LMFDB - Embedded newform 690.2.q.a.251.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(11,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 0, 9]))

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

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

chi := DirichletCharacter("690.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.q (of order $22$, degree $10$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			251.7
Character	$\chi$	$=$	690.251
Dual form			690.2.q.a.11.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.540641 + 0.841254i) q^{2} +(1.47579 + 0.906664i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(-1.56061 + 0.751335i) q^{6} +(-1.93677 - 1.67822i) q^{7} +(0.989821 + 0.142315i) q^{8} +(1.35592 + 2.67609i) q^{9} +O(q^{10})$	\(q+(-0.540641 + 0.841254i) q^{2} +(1.47579 + 0.906664i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(-1.56061 + 0.751335i) q^{6} +(-1.93677 - 1.67822i) q^{7} +(0.989821 + 0.142315i) q^{8} +(1.35592 + 2.67609i) q^{9} +(0.755750 - 0.654861i) q^{10} +(4.86446 - 3.12620i) q^{11} +(0.211665 - 1.71907i) q^{12} +(2.75804 + 3.18294i) q^{13} +(2.45891 - 0.722000i) q^{14} +(-1.16057 - 1.28572i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(1.02470 - 2.24378i) q^{17} +(-2.98434 - 0.306134i) q^{18} +(-1.20876 + 0.552021i) q^{19} +(0.142315 + 0.989821i) q^{20} +(-1.33669 - 4.23270i) q^{21} +5.78240i q^{22} +(4.03585 + 2.59074i) q^{23} +(1.33174 + 1.10746i) q^{24} +(0.841254 + 0.540641i) q^{25} +(-4.16877 + 0.599378i) q^{26} +(-0.425265 + 5.17872i) q^{27} +(-0.722000 + 2.45891i) q^{28} +(9.05831 + 4.13679i) q^{29} +(1.70907 - 0.281227i) q^{30} +(-1.06802 + 7.42827i) q^{31} +(-0.281733 - 0.959493i) q^{32} +(10.0133 - 0.203185i) q^{33} +(1.33359 + 2.07511i) q^{34} +(1.38551 + 2.15589i) q^{35} +(1.87099 - 2.34508i) q^{36} +(-0.831698 - 2.83250i) q^{37} +(0.189114 - 1.31532i) q^{38} +(1.18442 + 7.19797i) q^{39} +(-0.909632 - 0.415415i) q^{40} +(2.86232 - 9.74816i) q^{41} +(4.28344 + 1.16388i) q^{42} +(-8.83499 + 1.27028i) q^{43} +(-4.86446 - 3.12620i) q^{44} +(-0.547053 - 2.94970i) q^{45} +(-4.36141 + 1.99452i) q^{46} -1.54834i q^{47} +(-1.65165 + 0.521590i) q^{48} +(-0.0615513 - 0.428098i) q^{49} +(-0.909632 + 0.415415i) q^{50} +(3.54660 - 2.38229i) q^{51} +(1.74958 - 3.83104i) q^{52} +(-5.48005 + 6.32431i) q^{53} +(-4.12670 - 3.15758i) q^{54} +(-5.54817 + 1.62909i) q^{55} +(-1.67822 - 1.93677i) q^{56} +(-2.28437 - 0.281269i) q^{57} +(-8.37738 + 5.38382i) q^{58} +(2.63681 - 2.28481i) q^{59} +(-0.687409 + 1.58980i) q^{60} +(0.891151 + 0.128128i) q^{61} +(-5.67164 - 4.91451i) q^{62} +(1.86497 - 7.45851i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-1.74958 - 3.83104i) q^{65} +(-5.24269 + 8.53361i) q^{66} +(7.82353 - 12.1736i) q^{67} -2.46669 q^{68} +(3.60714 + 7.48255i) q^{69} -2.56271 q^{70} +(4.57179 - 7.11385i) q^{71} +(0.961271 + 2.84182i) q^{72} +(4.76049 + 10.4240i) q^{73} +(2.83250 + 0.831698i) q^{74} +(0.751335 + 1.56061i) q^{75} +(1.00427 + 0.870206i) q^{76} +(-14.6678 - 2.10891i) q^{77} +(-6.69567 - 2.89512i) q^{78} +(2.10799 - 1.82658i) q^{79} +(0.841254 - 0.540641i) q^{80} +(-5.32296 + 7.25714i) q^{81} +(6.65319 + 7.67819i) q^{82} +(-8.68171 + 2.54918i) q^{83} +(-3.29492 + 2.97422i) q^{84} +(-1.61534 + 1.86420i) q^{85} +(3.70793 - 8.11923i) q^{86} +(9.61749 + 14.3179i) q^{87} +(5.25985 - 2.40209i) q^{88} +(-1.22184 - 8.49808i) q^{89} +(2.77720 + 1.13452i) q^{90} -10.7932i q^{91} +(0.680064 - 4.74737i) q^{92} +(-8.31113 + 9.99424i) q^{93} +(1.30254 + 0.837094i) q^{94} +(1.31532 - 0.189114i) q^{95} +(0.454160 - 1.67145i) q^{96} +(-1.63510 + 5.56864i) q^{97} +(0.393416 + 0.179667i) q^{98} +(14.9618 + 8.77888i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9}+O(q^{10}) $ 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9	$ 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9} - 12 q^{11} - 12 q^{14} - 16 q^{16} - 8 q^{18} + 16 q^{20} + 62 q^{21} + 4 q^{23} + 2 q^{24} - 16 q^{25} + 42 q^{27} - 2 q^{30} - 4 q^{31} + 16 q^{33} + 2 q^{36} + 72 q^{38} - 124 q^{39} + 44 q^{41} + 44 q^{43} + 12 q^{44} - 2 q^{45} + 4 q^{46} + 70 q^{49} - 2 q^{51} - 52 q^{53} + 92 q^{54} + 10 q^{55} - 54 q^{56} - 38 q^{57} - 36 q^{58} - 44 q^{61} - 220 q^{63} + 16 q^{64} - 34 q^{66} - 44 q^{67} + 22 q^{69} - 12 q^{70} - 36 q^{72} - 28 q^{73} - 24 q^{74} - 88 q^{77} - 54 q^{78} - 44 q^{79} - 16 q^{80} - 66 q^{81} - 28 q^{82} + 4 q^{83} - 18 q^{84} + 158 q^{86} - 64 q^{87} + 80 q^{89} - 8 q^{90} - 4 q^{92} + 4 q^{93} + 24 q^{94} - 2 q^{96} - 88 q^{98} + 190 q^{99}+O(q^{100}) $ 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9 - 12 * q^11 - 12 * q^14 - 16 * q^16 - 8 * q^18 + 16 * q^20 + 62 * q^21 + 4 * q^23 + 2 * q^24 - 16 * q^25 + 42 * q^27 - 2 * q^30 - 4 * q^31 + 16 * q^33 + 2 * q^36 + 72 * q^38 - 124 * q^39 + 44 * q^41 + 44 * q^43 + 12 * q^44 - 2 * q^45 + 4 * q^46 + 70 * q^49 - 2 * q^51 - 52 * q^53 + 92 * q^54 + 10 * q^55 - 54 * q^56 - 38 * q^57 - 36 * q^58 - 44 * q^61 - 220 * q^63 + 16 * q^64 - 34 * q^66 - 44 * q^67 + 22 * q^69 - 12 * q^70 - 36 * q^72 - 28 * q^73 - 24 * q^74 - 88 * q^77 - 54 * q^78 - 44 * q^79 - 16 * q^80 - 66 * q^81 - 28 * q^82 + 4 * q^83 - 18 * q^84 + 158 * q^86 - 64 * q^87 + 80 * q^89 - 8 * q^90 - 4 * q^92 + 4 * q^93 + 24 * q^94 - 2 * q^96 - 88 * q^98 + 190 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{22}\right)$

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 $

$2$	−0.540641	+	0.841254i	−0.382291	+	0.594856i
$2$	−0.540641	+	0.841254i	−0.382291	+	0.594856i
$3$	1.47579	+	0.906664i	0.852048	+	0.523463i
$3$	1.47579	+	0.906664i	0.852048	+	0.523463i
$4$	−0.415415	−	0.909632i	−0.207708	−	0.454816i
$5$	−0.959493	−	0.281733i	−0.429098	−	0.125995i
$5$	−0.959493	−	0.281733i	−0.429098	−	0.125995i
$6$	−1.56061	+	0.751335i	−0.637115	+	0.306731i
$7$	−1.93677	−	1.67822i	−0.732030	−	0.634308i	0.206921	−	0.978358i	$-0.433656\pi$
$7$	−1.93677	−	1.67822i	−0.732030	−	0.634308i	−0.938951	+	0.344050i	$0.888201\pi$
$8$	0.989821	+	0.142315i	0.349955	+	0.0503159i
$9$	1.35592	+	2.67609i	0.451973	+	0.892031i
$10$	0.755750	−	0.654861i	0.238989	−	0.207085i
$11$	4.86446	−	3.12620i	1.46669	−	0.942585i	0.468438	−	0.883496i	$-0.344817\pi$
$11$	4.86446	−	3.12620i	1.46669	−	0.942585i	0.998253	−	0.0590884i	$-0.0188194\pi$
$12$	0.211665	−	1.71907i	0.0611024	−	0.496252i
$13$	2.75804	+	3.18294i	0.764941	+	0.882789i	0.995927	−	0.0901679i	$-0.0287404\pi$
$13$	2.75804	+	3.18294i	0.764941	+	0.882789i	−0.230985	+	0.972957i	$0.574195\pi$
$14$	2.45891	−	0.722000i	0.657170	−	0.192963i
$15$	−1.16057	−	1.28572i	−0.299659	−	0.331971i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	1.02470	−	2.24378i	0.248526	−	0.544197i	−0.743719	−	0.668493i	$-0.766940\pi$
$17$	1.02470	−	2.24378i	0.248526	−	0.544197i	0.992245	+	0.124296i	$0.0396671\pi$
$18$	−2.98434	−	0.306134i	−0.703416	−	0.0721564i
$19$	−1.20876	+	0.552021i	−0.277308	+	0.126642i	−0.549215	−	0.835681i	$-0.685073\pi$
$19$	−1.20876	+	0.552021i	−0.277308	+	0.126642i	0.271907	+	0.962324i	$0.412346\pi$
$20$	0.142315	+	0.989821i	0.0318226	+	0.221331i
$21$	−1.33669	−	4.23270i	−0.291689	−	0.923651i
$22$			5.78240i			1.23281i
$23$	4.03585	+	2.59074i	0.841533	+	0.540206i
$23$	4.03585	+	2.59074i	0.841533	+	0.540206i
$24$	1.33174	+	1.10746i	0.271840	+	0.226060i
$25$	0.841254	+	0.540641i	0.168251	+	0.108128i
$26$	−4.16877	+	0.599378i	−0.817563	+	0.117548i
$27$	−0.425265	+	5.17872i	−0.0818422	+	0.996645i
$28$	−0.722000	+	2.45891i	−0.136445	+	0.464689i
$29$	9.05831	+	4.13679i	1.68209	+	0.768183i	0.999294	+	0.0375693i	$0.0119615\pi$
$29$	9.05831	+	4.13679i	1.68209	+	0.768183i	0.682791	+	0.730613i	$0.260766\pi$
$30$	1.70907	−	0.281227i	0.312032	−	0.0513447i
$31$	−1.06802	+	7.42827i	−0.191823	+	1.33416i	0.635356	+	0.772219i	$0.280853\pi$
$31$	−1.06802	+	7.42827i	−0.191823	+	1.33416i	−0.827179	+	0.561938i	$0.810056\pi$
$32$	−0.281733	−	0.959493i	−0.0498038	−	0.169616i
$33$	10.0133	−	0.203185i	1.74310	−	0.0353699i
$34$	1.33359	+	2.07511i	0.228709	+	0.355879i
$35$	1.38551	+	2.15589i	0.234193	+	0.364412i
$36$	1.87099	−	2.34508i	0.311832	−	0.390846i
$37$	−0.831698	−	2.83250i	−0.136730	−	0.465661i	0.862450	−	0.506142i	$-0.168929\pi$
$37$	−0.831698	−	2.83250i	−0.136730	−	0.465661i	−0.999180	+	0.0404815i	$0.987111\pi$
$38$	0.189114	−	1.31532i	0.0306783	−	0.213372i
$39$	1.18442	+	7.19797i	0.189660	+	1.15260i
$40$	−0.909632	−	0.415415i	−0.143825	−	0.0656829i
$41$	2.86232	−	9.74816i	0.447019	−	1.52241i	−0.360611	−	0.932716i	$-0.617432\pi$
$41$	2.86232	−	9.74816i	0.447019	−	1.52241i	0.807630	−	0.589690i	$-0.200750\pi$
$42$	4.28344	+	1.16388i	0.660950	+	0.179591i
$43$	−8.83499	+	1.27028i	−1.34732	+	0.193716i	−0.777931	−	0.628350i	$-0.783731\pi$
$43$	−8.83499	+	1.27028i	−1.34732	+	0.193716i	−0.569392	+	0.822066i	$0.692821\pi$
$44$	−4.86446	−	3.12620i	−0.733345	−	0.471292i
$45$	−0.547053	−	2.94970i	−0.0815498	−	0.439715i
$46$	−4.36141	+	1.99452i	−0.643055	+	0.294075i
$47$		−	1.54834i		−	0.225848i	−0.993604	−	0.112924i	$-0.963978\pi$
$47$		−	1.54834i		−	0.225848i	0.993604	−	0.112924i	$-0.0360217\pi$
$48$	−1.65165	+	0.521590i	−0.238395	+	0.0752850i
$49$	−0.0615513	−	0.428098i	−0.00879304	−	0.0611569i
$50$	−0.909632	+	0.415415i	−0.128641	+	0.0587486i
$51$	3.54660	−	2.38229i	0.496623	−	0.333588i
$52$	1.74958	−	3.83104i	0.242623	−	0.531270i
$53$	−5.48005	+	6.32431i	−0.752742	+	0.868711i	−0.994831	−	0.101543i	$-0.967622\pi$
$53$	−5.48005	+	6.32431i	−0.752742	+	0.868711i	0.242089	+	0.970254i	$0.422167\pi$
$54$	−4.12670	−	3.15758i	−0.561573	−	0.429693i
$55$	−5.54817	+	1.62909i	−0.748115	+	0.219666i
$56$	−1.67822	−	1.93677i	−0.224262	−	0.258812i
$57$	−2.28437	−	0.281269i	−0.302572	−	0.0372550i
$58$	−8.37738	+	5.38382i	−1.10000	+	0.706930i
$59$	2.63681	−	2.28481i	0.343284	−	0.297457i	−0.466106	−	0.884729i	$-0.654343\pi$
$59$	2.63681	−	2.28481i	0.343284	−	0.297457i	0.809390	+	0.587272i	$0.199798\pi$
$60$	−0.687409	+	1.58980i	−0.0887441	+	0.205243i
$61$	0.891151	+	0.128128i	0.114100	+	0.0164051i	0.199128	−	0.979973i	$-0.436189\pi$
$61$	0.891151	+	0.128128i	0.114100	+	0.0164051i	−0.0850282	+	0.996379i	$0.527098\pi$
$62$	−5.67164	−	4.91451i	−0.720299	−	0.624143i
$63$	1.86497	−	7.45851i	0.234964	−	0.939684i
$64$	0.959493	+	0.281733i	0.119937	+	0.0352166i
$65$	−1.74958	−	3.83104i	−0.217008	−	0.475182i
$66$	−5.24269	+	8.53361i	−0.645331	+	1.05042i
$67$	7.82353	−	12.1736i	0.955796	−	1.48725i	0.0845390	−	0.996420i	$-0.473058\pi$
$67$	7.82353	−	12.1736i	0.955796	−	1.48725i	0.871257	−	0.490827i	$-0.163305\pi$
$68$	−2.46669			−0.299130
$69$	3.60714	+	7.48255i	0.434249	+	0.900793i
$70$	−2.56271			−0.306303
$71$	4.57179	−	7.11385i	0.542572	−	0.844258i	−0.456392	−	0.889779i	$-0.650858\pi$
$71$	4.57179	−	7.11385i	0.542572	−	0.844258i	0.998963	+	0.0455208i	$0.0144947\pi$
$72$	0.961271	+	2.84182i	0.113287	+	0.334912i
$73$	4.76049	+	10.4240i	0.557173	+	1.22004i	0.953351	+	0.301865i	$0.0976091\pi$
$73$	4.76049	+	10.4240i	0.557173	+	1.22004i	−0.396178	+	0.918174i	$0.629664\pi$
$74$	2.83250	+	0.831698i	0.329272	+	0.0966830i
$75$	0.751335	+	1.56061i	0.0867567	+	0.180203i
$76$	1.00427	+	0.870206i	0.115198	+	0.0998195i
$77$	−14.6678	−	2.10891i	−1.67155	−	0.240333i
$78$	−6.69567	−	2.89512i	−0.758135	−	0.327807i
$79$	2.10799	−	1.82658i	0.237167	−	0.205507i	−0.528165	−	0.849142i	$-0.677120\pi$
$79$	2.10799	−	1.82658i	0.237167	−	0.205507i	0.765333	+	0.643635i	$0.222574\pi$
$80$	0.841254	−	0.540641i	0.0940550	−	0.0604455i
$81$	−5.32296	+	7.25714i	−0.591440	+	0.806349i
$82$	6.65319	+	7.67819i	0.734721	+	0.847914i
$83$	−8.68171	+	2.54918i	−0.952941	+	0.279809i	−0.721011	−	0.692924i	$-0.756322\pi$
$83$	−8.68171	+	2.54918i	−0.952941	+	0.279809i	−0.231930	+	0.972732i	$0.574504\pi$
$84$	−3.29492	+	2.97422i	−0.359506	+	0.324514i
$85$	−1.61534	+	1.86420i	−0.175208	+	0.202201i
$86$	3.70793	−	8.11923i	0.399836	−	0.875519i
$87$	9.61749	+	14.3179i	1.03110	+	1.53504i
$88$	5.25985	−	2.40209i	0.560702	−	0.256064i
$89$	−1.22184	−	8.49808i	−0.129515	−	0.900794i	−0.946170	−	0.323669i	$-0.895084\pi$
$89$	−1.22184	−	8.49808i	−0.129515	−	0.900794i	0.816656	−	0.577125i	$-0.195826\pi$
$90$	2.77720	+	1.13452i	0.292743	+	0.119589i
$91$		−	10.7932i		−	1.13144i
$92$	0.680064	−	4.74737i	0.0709016	−	0.494947i
$93$	−8.31113	+	9.99424i	−0.861824	+	1.03635i
$94$	1.30254	+	0.837094i	0.134347	+	0.0863397i
$95$	1.31532	−	0.189114i	0.134949	−	0.0194027i
$96$	0.454160	−	1.67145i	0.0463525	−	0.170591i
$97$	−1.63510	+	5.56864i	−0.166019	+	0.565409i	0.833890	+	0.551931i	$0.186109\pi$
$97$	−1.63510	+	5.56864i	−0.166019	+	0.565409i	−0.999909	+	0.0134787i	$0.995709\pi$
$98$	0.393416	+	0.179667i	0.0397411	+	0.0181491i
$99$	14.9618	+	8.77888i	1.50372	+	0.882311i
$100$	0.142315	−	0.989821i	0.0142315	−	0.0989821i
$101$	5.23999	+	17.8458i	0.521398	+	1.77572i	0.624474	+	0.781046i	$0.285313\pi$
$101$	5.23999	+	17.8458i	0.521398	+	1.77572i	−0.103076	+	0.994674i	$0.532868\pi$
$102$	0.0866758	+	4.27156i	0.00858218	+	0.422947i
$103$	−6.19308	−	9.63662i	−0.610222	−	0.949524i	−0.999595	−	0.0284440i	$-0.990945\pi$
$103$	−6.19308	−	9.63662i	−0.610222	−	0.949524i	0.389373	−	0.921080i	$-0.372692\pi$
$104$	2.27698	+	3.54305i	0.223277	+	0.347425i
$105$	0.0900499	+	4.43784i	0.00878797	+	0.433088i
$106$	−2.35761	−	8.02929i	−0.228992	−	0.779873i
$107$	−2.24434	+	15.6098i	−0.216969	+	1.50905i	0.532169	+	0.846638i	$0.321377\pi$
$107$	−2.24434	+	15.6098i	−0.216969	+	1.50905i	−0.749138	+	0.662414i	$0.769532\pi$
$108$	4.88739	−	1.76448i	0.470289	−	0.169788i
$109$	0.323080	+	0.147546i	0.0309454	+	0.0141323i	0.430828	−	0.902434i	$-0.358222\pi$
$109$	0.323080	+	0.147546i	0.0309454	+	0.0141323i	−0.399882	+	0.916567i	$0.630949\pi$
$110$	1.62909	−	5.54817i	0.155328	−	0.528997i
$111$	1.34072	−	4.93426i	0.127255	−	0.468339i
$112$	2.53663	−	0.364712i	0.239689	−	0.0344621i
$113$	−14.4028	−	9.25609i	−1.35490	−	0.870740i	−0.356909	−	0.934139i	$-0.616170\pi$
$113$	−14.4028	−	9.25609i	−1.35490	−	0.870740i	−0.997988	+	0.0633992i	$0.979806\pi$
$114$	1.47164	−	1.76967i	0.137832	−	0.165745i
$115$	−3.14247	−	3.62282i	−0.293037	−	0.337830i
$116$		−	9.95821i		−	0.924597i
$117$	−4.77818	+	11.6966i	−0.441743	+	1.08135i
$118$	0.496537	+	3.45349i	0.0457099	+	0.317920i
$119$	−5.75017	+	2.62601i	−0.527117	+	0.240726i
$120$	−0.965785	−	1.43780i	−0.0881637	−	0.131252i
$121$	9.32030	−	20.4086i	0.847300	−	1.85533i
$122$	−0.589581	+	0.680412i	−0.0533781	+	0.0616016i
$123$	13.0625	−	11.7911i	1.17780	−	1.06317i
$124$	7.20067	−	2.11431i	0.646639	−	0.189870i
$125$	−0.654861	−	0.755750i	−0.0585725	−	0.0675963i
$126$	5.26622	+	5.60129i	0.469152	+	0.499003i
$127$	−3.31134	+	2.12807i	−0.293834	+	0.188836i	−0.679250	−	0.733907i	$-0.737695\pi$
$127$	−3.31134	+	2.12807i	−0.293834	+	0.188836i	0.385415	+	0.922743i	$0.374058\pi$
$128$	−0.755750	+	0.654861i	−0.0667995	+	0.0578821i
$129$	−14.1903	−	6.13570i	−1.24939	−	0.540218i
$130$	4.16877	+	0.599378i	0.365625	+	0.0525690i
$131$	−14.6769	−	12.7176i	−1.28232	−	1.11114i	−0.987838	−	0.155483i	$-0.950306\pi$
$131$	−14.6769	−	12.7176i	−1.28232	−	1.11114i	−0.294485	−	0.955656i	$-0.595148\pi$
$132$	−4.34452	−	9.02405i	−0.378142	−	0.785443i
$133$	3.26750	+	0.959424i	0.283328	+	0.0831926i
$134$	6.01140	+	13.1631i	0.519306	+	1.13712i
$135$	1.86705	−	4.84914i	0.160690	−	0.417347i
$136$	1.33359	−	2.07511i	0.114355	−	0.177939i
$137$	14.7205			1.25766			0.628830	−	0.777543i	$-0.283534\pi$
$137$	14.7205			1.25766			0.628830	+	0.777543i	$0.283534\pi$
$138$	−8.24489	−	1.01085i	−0.701852	−	0.0860491i
$139$	−6.38665			−0.541708			−0.270854	−	0.962620i	$-0.587306\pi$
$139$	−6.38665			−0.541708			−0.270854	+	0.962620i	$0.587306\pi$
$140$	1.38551	−	2.15589i	0.117097	−	0.182206i
$141$	1.40382	−	2.28502i	0.118223	−	0.192434i
$142$	3.51285	+	7.69207i	0.294792	+	0.645504i
$143$	23.3669	+	6.86113i	1.95404	+	0.573757i
$144$	−2.91040	−	0.727733i	−0.242533	−	0.0606444i
$145$	−7.52591	−	6.52124i	−0.624993	−	0.541560i
$146$	−11.3430	−	1.63087i	−0.938750	−	0.134972i
$147$	0.297305	−	0.687590i	0.0245213	−	0.0567115i
$148$	−2.23104	+	1.93320i	−0.183390	+	0.158908i
$149$	−1.91294	+	1.22937i	−0.156714	+	0.100714i	−0.616647	−	0.787239i	$-0.711510\pi$
$149$	−1.91294	+	1.22937i	−0.156714	+	0.100714i	0.459934	+	0.887953i	$0.347873\pi$
$150$	−1.71907	−	0.211665i	−0.140361	−	0.0172824i
$151$	−4.24042	−	4.89370i	−0.345080	−	0.398244i	0.556506	−	0.830844i	$-0.312142\pi$
$151$	−4.24042	−	4.89370i	−0.345080	−	0.398244i	−0.901586	+	0.432600i	$0.857596\pi$
$152$	−1.27501	+	0.374378i	−0.103417	+	0.0303661i
$153$	7.39398	−	0.300192i	0.597768	−	0.0242691i
$154$	9.70414	−	11.1992i	0.781982	−	0.902455i
$155$	3.11755	−	6.82648i	0.250408	−	0.548316i
$156$	6.05548	−	4.06754i	0.484826	−	0.325663i
$157$	2.74720	−	1.25461i	0.219251	−	0.100128i	−0.302762	−	0.953066i	$-0.597909\pi$
$157$	2.74720	−	1.25461i	0.219251	−	0.100128i	0.522012	+	0.852938i	$0.325181\pi$
$158$	0.396955	+	2.76088i	0.0315800	+	0.219644i
$159$	−13.8214	+	4.36480i	−1.09611	+	0.346151i
$160$			1.00000i			0.0790569i
$161$	−3.46868	−	11.7907i	−0.273371	−	0.929238i
$162$	−3.22728	−	8.40147i	−0.253559	−	0.660082i
$163$	11.1826	+	7.18665i	0.875892	+	0.562902i	0.899550	−	0.436818i	$-0.143895\pi$
$163$	11.1826	+	7.18665i	0.875892	+	0.562902i	−0.0236576	+	0.999720i	$0.507531\pi$
$164$	−10.0563	+	1.44588i	−0.785264	+	0.112904i
$165$	−9.66498	−	2.62613i	−0.752418	−	0.204444i
$166$	2.54918	−	8.68171i	0.197855	−	0.673831i
$167$	−4.11619	−	1.87980i	−0.318521	−	0.145464i	0.249738	−	0.968313i	$-0.419655\pi$
$167$	−4.11619	−	1.87980i	−0.318521	−	0.145464i	−0.568259	+	0.822850i	$0.692383\pi$
$168$	−0.720703	−	4.37985i	−0.0556035	−	0.337913i
$169$	−0.674271	+	4.68966i	−0.0518670	+	0.360743i
$170$	−0.694947	−	2.36677i	−0.0533000	−	0.181523i
$171$	−3.11624	−	2.48625i	−0.238305	−	0.190128i
$172$	4.82567	+	7.50889i	0.367954	+	0.572548i
$173$	−1.23651	−	1.92405i	−0.0940103	−	0.146283i	0.791063	−	0.611735i	$-0.209528\pi$
$173$	−1.23651	−	1.92405i	−0.0940103	−	0.146283i	−0.885073	+	0.465452i	$0.845892\pi$
$174$	−17.2446	+	0.349916i	−1.30731	+	0.0265271i
$175$	−0.722000	−	2.45891i	−0.0545781	−	0.185876i
$176$	−0.822921	+	5.72354i	−0.0620300	+	0.431428i
$177$	5.96294	−	0.981200i	0.448202	−	0.0737515i
$178$	7.80961	+	3.56653i	0.585355	+	0.267323i
$179$	6.78351	−	23.1025i	0.507023	−	1.72676i	−0.165057	−	0.986284i	$-0.552781\pi$
$179$	6.78351	−	23.1025i	0.507023	−	1.72676i	0.672080	−	0.740479i	$-0.265401\pi$
$180$	−2.45589	+	1.72297i	−0.183051	+	0.128422i
$181$	−19.4357	+	2.79443i	−1.44464	+	0.207708i	−0.819624	−	0.572902i	$-0.805817\pi$
$181$	−19.4357	+	2.79443i	−1.44464	+	0.207708i	−0.625018	+	0.780611i	$0.714908\pi$
$182$	9.07983	+	5.83525i	0.673042	+	0.432538i
$183$	1.19898	+	0.997065i	0.0886314	+	0.0737051i
$184$	3.62607	+	3.13873i	0.267317	+	0.231390i
$185$			2.95208i			0.217042i
$186$	−3.91435	−	12.3951i	−0.287014	−	0.908850i
$187$	−2.02989	−	14.1182i	−0.148440	−	1.03243i
$188$	−1.40842	+	0.643203i	−0.102719	+	0.0469104i
$189$	9.51467	−	9.31630i	0.692091	−	0.677661i
$190$	−0.552021	+	1.20876i	−0.0400478	+	0.0876925i
$191$	−4.30392	+	4.96699i	−0.311421	+	0.359399i	−0.889785	−	0.456380i	$-0.849146\pi$
$191$	−4.30392	+	4.96699i	−0.311421	+	0.359399i	0.578364	+	0.815779i	$0.303691\pi$
$192$	1.16057	+	1.28572i	0.0837573	+	0.0927886i
$193$	−11.4095	+	3.35015i	−0.821277	+	0.241149i	−0.665266	−	0.746606i	$-0.731682\pi$
$193$	−11.4095	+	3.35015i	−0.821277	+	0.241149i	−0.156011	+	0.987755i	$0.549864\pi$
$194$	−3.80063	−	4.38616i	−0.272870	−	0.314908i
$195$	0.891456	−	7.24009i	0.0638385	−	0.518474i
$196$	−0.363843	+	0.233828i	−0.0259888	+	0.0167020i
$197$	−16.4851	+	14.2844i	−1.17451	+	1.01772i	−0.175064	+	0.984557i	$0.556013\pi$
$197$	−16.4851	+	14.2844i	−1.17451	+	1.01772i	−0.999450	+	0.0331654i	$0.989441\pi$
$198$	−15.4742	+	7.84047i	−1.09971	+	0.557198i
$199$	2.48112	+	0.356731i	0.175882	+	0.0252880i	0.229693	−	0.973263i	$-0.426228\pi$
$199$	2.48112	+	0.356731i	0.175882	+	0.0252880i	−0.0538111	+	0.998551i	$0.517137\pi$
$200$	0.755750	+	0.654861i	0.0534396	+	0.0463056i
$201$	22.5833	−	10.8724i	1.59290	−	0.766883i
$202$	−17.8458	−	5.23999i	−1.25562	−	0.368684i
$203$	−10.6014	−	23.2138i	−0.744073	−	1.62929i
$204$	−3.64032	−	2.23646i	−0.254873	−	0.156584i
$205$	−5.49275	+	8.54688i	−0.383630	+	0.596940i
$206$	11.4551			0.798112
$207$	−1.46077	+	14.3131i	−0.101530	+	0.994832i
$208$	−4.21164			−0.292024
$209$	−4.15423	+	6.46410i	−0.287354	+	0.447131i
$210$	−3.78203	−	2.32352i	−0.260985	−	0.160338i
$211$	−5.75935	−	12.6112i	−0.396490	−	0.868192i	−0.997614	−	0.0690366i	$-0.978007\pi$
$211$	−5.75935	−	12.6112i	−0.396490	−	0.868192i	0.601124	−	0.799156i	$-0.294720\pi$
$212$	8.02929	+	2.35761i	0.551454	+	0.161921i
$213$	13.1969	−	6.35347i	0.904235	−	0.435333i
$214$	−11.9184	−	10.3273i	−0.814724	−	0.705962i
$215$	8.83499	+	1.27028i	0.602541	+	0.0866323i
$216$	−1.15794	+	5.06549i	−0.0787882	+	0.344663i
$217$	14.5348	−	12.5945i	0.986686	−	0.854969i
$218$	−0.298793	+	0.192023i	−0.0202368	+	0.0130054i
$219$	−2.42560	+	19.6998i	−0.163907	+	1.33119i
$220$	3.78667	+	4.37004i	0.255297	+	0.294628i
$221$	9.96799	−	2.92687i	0.670519	−	0.196882i
$222$	3.42611	+	3.79554i	0.229946	+	0.254740i
$223$	−1.34766	+	1.55529i	−0.0902463	+	0.104150i	−0.799076	−	0.601229i	$-0.794678\pi$
$223$	−1.34766	+	1.55529i	−0.0902463	+	0.104150i	0.708830	+	0.705379i	$0.249223\pi$
$224$	−1.06459	+	2.33113i	−0.0711309	+	0.155755i
$225$	−0.306134	+	2.98434i	−0.0204089	+	0.198956i
$226$	15.5734	−	7.11215i	1.03593	−	0.473093i
$227$	−0.0999327	−	0.695047i	−0.00663276	−	0.0461319i	0.986236	−	0.165342i	$-0.0528728\pi$
$227$	−0.0999327	−	0.695047i	−0.00663276	−	0.0461319i	−0.992869	+	0.119210i	$0.961964\pi$
$228$	0.693110	+	2.19478i	0.0459024	+	0.145353i
$229$			13.2875i			0.878063i	0.898472	+	0.439032i	$0.144678\pi$
$229$			13.2875i			0.878063i	−0.898472	+	0.439032i	$0.855322\pi$
$230$	4.74666	−	0.684972i	0.312986	−	0.0451657i
$231$	−19.7345	−	16.4111i	−1.29844	−	1.07977i
$232$	8.37738	+	5.38382i	0.550002	+	0.353465i
$233$	8.03888	−	1.15582i	0.526645	−	0.0757201i	0.126136	−	0.992013i	$-0.459742\pi$
$233$	8.03888	−	1.15582i	0.526645	−	0.0757201i	0.400509	+	0.916293i	$0.368833\pi$
$234$	−7.25651	−	10.3433i	−0.474373	−	0.676163i
$235$	−0.436217	+	1.48562i	−0.0284557	+	0.0969111i
$236$	−3.17371	−	1.44938i	−0.206591	−	0.0943469i
$237$	4.76705	−	0.784417i	0.309653	−	0.0509534i
$238$	0.899632	−	6.25708i	0.0583145	−	0.405586i
$239$	−4.21113	−	14.3418i	−0.272395	−	0.927693i	−0.976122	−	0.217223i	$-0.930300\pi$
$239$	−4.21113	−	14.3418i	−0.272395	−	0.927693i	0.703727	−	0.710471i	$-0.251518\pi$
$240$	1.73169	−	0.0351385i	0.111780	−	0.00226818i
$241$	0.330605	+	0.514431i	0.0212961	+	0.0331374i	0.851738	−	0.523967i	$-0.175549\pi$
$241$	0.330605	+	0.514431i	0.0212961	+	0.0331374i	−0.830442	+	0.557105i	$0.811912\pi$
$242$	12.1299	+	18.8745i	0.779738	+	1.21330i
$243$	−14.4354	+	5.88388i	−0.926029	+	0.377451i
$244$	−0.253648	−	0.863845i	−0.0162381	−	0.0553020i
$245$	−0.0615513	+	0.428098i	−0.00393237	+	0.0273502i
$246$	2.85718	+	17.3636i	0.182167	+	1.10706i
$247$	−5.09085	−	2.32491i	−0.323923	−	0.147931i
$248$	−2.11431	+	7.20067i	−0.134259	+	0.457243i
$249$	−15.1236	−	4.10934i	−0.958422	−	0.260419i
$250$	0.989821	−	0.142315i	0.0626018	−	0.00900078i
$251$	6.85669	+	4.40653i	0.432790	+	0.278138i	0.738844	−	0.673877i	$-0.235372\pi$
$251$	6.85669	+	4.40653i	0.432790	+	0.278138i	−0.306053	+	0.952014i	$0.599009\pi$
$252$	−7.55924	+	1.40194i	−0.476187	+	0.0883139i
$253$	27.7314	−	0.0143353i	1.74346	−	0.000901254i
$254$		−	3.93620i		−	0.246979i
$255$	−4.07411	+	1.28660i	−0.255131	+	0.0805701i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	−3.38402	+	1.54543i	−0.211089	+	0.0964012i	−0.518154	−	0.855287i	$-0.673381\pi$
$257$	−3.38402	+	1.54543i	−0.211089	+	0.0964012i	0.307065	+	0.951689i	$0.400653\pi$
$258$	12.8335	−	8.62044i	0.798982	−	0.536685i
$259$	−3.14276	+	6.88168i	−0.195282	+	0.427607i
$260$	−2.75804	+	3.18294i	−0.171046	+	0.197398i
$261$	1.21190	+	29.8500i	0.0750145	+	1.84767i
$262$	18.6336	−	5.47132i	1.15119	−	0.338019i
$263$	−5.80137	−	6.69514i	−0.357728	−	0.412840i	0.548149	−	0.836381i	$-0.315333\pi$
$263$	−5.80137	−	6.69514i	−0.357728	−	0.412840i	−0.905877	+	0.423541i	$0.860787\pi$
$264$	9.94034	+	1.22393i	0.611786	+	0.0753278i
$265$	7.03983	−	4.52422i	0.432453	−	0.277921i
$266$	−2.57366	+	2.23009i	−0.157801	+	0.136736i
$267$	5.90172	−	13.6492i	0.361180	−	0.835317i
$268$	−14.3235	−	2.05942i	−0.874950	−	0.125799i
$269$	1.40427	+	1.21680i	0.0856196	+	0.0741898i	0.696619	−	0.717441i	$-0.254687\pi$
$269$	1.40427	+	1.21680i	0.0856196	+	0.0741898i	−0.610999	+	0.791631i	$0.709232\pi$
$270$	3.06995	+	4.19231i	0.186831	+	0.255136i
$271$	−26.9474	−	7.91249i	−1.63694	−	0.480649i	−0.671442	−	0.741057i	$-0.734325\pi$
$271$	−26.9474	−	7.91249i	−1.63694	−	0.480649i	−0.965499	+	0.260408i	$0.916143\pi$
$272$	1.02470	+	2.24378i	0.0621316	+	0.136049i
$273$	9.78582	−	15.9285i	0.592265	−	0.964039i
$274$	−7.95853	+	12.3837i	−0.480792	+	0.748127i
$275$	5.78240			0.348692
$276$	5.30790	−	6.38954i	0.319498	−	0.384605i
$277$	−12.6601			−0.760674			−0.380337	−	0.924848i	$-0.624192\pi$
$277$	−12.6601			−0.760674			−0.380337	+	0.924848i	$0.624192\pi$
$278$	3.45288	−	5.37279i	0.207090	−	0.322238i
$279$	−21.3269	+	7.21401i	−1.27681	+	0.431891i
$280$	1.06459	+	2.33113i	0.0636214	+	0.139311i
$281$	−7.07815	−	2.07833i	−0.422247	−	0.123983i	0.0637043	−	0.997969i	$-0.479709\pi$
$281$	−7.07815	−	2.07833i	−0.422247	−	0.123983i	−0.485951	+	0.873986i	$0.661527\pi$
$282$	1.16332	+	2.41635i	0.0692747	+	0.143891i
$283$	−3.58601	−	3.10729i	−0.213166	−	0.184709i	0.541733	−	0.840551i	$-0.317769\pi$
$283$	−3.58601	−	3.10729i	−0.213166	−	0.184709i	−0.754899	+	0.655841i	$0.772314\pi$
$284$	−8.37017	−	1.20345i	−0.496678	−	0.0714116i
$285$	2.11260	+	0.913458i	0.125139	+	0.0541086i
$286$	−18.4050	+	15.9481i	−1.08831	+	0.943028i
$287$	−21.9032	+	14.0763i	−1.29291	+	0.830900i
$288$	2.18569	−	2.05494i	0.128793	−	0.121088i
$289$	7.14809	+	8.24934i	0.420476	+	0.485255i
$290$	9.55483	−	2.80555i	0.561079	−	0.164748i
$291$	−7.46195	+	6.73566i	−0.437427	+	0.394851i
$292$	7.50444	−	8.66058i	0.439164	−	0.506822i
$293$	−4.46524	+	9.77751i	−0.260862	+	0.571208i	−0.994063	−	0.108803i	$-0.965298\pi$
$293$	−4.46524	+	9.77751i	−0.260862	+	0.571208i	0.733201	+	0.680012i	$0.238025\pi$
$294$	0.417703	+	0.621848i	0.0243609	+	0.0362669i
$295$	−3.17371	+	1.44938i	−0.184780	+	0.0843864i
$296$	−0.420125	−	2.92204i	−0.0244193	−	0.169840i
$297$	14.1210	+	26.5212i	0.819386	+	1.53891i
$298$		−	2.27391i		−	0.131724i
$299$	2.88485	+	19.9912i	0.166835	+	1.15612i
$300$	1.10746	−	1.33174i	0.0639394	−	0.0768879i
$301$	19.2431	+	12.3668i	1.10916	+	0.712812i
$302$	6.40938	−	0.921530i	0.368819	−	0.0530281i
$303$	−8.44698	+	31.0875i	−0.485266	+	1.78593i
$304$	0.374378	−	1.27501i	0.0214721	−	0.0731271i
$305$	−0.818955	−	0.374004i	−0.0468932	−	0.0214154i
$306$	−3.74495	+	6.38251i	−0.214085	+	0.364864i
$307$	−0.433913	+	3.01793i	−0.0247647	+	0.172242i	−0.998450	−	0.0556539i	$-0.982276\pi$
$307$	−0.433913	+	3.01793i	−0.0247647	+	0.172242i	0.973685	+	0.227896i	$0.0731847\pi$
$308$	4.17489	+	14.2184i	0.237886	+	0.810167i
$309$	−0.402514	−	19.8367i	−0.0228982	−	1.12847i
$310$	4.05733	+	6.31332i	0.230441	+	0.358573i
$311$	−5.94289	−	9.24731i	−0.336990	−	0.524367i	0.630859	−	0.775897i	$-0.282703\pi$
$311$	−5.94289	−	9.24731i	−0.336990	−	0.524367i	−0.967849	+	0.251530i	$0.919066\pi$
$312$	0.147991	+	7.29327i	0.00837831	+	0.412900i
$313$	3.37499	+	11.4941i	0.190766	+	0.649688i	0.998213	+	0.0597488i	$0.0190300\pi$
$313$	3.37499	+	11.4941i	0.190766	+	0.649688i	−0.807448	+	0.589939i	$0.799152\pi$
$314$	−0.429809	+	2.98938i	−0.0242555	+	0.168701i
$315$	−3.89073	+	6.63096i	−0.219218	+	0.373613i
$316$	−2.53721	−	1.15870i	−0.142729	−	0.0651822i
$317$	3.61922	−	12.3259i	0.203276	−	0.692294i	−0.793241	−	0.608907i	$-0.791608\pi$
$317$	3.61922	−	12.3259i	0.203276	−	0.692294i	0.996517	−	0.0833866i	$-0.0265736\pi$
$318$	3.80053	−	13.9871i	0.213123	−	0.784359i
$319$	56.9962	−	8.19482i	3.19118	−	0.458822i
$320$	−0.841254	−	0.540641i	−0.0470275	−	0.0302227i
$321$	−17.4650	+	21.0019i	−0.974801	+	1.17221i
$322$	11.7943	+	3.45649i	0.657270	+	0.192623i
$323$			3.27784i			0.182384i
$324$	8.81256	+	1.82721i	0.489587	+	0.101512i
$325$	0.599378	+	4.16877i	0.0332475	+	0.231242i
$326$	−12.0916	+	5.52204i	−0.669691	+	0.305838i
$327$	0.343024	+	0.510672i	0.0189693	+	0.0282402i
$328$	4.22049	−	9.24158i	0.233038	−	0.510281i
$329$	−2.59845	+	2.99877i	−0.143257	+	0.165328i
$330$	7.43452	−	6.71090i	0.409257	−	0.369423i
$331$	−10.6216	+	3.11878i	−0.583816	+	0.171424i	−0.560286	−	0.828299i	$-0.689309\pi$
$331$	−10.6216	+	3.11878i	−0.583816	+	0.171424i	−0.0235300	+	0.999723i	$0.507491\pi$
$332$	5.92533	+	6.83819i	0.325195	+	0.375295i
$333$	6.45233	−	6.06635i	0.353586	−	0.332434i
$334$	3.80677	−	2.44646i	0.208297	−	0.133865i
$335$	−10.9363	+	9.47638i	−0.597516	+	0.517750i
$336$	4.07421	+	1.76163i	0.222266	+	0.0961049i
$337$	−5.50374	−	0.791318i	−0.299808	−	0.0431058i	−0.00923052	−	0.999957i	$-0.502938\pi$
$337$	−5.50374	−	0.791318i	−0.299808	−	0.0431058i	−0.290577	+	0.956852i	$0.593847\pi$
$338$	−3.58065	−	3.10265i	−0.194762	−	0.168762i
$339$	−12.8633	−	26.7185i	−0.698639	−	1.45115i
$340$	2.36677	+	0.694947i	0.128356	+	0.0376888i
$341$	18.0269	+	39.4734i	0.976212	+	2.13761i
$342$	3.77633	−	1.27738i	0.204201	−	0.0690726i
$343$	−10.2978	+	16.0237i	−0.556028	+	0.865197i
$344$	−8.92584			−0.481249
$345$	−1.35295	−	8.19570i	−0.0728405	−	0.441242i
$346$	2.28712			0.122957
$347$	14.6361	−	22.7742i	0.785708	−	1.22259i	−0.185098	−	0.982720i	$-0.559260\pi$
$347$	14.6361	−	22.7742i	0.785708	−	1.22259i	0.970806	−	0.239865i	$-0.0771033\pi$
$348$	9.02875	−	14.6962i	0.483992	−	0.787801i
$349$	−1.72610	−	3.77963i	−0.0923960	−	0.202319i	0.857792	−	0.513998i	$-0.171836\pi$
$349$	−1.72610	−	3.77963i	−0.0923960	−	0.202319i	−0.950188	+	0.311679i	$0.899109\pi$
$350$	2.45891	+	0.722000i	0.131434	+	0.0385925i
$351$	−17.6565	+	12.9295i	−0.942432	+	0.690126i
$352$	−4.37004	−	3.78667i	−0.232924	−	0.201830i
$353$	3.63698	+	0.522919i	0.193577	+	0.0278321i	0.238421	−	0.971162i	$-0.423370\pi$
$353$	3.63698	+	0.522919i	0.193577	+	0.0278321i	−0.0448444	+	0.998994i	$0.514279\pi$
$354$	−2.39837	+	5.54682i	−0.127472	+	0.294810i
$355$	−6.39080	+	5.53766i	−0.339189	+	0.293909i
$356$	−7.22255	+	4.64165i	−0.382795	+	0.246007i
$357$	−10.8670	−	1.33802i	−0.575141	−	0.0708157i
$358$	15.7676	+	18.1968i	0.833345	+	0.961731i
$359$	18.5419	−	5.44439i	0.978603	−	0.287344i	0.246955	−	0.969027i	$-0.420570\pi$
$359$	18.5419	−	5.44439i	0.978603	−	0.287344i	0.731648	+	0.681683i	$0.238752\pi$
$360$	−0.121698	−	2.99753i	−0.00641406	−	0.157984i
$361$	−11.2860	+	13.0247i	−0.593999	+	0.685512i
$362$	8.15689	−	17.8611i	0.428717	−	0.938759i
$363$	32.2586	−	21.6685i	1.69314	−	1.13730i
$364$	−9.81786	+	4.48366i	−0.514595	+	0.235008i
$365$	−1.63087	−	11.3430i	−0.0853637	−	0.593717i
$366$	−1.48700	+	0.469595i	−0.0777269	+	0.0245461i
$367$			20.3602i			1.06279i	0.847124	+	0.531396i	$0.178332\pi$
$367$			20.3602i			1.06279i	−0.847124	+	0.531396i	$0.821668\pi$
$368$	−4.60087	+	1.35352i	−0.239837	+	0.0705571i
$369$	29.9681	−	5.55789i	1.56007	−	0.289332i
$370$	−2.48345	−	1.59602i	−0.129109	−	0.0829730i
$371$	21.2272	−	3.05201i	1.10206	−	0.158452i
$372$	12.5437	+	3.40831i	0.650358	+	0.176713i
$373$	2.33776	−	7.96167i	0.121044	−	0.412240i	−0.876570	−	0.481275i	$-0.840174\pi$
$373$	2.33776	−	7.96167i	0.121044	−	0.412240i	0.997614	+	0.0690352i	$0.0219921\pi$
$374$	12.9744	+	5.92523i	0.670892	+	0.306386i
$375$	−0.281227	−	1.70907i	−0.0145225	−	0.0882559i
$376$	0.220351	−	1.53258i	0.0113638	−	0.0790366i
$377$	11.8160	+	40.2415i	0.608553	+	2.07254i
$378$	2.69335	+	13.0410i	0.138531	+	0.670758i
$379$	8.75631	+	13.6251i	0.449781	+	0.699874i	0.989908	−	0.141710i	$-0.0452601\pi$
$379$	8.75631	+	13.6251i	0.449781	+	0.699874i	−0.540127	+	0.841584i	$0.681624\pi$
$380$	−0.718426	−	1.11789i	−0.0368545	−	0.0573467i
$381$	−6.81630	+	0.138312i	−0.349210	+	0.00708595i
$382$	−1.85162	−	6.30605i	−0.0947372	−	0.322645i
$383$	−1.44592	+	10.0566i	−0.0738832	+	0.513869i	0.918951	+	0.394371i	$0.129038\pi$
$383$	−1.44592	+	10.0566i	−0.0738832	+	0.513869i	−0.992834	+	0.119498i	$0.961872\pi$
$384$	−1.70907	+	0.281227i	−0.0872155	+	0.0143513i
$385$	13.4795	+	6.15588i	0.686979	+	0.313733i
$386$	3.35015	−	11.4095i	0.170518	−	0.580731i
$387$	−15.3789	−	21.9209i	−0.781755	−	1.11430i
$388$	5.74465	−	0.825957i	0.291641	−	0.0419316i
$389$	17.9718	+	11.5498i	0.911206	+	0.585596i	0.910094	−	0.414403i	$-0.136010\pi$
$389$	17.9718	+	11.5498i	0.911206	+	0.585596i	0.00111240	+	0.999999i	$0.499646\pi$
$390$	5.60880	+	4.66423i	0.284012	+	0.236182i
$391$	9.94858	−	6.40084i	0.503121	−	0.323704i
$392$		−	0.432501i		−	0.0218446i
$393$	−10.1294	−	32.0755i	−0.510961	−	1.61799i
$394$	−3.10430	−	21.5909i	−0.156392	−	1.08773i
$395$	−2.53721	+	1.15870i	−0.127661	+	0.0583008i
$396$	1.77019	−	17.2566i	0.0889552	−	0.867179i
$397$	0.334270	−	0.731949i	0.0167765	−	0.0367355i	−0.901058	−	0.433698i	$-0.857208\pi$
$397$	0.334270	−	0.731949i	0.0167765	−	0.0367355i	0.917835	+	0.396963i	$0.129936\pi$
$398$	−1.64150	+	1.89439i	−0.0822807	+	0.0949570i
$399$	3.95227	+	4.37843i	0.197861	+	0.219196i
$400$	−0.959493	+	0.281733i	−0.0479746	+	0.0140866i
$401$	9.60368	+	11.0832i	0.479585	+	0.553471i	0.943053	−	0.332643i	$-0.107940\pi$
$401$	9.60368	+	11.0832i	0.479585	+	0.553471i	−0.463468	+	0.886114i	$0.653395\pi$
$402$	−3.06297	+	24.8764i	−0.152767	+	1.24072i
$403$	−26.5894	+	17.0880i	−1.32451	+	0.851213i
$404$	14.0563	−	12.1799i	0.699327	−	0.605970i
$405$	7.15192	−	5.46352i	0.355382	−	0.271485i
$406$	25.2603	+	3.63188i	1.25365	+	0.180247i
$407$	−12.9007	−	11.1786i	−0.639466	−	0.554101i
$408$	3.84954	−	1.85331i	0.190580	−	0.0917526i
$409$	−17.7898	−	5.22354i	−0.879647	−	0.258288i	−0.189434	−	0.981894i	$-0.560665\pi$
$409$	−17.7898	−	5.22354i	−0.879647	−	0.258288i	−0.690213	+	0.723606i	$0.742483\pi$
$410$	−4.22049	−	9.24158i	−0.208435	−	0.456409i
$411$	21.7244	+	13.3466i	1.07159	+	0.658339i
$412$	−6.19308	+	9.63662i	−0.305111	+	0.474762i
$413$	−8.94131			−0.439973
$414$	−11.2512	−	8.96715i	−0.552968	−	0.440711i
$415$	9.04822			0.444160
$416$	2.27698	−	3.54305i	0.111638	−	0.173713i
$417$	−9.42536	−	5.79054i	−0.461562	−	0.283564i
$418$	−3.19200	−	6.98951i	−0.156126	−	0.341868i
$419$	4.85132	+	1.42448i	0.237003	+	0.0695902i	0.398077	−	0.917352i	$-0.369678\pi$
$419$	4.85132	+	1.42448i	0.237003	+	0.0695902i	−0.161074	+	0.986942i	$0.551496\pi$
$420$	3.99939	−	1.92546i	0.195150	−	0.0939526i
$421$	21.8578	+	18.9399i	1.06529	+	0.923076i	0.997213	−	0.0746045i	$-0.0237694\pi$
$421$	21.8578	+	18.9399i	1.06529	+	0.923076i	0.0680731	+	0.997680i	$0.478315\pi$
$422$	13.7230	+	1.97307i	0.668024	+	0.0960474i
$423$	4.14350	−	2.09942i	0.201464	−	0.102077i
$424$	−6.32431	+	5.48005i	−0.307136	+	0.266135i
$425$	2.07511	−	1.33359i	0.100658	−	0.0646888i
$426$	−1.78989	+	14.5369i	−0.0867205	+	0.704314i
$427$	−1.51093	−	1.74370i	−0.0731188	−	0.0843836i
$428$	15.1315	−	4.44300i	0.731407	−	0.214761i
$429$	28.2639	+	31.3115i	1.36459	+	1.51173i
$430$	−5.84518	+	6.74570i	−0.281880	+	0.325307i
$431$	0.894471	−	1.95862i	0.0430852	−	0.0943433i	−0.886865	−	0.462028i	$-0.847122\pi$
$431$	0.894471	−	1.95862i	0.0430852	−	0.0943433i	0.929951	+	0.367684i	$0.119849\pi$
$432$	−3.63533	−	3.71273i	−0.174905	−	0.178629i
$433$	−24.3569	+	11.1234i	−1.17052	+	0.534558i	−0.903272	−	0.429069i	$-0.858842\pi$
$433$	−24.3569	+	11.1234i	−1.17052	+	0.534558i	−0.267248	+	0.963628i	$0.586114\pi$
$434$	2.73704	+	19.0365i	0.131382	+	0.913783i
$435$	−5.19410	−	16.4475i	−0.249038	−	0.788596i
$436$		−	0.355177i		−	0.0170099i
$437$	−6.30850	−	0.903698i	−0.301777	−	0.0432297i
$438$	−15.2612	−	12.6911i	−0.729207	−	0.606403i
$439$	−7.32089	−	4.70485i	−0.349407	−	0.224550i	0.354151	−	0.935188i	$-0.384770\pi$
$439$	−7.32089	−	4.70485i	−0.349407	−	0.224550i	−0.703558	+	0.710638i	$0.748406\pi$
$440$	−5.72354	+	0.822921i	−0.272859	+	0.0392312i
$441$	1.06217	−	0.745184i	0.0505797	−	0.0354850i
$442$	−2.92687	+	9.96799i	−0.139217	+	0.474129i
$443$	−10.8529	−	4.95634i	−0.515636	−	0.235483i	0.140562	−	0.990072i	$-0.455109\pi$
$443$	−10.8529	−	4.95634i	−0.515636	−	0.235483i	−0.656198	+	0.754589i	$0.727836\pi$
$444$	−5.04531	+	0.830205i	−0.239440	+	0.0393998i
$445$	−1.22184	+	8.49808i	−0.0579207	+	0.402848i
$446$	−0.579789	−	1.97458i	−0.0274538	−	0.0934991i
$447$	−3.93772	+	0.0799019i	−0.186248	+	0.00377923i
$448$	−1.38551	−	2.15589i	−0.0654591	−	0.101856i
$449$	6.99131	+	10.8787i	0.329940	+	0.513397i	0.966103	−	0.258158i	$-0.0831155\pi$
$449$	6.99131	+	10.8787i	0.329940	+	0.513397i	−0.636162	+	0.771555i	$0.719479\pi$
$450$	−2.34508	−	1.87099i	−0.110548	−	0.0881994i
$451$	−16.5511	−	56.3677i	−0.779359	−	2.65425i
$452$	−2.43651	+	16.9463i	−0.114604	+	0.797088i
$453$	−1.82102	−	11.0667i	−0.0855592	−	0.519960i
$454$	0.638738	+	0.291702i	0.0299775	+	0.0136903i
$455$	−3.04080	+	10.3560i	−0.142555	+	0.485497i
$456$	−2.22109	−	0.603506i	−0.104012	−	0.0282618i
$457$	−38.6057	+	5.55066i	−1.80590	+	0.259649i	−0.961251	−	0.275674i	$-0.911099\pi$
$457$	−38.6057	+	5.55066i	−1.80590	+	0.259649i	−0.844648	+	0.535323i	$0.820190\pi$
$458$	−11.1782	−	7.18377i	−0.522321	−	0.335676i
$459$	11.1841	+	6.26084i	0.522031	+	0.292231i
$460$	−1.99001	+	4.36347i	−0.0927845	+	0.203448i
$461$		−	14.0773i		−	0.655645i	−0.944739	−	0.327822i	$-0.893685\pi$
$461$		−	14.0773i		−	0.655645i	0.944739	−	0.327822i	$-0.106315\pi$
$462$	24.4752	−	7.72924i	1.13869	−	0.359597i
$463$	4.59339	+	31.9478i	0.213473	+	1.48474i	0.761438	+	0.648237i	$0.224494\pi$
$463$	4.59339	+	31.9478i	0.213473	+	1.48474i	−0.547965	+	0.836501i	$0.684597\pi$
$464$	−9.05831	+	4.13679i	−0.420521	+	0.192046i
$465$	10.7902	−	7.24789i	0.500382	−	0.336113i
$466$	−3.37381	+	7.38762i	−0.156289	+	0.342225i
$467$	−8.99451	+	10.3802i	−0.416216	+	0.480339i	−0.924680	−	0.380744i	$-0.875668\pi$
$467$	−8.99451	+	10.3802i	−0.416216	+	0.480339i	0.508464	+	0.861083i	$0.330213\pi$
$468$	12.6245	−	0.512549i	0.583568	−	0.0236926i
$469$	−35.5824	+	10.4479i	−1.64304	+	0.482441i
$470$	−1.01395	−	1.17016i	−0.0467698	−	0.0539752i
$471$	5.19180	+	0.639255i	0.239226	+	0.0294553i
$472$	2.93514	−	1.88630i	0.135101	−	0.0868239i
$473$	−39.0063	+	33.7992i	−1.79351	+	1.55409i
$474$	−1.91737	+	4.43439i	−0.0880677	+	0.203678i
$475$	−1.31532	−	0.189114i	−0.0603509	−	0.00867714i
$476$	4.77741	+	4.13965i	0.218972	+	0.189741i
$477$	−24.3550	−	6.08986i	−1.11514	−	0.278836i
$478$	14.3418	+	4.21113i	0.655978	+	0.192613i
$479$	−6.02735	−	13.1981i	−0.275397	−	0.603035i	0.720508	−	0.693447i	$-0.243909\pi$
$479$	−6.02735	−	13.1981i	−0.275397	−	0.603035i	−0.995904	+	0.0904123i	$0.971182\pi$
$480$	−0.906664	+	1.47579i	−0.0413834	+	0.0673603i
$481$	6.72185	−	10.4594i	0.306490	−	0.476907i
$482$	−0.611505			−0.0278533
$483$	5.57116	−	20.5456i	0.253496	−	0.934855i
$484$	−22.4361			−1.01982
$485$	3.13773	−	4.88241i	0.142477	−	0.221699i
$486$	2.85451	−	15.3249i	0.129483	−	0.695150i
$487$	−15.3077	−	33.5191i	−0.693656	−	1.51890i	−0.847497	−	0.530800i	$-0.821892\pi$
$487$	−15.3077	−	33.5191i	−0.693656	−	1.51890i	0.153841	−	0.988096i	$-0.450836\pi$
$488$	0.863845	+	0.253648i	0.0391044	+	0.0114821i
$489$	9.98737	+	20.7449i	0.451644	+	0.938116i
$490$	−0.326862	−	0.283228i	−0.0147661	−	0.0127949i
$491$	−24.3602	−	3.50247i	−1.09936	−	0.158064i	−0.431328	−	0.902195i	$-0.641955\pi$
$491$	−24.3602	−	3.50247i	−1.09936	−	0.158064i	−0.668034	+	0.744131i	$0.732864\pi$
$492$	−16.1519	−	6.98386i	−0.728184	−	0.314857i
$493$	18.5641	−	16.0859i	0.836085	−	0.724472i
$494$	4.70816	−	3.02575i	0.211830	−	0.136135i
$495$	−11.8825	−	12.6385i	−0.534077	−	0.568059i
$496$	−4.91451	−	5.67164i	−0.220668	−	0.254664i
$497$	−20.7931	+	6.10541i	−0.932698	+	0.273865i
$498$	11.6335	−	10.5011i	0.521307	−	0.470567i
$499$	5.53356	−	6.38607i	0.247716	−	0.285880i	−0.618251	−	0.785981i	$-0.712158\pi$
$499$	5.53356	−	6.38607i	0.247716	−	0.285880i	0.865967	+	0.500101i	$0.166704\pi$
$500$	−0.415415	+	0.909632i	−0.0185779	+	0.0406800i
$501$	−4.37029	−	6.50620i	−0.195250	−	0.290676i
$502$	−7.41401	+	3.38587i	−0.330904	+	0.151119i
$503$	0.533344	+	3.70949i	0.0237806	+	0.165398i	0.998251	−	0.0591183i	$-0.0188289\pi$
$503$	0.533344	+	3.70949i	0.0237806	+	0.165398i	−0.974470	+	0.224516i	$0.927920\pi$
$504$	2.90745	−	7.11718i	0.129508	−	0.317024i
$505$		−	18.5992i		−	0.827651i
$506$	−14.9807	+	23.3369i	−0.665972	+	1.03745i
$507$	−5.24703	+	6.30962i	−0.233029	+	0.280220i
$508$	3.31134	+	2.12807i	0.146917	+	0.0944179i
$509$	8.77011	−	1.26095i	0.388728	−	0.0558907i	0.0548200	−	0.998496i	$-0.482542\pi$
$509$	8.77011	−	1.26095i	0.388728	−	0.0558907i	0.333908	+	0.942606i	$0.391632\pi$
$510$	1.12027	−	4.12295i	0.0496064	−	0.182567i
$511$	8.27383	−	28.1781i	0.366012	−	1.24652i
$512$	0.909632	+	0.415415i	0.0402004	+	0.0183589i
$513$	−2.34472	−	6.49457i	−0.103522	−	0.286742i
$514$	0.529440	−	3.68234i	0.0233526	−	0.162421i
$515$	3.22727	+	10.9911i	0.142210	+	0.484324i
$516$	0.313640	+	15.4568i	0.0138073	+	0.680449i
$517$	−4.84041	−	7.53183i	−0.212881	−	0.331249i
$518$	−4.09014	−	6.36438i	−0.179710	−	0.279635i
$519$	−0.0803661	−	3.96060i	−0.00352768	−	0.173851i
$520$	−1.18656	−	4.04104i	−0.0520339	−	0.177211i
$521$	−4.25871	+	29.6200i	−0.186577	+	1.29767i	0.654212	+	0.756311i	$0.273000\pi$
$521$	−4.25871	+	29.6200i	−0.186577	+	1.29767i	−0.840789	+	0.541363i	$0.817909\pi$
$522$	−25.7667	−	15.1186i	−1.12778	−	0.661725i
$523$	−18.9348	−	8.64722i	−0.827960	−	0.378117i	−0.0440791	−	0.999028i	$-0.514035\pi$
$523$	−18.9348	−	8.64722i	−0.827960	−	0.378117i	−0.783881	+	0.620911i	$0.786763\pi$
$524$	−5.47132	+	18.6336i	−0.239016	+	0.814013i
$525$	1.16388	−	4.28344i	0.0507959	−	0.186945i
$526$	8.76877	−	1.26076i	0.382336	−	0.0549717i
$527$	15.5730	+	10.0082i	0.678371	+	0.435963i
$528$	−6.40379	+	7.70064i	−0.278689	+	0.335127i
$529$	9.57617	+	20.9116i	0.416355	+	0.909202i
$530$			8.36826i			0.363494i
$531$	9.68968	+	3.95834i	0.420496	+	0.171777i
$532$	−0.484645	−	3.37078i	−0.0210120	−	0.146142i
$533$	38.9222	−	17.7752i	1.68591	−	0.769928i
$534$	8.29171	+	12.3442i	0.358818	+	0.534184i
$535$	6.55121	−	14.3451i	0.283234	−	0.620195i
$536$	9.47638	−	10.9363i	0.409317	−	0.472378i
$537$	30.9573	−	27.9441i	1.33590	−	1.20588i
$538$	−1.78284	+	0.523490i	−0.0768638	+	0.0225693i
$539$	−1.63774	−	1.89005i	−0.0705423	−	0.0814101i
$540$	−5.18653	+	0.316073i	−0.223193	+	0.0136016i
$541$	2.64126	−	1.69743i	0.113557	−	0.0729784i	−0.482630	−	0.875824i	$-0.660318\pi$
$541$	2.64126	−	1.69743i	0.113557	−	0.0729784i	0.596186	+	0.802846i	$0.296682\pi$
$542$	21.2253	−	18.3918i	0.911705	−	0.789997i
$543$	−31.2166	−	13.4976i	−1.33963	−	0.579239i
$544$	−2.44158	−	0.351047i	−0.104682	−	0.0150510i
$545$	−0.268424	−	0.232591i	−0.0114980	−	0.00996311i
$546$	8.10932	+	16.8440i	0.347047	+	0.720856i
$547$	13.1059	+	3.84823i	0.560367	+	0.164538i	0.549636	−	0.835404i	$-0.314766\pi$
$547$	13.1059	+	3.84823i	0.560367	+	0.164538i	0.0107301	+	0.999942i	$0.496584\pi$
$548$	−6.11513	−	13.3903i	−0.261226	−	0.572004i
$549$	0.865446	+	2.55853i	0.0369363	+	0.109196i
$550$	−3.12620	+	4.86446i	−0.133302	+	0.207421i
$551$	−13.2329			−0.563740
$552$	2.50555	+	7.91974i	0.106643	+	0.337086i
$553$	−7.14810			−0.303968
$554$	6.84459	−	10.6504i	0.290799	−	0.452491i
$555$	−2.67655	+	4.35666i	−0.113613	+	0.184930i
$556$	2.65311	+	5.80950i	0.112517	+	0.246378i
$557$	0.741256	+	0.217652i	0.0314080	+	0.00922222i	0.297399	−	0.954753i	$-0.403881\pi$
$557$	0.741256	+	0.217652i	0.0314080	+	0.00922222i	−0.265991	+	0.963976i	$0.585699\pi$
$558$	5.46139	−	21.8415i	0.231199	−	0.924626i
$559$	−28.4104	−	24.6178i	−1.20163	−	1.04122i
$560$	−2.53663	−	0.364712i	−0.107192	−	0.0154119i
$561$	9.80478	−	22.6760i	0.413958	−	0.957380i
$562$	5.57514	−	4.83089i	0.235173	−	0.203779i
$563$	29.4323	−	18.9150i	1.24042	−	0.797172i	0.254943	−	0.966956i	$-0.417943\pi$
$563$	29.4323	−	18.9150i	1.24042	−	0.797172i	0.985481	+	0.169784i	$0.0543070\pi$
$564$	−2.66170	−	0.327729i	−0.112078	−	0.0137999i
$565$	11.2116	+	12.9389i	0.471676	+	0.544343i
$566$	4.55276	−	1.33681i	0.191367	−	0.0561904i
$567$	22.4884	−	5.12230i	0.944425	−	0.215116i
$568$	5.53766	−	6.39080i	0.232355	−	0.268152i
$569$	10.8605	−	23.7812i	0.455297	−	0.996961i	−0.533238	−	0.845965i	$-0.679025\pi$
$569$	10.8605	−	23.7812i	0.455297	−	0.996961i	0.988534	−	0.150995i	$-0.0482478\pi$
$570$	−1.91060	+	1.28338i	−0.0800264	+	0.0537547i
$571$	−8.65904	+	3.95445i	−0.362369	+	0.165489i	−0.588276	−	0.808660i	$-0.700193\pi$
$571$	−8.65904	+	3.95445i	−0.362369	+	0.165489i	0.225906	+	0.974149i	$0.427466\pi$
$572$	−3.46584	−	24.1055i	−0.144914	−	1.00790i
$573$	−10.8551	+	3.42803i	−0.453478	+	0.143208i
$574$		−	26.0364i		−	1.08674i
$575$	1.99452	+	4.36141i	0.0831770	+	0.181883i
$576$	0.547053	+	2.94970i	0.0227939	+	0.122904i
$577$	5.62370	+	3.61413i	0.234118	+	0.150458i	0.652440	−	0.757840i	$-0.273745\pi$
$577$	5.62370	+	3.61413i	0.234118	+	0.150458i	−0.418322	+	0.908299i	$0.637382\pi$
$578$	−10.8043	+	1.55343i	−0.449401	+	0.0646141i
$579$	−19.8756	−	5.40051i	−0.826001	−	0.224438i
$580$	−2.80555	+	9.55483i	−0.116494	+	0.396743i
$581$	21.0925	+	9.63264i	0.875066	+	0.399629i
$582$	−1.63216	−	9.91896i	−0.0676553	−	0.411154i
$583$	−6.88642	+	47.8961i	−0.285206	+	1.98365i
$584$	3.22854	+	10.9954i	0.133598	+	0.454993i
$585$	7.87994	−	9.87662i	0.325795	−	0.408348i
$586$	−5.81128	−	9.04252i	−0.240062	−	0.373543i
$587$	−5.47855	−	8.52478i	−0.226124	−	0.351856i	0.709590	−	0.704614i	$-0.248880\pi$
$587$	−5.47855	−	8.52478i	−0.226124	−	0.351856i	−0.935714	+	0.352759i	$0.885244\pi$
$588$	−0.748959	+	0.0151974i	−0.0308865	+	0.000626731i
$589$	−2.80958	−	9.56855i	−0.115767	−	0.394265i
$590$	0.496537	−	3.45349i	0.0204421	−	0.142178i
$591$	−37.2797	+	6.13437i	−1.53348	+	0.252334i
$592$	2.68531	+	1.22634i	0.110366	+	0.0504023i
$593$	12.2671	−	41.7781i	0.503751	−	1.71562i	−0.177995	−	0.984031i	$-0.556961\pi$
$593$	12.2671	−	41.7781i	0.503751	−	1.71562i	0.681746	−	0.731589i	$-0.261221\pi$
$594$	−29.9454	−	2.45905i	−1.22868	−	0.100896i
$595$	6.25708	−	0.899632i	0.256515	−	0.0368813i
$596$	1.91294	+	1.22937i	0.0783570	+	0.0503570i
$597$	3.33818	+	2.77600i	0.136623	+	0.113614i
$598$	−18.3774	−	8.38118i	−0.751506	−	0.342732i
$599$		−	15.7761i		−	0.644595i	−0.946638	−	0.322298i	$-0.895545\pi$
$599$		−	15.7761i		−	0.644595i	0.946638	−	0.322298i	$-0.104455\pi$
$600$	0.521590	+	1.65165i	0.0212938	+	0.0674283i
$601$	6.84193	+	47.5867i	0.279088	+	1.94110i	0.333909	+	0.942605i	$0.391632\pi$
$601$	6.84193	+	47.5867i	0.279088	+	1.94110i	−0.0548210	+	0.998496i	$0.517459\pi$
$602$	−20.8073	+	9.50236i	−0.848041	+	0.387287i
$603$	43.1859	+	4.43001i	1.75867	+	0.180404i
$604$	−2.68993	+	5.89013i	−0.109452	+	0.239666i
$605$	−14.6925	+	16.9561i	−0.597337	+	0.689363i
$606$	−21.5857	−	23.9132i	−0.876859	−	0.971409i
$607$	31.1060	−	9.13355i	1.26255	−	0.370719i	0.419110	−	0.907936i	$-0.362342\pi$
$607$	31.1060	−	9.13355i	1.26255	−	0.370719i	0.843444	+	0.537216i	$0.180524\pi$
$608$	0.870206	+	1.00427i	0.0352915	+	0.0407286i
$609$	5.40170	−	43.8707i	0.218888	−	1.77773i
$610$	0.757393	−	0.486747i	0.0306659	−	0.0197078i
$611$	4.92827	−	4.27037i	0.199376	−	0.172761i
$612$	−3.34464	−	6.60110i	−0.135199	−	0.266834i
$613$	5.51748	+	0.793294i	0.222849	+	0.0320408i	0.252835	−	0.967509i	$-0.418637\pi$
$613$	5.51748	+	0.793294i	0.222849	+	0.0320408i	−0.0299858	+	0.999550i	$0.509546\pi$
$614$	−2.30425	−	1.99665i	−0.0929921	−	0.0805781i
$615$	−15.8553	+	7.63333i	−0.639347	+	0.307806i
$616$	−14.2184	−	4.17489i	−0.572874	−	0.168211i
$617$	−9.86851	−	21.6090i	−0.397291	−	0.869946i	−0.997538	−	0.0701314i	$-0.977658\pi$
$617$	−9.86851	−	21.6090i	−0.397291	−	0.869946i	0.600247	−	0.799815i	$-0.295069\pi$
$618$	16.9053	+	10.3859i	0.680030	+	0.417782i
$619$	6.65486	−	10.3552i	0.267481	−	0.416209i	−0.681367	−	0.731942i	$-0.738614\pi$
$619$	6.65486	−	10.3552i	0.267481	−	0.416209i	0.948848	+	0.315733i	$0.102250\pi$
$620$	−7.50466			−0.301394
$621$	−15.1330	+	19.7988i	−0.607267	+	0.794498i
$622$	10.9923			0.440751
$623$	−11.8952	+	18.5093i	−0.476572	+	0.741561i
$624$	−6.21550	−	3.81854i	−0.248819	−	0.152864i
$625$	0.415415	+	0.909632i	0.0166166	+	0.0363853i
$626$	−11.4941	−	3.37499i	−0.459399	−	0.134892i
$627$	−11.9915	+	5.77318i	−0.478896	+	0.230558i
$628$	−2.28246	−	1.97776i	−0.0910800	−	0.0789213i
$629$	−7.20776	−	1.03632i	−0.287392	−	0.0413208i
$630$	−3.47483	−	6.85806i	−0.138441	−	0.273232i
$631$	36.0577	−	31.2442i	1.43544	−	1.24381i	0.512595	−	0.858630i	$-0.328684\pi$
$631$	36.0577	−	31.2442i	1.43544	−	1.24381i	0.922841	−	0.385182i	$-0.125861\pi$
$632$	2.34648	−	1.50799i	0.0933381	−	0.0599847i
$633$	2.93454	−	23.8333i	0.116638	−	0.947290i
$634$	8.41254	+	9.70859i	0.334105	+	0.385577i
$635$	3.77676	−	1.10896i	0.149876	−	0.0440076i
$636$	9.71199	+	10.7592i	0.385106	+	0.426631i
$637$	1.19285	−	1.37662i	0.0472625	−	0.0545439i
$638$	−23.9206	+	52.3787i	−0.947024	+	2.07369i
$639$	25.2363	+	2.58874i	0.998333	+	0.102409i
$640$	0.909632	−	0.415415i	0.0359564	−	0.0164207i
$641$	6.44662	+	44.8372i	0.254626	+	1.77096i	0.569657	+	0.821883i	$0.307076\pi$
$641$	6.44662	+	44.8372i	0.254626	+	1.77096i	−0.315031	+	0.949081i	$0.602015\pi$
$642$	−8.22562	−	26.0470i	−0.324639	−	1.02799i
$643$			30.6594i			1.20909i	0.796572	+	0.604543i	$0.206644\pi$
$643$			30.6594i			1.20909i	−0.796572	+	0.604543i	$0.793356\pi$
$644$	−9.28426	+	8.05326i	−0.365851	+	0.317343i
$645$	11.8869	+	9.88504i	0.468046	+	0.389223i
$646$	−2.75750	−	1.77214i	−0.108492	−	0.0697237i
$647$	−36.7534	+	5.28434i	−1.44493	+	0.207749i	−0.819744	−	0.572730i	$-0.805884\pi$
$647$	−36.7534	+	5.28434i	−1.44493	+	0.207749i	−0.625182	+	0.780479i	$0.714975\pi$
$648$	−6.30158	+	6.42574i	−0.247549	+	0.252427i
$649$	5.68390	−	19.3576i	0.223113	−	0.759852i
$650$	−3.83104	−	1.74958i	−0.150266	−	0.0686241i
$651$	32.8693	−	5.40863i	1.28825	−	0.211981i
$652$	1.89177	−	13.1575i	0.0740873	−	0.515289i
$653$	1.26295	+	4.30120i	0.0494229	+	0.168319i	0.980506	−	0.196487i	$-0.0629534\pi$
$653$	1.26295	+	4.30120i	0.0494229	+	0.168319i	−0.931083	+	0.364806i	$0.881135\pi$
$654$	−0.615057	+	0.0124804i	−0.0240506	+	0.000488021i
$655$	10.4994	+	16.3374i	0.410245	+	0.638354i
$656$	5.49275	+	8.54688i	0.214456	+	0.333700i
$657$	−21.4408	+	26.8736i	−0.836486	+	1.04844i
$658$	−1.11790	−	3.80721i	−0.0435802	−	0.148421i
$659$	−3.84254	+	26.7255i	−0.149684	+	1.04108i	0.767052	+	0.641585i	$0.221723\pi$
$659$	−3.84254	+	26.7255i	−0.149684	+	1.04108i	−0.916737	+	0.399492i	$0.869186\pi$
$660$	1.62616	+	9.88251i	0.0632984	+	0.384676i
$661$	10.5642	+	4.82451i	0.410900	+	0.187652i	0.610130	−	0.792301i	$-0.291117\pi$
$661$	10.5642	+	4.82451i	0.410900	+	0.187652i	−0.199231	+	0.979953i	$0.563844\pi$
$662$	3.11878	−	10.6216i	0.121215	−	0.412820i
$663$	17.3644	+	4.71818i	0.674376	+	0.183239i
$664$	−8.95613	+	1.28770i	−0.347565	+	0.0499723i
$665$	−2.86484	−	1.84112i	−0.111094	−	0.0713956i
$666$	1.61495	+	8.70777i	0.0625779	+	0.337419i
$667$	25.8406	+	40.1632i	1.00055	+	1.55512i
$668$			4.52512i			0.175082i
$669$	−3.39900	+	1.07340i	−0.131413	+	0.0415001i
$670$	−2.05942	−	14.3235i	−0.0795622	−	0.553367i
$671$	4.73552	−	2.16264i	0.182813	−	0.0834878i
$672$	−3.68466	+	2.47503i	−0.142139	+	0.0954764i
$673$	14.4316	−	31.6008i	0.556298	−	1.21812i	−0.397480	−	0.917611i	$-0.630115\pi$
$673$	14.4316	−	31.6008i	0.556298	−	1.21812i	0.953778	−	0.300512i	$-0.0971575\pi$
$674$	3.64124	−	4.20222i	0.140255	−	0.161863i
$675$	−3.15758	+	4.12670i	−0.121535	+	0.158837i
$676$	4.54596	−	1.33482i	0.174845	−	0.0513391i
$677$	−18.1373	−	20.9315i	−0.697071	−	0.804463i	0.291282	−	0.956637i	$-0.405918\pi$
$677$	−18.1373	−	20.9315i	−0.697071	−	0.804463i	−0.988354	+	0.152174i	$0.951373\pi$
$678$	29.4315	+	3.62383i	1.13031	+	0.139172i
$679$	12.5122	−	8.04111i	0.480174	−	0.308589i
$680$	−1.86420	+	1.61534i	−0.0714888	+	0.0619454i
$681$	0.482694	−	1.11635i	0.0184969	−	0.0427786i
$682$	−42.9532	−	6.17574i	−1.64476	−	0.236481i
$683$	12.0251	+	10.4198i	0.460128	+	0.398704i	0.853844	−	0.520529i	$-0.174265\pi$
$683$	12.0251	+	10.4198i	0.460128	+	0.398704i	−0.393716	+	0.919232i	$0.628811\pi$
$684$	−0.967043	+	3.86746i	−0.0369758	+	0.147876i
$685$	−14.1243	−	4.14726i	−0.539660	−	0.158458i
$686$	−7.91256	−	17.3261i	−0.302103	−	0.661513i
$687$	−12.0473	+	19.6096i	−0.459634	+	0.748153i
$688$	4.82567	−	7.50889i	0.183977	−	0.286274i
$689$	−35.2441			−1.34269
$690$	7.62612	+	3.29275i	0.290322	+	0.125353i
$691$	30.9086			1.17582			0.587910	−	0.808926i	$-0.299951\pi$
$691$	30.9086			1.17582			0.587910	+	0.808926i	$0.299951\pi$
$692$	−1.23651	+	1.92405i	−0.0470052	+	0.0731415i
$693$	−14.2447	−	42.1119i	−0.541112	−	1.59970i
$694$	11.2460	+	24.6254i	0.426893	+	0.934766i
$695$	6.12794	+	1.79933i	0.232446	+	0.0682523i
$696$	7.48195	+	15.5409i	0.283603	+	0.589075i
$697$	−18.9397	−	16.4114i	−0.717393	−	0.621624i
$698$	4.11283	+	0.591336i	0.155673	+	0.0223824i
$699$	12.9116	+	5.58282i	0.488363	+	0.211162i
$700$	−1.93677	+	1.67822i	−0.0732030	+	0.0634308i
$701$	−17.8784	+	11.4898i	−0.675259	+	0.433963i	−0.832818	−	0.553547i	$-0.813274\pi$
$701$	−17.8784	+	11.4898i	−0.675259	+	0.433963i	0.157559	+	0.987510i	$0.449638\pi$
$702$	−1.33118	−	21.8438i	−0.0502423	−	0.824440i
$703$	2.56892	+	2.96470i	0.0968888	+	0.111816i
$704$	5.54817	−	1.62909i	0.209105	−	0.0613986i
$705$	−1.99072	+	1.79696i	−0.0749750	+	0.0676775i
$706$	−2.40621	+	2.77691i	−0.0905588	+	0.104510i
$707$	19.8005	−	43.3570i	0.744673	−	1.63061i
$708$	−3.36963	−	5.01648i	−0.126638	−	0.188531i
$709$	7.37602	−	3.36852i	0.277012	−	0.126507i	−0.272065	−	0.962279i	$-0.587707\pi$
$709$	7.37602	−	3.36852i	0.277012	−	0.126507i	0.549077	+	0.835772i	$0.314979\pi$
$710$	−1.20345	−	8.37017i	−0.0451646	−	0.314127i
$711$	7.74637	+	3.16448i	0.290512	+	0.118677i
$712$		−	8.58547i		−	0.321754i
$713$	−23.5551	+	27.2124i	−0.882145	+	1.01911i
$714$	7.00074	−	8.41848i	0.261996	−	0.315054i
$715$	−20.4873	−	13.1664i	−0.766183	−	0.492396i
$716$	−23.8328	+	3.42663i	−0.890672	+	0.128059i
$717$	6.78844	−	24.9836i	0.253519	−	0.933028i
$718$	−5.44439	+	18.5419i	−0.203183	+	0.691977i
$719$	9.70419	+	4.43176i	0.361905	+	0.165277i	0.588065	−	0.808814i	$-0.299890\pi$
$719$	9.70419	+	4.43176i	0.361905	+	0.165277i	−0.226160	+	0.974090i	$0.572617\pi$
$720$	2.58748	+	1.51821i	0.0964296	+	0.0565803i
$721$	−4.17780	+	29.0573i	−0.155589	+	1.08215i
$722$	−4.85543	−	16.5361i	−0.180700	−	0.615409i
$723$	0.0214874	+	1.05894i	0.000799124	+	0.0393824i
$724$	10.6158	+	16.5185i	0.394532	+	0.613903i
$725$	5.38382	+	8.37738i	0.199950	+	0.311128i
$726$	0.788371	+	38.8525i	0.0292592	+	1.44195i
$727$	−3.56706	−	12.1483i	−0.132295	−	0.450556i	0.866524	−	0.499135i	$-0.166349\pi$
$727$	−3.56706	−	12.1483i	−0.132295	−	0.450556i	−0.998819	+	0.0485794i	$0.984531\pi$
$728$	1.53603	−	10.6834i	0.0569292	−	0.395952i
$729$	−26.6383	−	4.40465i	−0.986604	−	0.163135i
$730$	10.4240	+	4.76049i	0.385810	+	0.176194i
$731$	−6.20299	+	21.1254i	−0.229426	+	0.781353i
$732$	0.408886	−	1.50483i	0.0151129	−	0.0556201i
$733$	6.74269	−	0.969452i	0.249047	−	0.0358075i	−0.0166607	−	0.999861i	$-0.505304\pi$
$733$	6.74269	−	0.969452i	0.249047	−	0.0358075i	0.265708	+	0.964054i	$0.414394\pi$
$734$	−17.1281	−	11.0075i	−0.632208	−	0.406296i
$735$	−0.478978	+	0.575978i	−0.0176674	+	0.0212453i
$736$	1.34876	−	4.60226i	0.0497161	−	0.169642i
$737$		−	83.6762i		−	3.08225i
$738$	−11.5264	+	28.2156i	−0.424291	+	1.03863i
$739$	2.48560	+	17.2877i	0.0914341	+	0.635938i	0.983076	+	0.183197i	$0.0586447\pi$
$739$	2.48560	+	17.2877i	0.0914341	+	0.635938i	−0.891642	+	0.452741i	$0.850446\pi$
$740$	2.68531	−	1.22634i	0.0987140	−	0.0450812i
$741$	−5.40511	−	8.04677i	−0.198562	−	0.295606i
$742$	−8.90876	+	19.5075i	−0.327051	+	0.716142i
$743$	0.824757	−	0.951820i	0.0302574	−	0.0349189i	−0.740419	−	0.672145i	$-0.765373\pi$
$743$	0.824757	−	0.951820i	0.0302574	−	0.0349189i	0.770677	+	0.637227i	$0.219918\pi$
$744$	−9.64886	+	8.70972i	−0.353745	+	0.319314i
$745$	2.18180	−	0.640636i	0.0799351	−	0.0234711i
$746$	5.43390	+	6.27105i	0.198949	+	0.229599i
$747$	−18.5935	−	19.7766i	−0.680302	−	0.723587i
$748$	−11.9991	+	7.71137i	−0.438732	+	0.281956i
$749$	30.5434	−	26.4660i	1.11603	−	0.967047i
$750$	1.58980	+	0.687409i	0.0580513	+	0.0251006i
$751$	−34.0221	−	4.89163i	−1.24148	−	0.178498i	−0.509890	−	0.860240i	$-0.670314\pi$
$751$	−34.0221	−	4.89163i	−1.24148	−	0.178498i	−0.731593	+	0.681741i	$0.761223\pi$
$752$	1.17016	+	1.01395i	0.0426712	+	0.0369748i
$753$	6.12380	+	12.7198i	0.223164	+	0.463536i
$754$	−40.2415	−	11.8160i	−1.46551	−	0.430312i
$755$	2.68993	+	5.89013i	0.0978967	+	0.214364i
$756$	−12.4269	−	4.78472i	−0.451964	−	0.174019i
$757$	21.4958	−	33.4482i	0.781280	−	1.21570i	−0.190935	−	0.981603i	$-0.561152\pi$
$757$	21.4958	−	33.4482i	0.781280	−	1.21570i	0.972214	−	0.234092i	$-0.0752118\pi$
$758$	−16.1962			−0.588271
$759$	40.9388	+	25.1219i	1.48598	+	0.911868i
$760$	1.32884			0.0482022
$761$	−16.1793	+	25.1754i	−0.586498	+	0.912608i	0.413500	+	0.910504i	$0.364306\pi$
$761$	−16.1793	+	25.1754i	−0.586498	+	0.912608i	−0.999998	+	0.00210408i	$0.999330\pi$
$762$	3.56881	−	5.80901i	0.129285	−	0.210438i
$763$	−0.378117	−	0.827961i	−0.0136888	−	0.0299742i
$764$	6.30605	+	1.85162i	0.228145	+	0.0669893i
$765$	−7.17905	−	1.79509i	−0.259559	−	0.0649017i
$766$	−7.67844	−	6.65340i	−0.277433	−	0.240397i
$767$	14.5448	+	2.09123i	0.525184	+	0.0755100i
$768$	0.687409	−	1.58980i	0.0248047	−	0.0573670i
$769$	6.00967	−	5.20741i	0.216714	−	0.187784i	−0.539738	−	0.841833i	$-0.681477\pi$
$769$	6.00967	−	5.20741i	0.216714	−	0.187784i	0.756452	+	0.654049i	$0.226931\pi$
$770$	−12.4662	+	8.01155i	−0.449251	+	0.288716i
$771$	−6.39529	−	0.787437i	−0.230321	−	0.0283589i
$772$	7.78710	+	8.98679i	0.280264	+	0.323442i
$773$	11.2206	−	3.29466i	0.403576	−	0.118501i	−0.0736438	−	0.997285i	$-0.523463\pi$
$773$	11.2206	−	3.29466i	0.403576	−	0.118501i	0.477220	+	0.878784i	$0.341645\pi$
$774$	26.7555	−	1.08626i	0.961706	−	0.0390448i
$775$	−4.91451	+	5.67164i	−0.176534	+	0.203731i
$776$	−2.41096	+	5.27926i	−0.0865483	+	0.189514i
$777$	−10.8774	+	7.30650i	−0.390226	+	0.262119i
$778$	−19.4326	+	8.87456i	−0.696691	+	0.318168i
$779$	1.92134	+	13.3632i	0.0688391	+	0.478787i
$780$	−6.95614	+	2.19675i	−0.249070	+	0.0786561i
$781$		−	48.8974i		−	1.74969i
$782$	0.00611525	+	11.8298i	0.000218681	+	0.423034i
$783$	−25.2755	+	45.1512i	−0.903271	+	1.61357i
$784$	0.363843	+	0.233828i	0.0129944	+	0.00835098i
$785$	−2.98938	+	0.429809i	−0.106696	+	0.0153405i
$786$	32.4600	+	8.81990i	1.15781	+	0.314595i
$787$	13.3752	−	45.5516i	0.476773	−	1.62374i	−0.272978	−	0.962020i	$-0.588009\pi$
$787$	13.3752	−	45.5516i	0.476773	−	1.62374i	0.749751	−	0.661720i	$-0.230173\pi$
$788$	19.8417	+	9.06141i	0.706832	+	0.322799i
$789$	−2.49137	−	15.1405i	−0.0886951	−	0.539017i
$790$	0.396955	−	2.76088i	0.0141230	−	0.0982277i
$791$	12.3611	+	42.0979i	0.439509	+	1.49683i
$792$	13.5602	+	10.8188i	0.481840	+	0.384430i
$793$	2.05000	+	3.18986i	0.0727976	+	0.113275i
$794$	0.435035	+	0.676928i	0.0154388	+	0.0240233i
$795$	14.4913	−	0.294048i	0.513952	−	0.0104288i
$796$	−0.706200	−	2.40510i	−0.0250306	−	0.0852464i
$797$	4.30236	−	29.9236i	0.152398	−	1.05995i	−0.759788	−	0.650171i	$-0.774697\pi$
$797$	4.30236	−	29.9236i	0.152398	−	1.05995i	0.912186	−	0.409777i	$-0.134394\pi$
$798$	−5.82013	+	0.957701i	−0.206030	+	0.0339022i
$799$	−3.47413	−	1.58658i	−0.122906	−	0.0561292i
$800$	0.281733	−	0.959493i	0.00996075	−	0.0339232i
$801$	21.0849	−	14.7925i	0.745000	−	0.522666i
$802$	−14.5160	+	2.08708i	−0.512576	+	0.0736973i
$803$	55.7448	+	35.8250i	1.96719	+	1.26424i
$804$	−19.2714	−	16.0259i	−0.679649	−	0.565190i
$805$	0.00635330	+	12.2903i	0.000223924	+	0.433178i
$806$		−	31.6069i		−	1.11331i
$807$	0.969171	+	3.06894i	0.0341164	+	0.108032i
$808$	2.64694	+	18.4098i	0.0931189	+	0.647656i
$809$	1.34769	−	0.615469i	0.0473822	−	0.0216387i	−0.391583	−	0.920143i	$-0.628072\pi$
$809$	1.34769	−	0.615469i	0.0473822	−	0.0216387i	0.438965	+	0.898504i	$0.355345\pi$
$810$	0.729588	+	8.97038i	0.0256351	+	0.315187i
$811$	1.80539	−	3.95326i	0.0633960	−	0.138818i	−0.875282	−	0.483613i	$-0.839324\pi$
$811$	1.80539	−	3.95326i	0.0633960	−	0.138818i	0.938678	+	0.344795i	$0.112052\pi$
$812$	−16.7121	+	19.2868i	−0.586479	+	0.676833i
$813$	−32.5948	−	36.1095i	−1.14315	−	1.26641i
$814$	16.3787	−	4.80921i	0.574072	−	0.168563i
$815$	−8.70495	−	10.0461i	−0.304921	−	0.351898i
$816$	−0.522112	+	4.24041i	−0.0182776	+	0.148444i
$817$	9.97814	−	6.41256i	0.349091	−	0.224347i
$818$	14.0122	−	12.1416i	0.489925	−	0.424522i
$819$	28.8837	−	14.6347i	1.00928	−	0.511379i
$820$	10.0563	+	1.44588i	0.351181	+	0.0504922i
$821$	−15.4202	−	13.3617i	−0.538168	−	0.466325i	0.342862	−	0.939386i	$-0.388604\pi$
$821$	−15.4202	−	13.3617i	−0.538168	−	0.466325i	−0.881030	+	0.473061i	$0.843149\pi$
$822$	−22.9730	+	11.0601i	−0.801275	+	0.385764i
$823$	12.7841	+	3.75374i	0.445625	+	0.130847i	0.496843	−	0.867840i	$-0.334492\pi$
$823$	12.7841	+	3.75374i	0.445625	+	0.130847i	−0.0512186	+	0.998687i	$0.516311\pi$
$824$	−4.75861	−	10.4199i	−0.165774	−	0.362994i
$825$	8.53361	+	5.24269i	0.297102	+	0.182527i
$826$	4.83404	−	7.52191i	0.168198	−	0.261721i
$827$	−19.0027			−0.660788			−0.330394	−	0.943843i	$-0.607182\pi$
$827$	−19.0027			−0.660788			−0.330394	+	0.943843i	$0.607182\pi$
$828$	13.6265	−	4.61714i	0.473554	−	0.160457i
$829$	1.73926			0.0604069			0.0302035	−	0.999544i	$-0.490384\pi$
$829$	1.73926			0.0604069			0.0302035	+	0.999544i	$0.490384\pi$
$830$	−4.89184	+	7.61185i	−0.169798	+	0.264211i
$831$	−18.6837	−	11.4785i	−0.648131	−	0.398184i
$832$	1.74958	+	3.83104i	0.0606557	+	0.132817i
$833$	−1.02363	−	0.300565i	−0.0354667	−	0.0104140i
$834$	9.96705	−	4.79851i	0.345131	−	0.166159i
$835$	3.41986	+	2.96332i	0.118349	+	0.102550i
$836$	7.60568	+	1.09353i	0.263048	+	0.0378206i
$837$	−38.0148	−	8.68998i	−1.31398	−	0.300370i
$838$	−3.82117	+	3.31106i	−0.132000	+	0.114379i
$839$	−34.7437	+	22.3284i	−1.19949	+	0.770863i	−0.978867	−	0.204497i	$-0.934444\pi$
$839$	−34.7437	+	22.3284i	−1.19949	+	0.770863i	−0.220619	+	0.975360i	$0.570808\pi$
$840$	−0.542437	+	4.40548i	−0.0187158	+	0.152004i
$841$	45.9489	+	53.0279i	1.58445	+	1.82855i
$842$	−27.7505	+	8.14829i	−0.956346	+	0.280809i
$843$	−8.56152	−	9.48469i	−0.294874	−	0.326670i
$844$	−9.07905	+	10.4778i	−0.312514	+	0.360660i
$845$	1.96819	−	4.30973i	0.0677077	−	0.148259i
$846$	−0.473998	+	4.62076i	−0.0162964	+	0.158865i
$847$	−52.3014	+	23.8853i	−1.79710	+	0.820707i
$848$	−1.19093	−	8.28309i	−0.0408966	−	0.284442i
$849$	−2.47493	−	7.83702i	−0.0849393	−	0.268966i
$850$			2.46669i			0.0846068i
$851$	3.98166	−	13.5863i	0.136490	−	0.465732i
$852$	−11.2615	−	9.36498i	−0.385813	−	0.320839i
$853$	−43.7024	−	28.0859i	−1.49634	−	0.961641i	−0.995364	−	0.0961824i	$-0.969337\pi$
$853$	−43.7024	−	28.0859i	−1.49634	−	0.961641i	−0.500980	−	0.865459i	$-0.667027\pi$
$854$	2.28376	−	0.328356i	0.0781488	−	0.0112361i
$855$	2.28955	+	3.26349i	0.0783010	+	0.111609i
$856$	−4.44300	+	15.1315i	−0.151859	+	0.517183i
$857$	47.9557	+	21.9006i	1.63813	+	0.748111i	0.999766	−	0.0216207i	$-0.00688263\pi$
$857$	47.9557	+	21.9006i	1.63813	+	0.748111i	0.638368	+	0.769731i	$0.279610\pi$
$858$	−41.6215	+	6.84881i	−1.42094	+	0.233815i
$859$	5.28014	−	36.7242i	0.180156	−	1.25301i	−0.676235	−	0.736686i	$-0.736390\pi$
$859$	5.28014	−	36.7242i	0.180156	−	1.25301i	0.856391	−	0.516327i	$-0.172701\pi$
$860$	−2.51470	−	8.56428i	−0.0857506	−	0.292040i
$861$	−45.0871	+	0.914879i	−1.53656	+	0.0311790i
$862$	1.16411	+	1.81139i	0.0396496	+	0.0616961i
$863$	−8.42143	−	13.1040i	−0.286669	−	0.446065i	0.667815	−	0.744327i	$-0.267230\pi$
$863$	−8.42143	−	13.1040i	−0.286669	−	0.446065i	−0.954484	+	0.298262i	$0.903593\pi$
$864$	5.08876	−	1.05098i	0.173123	−	0.0357549i
$865$	0.644357	+	2.19448i	0.0219088	+	0.0746145i
$866$	3.81072	−	26.5041i	0.129494	−	0.900648i
$867$	3.06971	+	18.6552i	0.104253	+	0.633564i
$868$	−17.4943	−	7.98938i	−0.593795	−	0.271177i
$869$	4.54397	−	15.4753i	0.154144	−	0.524965i
$870$	16.6446	+	4.52262i	0.564306	+	0.153331i
$871$	60.3256	−	8.67351i	2.04405	−	0.293891i
$872$	0.298793	+	0.192023i	0.0101184	+	0.00650272i
$873$	−17.1193	+	3.17494i	−0.579399	+	0.107456i
$874$	4.17087	−	4.81847i	0.141082	−	0.162987i
$875$			2.56271i			0.0866355i
$876$	18.9272	−	5.97721i	0.639492	−	0.201951i
$877$	6.74357	+	46.9025i	0.227714	+	1.58379i	0.707702	+	0.706511i	$0.249732\pi$
$877$	6.74357	+	46.9025i	0.227714	+	1.58379i	−0.479988	+	0.877275i	$0.659359\pi$
$878$	7.91595	−	3.61509i	0.267150	−	0.122003i
$879$	−15.4547	+	10.3811i	−0.521274	+	0.350146i
$880$	2.40209	−	5.25985i	0.0809746	−	0.177310i
$881$	19.7641	−	22.8090i	0.665868	−	0.768453i	−0.317856	−	0.948139i	$-0.602963\pi$
$881$	19.7641	−	22.8090i	0.665868	−	0.768453i	0.983724	+	0.179686i	$0.0575082\pi$
$882$	0.0526346	+	1.29643i	0.00177230	+	0.0436532i
$883$	27.7570	−	8.15018i	0.934096	−	0.274275i	0.220945	−	0.975286i	$-0.429086\pi$
$883$	27.7570	−	8.15018i	0.934096	−	0.274275i	0.713151	+	0.701011i	$0.247268\pi$
$884$	−6.80322	−	7.85134i	−0.228817	−	0.264069i
$885$	−5.99784	−	0.738500i	−0.201615	−	0.0248244i
$886$	10.0371	−	6.45042i	0.337201	−	0.216706i
$887$	16.0327	−	13.8924i	0.538325	−	0.466462i	−0.342757	−	0.939424i	$-0.611361\pi$
$887$	16.0327	−	13.8924i	0.538325	−	0.466462i	0.881083	+	0.472962i	$0.156815\pi$
$888$	2.02929	−	4.69323i	0.0680985	−	0.157494i
$889$	9.98468	+	1.43558i	0.334876	+	0.0481478i
$890$	−6.48846	−	5.62228i	−0.217494	−	0.188459i
$891$	−3.20608	+	51.9427i	−0.107408	+	1.74015i
$892$	1.97458	+	0.579789i	0.0661138	+	0.0194128i
$893$	0.854715	+	1.87156i	0.0286019	+	0.0626295i
$894$	2.06168	−	3.35582i	0.0689528	−	0.112235i
$895$	−13.0175	+	20.2556i	−0.435126	+	0.677069i
$896$	2.56271			0.0856142
$897$	−13.8679	+	32.1185i	−0.463035	+	1.07240i
$898$	−12.9315			−0.431531
$899$	−40.4037	+	62.8694i	−1.34754	+	2.09681i
$900$	2.84182	−	0.961271i	0.0947274	−	0.0320424i
$901$	8.57496	+	18.7765i	0.285673	+	0.625538i
$902$	56.3677	+	16.5511i	1.87684	+	0.551090i
$903$	17.1863	+	35.6979i	0.571925	+	1.18795i
$904$	−12.9389	−	11.2116i	−0.430341	−	0.372892i
$905$	19.4357	+	2.79443i	0.646063	+	0.0928899i
$906$	10.2944	+	4.45117i	0.342010	+	0.147880i
$907$	17.4730	−	15.1404i	0.580181	−	0.502730i	−0.314606	−	0.949222i	$-0.601872\pi$
$907$	17.4730	−	15.1404i	0.580181	−	0.502730i	0.894788	+	0.446492i	$0.147327\pi$
$908$	−0.590723	+	0.379635i	−0.0196038	+	0.0125986i
$909$	−40.6519	+	38.2201i	−1.34834	+	1.26768i
$910$	−7.06805	−	8.15697i	−0.234304	−	0.270401i
$911$	−32.1937	+	9.45293i	−1.06663	+	0.313190i	−0.767517	−	0.641029i	$-0.778508\pi$
$911$	−32.1937	+	9.45293i	−1.06663	+	0.313190i	−0.299110	+	0.954219i	$0.596690\pi$
$912$	1.70851	−	1.54222i	0.0565746	−	0.0510680i
$913$	−34.2626	+	39.5411i	−1.13393	+	1.30862i
$914$	16.2023	−	35.4781i	0.535925	−	1.17351i
$915$	−0.869510	−	1.29447i	−0.0287451	−	0.0427938i
$916$	12.0867	−	5.51983i	0.399357	−	0.182380i
$917$	7.08281	+	49.2620i	0.233895	+	1.62678i
$918$	−11.3136	+	6.02384i	−0.373403	+	0.198816i
$919$		−	18.9768i		−	0.625986i	−0.949755	−	0.312993i	$-0.898668\pi$
$919$		−	18.9768i		−	0.625986i	0.949755	−	0.312993i	$-0.101332\pi$
$920$	−2.59491	−	4.03317i	−0.0855516	−	0.132970i
$921$	−3.37662	+	4.06042i	−0.111263	+	0.133795i
$922$	11.8426	+	7.61075i	0.390014	+	0.250647i
$923$	35.2521	−	5.06849i	1.16034	−	0.166831i
$924$	−6.73002	+	24.7686i	−0.221401	+	0.814826i
$925$	0.831698	−	2.83250i	0.0273461	−	0.0931322i
$926$	−29.3595	−	13.4081i	−0.964814	−	0.440616i
$927$	17.3912	−	29.6397i	0.571201	−	0.973497i
$928$	1.41720	−	9.85685i	0.0465219	−	0.323567i
$929$	−10.0920	−	34.3703i	−0.331108	−	1.12765i	−0.941909	−	0.335868i	$-0.890971\pi$
$929$	−10.0920	−	34.3703i	−0.331108	−	1.12765i	0.610801	−	0.791784i	$-0.290848\pi$
$930$	0.263702	+	12.9958i	0.00864714	+	0.426148i
$931$	0.310720	+	0.483490i	0.0101834	+	0.0158457i
$932$	−4.39084	−	6.83228i	−0.143827	−	0.223799i
$933$	−0.386253	−	19.0353i	−0.0126454	−	0.623188i
$934$	−3.86959	−	13.1786i	−0.126617	−	0.431218i
$935$	−2.02989	+	14.1182i	−0.0663846	+	0.461715i
$936$	−6.39414	+	10.8975i	−0.208999	+	0.356197i
$937$	−10.0806	−	4.60364i	−0.329318	−	0.150394i	0.243894	−	0.969802i	$-0.421575\pi$
$937$	−10.0806	−	4.60364i	−0.329318	−	0.150394i	−0.573211	+	0.819408i	$0.694303\pi$
$938$	10.4479	−	35.5824i	0.341137	−	1.16181i
$939$	−5.44056	+	20.0229i	−0.177546	+	0.653424i
$940$	1.53258	−	0.220351i	0.0499872	−	0.00718707i
$941$	18.7755	+	12.0663i	0.612063	+	0.393349i	0.809630	−	0.586940i	$-0.199668\pi$
$941$	18.7755	+	12.0663i	0.612063	+	0.393349i	−0.197567	+	0.980289i	$0.563304\pi$
$942$	−3.34468	+	4.02201i	−0.108975	+	0.131044i
$943$	36.8068	−	31.9266i	1.19859	−	1.03967i
$944$			3.48900i			0.113557i
$945$	−11.7540	+	6.25833i	−0.382357	+	0.203584i
$946$	−7.34526	−	51.0874i	−0.238815	−	1.66100i
$947$	−3.53928	+	1.61633i	−0.115011	+	0.0525238i	−0.472090	−	0.881551i	$-0.656500\pi$
$947$	−3.53928	+	1.61633i	−0.115011	+	0.0525238i	0.357079	+	0.934074i	$0.383773\pi$
$948$	−2.69384	−	4.01040i	−0.0874917	−	0.130252i
$949$	−20.0494	+	43.9022i	−0.650833	+	1.42512i
$950$	0.870206	−	1.00427i	0.0282332	−	0.0325829i
$951$	16.5167	−	14.9091i	0.535591	−	0.483461i
$952$	−6.06536	+	1.78095i	−0.196579	+	0.0577209i
$953$	12.5868	+	14.5260i	0.407727	+	0.470542i	0.922059	−	0.387049i	$-0.126506\pi$
$953$	12.5868	+	14.5260i	0.407727	+	0.470542i	−0.514332	+	0.857591i	$0.671960\pi$
$954$	18.2904	−	17.1963i	0.592174	−	0.556750i
$955$	5.52895	−	3.55324i	0.178912	−	0.114980i
$956$	−11.2964	+	9.78837i	−0.365351	+	0.316579i
$957$	91.5445	+	39.5826i	2.95921	+	1.27952i
$958$	14.3615	+	2.06488i	0.464000	+	0.0667132i
$959$	−28.5103	−	24.7043i	−0.920645	−	0.797744i
$960$	−0.751335	−	1.56061i	−0.0242492	−	0.0503684i
$961$	−24.2943	−	7.13345i	−0.783687	−	0.230111i
$962$	5.16490	+	11.3096i	0.166523	+	0.364635i
$963$	−44.8163	+	15.1595i	−1.44419	+	0.488508i
$964$	0.330605	−	0.514431i	0.0106481	−	0.0165687i
$965$	11.8912			0.382792
$966$	14.2720	+	15.7945i	0.459195	+	0.508180i
$967$	−35.7816			−1.15066			−0.575330	−	0.817921i	$-0.695126\pi$
$967$	−35.7816			−1.15066			−0.575330	+	0.817921i	$0.695126\pi$
$968$	12.1299	−	18.8745i	0.389869	−	0.606648i
$969$	−2.97190	+	4.83741i	−0.0954713	+	0.155400i
$970$	2.41096	+	5.27926i	0.0774111	+	0.169507i
$971$	24.9147	+	7.31561i	0.799551	+	0.234769i	0.655889	−	0.754858i	$-0.272294\pi$
$971$	24.9147	+	7.31561i	0.799551	+	0.234769i	0.143662	+	0.989627i	$0.454112\pi$
$972$	11.3488	+	10.6866i	0.364014	+	0.342774i
$973$	12.3695	+	10.7182i	0.396547	+	0.343610i
$974$	36.4740	+	5.24417i	1.16870	+	0.168034i
$975$	−2.89512	+	6.69567i	−0.0927179	+	0.214433i
$976$	−0.680412	+	0.589581i	−0.0217795	+	0.0188720i
$977$	20.6070	−	13.2433i	0.659277	−	0.423692i	−0.167768	−	0.985826i	$-0.553656\pi$
$977$	20.6070	−	13.2433i	0.659277	−	0.423692i	0.827046	+	0.562135i	$0.190020\pi$
$978$	−22.8513	−	2.81363i	−0.730704	−	0.0899699i
$979$	−32.5103	−	37.5189i	−1.03903	−	1.19911i
$980$	0.414981	−	0.121850i	0.0132561	−	0.00389234i
$981$	0.0432243	+	1.06465i	0.00138005	+	0.0339917i
$982$	16.1166	−	18.5995i	0.514301	−	0.593535i
$983$	15.9665	−	34.9618i	0.509252	−	1.11511i	−0.464098	−	0.885784i	$-0.653621\pi$
$983$	15.9665	−	34.9618i	0.509252	−	1.11511i	0.973350	−	0.229323i	$-0.0736513\pi$
$984$	14.6076	−	9.81208i	0.465673	−	0.312798i
$985$	19.8417	−	9.06141i	0.632210	−	0.288720i
$986$	3.49580	+	24.3138i	0.111329	+	0.774309i
$987$	−6.55365	+	2.06964i	−0.208605	+	0.0658773i
$988$			5.59660i			0.178052i
$989$	−38.9476	−	17.7625i	−1.23846	−	0.564814i
$990$	17.0563	−	3.16328i	0.542086	−	0.100535i
$991$	8.27240	+	5.31635i	0.262782	+	0.168879i	0.665397	−	0.746490i	$-0.268262\pi$
$991$	8.27240	+	5.31635i	0.262782	+	0.168879i	−0.402615	+	0.915369i	$0.631899\pi$
$992$	7.42827	−	1.06802i	0.235848	−	0.0339098i
$993$	−18.5029	−	5.02755i	−0.587173	−	0.159544i
$994$	6.10541	−	20.7931i	0.193652	−	0.659517i
$995$	−2.28011	−	1.04129i	−0.0722845	−	0.0330112i
$996$	2.54460	+	15.4640i	0.0806288	+	0.489996i
$997$	−1.90121	+	13.2232i	−0.0602120	+	0.418783i	0.937314	+	0.348486i	$0.113304\pi$
$997$	−1.90121	+	13.2232i	−0.0602120	+	0.418783i	−0.997526	+	0.0702977i	$0.977605\pi$
$998$	2.38063	+	8.10769i	0.0753576	+	0.256645i
$999$	15.0224	−	3.10257i	0.475289	−	0.0981610i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.q.a.251.7	yes	160
3.2	odd	2		690.2.q.b.251.11	yes	160
23.11	odd	22		690.2.q.b.11.11	yes	160
69.11	even	22	inner	690.2.q.a.11.7	✓	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.q.a.11.7	✓	160	69.11	even	22	inner
690.2.q.a.251.7	yes	160	1.1	even	1	trivial
690.2.q.b.11.11	yes	160	23.11	odd	22
690.2.q.b.251.11	yes	160	3.2	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.q (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.540641 + 0.841254i) q^{2} +(1.47579 + 0.906664i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(-1.56061 + 0.751335i) q^{6} +(-1.93677 - 1.67822i) q^{7} +(0.989821 + 0.142315i) q^{8} +(1.35592 + 2.67609i) q^{9} +O(q^{10})\)	\(q+(-0.540641 + 0.841254i) q^{2} +(1.47579 + 0.906664i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-0.959493 - 0.281733i) q^{5} +(-1.56061 + 0.751335i) q^{6} +(-1.93677 - 1.67822i) q^{7} +(0.989821 + 0.142315i) q^{8} +(1.35592 + 2.67609i) q^{9} +(0.755750 - 0.654861i) q^{10} +(4.86446 - 3.12620i) q^{11} +(0.211665 - 1.71907i) q^{12} +(2.75804 + 3.18294i) q^{13} +(2.45891 - 0.722000i) q^{14} +(-1.16057 - 1.28572i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(1.02470 - 2.24378i) q^{17} +(-2.98434 - 0.306134i) q^{18} +(-1.20876 + 0.552021i) q^{19} +(0.142315 + 0.989821i) q^{20} +(-1.33669 - 4.23270i) q^{21} +5.78240i q^{22} +(4.03585 + 2.59074i) q^{23} +(1.33174 + 1.10746i) q^{24} +(0.841254 + 0.540641i) q^{25} +(-4.16877 + 0.599378i) q^{26} +(-0.425265 + 5.17872i) q^{27} +(-0.722000 + 2.45891i) q^{28} +(9.05831 + 4.13679i) q^{29} +(1.70907 - 0.281227i) q^{30} +(-1.06802 + 7.42827i) q^{31} +(-0.281733 - 0.959493i) q^{32} +(10.0133 - 0.203185i) q^{33} +(1.33359 + 2.07511i) q^{34} +(1.38551 + 2.15589i) q^{35} +(1.87099 - 2.34508i) q^{36} +(-0.831698 - 2.83250i) q^{37} +(0.189114 - 1.31532i) q^{38} +(1.18442 + 7.19797i) q^{39} +(-0.909632 - 0.415415i) q^{40} +(2.86232 - 9.74816i) q^{41} +(4.28344 + 1.16388i) q^{42} +(-8.83499 + 1.27028i) q^{43} +(-4.86446 - 3.12620i) q^{44} +(-0.547053 - 2.94970i) q^{45} +(-4.36141 + 1.99452i) q^{46} -1.54834i q^{47} +(-1.65165 + 0.521590i) q^{48} +(-0.0615513 - 0.428098i) q^{49} +(-0.909632 + 0.415415i) q^{50} +(3.54660 - 2.38229i) q^{51} +(1.74958 - 3.83104i) q^{52} +(-5.48005 + 6.32431i) q^{53} +(-4.12670 - 3.15758i) q^{54} +(-5.54817 + 1.62909i) q^{55} +(-1.67822 - 1.93677i) q^{56} +(-2.28437 - 0.281269i) q^{57} +(-8.37738 + 5.38382i) q^{58} +(2.63681 - 2.28481i) q^{59} +(-0.687409 + 1.58980i) q^{60} +(0.891151 + 0.128128i) q^{61} +(-5.67164 - 4.91451i) q^{62} +(1.86497 - 7.45851i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-1.74958 - 3.83104i) q^{65} +(-5.24269 + 8.53361i) q^{66} +(7.82353 - 12.1736i) q^{67} -2.46669 q^{68} +(3.60714 + 7.48255i) q^{69} -2.56271 q^{70} +(4.57179 - 7.11385i) q^{71} +(0.961271 + 2.84182i) q^{72} +(4.76049 + 10.4240i) q^{73} +(2.83250 + 0.831698i) q^{74} +(0.751335 + 1.56061i) q^{75} +(1.00427 + 0.870206i) q^{76} +(-14.6678 - 2.10891i) q^{77} +(-6.69567 - 2.89512i) q^{78} +(2.10799 - 1.82658i) q^{79} +(0.841254 - 0.540641i) q^{80} +(-5.32296 + 7.25714i) q^{81} +(6.65319 + 7.67819i) q^{82} +(-8.68171 + 2.54918i) q^{83} +(-3.29492 + 2.97422i) q^{84} +(-1.61534 + 1.86420i) q^{85} +(3.70793 - 8.11923i) q^{86} +(9.61749 + 14.3179i) q^{87} +(5.25985 - 2.40209i) q^{88} +(-1.22184 - 8.49808i) q^{89} +(2.77720 + 1.13452i) q^{90} -10.7932i q^{91} +(0.680064 - 4.74737i) q^{92} +(-8.31113 + 9.99424i) q^{93} +(1.30254 + 0.837094i) q^{94} +(1.31532 - 0.189114i) q^{95} +(0.454160 - 1.67145i) q^{96} +(-1.63510 + 5.56864i) q^{97} +(0.393416 + 0.179667i) q^{98} +(14.9618 + 8.77888i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9}+O(q^{10}) \) 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9	\( 160 q + 16 q^{4} - 16 q^{5} - 2 q^{6} + 42 q^{9} - 12 q^{11} - 12 q^{14} - 16 q^{16} - 8 q^{18} + 16 q^{20} + 62 q^{21} + 4 q^{23} + 2 q^{24} - 16 q^{25} + 42 q^{27} - 2 q^{30} - 4 q^{31} + 16 q^{33} + 2 q^{36} + 72 q^{38} - 124 q^{39} + 44 q^{41} + 44 q^{43} + 12 q^{44} - 2 q^{45} + 4 q^{46} + 70 q^{49} - 2 q^{51} - 52 q^{53} + 92 q^{54} + 10 q^{55} - 54 q^{56} - 38 q^{57} - 36 q^{58} - 44 q^{61} - 220 q^{63} + 16 q^{64} - 34 q^{66} - 44 q^{67} + 22 q^{69} - 12 q^{70} - 36 q^{72} - 28 q^{73} - 24 q^{74} - 88 q^{77} - 54 q^{78} - 44 q^{79} - 16 q^{80} - 66 q^{81} - 28 q^{82} + 4 q^{83} - 18 q^{84} + 158 q^{86} - 64 q^{87} + 80 q^{89} - 8 q^{90} - 4 q^{92} + 4 q^{93} + 24 q^{94} - 2 q^{96} - 88 q^{98} + 190 q^{99}+O(q^{100}) \) 160 * q + 16 * q^4 - 16 * q^5 - 2 * q^6 + 42 * q^9 - 12 * q^11 - 12 * q^14 - 16 * q^16 - 8 * q^18 + 16 * q^20 + 62 * q^21 + 4 * q^23 + 2 * q^24 - 16 * q^25 + 42 * q^27 - 2 * q^30 - 4 * q^31 + 16 * q^33 + 2 * q^36 + 72 * q^38 - 124 * q^39 + 44 * q^41 + 44 * q^43 + 12 * q^44 - 2 * q^45 + 4 * q^46 + 70 * q^49 - 2 * q^51 - 52 * q^53 + 92 * q^54 + 10 * q^55 - 54 * q^56 - 38 * q^57 - 36 * q^58 - 44 * q^61 - 220 * q^63 + 16 * q^64 - 34 * q^66 - 44 * q^67 + 22 * q^69 - 12 * q^70 - 36 * q^72 - 28 * q^73 - 24 * q^74 - 88 * q^77 - 54 * q^78 - 44 * q^79 - 16 * q^80 - 66 * q^81 - 28 * q^82 + 4 * q^83 - 18 * q^84 + 158 * q^86 - 64 * q^87 + 80 * q^89 - 8 * q^90 - 4 * q^92 + 4 * q^93 + 24 * q^94 - 2 * q^96 - 88 * q^98 + 190 * q^99

Introduction

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