0.867229	−	0.203832i
$587$	−36.7161			−1.51543			−0.757717	−	0.652583i	$-0.773685\pi$
$587$	−36.7161			−1.51543			−0.757717	+	0.652583i	$0.773685\pi$
$588$	−1.09233	−	2.19535i	−0.0450469	−	0.0905348i
$589$	31.7412			1.30787
$590$	−6.74915	−	28.7151i	−0.277858	−	1.18218i
$591$	1.59920			0.0657822
$592$	20.0410	+	15.1533i	0.823681	+	0.622797i
$593$		−	29.6072i		−	1.21582i	−0.794005	−	0.607912i	$-0.792007\pi$
$593$		−	29.6072i		−	1.21582i	0.794005	−	0.607912i	$-0.207993\pi$
$594$	−19.4804	+	4.57864i	−0.799290	+	0.187864i
$595$		−	49.0423i		−	2.01054i
$596$	7.20792	+	14.4864i	0.295248	+	0.593387i
$597$	0.634021			0.0259488
$598$	7.92698	+	33.7263i	0.324159	+	1.37917i
$599$			17.3922i			0.710625i	0.934748	+	0.355312i	$0.115625\pi$
$599$			17.3922i			0.710625i	−0.934748	+	0.355312i	$0.884375\pi$
$600$	9.64041	+	11.6202i	0.393568	+	0.474393i
$601$	−13.4856			−0.550087			−0.275044	−	0.961432i	$-0.588692\pi$
$601$	−13.4856			−0.550087			−0.275044	+	0.961432i	$0.588692\pi$
$602$	9.30586	+	39.5929i	0.379279	+	1.61369i
$603$	9.31243			0.379231
$604$	3.29639	−	1.64016i	0.134128	−	0.0667373i
$605$			73.6060i			2.99251i
$606$	−8.96934	+	2.10814i	−0.364355	+	0.0856373i
$607$	−20.8308			−0.845495			−0.422748	−	0.906247i	$-0.638934\pi$
$607$	−20.8308			−0.845495			−0.422748	+	0.906247i	$0.638934\pi$
$608$	24.4199	+	10.8045i	0.990356	+	0.438179i
$609$	2.56918			0.104108
$610$	4.95393	+	21.0771i	0.200579	+	0.853387i
$611$	12.7718			0.516691
$612$	9.57216	+	19.2381i	0.386932	+	0.777653i
$613$	22.1615			0.895093			0.447546	−	0.894261i	$-0.352298\pi$
$613$	22.1615			0.895093			0.447546	+	0.894261i	$0.352298\pi$
$614$	5.96320	−	1.40158i	0.240655	−	0.0565633i
$615$		−	10.9625i		−	0.442049i
$616$	36.4992	−	30.2806i	1.47060	−	1.22004i
$617$	−6.72558			−0.270762			−0.135381	−	0.990794i	$-0.543226\pi$
$617$	−6.72558			−0.270762			−0.135381	+	0.990794i	$0.543226\pi$
$618$	0.729257	+	3.10271i	0.0293350	+	0.124809i
$619$	4.03542			0.162197			0.0810986	−	0.996706i	$-0.474157\pi$
$619$	4.03542			0.162197			0.0810986	+	0.996706i	$0.474157\pi$
$620$	49.3004	−	24.5301i	1.97995	−	0.985153i
$621$		−	19.2820i		−	0.773761i
$622$	3.11168	+	13.2390i	0.124767	+	0.530837i
$623$			6.83349i			0.273778i
$624$	−3.65533	+	4.83436i	−0.146330	+	0.193529i
$625$	54.6159			2.18464
$626$	−7.18072	−	30.5512i	−0.286999	−	1.22107i
$627$		−	11.5281i		−	0.460387i
$628$	−35.7378	+	17.7818i	−1.42609	+	0.709572i
$629$	−24.1522			−0.963009
$630$	49.0629	−	11.5317i	1.95471	−	0.459433i
$631$		−	8.05486i		−	0.320659i	−0.987064	−	0.160330i	$-0.948744\pi$
$631$		−	8.05486i		−	0.320659i	0.987064	−	0.160330i	$-0.0512557\pi$
$632$	32.2763	−	26.7772i	1.28388	−	1.06514i
$633$	8.07336			0.320887
$634$	1.55707	−	0.365972i	0.0618392	−	0.0145346i
$635$	−3.40666			−0.135189
$636$	−0.682957	+	0.339815i	−0.0270810	+	0.0134745i
$637$		−	9.02561i		−	0.357608i
$638$	3.16667	+	13.4730i	0.125370	+	0.533400i
$639$	6.85136			0.271036
$640$	46.2788	−	2.09056i	1.82933	−	0.0826366i
$641$			19.8280i			0.783159i	0.920144	+	0.391579i	$0.128071\pi$
$641$			19.8280i			0.783159i	−0.920144	+	0.391579i	$0.871929\pi$
$642$	−4.65723	+	1.09463i	−0.183806	+	0.0432015i
$643$	−11.3976			−0.449476			−0.224738	−	0.974419i	$-0.572153\pi$
$643$	−11.3976			−0.449476			−0.224738	+	0.974419i	$0.572153\pi$
$644$	20.3564	+	40.9121i	0.802153	+	1.61216i
$645$	17.1516			0.675345
$646$	−24.9884	+	5.87324i	−0.983156	+	0.231079i
$647$	−11.0560			−0.434658			−0.217329	−	0.976098i	$-0.569734\pi$
$647$	−11.0560			−0.434658			−0.217329	+	0.976098i	$0.569734\pi$
$648$	−15.6513	+	12.9847i	−0.614839	+	0.510085i
$649$			27.4202i			1.07634i
$650$	12.7156	+	54.1002i	0.498748	+	2.12199i
$651$			9.50215i			0.372419i
$652$	5.38362	−	2.67870i	0.210839	−	0.104906i
$653$	−24.0978			−0.943021			−0.471510	−	0.881861i	$-0.656291\pi$
$653$	−24.0978			−0.943021			−0.471510	+	0.881861i	$0.656291\pi$
$654$	8.50211	−	1.99832i	0.332459	−	0.0781407i
$655$			25.9578i			1.01426i
$656$	−18.8284	−	14.2364i	−0.735127	−	0.555840i
$657$		−	15.7115i		−	0.612963i
$658$	16.3988	−	3.85436i	0.639294	−	0.150259i
$659$	3.41601			0.133069			0.0665345	−	0.997784i	$-0.478806\pi$
$659$	3.41601			0.133069			0.0665345	+	0.997784i	$0.478806\pi$
$660$	−8.90909	−	17.9054i	−0.346786	−	0.696967i
$661$		−	18.5312i		−	0.720782i	−0.932801	−	0.360391i	$-0.882643\pi$
$661$		−	18.5312i		−	0.720782i	0.932801	−	0.360391i	$-0.117357\pi$
$662$	2.00548	−	0.471365i	0.0779452	−	0.0183201i
$663$		−	5.82606i		−	0.226266i
$664$	−33.8963	+	28.1212i	−1.31543	+	1.09131i
$665$			60.2075i			2.33475i
$666$	−5.67907	−	24.1623i	−0.220060	−	0.936271i
$667$	−13.3358			−0.516363
$668$	11.9745	−	22.9044i	0.463309	−	0.886197i
$669$	−7.02585			−0.271635
$670$	4.41577	+	18.7874i	0.170596	+	0.725822i
$671$		−	20.1267i		−	0.776981i
$672$	−3.23446	+	7.31041i	−0.124772	+	0.282005i
$673$		−	19.0484i		−	0.734263i	−0.930169	−	0.367132i	$-0.880340\pi$
$673$		−	19.0484i		−	0.734263i	0.930169	−	0.367132i	$-0.119660\pi$
$674$	−30.0689	+	7.06735i	−1.15821	+	0.272224i
$675$		−	30.9302i		−	1.19050i
$676$	3.30525	−	1.64457i	0.127125	−	0.0632527i
$677$	−44.9999			−1.72949			−0.864744	−	0.502213i	$-0.832519\pi$
$677$	−44.9999			−1.72949			−0.864744	+	0.502213i	$0.832519\pi$
$678$	−12.1372	+	2.85271i	−0.466127	+	0.109558i
$679$		−	31.5781i		−	1.21186i
$680$	−34.2731	+	28.4338i	−1.31431	+	1.09038i
$681$		−	12.2545i		−	0.469595i
$682$	−49.8301	+	11.7120i	−1.90809	+	0.448475i
$683$	12.3014			0.470699			0.235350	−	0.971911i	$-0.424376\pi$
$683$	12.3014			0.470699			0.235350	+	0.971911i	$0.424376\pi$
$684$	−11.7514	−	23.6179i	−0.449327	−	0.903053i
$685$			19.5142i			0.745601i
$686$	4.33150	+	18.4289i	0.165378	+	0.703619i
$687$			3.24543i			0.123821i
$688$	22.2741	−	29.4586i	0.849190	−	1.12310i
$689$	−2.80780			−0.106969
$690$	18.7594	−	4.40918i	0.714158	−	0.167855i
$691$	−19.7121			−0.749885			−0.374942	−	0.927048i	$-0.622338\pi$
$691$	−19.7121			−0.749885			−0.374942	+	0.927048i	$0.622338\pi$
$692$	29.1085	−	14.4833i	1.10654	−	0.550574i
$693$	−46.8505			−1.77970
$694$	−29.1609	+	6.85394i	−1.10693	+	0.260172i
$695$		−	21.9944i		−	0.834294i
$696$	−1.48956	−	1.79546i	−0.0564616	−	0.0680568i
$697$	22.6908			0.859476
$698$	6.85710	+	29.1744i	0.259545	+	1.10427i
$699$			2.10696i			0.0796924i
$700$	32.6535	+	65.6268i	1.23419	+	2.48046i
$701$	0.0611077			0.00230800			0.00115400	−	0.999999i	$-0.499633\pi$
$701$	0.0611077			0.00230800			0.00115400	+	0.999999i	$0.499633\pi$
$702$	12.0864	−	2.84076i	0.456170	−	0.107218i
$703$	29.6508			1.11830
$704$	−42.3231	−	7.95126i	−1.59511	−	0.299674i
$705$		−	7.10397i		−	0.267551i
$706$	20.1418	−	4.73409i	0.758046	−	0.178170i
$707$	−44.7317			−1.68231
$708$	−2.05895	−	4.13806i	−0.0773800	−	0.155518i
$709$			29.5642i			1.11031i	0.831748	+	0.555153i	$0.187340\pi$
$709$			29.5642i			1.11031i	−0.831748	+	0.555153i	$0.812660\pi$
$710$	3.24878	+	13.8223i	0.121925	+	0.518743i
$711$	−41.4299			−1.55374
$712$	4.77557	−	3.96192i	0.178972	−	0.148479i
$713$		−	49.3226i		−	1.84715i
$714$	−1.75823	−	7.48062i	−0.0658002	−	0.279955i
$715$		−	73.6134i		−	2.75298i
$716$	15.5544	+	31.2611i	0.581294	+	1.16828i
$717$	−6.47194			−0.241699
$718$	3.84331	+	16.3519i	0.143431	+	0.610246i
$719$	−18.3064			−0.682713			−0.341356	−	0.939934i	$-0.610886\pi$
$719$	−18.3064			−0.682713			−0.341356	+	0.939934i	$0.610886\pi$
$720$	−36.5046	−	27.6016i	−1.36045	−	1.02865i
$721$			15.4738i			0.576273i
$722$	4.52015	−	1.06241i	0.168222	−	0.0395387i
$723$	9.01979			0.335450
$724$	16.8238	−	8.37091i	0.625251	−	0.311102i
$725$	−21.3919			−0.794473
$726$	2.63888	+	11.2274i	0.0979379	+	0.416689i
$727$	−36.8308			−1.36598			−0.682989	−	0.730429i	$-0.739320\pi$
$727$	−36.8308			−1.36598			−0.682989	+	0.730429i	$0.739320\pi$
$728$	−22.6455	+	18.7872i	−0.839297	+	0.696301i
$729$	16.5122			0.611565
$730$	31.6973	−	7.45008i	1.17317	−	0.275740i
$731$			35.5016i			1.31307i
$732$	1.51129	+	3.03737i	0.0558587	+	0.112264i
$733$	11.4130			0.421549			0.210774	−	0.977535i	$-0.432401\pi$
$733$	11.4130			0.421549			0.210774	+	0.977535i	$0.432401\pi$
$734$	1.06839	+	4.54560i	0.0394350	+	0.167781i
$735$	−5.02026			−0.185175
$736$	16.7891	−	37.9460i	0.618853	−	1.39871i
$737$		−	17.9403i		−	0.660838i
$738$	5.33546	+	22.7004i	0.196401	+	0.835612i
$739$	42.0638			1.54734			0.773671	−	0.633587i	$-0.218418\pi$
$739$	42.0638			1.54734			0.773671	+	0.633587i	$0.218418\pi$
$740$	46.0536	−	22.9146i	1.69296	−	0.842357i
$741$			7.15246i			0.262752i
$742$	−3.60519	+	0.847358i	−0.132351	+	0.0311075i
$743$			33.8468i			1.24172i	0.783921	+	0.620860i	$0.213216\pi$
$743$			33.8468i			1.24172i	−0.783921	+	0.620860i	$0.786784\pi$
$744$	6.64055	−	5.50916i	0.243454	−	0.201976i
$745$	33.1271			1.21368
$746$	−1.46337	−	6.22607i	−0.0535777	−	0.227953i
$747$	43.5094			1.59192
$748$	37.0618	−	18.4406i	1.35512	−	0.674256i
$749$	−23.2264			−0.848675
$750$	17.3047	−	4.06726i	0.631877	−	0.148515i
$751$	−2.74827			−0.100286			−0.0501428	−	0.998742i	$-0.515968\pi$
$751$	−2.74827			−0.100286			−0.0501428	+	0.998742i	$0.515968\pi$
$752$	−12.2013	−	9.22561i	−0.444937	−	0.336423i
$753$	−1.15149			−0.0419626
$754$	−1.96472	−	8.35914i	−0.0715508	−	0.304422i
$755$		−	7.53808i		−	0.274339i
$756$	14.6615	−	7.29502i	0.533233	−	0.265317i
$757$	6.57654			0.239028			0.119514	−	0.992832i	$-0.461866\pi$
$757$	6.57654			0.239028			0.119514	+	0.992832i	$0.461866\pi$
$758$	−41.7273	+	9.80753i	−1.51561	+	0.356226i
$759$	−17.9135			−0.650218
$760$	42.0759	−	34.9071i	1.52625	−	1.26622i
$761$	−16.9887			−0.615841			−0.307921	−	0.951412i	$-0.599633\pi$
$761$	−16.9887			−0.615841			−0.307921	+	0.951412i	$0.599633\pi$
$762$	−0.519632	+	0.122133i	−0.0188243	+	0.00442443i
$763$	42.4015			1.53504
$764$	7.75839	+	15.5927i	0.280689	+	0.564126i
$765$	43.9930			1.59057
$766$	−3.45501	−	14.6998i	−0.124835	−	0.531124i
$767$		−	17.0125i		−	0.614287i
$768$	6.98414	−	1.97804i	0.252019	−	0.0713764i
$769$		−	47.2709i		−	1.70463i	−0.523026	−	0.852317i	$-0.675197\pi$
$769$		−	47.2709i		−	1.70463i	0.523026	−	0.852317i	$-0.324803\pi$
$770$	−22.2156	−	94.5189i	−0.800594	−	3.40623i
$771$	1.24245			0.0447457
$772$	1.44171	+	2.89755i	0.0518884	+	0.104285i
$773$		−	11.1338i		−	0.400455i	−0.979749	−	0.200227i	$-0.935832\pi$
$773$		−	11.1338i		−	0.400455i	0.979749	−	0.200227i	$-0.0641681\pi$
$774$	−35.5165	+	8.34775i	−1.27662	+	0.300054i
$775$		−	79.1182i		−	2.84201i
$776$	−22.0683	+	18.3084i	−0.792206	+	0.657233i
$777$			8.87635i			0.318437i
$778$	−10.6278	−	45.2173i	−0.381026	−	1.62112i
$779$	−27.8567			−0.998071
$780$	5.52753	+	11.1092i	0.197917	+	0.397773i
$781$		−	13.1990i		−	0.472299i
$782$	9.12642	+	38.8295i	0.326360	+	1.38854i
$783$			4.77909i			0.170791i
$784$	−6.51959	+	8.62250i	−0.232843	+	0.307946i
$785$			81.7240i			2.91686i
$786$	0.930624	+	3.95945i	0.0331943	+	0.141229i
$787$	−28.1723			−1.00424			−0.502118	−	0.864799i	$-0.667446\pi$
$787$	−28.1723			−1.00424			−0.502118	+	0.864799i	$0.667446\pi$
$788$	−3.14051	−	6.31178i	−0.111876	−	0.224848i
$789$	0.841859			0.0299710
$790$	−19.6452	−	83.5831i	−0.698946	−	2.97375i
$791$	−60.5303			−2.15221
$792$	27.1630	+	32.7413i	0.965195	+	1.16341i
$793$			12.4873i			0.443438i
$794$	−34.9593	+	8.21677i	−1.24066	+	0.291602i
$795$			1.56177i			0.0553901i
$796$	−1.24509	−	2.50238i	−0.0441312	−	0.0886946i
$797$			5.40908i			0.191599i	0.995401	+	0.0957997i	$0.0305408\pi$
$797$			5.40908i			0.191599i	−0.995401	+	0.0957997i	$0.969459\pi$
$798$	2.15852	+	9.18369i	0.0764108	+	0.325099i
$799$	14.7043			0.520200
$800$	26.9313	−	60.8690i	0.952164	−	2.15204i
$801$	−6.12993			−0.216590
$802$	−2.88708	−	12.2834i	−0.101946	−	0.433743i
$803$	−30.2679			−1.06813
$804$	1.34711	+	2.70741i	0.0475089	+	0.0954831i
$805$	93.5564			3.29743
$806$	30.9164	−	7.26655i	1.08898	−	0.255953i
$807$	5.41769			0.190712
$808$	25.9345	+	31.2606i	0.912374	+	1.09974i
$809$	3.70771			0.130356			0.0651781	−	0.997874i	$-0.479238\pi$
$809$	3.70771			0.130356			0.0651781	+	0.997874i	$0.479238\pi$
$810$	9.52628	+	40.5307i	0.334719	+	1.42410i
$811$	−29.3963			−1.03224			−0.516121	−	0.856516i	$-0.672625\pi$
$811$	−29.3963			−1.03224			−0.516121	+	0.856516i	$0.672625\pi$
$812$	−5.04537	−	10.1401i	−0.177058	−	0.355849i
$813$			0.325863i			0.0114285i
$814$	−46.5483	+	10.9406i	−1.63152	+	0.383469i
$815$		−	12.3111i		−	0.431239i
$816$	−4.20842	+	5.56585i	−0.147324	+	0.194844i
$817$		−	43.5841i		−	1.52481i
$818$	11.0503	−	2.59725i	0.386366	−	0.0908108i
$819$	29.0678			1.01571
$820$	−43.2671	+	21.5281i	−1.51095	+	0.751795i
$821$		−	1.22486i		−	0.0427478i	−0.999772	−	0.0213739i	$-0.993196\pi$
$821$		−	1.22486i		−	0.0427478i	0.999772	−	0.0213739i	$-0.00680405\pi$
$822$	0.699612	+	2.97659i	0.0244018	+	0.103820i
$823$	−38.1585			−1.33012			−0.665061	−	0.746789i	$-0.731595\pi$
$823$	−38.1585			−1.33012			−0.665061	+	0.746789i	$0.731595\pi$
$824$	10.8138	−	8.97139i	0.376717	−	0.312533i
$825$	−28.7349			−1.00042
$826$	−5.13417	−	21.8439i	−0.178641	−	0.760048i
$827$	35.4902			1.23412			0.617058	−	0.786918i	$-0.288324\pi$
$827$	35.4902			1.23412			0.617058	+	0.786918i	$0.288324\pi$
$828$	−36.6998	+	18.2605i	−1.27541	+	0.634597i
$829$			13.9873i			0.485798i	0.970052	+	0.242899i	$0.0780983\pi$
$829$			13.9873i			0.485798i	−0.970052	+	0.242899i	$0.921902\pi$
$830$	20.6313	+	87.7783i	0.716122	+	3.04683i
$831$	10.1400			0.351754
$832$	26.2588	+	4.93326i	0.910361	+	0.171030i
$833$		−	10.3913i		−	0.360037i
$834$	−0.788528	−	3.35489i	−0.0273045	−	0.116170i
$835$	−31.0622	−	42.8384i	−1.07495	−	1.48248i
$836$	−45.4995	+	22.6389i	−1.57363	+	0.782984i
$837$	−17.6755			−0.610956
$838$	−4.68071	−	19.9147i	−0.161693	−	0.687941i
$839$		−	8.51876i		−	0.294100i	−0.989129	−	0.147050i	$-0.953022\pi$
$839$		−	8.51876i		−	0.294100i	0.989129	−	0.147050i	$-0.0469779\pi$
$840$	10.4499	+	12.5960i	0.360557	+	0.434602i
$841$	−25.6947			−0.886024
$842$	−51.9572	+	12.2119i	−1.79056	+	0.420851i
$843$			8.17116i			0.281430i
$844$	−15.8545	−	31.8643i	−0.545735	−	1.09681i
$845$		−	7.55833i		−	0.260014i
$846$	3.45752	+	14.7105i	0.118872	+	0.505756i
$847$			55.9931i			1.92395i
$848$	2.68239	+	2.02819i	0.0921137	+	0.0696485i
$849$	5.29341			0.181669
$850$	14.6397	+	62.2862i	0.502136	+	2.13640i
$851$		−	46.0743i		−	1.57941i
$852$	0.991099	+	1.99190i	0.0339545	+	0.0682415i
$853$	−43.4439			−1.48749			−0.743745	−	0.668464i	$-0.766952\pi$
$853$	−43.4439			−1.48749			−0.743745	+	0.668464i	$0.766952\pi$
$854$	3.76852	+	16.0336i	0.128956	+	0.548660i
$855$	−54.0087			−1.84706
$856$	13.4662	+	16.2317i	0.460266	+	0.554789i
$857$	−0.371375			−0.0126859			−0.00634297	−	0.999980i	$-0.502019\pi$
$857$	−0.371375			−0.0126859			−0.00634297	+	0.999980i	$0.502019\pi$
$858$	−2.63914	−	11.2285i	−0.0900987	−	0.383336i
$859$			31.0646i			1.05991i	0.848025	+	0.529956i	$0.177791\pi$
$859$			31.0646i			1.05991i	−0.848025	+	0.529956i	$0.822209\pi$
$860$	−33.6825	−	67.6948i	−1.14856	−	2.30837i
$861$		−	8.33929i		−	0.284202i
$862$	10.1169	+	43.0435i	0.344582	+	1.46607i
$863$			3.14072i			0.106911i	0.998570	+	0.0534557i	$0.0170236\pi$
$863$			3.14072i			0.106911i	−0.998570	+	0.0534557i	$0.982976\pi$
$864$	−13.5986	−	6.01663i	−0.462632	−	0.204690i
$865$		−	66.5644i		−	2.26326i
$866$	16.6456	−	3.91235i	0.565640	−	0.132947i
$867$			1.00492i			0.0341288i
$868$	37.5035	−	18.6604i	1.27295	−	0.633375i
$869$			79.8140i			2.70751i
$870$	−4.64956	+	1.09282i	−0.157635	+	0.0370502i
$871$			11.1308i			0.377153i
$872$	−24.5836	−	29.6322i	−0.832505	−	1.00347i
$873$	28.3269			0.958721
$874$	−11.2042	−	47.6696i	−0.378987	−	1.61245i
$875$	86.3013			2.91752
$876$	4.56782	−	2.27278i	0.154332	−	0.0767902i
$877$	45.3738			1.53216			0.766082	−	0.642743i	$-0.222204\pi$
$877$	45.3738			1.53216			0.766082	+	0.642743i	$0.222204\pi$
$878$	−4.39249	+	1.03240i	−0.148239	+	0.0348419i
$879$		−	6.91818i		−	0.233344i
$880$	−53.1741	+	70.3255i	−1.79250	+	2.37067i
$881$			37.5825i			1.26619i	0.774075	+	0.633094i	$0.218215\pi$
$881$			37.5825i			1.26619i	−0.774075	+	0.633094i	$0.781785\pi$
$882$	10.3956	−	2.44338i	0.350040	−	0.0822728i
$883$		−	31.9319i		−	1.07460i	−0.843393	−	0.537298i	$-0.819445\pi$
$883$		−	31.9319i		−	1.07460i	0.843393	−	0.537298i	$-0.180555\pi$
$884$	−22.9946	+	11.4413i	−0.773391	+	0.384811i
$885$	−9.46278			−0.318088
$886$	−31.7734	+	7.46798i	−1.06745	+	0.250892i
$887$	−22.0611			−0.740739			−0.370369	−	0.928885i	$-0.620769\pi$
$887$	−22.0611			−0.740739			−0.370369	+	0.928885i	$0.620769\pi$
$888$	6.20322	−	5.14634i	0.208166	−	0.172700i
$889$	−2.59149			−0.0869159
$890$	−2.90669	−	12.3669i	−0.0974325	−	0.414539i
$891$		−	38.7031i		−	1.29660i
$892$	13.7974	+	27.7299i	0.461972	+	0.928467i
$893$	−18.0519			−0.604085
$894$	5.05301	−	1.18765i	0.168998	−	0.0397210i
$895$	71.4868			2.38954
$896$	35.2049	−	1.59032i	1.17611	−	0.0531288i
$897$	11.1142			0.371092
$898$	50.3568	−	11.8358i	1.68043	−	0.394965i
$899$			12.2247i			0.407717i
$900$	−58.8701	+	29.2916i	−1.96234	+	0.976387i
$901$	−3.23265			−0.107695
$902$	43.7319	−	10.2787i	1.45611	−	0.342243i
$903$	13.0475			0.434193
$904$	35.0943	+	42.3015i	1.16722	+	1.40693i
$905$		−	38.4721i		−	1.27886i
$906$	−0.270250	−	1.14981i	−0.00897846	−	0.0382000i
$907$			41.2005i			1.36804i	0.729463	+	0.684020i	$0.239770\pi$
$907$			41.2005i			1.36804i	−0.729463	+	0.684020i	$0.760230\pi$
$908$	−48.3667	+	24.0655i	−1.60511	+	0.798642i
$909$		−	40.1262i		−	1.33090i
$910$	13.7834	+	58.6431i	0.456915	+	1.94400i
$911$			36.8365i			1.22045i	0.792229	+	0.610224i	$0.208921\pi$
$911$			36.8365i			1.22045i	−0.792229	+	0.610224i	$0.791079\pi$
$912$	5.16653	−	6.83300i	0.171081	−	0.226263i
$913$		−	83.8201i		−	2.77404i
$914$	−6.94486	−	29.5478i	−0.229715	−	0.977353i
$915$	6.94576			0.229620
$916$	12.8092	−	6.37339i	0.423228	−	0.210583i
$917$			19.7465i			0.652086i
$918$	13.9152	−	3.27060i	0.459269	−	0.107946i
$919$			30.0188i			0.990228i	0.868828	+	0.495114i	$0.164874\pi$
$919$			30.0188i			0.990228i	−0.868828	+	0.495114i	$0.835126\pi$
$920$	−54.2422	−	65.3817i	−1.78831	−	2.15557i
$921$		−	1.96512i		−	0.0647528i
$922$	−44.1641	+	10.3803i	−1.45447	+	0.341856i
$923$			8.18918i			0.269550i
$924$	−6.77727	−	13.6209i	−0.222956	−	0.448095i
$925$		−	73.9076i		−	2.43007i
$926$	−0.614905	+	0.144526i	−0.0202070	+	0.00474943i
$927$	−13.8806			−0.455900
$928$	−4.16120	+	9.40499i	−0.136598	+	0.308734i
$929$	40.3097			1.32252			0.661260	−	0.750157i	$-0.270022\pi$
$929$	40.3097			1.32252			0.661260	+	0.750157i	$0.270022\pi$
$930$	−4.04183	−	17.1965i	−0.132537	−	0.563895i
$931$			12.7570i			0.418094i
$932$	8.31582	−	4.13765i	0.272394	−	0.135533i
$933$	4.36280			0.142832
$934$	−3.09598	−	13.1722i	−0.101304	−	0.431008i
$935$		−	84.7518i		−	2.77168i
$936$	−16.8529	−	20.3140i	−0.550856	−	0.663982i
$937$			26.1507i			0.854305i	0.904180	+	0.427152i	$0.140483\pi$
$937$			26.1507i			0.854305i	−0.904180	+	0.427152i	$0.859517\pi$
$938$	3.35914	+	14.2919i	0.109680	+	0.466646i
$939$	−10.0679			−0.328553
$940$	−28.0383	+	13.9508i	−0.914507	+	0.455026i
$941$			13.1344i			0.428169i	0.976815	+	0.214085i	$0.0686768\pi$
$941$			13.1344i			0.428169i	−0.976815	+	0.214085i	$0.931323\pi$
$942$	2.92992	+	12.4657i	0.0954619	+	0.406154i
$943$			43.2866i			1.40960i
$944$	−12.2889	+	16.2527i	−0.399969	+	0.528980i
$945$		−	33.5274i		−	1.09065i
$946$	16.0818	+	68.4220i	0.522865	+	2.22459i
$947$			35.6303i			1.15783i	0.815389	+	0.578914i	$0.196523\pi$
$947$			35.6303i			1.15783i	−0.815389	+	0.578914i	$0.803477\pi$
$948$	−5.99314	−	12.0450i	−0.194648	−	0.391202i
$949$	18.7794			0.609604
$950$	−17.9726	−	76.4666i	−0.583108	−	2.48090i
$951$		−	0.513118i		−	0.0166390i
$952$	−26.0720	+	21.6299i	−0.844998	+	0.701031i
$953$			47.0633i			1.52453i	0.647266	+	0.762264i	$0.275912\pi$
$953$			47.0633i			1.52453i	−0.647266	+	0.762264i	$0.724088\pi$
$954$	−0.760116	−	3.23401i	−0.0246097	−	0.104705i
$955$	35.6570			1.15383
$956$	12.7096	+	25.5437i	0.411059	+	0.826143i
$957$	4.43989			0.143521
$958$	−31.7970	+	7.47353i	−1.02732	+	0.241459i
$959$			14.8448i			0.479362i
$960$	2.74400	−	14.6058i	0.0885622	−	0.471400i
$961$	−14.2133			−0.458494
$962$	28.8803	−	6.78799i	0.931139	−	0.218853i
$963$		−	20.8351i		−	0.671401i
$964$	−17.7131	−	35.5997i	−0.570501	−	1.14659i
$965$	6.62602			0.213299
$966$	14.2705	−	3.35412i	0.459147	−	0.107917i
$967$		−	27.9462i		−	0.898689i	−0.893359	−	0.449345i	$-0.851658\pi$
$967$		−	27.9462i		−	0.898689i	0.893359	−	0.449345i	$-0.148342\pi$
$968$	39.1306	−	32.4637i	1.25771	−	1.04342i
$969$			8.23470i			0.264537i
$970$	13.4321	+	57.1484i	0.431278	+	1.83492i
$971$	−16.9832			−0.545018			−0.272509	−	0.962153i	$-0.587853\pi$
$971$	−16.9832			−0.545018			−0.272509	+	0.962153i	$0.587853\pi$
$972$	9.93215	+	19.9616i	0.318574	+	0.640267i
$973$		−	16.7314i		−	0.536384i
$974$	−17.9290	+	4.21401i	−0.574483	+	0.135026i
$975$	17.8282			0.570960
$976$	9.02015	−	11.9296i	0.288728	−	0.381858i
$977$			17.5597i			0.561784i	0.959739	+	0.280892i	$0.0906304\pi$
$977$			17.5597i			0.561784i	−0.959739	+	0.280892i	$0.909370\pi$
$978$	−0.441370	−	1.87786i	−0.0141134	−	0.0600474i
$979$			11.8092i			0.377424i
$980$	9.85883	+	19.8142i	0.314929	+	0.632941i
$981$			38.0359i			1.21439i
$982$	−9.08365	−	38.6475i	−0.289871	−	1.23329i
$983$	43.8125			1.39740			0.698700	−	0.715414i	$-0.253762\pi$
$983$	43.8125			1.39740			0.698700	+	0.715414i	$0.253762\pi$
$984$	−5.82789	+	4.83496i	−0.185786	+	0.154133i
$985$	−14.4336			−0.459892
$986$	−2.26200	−	9.62396i	−0.0720368	−	0.306489i
$987$		−	5.40409i		−	0.172014i
$988$	28.2296	−	14.0460i	0.898104	−	0.446864i
$989$	−67.7253			−2.15354
$990$	84.7875	−	19.9283i	2.69472	−	0.633363i
$991$	−19.3421			−0.614421			−0.307210	−	0.951642i	$-0.599395\pi$
$991$	−19.3421			−0.614421			−0.307210	+	0.951642i	$0.599395\pi$
$992$	−34.7846	−	15.3903i	−1.10441	−	0.488642i
$993$		−	0.660888i		−	0.0209726i
$994$	2.47139	+	10.5148i	0.0783878	+	0.333510i
$995$	−5.72237			−0.181411
$996$	6.29395	+	12.6495i	0.199431	+	0.400816i
$997$	12.1424			0.384552			0.192276	−	0.981341i	$-0.438413\pi$
$997$	12.1424			0.384552			0.192276	+	0.981341i	$0.438413\pi$
$998$	−48.1085	+	11.3074i	−1.52285	+	0.357928i
$999$	−16.5115			−0.522399

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	668.2.b.b.667.7	yes	60
4.3	odd	2	inner	668.2.b.b.667.5	✓	60
167.166	odd	2	inner	668.2.b.b.667.8	yes	60
668.667	even	2	inner	668.2.b.b.667.6	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
668.2.b.b.667.5	✓	60	4.3	odd	2	inner
668.2.b.b.667.6	yes	60	668.667	even	2	inner
668.2.b.b.667.7	yes	60	1.1	even	1	trivial
668.2.b.b.667.8	yes	60	167.166	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 668 = 2^{2} \cdot 167 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	668.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37670 + 0.323577i) q^{2} +0.453678i q^{3} +(1.79060 - 0.890936i) q^{4} -4.09468i q^{5} +(-0.146800 - 0.624578i) q^{6} -3.11488i q^{7} +(-2.17682 + 1.80595i) q^{8} +2.79418 q^{9} +O(q^{10})\)	\(q+(-1.37670 + 0.323577i) q^{2} +0.453678i q^{3} +(1.79060 - 0.890936i) q^{4} -4.09468i q^{5} +(-0.146800 - 0.624578i) q^{6} -3.11488i q^{7} +(-2.17682 + 1.80595i) q^{8} +2.79418 q^{9} +(1.32494 + 5.63714i) q^{10} -5.38294i q^{11} +(0.404198 + 0.812354i) q^{12} +3.33978i q^{13} +(1.00790 + 4.28825i) q^{14} +1.85767 q^{15} +(2.41247 - 3.19061i) q^{16} +3.84512i q^{17} +(-3.84674 + 0.904131i) q^{18} -4.72052i q^{19} +(-3.64809 - 7.33191i) q^{20} +1.41315 q^{21} +(1.74180 + 7.41068i) q^{22} -7.33522 q^{23} +(-0.819318 - 0.987577i) q^{24} -11.7664 q^{25} +(-1.08067 - 4.59786i) q^{26} +2.62869i q^{27} +(-2.77516 - 5.57749i) q^{28} +1.81805 q^{29} +(-2.55744 + 0.601098i) q^{30} +6.72408i q^{31} +(-2.28883 + 5.17313i) q^{32} +2.44212 q^{33} +(-1.24419 - 5.29357i) q^{34} -12.7544 q^{35} +(5.00324 - 2.48943i) q^{36} +6.28125i q^{37} +(1.52745 + 6.49873i) q^{38} -1.51518 q^{39} +(7.39476 + 8.91339i) q^{40} -5.90120i q^{41} +(-1.94548 + 0.457263i) q^{42} +9.23290 q^{43} +(-4.79585 - 9.63867i) q^{44} -11.4413i q^{45} +(10.0984 - 2.37351i) q^{46} -3.82414i q^{47} +(1.44751 + 1.09448i) q^{48} -2.70246 q^{49} +(16.1988 - 3.80733i) q^{50} -1.74445 q^{51} +(2.97553 + 5.98019i) q^{52} +0.840714i q^{53} +(-0.850584 - 3.61891i) q^{54} -22.0414 q^{55} +(5.62530 + 6.78054i) q^{56} +2.14160 q^{57} +(-2.50290 + 0.588279i) q^{58} -5.09391 q^{59} +(3.32633 - 1.65506i) q^{60} +3.73897 q^{61} +(-2.17576 - 9.25704i) q^{62} -8.70352i q^{63} +(1.47712 - 7.86245i) q^{64} +13.6753 q^{65} +(-3.36206 + 0.790214i) q^{66} +3.33280 q^{67} +(3.42576 + 6.88506i) q^{68} -3.32783i q^{69} +(17.5590 - 4.12704i) q^{70} +2.45201 q^{71} +(-6.08243 + 5.04613i) q^{72} -5.62294i q^{73} +(-2.03247 - 8.64738i) q^{74} -5.33815i q^{75} +(-4.20568 - 8.45255i) q^{76} -16.7672 q^{77} +(2.08595 - 0.490279i) q^{78} -14.8272 q^{79} +(-13.0645 - 9.87827i) q^{80} +7.18995 q^{81} +(1.90949 + 8.12417i) q^{82} +15.5714 q^{83} +(2.53038 - 1.25903i) q^{84} +15.7445 q^{85} +(-12.7109 + 2.98755i) q^{86} +0.824808i q^{87} +(9.72129 + 11.7177i) q^{88} -2.19382 q^{89} +(3.70213 + 15.7511i) q^{90} +10.4030 q^{91} +(-13.1344 + 6.53521i) q^{92} -3.05057 q^{93} +(1.23740 + 5.26469i) q^{94} -19.3290 q^{95} +(-2.34693 - 1.03839i) q^{96} +10.1378 q^{97} +(3.72047 - 0.874454i) q^{98} -15.0409i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 2 q^{2} + 2 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9}+O(q^{10}) \) 60 * q - 2 * q^2 + 2 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9	\( 60 q - 2 q^{2} + 2 q^{4} - 8 q^{6} - 8 q^{8} - 16 q^{9} + 18 q^{12} + 10 q^{14} + 10 q^{16} - 20 q^{18} + 20 q^{22} + 10 q^{24} - 188 q^{25} + 4 q^{29} + 18 q^{32} + 8 q^{33} + 30 q^{36} - 36 q^{38} + 14 q^{42} + 28 q^{44} - 28 q^{48} + 72 q^{49} - 40 q^{50} - 74 q^{54} + 50 q^{56} + 8 q^{57} - 22 q^{58} + 36 q^{61} + 104 q^{62} + 8 q^{64} + 24 q^{65} + 24 q^{66} + 90 q^{72} - 36 q^{76} - 84 q^{81} - 110 q^{84} - 16 q^{85} - 20 q^{88} + 28 q^{89} + 72 q^{93} + 90 q^{94} + 2 q^{96} - 4 q^{97} - 114 q^{98}+O(q^{100}) \) 60 * q - 2 * q^2 + 2 * q^4 - 8 * q^6 - 8 * q^8 - 16 * q^9 + 18 * q^12 + 10 * q^14 + 10 * q^16 - 20 * q^18 + 20 * q^22 + 10 * q^24 - 188 * q^25 + 4 * q^29 + 18 * q^32 + 8 * q^33 + 30 * q^36 - 36 * q^38 + 14 * q^42 + 28 * q^44 - 28 * q^48 + 72 * q^49 - 40 * q^50 - 74 * q^54 + 50 * q^56 + 8 * q^57 - 22 * q^58 + 36 * q^61 + 104 * q^62 + 8 * q^64 + 24 * q^65 + 24 * q^66 + 90 * q^72 - 36 * q^76 - 84 * q^81 - 110 * q^84 - 16 * q^85 - 20 * q^88 + 28 * q^89 + 72 * q^93 + 90 * q^94 + 2 * q^96 - 4 * q^97 - 114 * q^98

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