LMFDB - Embedded newform 880.2.cz.a.147.113

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [880,2,Mod(147,880)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(880, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 15, 5, 4]))

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

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

chi := DirichletCharacter("880.147");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 880 = 2^{4} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	880.cz (of order $20$, degree $8$, 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:	$7.02683537787$
Analytic rank:	$0$
Dimension:	$1120$
Relative dimension:	$140$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			147.113
Character	$\chi$	$=$	880.147
Dual form			880.2.cz.a.443.113

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.15398 - 0.817511i) q^{2} +(0.618224 + 0.200873i) q^{3} +(0.663353 - 1.88679i) q^{4} +(-2.02895 - 0.939878i) q^{5} +(0.877636 - 0.273601i) q^{6} +(-1.18591 + 2.32748i) q^{7} +(-0.776970 - 2.71962i) q^{8} +(-2.08520 - 1.51499i) q^{9} +O(q^{10})$	\(q+(1.15398 - 0.817511i) q^{2} +(0.618224 + 0.200873i) q^{3} +(0.663353 - 1.88679i) q^{4} +(-2.02895 - 0.939878i) q^{5} +(0.877636 - 0.273601i) q^{6} +(-1.18591 + 2.32748i) q^{7} +(-0.776970 - 2.71962i) q^{8} +(-2.08520 - 1.51499i) q^{9} +(-3.10973 + 0.574083i) q^{10} +(2.29349 - 2.39581i) q^{11} +(0.789106 - 1.03321i) q^{12} +(-2.56289 - 1.86205i) q^{13} +(0.534219 + 3.65536i) q^{14} +(-1.06555 - 0.988617i) q^{15} +(-3.11993 - 2.50321i) q^{16} +(-5.65584 - 0.895798i) q^{17} +(-3.64480 - 0.0435951i) q^{18} +(4.21517 - 2.14774i) q^{19} +(-3.11926 + 3.20472i) q^{20} +(-1.20069 + 1.20069i) q^{21} +(0.688047 - 4.63968i) q^{22} +(-1.65259 + 1.65259i) q^{23} +(0.0659563 - 1.83741i) q^{24} +(3.23326 + 3.81393i) q^{25} +(-4.47977 - 0.0535821i) q^{26} +(-2.13105 - 2.93314i) q^{27} +(3.60478 + 3.78150i) q^{28} +(-0.854255 - 0.435264i) q^{29} +(-2.03783 - 0.269750i) q^{30} +(2.42909 - 3.34336i) q^{31} +(-5.64674 - 0.338088i) q^{32} +(1.89914 - 1.02045i) q^{33} +(-7.25907 + 3.58998i) q^{34} +(4.59369 - 3.60772i) q^{35} +(-4.24168 + 2.92936i) q^{36} +(-2.28283 - 7.02584i) q^{37} +(3.10844 - 5.92440i) q^{38} +(-1.21040 - 1.66598i) q^{39} +(-0.979677 + 6.24822i) q^{40} +(6.45452 + 2.09720i) q^{41} +(-0.403997 + 2.36714i) q^{42} -2.73314 q^{43} +(-2.99899 - 5.91659i) q^{44} +(2.80686 + 5.03366i) q^{45} +(-0.556050 + 3.25807i) q^{46} +(-1.41655 - 2.78013i) q^{47} +(-1.42599 - 2.17425i) q^{48} +(0.103724 + 0.142763i) q^{49} +(6.84905 + 1.75798i) q^{50} +(-3.31664 - 1.68991i) q^{51} +(-5.21338 + 3.60043i) q^{52} +(-4.08050 + 5.61633i) q^{53} +(-4.85707 - 1.64264i) q^{54} +(-6.90514 + 2.70537i) q^{55} +(7.25127 + 1.41684i) q^{56} +(3.03734 - 0.481068i) q^{57} +(-1.34163 + 0.196075i) q^{58} +(-1.05990 - 0.540048i) q^{59} +(-2.57214 + 1.35466i) q^{60} +(9.69978 + 1.53629i) q^{61} +(0.0698994 - 5.84399i) q^{62} +(5.99896 - 3.05662i) q^{63} +(-6.79263 + 4.22612i) q^{64} +(3.44987 + 6.18680i) q^{65} +(1.35735 - 2.73015i) q^{66} +14.3088 q^{67} +(-5.44200 + 10.0771i) q^{68} +(-1.35363 + 0.689710i) q^{69} +(2.35169 - 7.91864i) q^{70} +(-6.10934 + 4.43870i) q^{71} +(-2.50004 + 6.84804i) q^{72} +(6.79020 - 13.3265i) q^{73} +(-8.37805 - 6.24146i) q^{74} +(1.23276 + 3.00734i) q^{75} +(-1.25618 - 9.37783i) q^{76} +(2.85632 + 8.17926i) q^{77} +(-2.75874 - 0.932992i) q^{78} +(4.19372 + 3.04692i) q^{79} +(3.97746 + 8.01123i) q^{80} +(1.66115 + 5.11249i) q^{81} +(9.16288 - 2.85650i) q^{82} +(4.97411 + 6.84628i) q^{83} +(1.46896 + 3.06192i) q^{84} +(10.6335 + 7.13333i) q^{85} +(-3.15400 + 2.23437i) q^{86} +(-0.440688 - 0.440688i) q^{87} +(-8.29766 - 4.37594i) q^{88} -2.99274 q^{89} +(7.35414 + 3.51412i) q^{90} +(7.37322 - 3.75685i) q^{91} +(2.02183 + 4.21433i) q^{92} +(2.17332 - 1.57901i) q^{93} +(-3.90746 - 2.05018i) q^{94} +(-10.5710 + 0.395898i) q^{95} +(-3.42304 - 1.34329i) q^{96} +(-2.76685 - 17.4692i) q^{97} +(0.236406 + 0.0799513i) q^{98} +(-8.41200 + 1.52114i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1120 q - 6 q^{2} - 6 q^{5} - 12 q^{6} - 12 q^{7} - 6 q^{8} + 264 q^{9}+O(q^{10}) $ 1120 * q - 6 * q^2 - 6 * q^5 - 12 * q^6 - 12 * q^7 - 6 * q^8 + 264 * q^9	$ 1120 q - 6 q^{2} - 6 q^{5} - 12 q^{6} - 12 q^{7} - 6 q^{8} + 264 q^{9} - 8 q^{10} - 16 q^{11} - 44 q^{12} - 12 q^{13} - 24 q^{15} - 12 q^{16} - 12 q^{17} - 10 q^{18} - 6 q^{20} - 32 q^{21} - 10 q^{22} - 32 q^{23} - 24 q^{24} + 20 q^{26} - 22 q^{28} + 36 q^{30} - 36 q^{32} - 16 q^{33} - 32 q^{34} + 14 q^{35} + 20 q^{36} - 12 q^{37} - 26 q^{38} - 88 q^{40} - 6 q^{42} + 32 q^{43} + 80 q^{44} - 8 q^{45} - 12 q^{46} - 18 q^{48} + 16 q^{50} - 12 q^{51} + 34 q^{52} - 168 q^{54} - 16 q^{55} - 80 q^{56} - 24 q^{57} + 38 q^{58} + 16 q^{59} - 32 q^{60} - 12 q^{61} + 96 q^{62} + 36 q^{63} - 32 q^{65} - 24 q^{66} - 32 q^{67} - 38 q^{68} + 36 q^{69} - 42 q^{70} - 56 q^{71} - 76 q^{72} + 100 q^{74} + 30 q^{75} - 32 q^{76} - 108 q^{78} + 102 q^{80} - 240 q^{81} - 18 q^{82} + 24 q^{84} + 14 q^{85} - 4 q^{86} - 32 q^{87} - 98 q^{88} - 44 q^{90} - 28 q^{91} - 48 q^{92} - 36 q^{93} - 48 q^{94} - 120 q^{95} + 20 q^{96} - 12 q^{97} - 284 q^{98} + 20 q^{99}+O(q^{100}) $ 1120 * q - 6 * q^2 - 6 * q^5 - 12 * q^6 - 12 * q^7 - 6 * q^8 + 264 * q^9 - 8 * q^10 - 16 * q^11 - 44 * q^12 - 12 * q^13 - 24 * q^15 - 12 * q^16 - 12 * q^17 - 10 * q^18 - 6 * q^20 - 32 * q^21 - 10 * q^22 - 32 * q^23 - 24 * q^24 + 20 * q^26 - 22 * q^28 + 36 * q^30 - 36 * q^32 - 16 * q^33 - 32 * q^34 + 14 * q^35 + 20 * q^36 - 12 * q^37 - 26 * q^38 - 88 * q^40 - 6 * q^42 + 32 * q^43 + 80 * q^44 - 8 * q^45 - 12 * q^46 - 18 * q^48 + 16 * q^50 - 12 * q^51 + 34 * q^52 - 168 * q^54 - 16 * q^55 - 80 * q^56 - 24 * q^57 + 38 * q^58 + 16 * q^59 - 32 * q^60 - 12 * q^61 + 96 * q^62 + 36 * q^63 - 32 * q^65 - 24 * q^66 - 32 * q^67 - 38 * q^68 + 36 * q^69 - 42 * q^70 - 56 * q^71 - 76 * q^72 + 100 * q^74 + 30 * q^75 - 32 * q^76 - 108 * q^78 + 102 * q^80 - 240 * q^81 - 18 * q^82 + 24 * q^84 + 14 * q^85 - 4 * q^86 - 32 * q^87 - 98 * q^88 - 44 * q^90 - 28 * q^91 - 48 * q^92 - 36 * q^93 - 48 * q^94 - 120 * q^95 + 20 * q^96 - 12 * q^97 - 284 * q^98 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/880\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$321$	$661$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{5}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	1.15398	−	0.817511i	0.815989	−	0.578067i
$2$	1.15398	−	0.817511i	0.815989	−	0.578067i
$3$	0.618224	+	0.200873i	0.356932	+	0.115974i	0.481994	−	0.876175i	$-0.339913\pi$
$3$	0.618224	+	0.200873i	0.356932	+	0.115974i	−0.125062	+	0.992149i	$0.539913\pi$
$4$	0.663353	−	1.88679i	0.331676	−	0.943393i
$5$	−2.02895	−	0.939878i	−0.907373	−	0.420326i
$5$	−2.02895	−	0.939878i	−0.907373	−	0.420326i
$6$	0.877636	−	0.273601i	0.358293	−	0.111697i
$7$	−1.18591	+	2.32748i	−0.448232	+	0.879704i	0.550754	+	0.834668i	$0.314340\pi$
$7$	−1.18591	+	2.32748i	−0.448232	+	0.879704i	−0.998985	+	0.0450362i	$0.985660\pi$
$8$	−0.776970	−	2.71962i	−0.274701	−	0.961530i
$9$	−2.08520	−	1.51499i	−0.695067	−	0.504995i
$10$	−3.10973	+	0.574083i	−0.983383	+	0.181541i
$11$	2.29349	−	2.39581i	0.691513	−	0.722364i
$11$	2.29349	−	2.39581i	0.691513	−	0.722364i
$12$	0.789106	−	1.03321i	0.227795	−	0.298261i
$13$	−2.56289	−	1.86205i	−0.710817	−	0.516439i	0.172620	−	0.984988i	$-0.444777\pi$
$13$	−2.56289	−	1.86205i	−0.710817	−	0.516439i	−0.883437	+	0.468550i	$0.844777\pi$
$14$	0.534219	+	3.65536i	0.142776	+	0.976937i
$15$	−1.06555	−	0.988617i	−0.275123	−	0.255260i
$16$	−3.11993	−	2.50321i	−0.779982	−	0.625802i
$17$	−5.65584	−	0.895798i	−1.37174	−	0.217263i	−0.573307	−	0.819341i	$-0.694340\pi$
$17$	−5.65584	−	0.895798i	−1.37174	−	0.217263i	−0.798437	+	0.602078i	$0.794340\pi$
$18$	−3.64480	−	0.0435951i	−0.859088	−	0.0102755i
$19$	4.21517	−	2.14774i	0.967026	−	0.492724i	0.102182	−	0.994766i	$-0.467417\pi$
$19$	4.21517	−	2.14774i	0.967026	−	0.492724i	0.864844	+	0.502041i	$0.167417\pi$
$20$	−3.11926	+	3.20472i	−0.697487	+	0.716597i
$21$	−1.20069	+	1.20069i	−0.262011	+	0.262011i
$22$	0.688047	−	4.63968i	0.146692	−	0.989182i
$23$	−1.65259	+	1.65259i	−0.344589	+	0.344589i	−0.858089	−	0.513501i	$-0.828348\pi$
$23$	−1.65259	+	1.65259i	−0.344589	+	0.344589i	0.513501	+	0.858089i	$0.328348\pi$
$24$	0.0659563	−	1.83741i	0.0134633	−	0.375059i
$25$	3.23326	+	3.81393i	0.646651	+	0.762786i
$26$	−4.47977	−	0.0535821i	−0.878555	−	0.0105083i
$27$	−2.13105	−	2.93314i	−0.410121	−	0.564483i
$28$	3.60478	+	3.78150i	0.681239	+	0.714636i
$29$	−0.854255	−	0.435264i	−0.158631	−	0.0808266i	0.372873	−	0.927883i	$-0.378373\pi$
$29$	−0.854255	−	0.435264i	−0.158631	−	0.0808266i	−0.531504	+	0.847056i	$0.678373\pi$
$30$	−2.03783	−	0.269750i	−0.372055	−	0.0492494i
$31$	2.42909	−	3.34336i	0.436278	−	0.600485i	−0.533102	−	0.846051i	$-0.678974\pi$
$31$	2.42909	−	3.34336i	0.436278	−	0.600485i	0.969380	+	0.245566i	$0.0789738\pi$
$32$	−5.64674	−	0.338088i	−0.998212	−	0.0597660i
$33$	1.89914	−	1.02045i	0.330599	−	0.177637i
$34$	−7.25907	+	3.58998i	−1.24492	+	0.615676i
$35$	4.59369	−	3.60772i	0.776476	−	0.609816i
$36$	−4.24168	+	2.92936i	−0.706946	+	0.488226i
$37$	−2.28283	−	7.02584i	−0.375296	−	1.15504i	−0.943279	−	0.332001i	$-0.892276\pi$
$37$	−2.28283	−	7.02584i	−0.375296	−	1.15504i	0.567983	−	0.823040i	$-0.307724\pi$
$38$	3.10844	−	5.92440i	0.504255	−	0.961064i
$39$	−1.21040	−	1.66598i	−0.193820	−	0.266770i
$40$	−0.979677	+	6.24822i	−0.154900	+	0.987930i
$41$	6.45452	+	2.09720i	1.00803	+	0.327528i	0.766068	−	0.642759i	$-0.222210\pi$
$41$	6.45452	+	2.09720i	1.00803	+	0.327528i	0.241958	+	0.970287i	$0.422210\pi$
$42$	−0.403997	+	2.36714i	−0.0623381	+	0.365258i
$43$	−2.73314			−0.416801			−0.208400	−	0.978044i	$-0.566826\pi$
$43$	−2.73314			−0.416801			−0.208400	+	0.978044i	$0.566826\pi$
$44$	−2.99899	−	5.91659i	−0.452115	−	0.891960i
$45$	2.80686	+	5.03366i	0.418422	+	0.750374i
$46$	−0.556050	+	3.25807i	−0.0819851	+	0.480376i
$47$	−1.41655	−	2.78013i	−0.206625	−	0.405524i	0.764317	−	0.644841i	$-0.223076\pi$
$47$	−1.41655	−	2.78013i	−0.206625	−	0.405524i	−0.970941	+	0.239317i	$0.923076\pi$
$48$	−1.42599	−	2.17425i	−0.205823	−	0.313827i
$49$	0.103724	+	0.142763i	0.0148177	+	0.0203948i
$50$	6.84905	+	1.75798i	0.968602	+	0.248617i
$51$	−3.31664	−	1.68991i	−0.464422	−	0.236635i
$52$	−5.21338	+	3.60043i	−0.722966	+	0.499289i
$53$	−4.08050	+	5.61633i	−0.560500	+	0.771463i	−0.991390	−	0.130942i	$-0.958200\pi$
$53$	−4.08050	+	5.61633i	−0.560500	+	0.771463i	0.430890	+	0.902405i	$0.358200\pi$
$54$	−4.85707	−	1.64264i	−0.660964	−	0.223535i
$55$	−6.90514	+	2.70537i	−0.931089	+	0.364792i
$56$	7.25127	+	1.41684i	0.968991	+	0.189333i
$57$	3.03734	−	0.481068i	0.402306	−	0.0637190i
$58$	−1.34163	+	0.196075i	−0.176164	+	0.0257458i
$59$	−1.05990	−	0.540048i	−0.137988	−	0.0703083i	0.383634	−	0.923485i	$-0.374673\pi$
$59$	−1.05990	−	0.540048i	−0.137988	−	0.0703083i	−0.521621	+	0.853177i	$0.674673\pi$
$60$	−2.57214	+	1.35466i	−0.332062	+	0.174886i
$61$	9.69978	+	1.53629i	1.24193	+	0.196702i	0.742615	−	0.669719i	$-0.233585\pi$
$61$	9.69978	+	1.53629i	1.24193	+	0.196702i	0.499314	+	0.866421i	$0.333585\pi$
$62$	0.0698994	−	5.84399i	0.00887723	−	0.742187i
$63$	5.99896	−	3.05662i	0.755797	−	0.385098i
$64$	−6.79263	+	4.22612i	−0.849079	+	0.528266i
$65$	3.44987	+	6.18680i	0.427903	+	0.767378i
$66$	1.35735	−	2.73015i	0.167079	−	0.336058i
$67$	14.3088			1.74810			0.874051	−	0.485835i	$-0.161484\pi$
$67$	14.3088			1.74810			0.874051	+	0.485835i	$0.161484\pi$
$68$	−5.44200	+	10.0771i	−0.659939	+	1.22203i
$69$	−1.35363	+	0.689710i	−0.162958	+	0.0830313i
$70$	2.35169	−	7.91864i	0.281081	−	0.946459i
$71$	−6.10934	+	4.43870i	−0.725046	+	0.526777i	−0.887992	−	0.459858i	$-0.847900\pi$
$71$	−6.10934	+	4.43870i	−0.725046	+	0.526777i	0.162947	+	0.986635i	$0.447900\pi$
$72$	−2.50004	+	6.84804i	−0.294633	+	0.807050i
$73$	6.79020	−	13.3265i	0.794733	−	1.55975i	−0.0335482	−	0.999437i	$-0.510681\pi$
$73$	6.79020	−	13.3265i	0.794733	−	1.55975i	0.828281	−	0.560313i	$-0.189319\pi$
$74$	−8.37805	−	6.24146i	−0.973929	−	0.725555i
$75$	1.23276	+	3.00734i	0.142347	+	0.347257i
$76$	−1.25618	−	9.37783i	−0.144093	−	1.07571i
$77$	2.85632	+	8.17926i	0.325508	+	0.932113i
$78$	−2.75874	−	0.932992i	−0.312366	−	0.105641i
$79$	4.19372	+	3.04692i	0.471830	+	0.342805i	0.798154	−	0.602453i	$-0.205810\pi$
$79$	4.19372	+	3.04692i	0.471830	+	0.342805i	−0.326324	+	0.945258i	$0.605810\pi$
$80$	3.97746	+	8.01123i	0.444693	+	0.895683i
$81$	1.66115	+	5.11249i	0.184572	+	0.568054i
$82$	9.16288	−	2.85650i	1.01187	−	0.315448i
$83$	4.97411	+	6.84628i	0.545980	+	0.751477i	0.989460	−	0.144808i	$-0.0462563\pi$
$83$	4.97411	+	6.84628i	0.545980	+	0.751477i	−0.443480	+	0.896284i	$0.646256\pi$
$84$	1.46896	+	3.06192i	0.160277	+	0.334082i
$85$	10.6335	+	7.13333i	1.15336	+	0.773719i
$86$	−3.15400	+	2.23437i	−0.340105	+	0.240939i
$87$	−0.440688	−	0.440688i	−0.0472467	−	0.0472467i
$88$	−8.29766	−	4.37594i	−0.884533	−	0.466477i
$89$	−2.99274			−0.317229			−0.158615	−	0.987341i	$-0.550703\pi$
$89$	−2.99274			−0.317229			−0.158615	+	0.987341i	$0.550703\pi$
$90$	7.35414	+	3.51412i	0.775194	+	0.370421i
$91$	7.37322	−	3.75685i	0.772924	−	0.393824i
$92$	2.02183	+	4.21433i	0.210791	+	0.439374i
$93$	2.17332	−	1.57901i	0.225362	−	0.163735i
$94$	−3.90746	−	2.05018i	−0.403024	−	0.211460i
$95$	−10.5710	+	0.395898i	−1.08456	+	0.0406182i
$96$	−3.42304	−	1.34329i	−0.349363	−	0.137099i
$97$	−2.76685	−	17.4692i	−0.280931	−	1.77373i	−0.575206	−	0.818009i	$-0.695078\pi$
$97$	−2.76685	−	17.4692i	−0.280931	−	1.77373i	0.294275	−	0.955721i	$-0.404922\pi$
$98$	0.236406	+	0.0799513i	0.0238806	+	0.00807630i
$99$	−8.41200	+	1.52114i	−0.845438	+	0.152880i
$100$	9.34086	−	3.57049i	0.934086	−	0.357049i
$101$	13.1364	−	2.08060i	1.30712	−	0.207028i	0.536272	−	0.844045i	$-0.319832\pi$
$101$	13.1364	−	2.08060i	1.30712	−	0.207028i	0.770849	+	0.637018i	$0.219832\pi$
$102$	−5.20886	+	0.761258i	−0.515754	+	0.0753758i
$103$	−8.05755	−	4.10552i	−0.793934	−	0.404529i	0.00947678	−	0.999955i	$-0.496983\pi$
$103$	−8.05755	−	4.10552i	−0.793934	−	0.404529i	−0.803410	+	0.595426i	$0.796983\pi$
$104$	−3.07277	+	8.41683i	−0.301309	+	0.825338i
$105$	3.56463	−	1.30763i	0.347872	−	0.127612i
$106$	−0.117420	+	9.81701i	−0.0114049	+	0.953512i
$107$	−15.6930	−	5.09896i	−1.51710	−	0.492935i	−0.572148	−	0.820150i	$-0.693890\pi$
$107$	−15.6930	−	5.09896i	−1.51710	−	0.492935i	−0.944950	+	0.327216i	$0.893890\pi$
$108$	−6.94785	+	2.07513i	−0.668557	+	0.199680i
$109$	−3.85263	+	3.85263i	−0.369015	+	0.369015i	−0.867118	−	0.498103i	$-0.834030\pi$
$109$	−3.85263	+	3.85263i	−0.369015	+	0.369015i	0.498103	+	0.867118i	$0.334030\pi$
$110$	−5.75674	+	8.76698i	−0.548884	+	0.835899i
$111$		−	4.80211i		−	0.455796i
$112$	9.52612	−	4.29298i	0.900133	−	0.405649i
$113$	1.99462	+	3.91467i	0.187638	+	0.368261i	0.965592	−	0.260060i	$-0.0837424\pi$
$113$	1.99462	+	3.91467i	0.187638	+	0.368261i	−0.777954	+	0.628321i	$0.783742\pi$
$114$	3.11176	−	3.03820i	0.291443	−	0.284554i
$115$	4.90625	−	1.79978i	0.457510	−	0.167831i
$116$	−1.38792	+	1.32306i	−0.128865	+	0.122843i
$117$	2.52316	+	7.76548i	0.233266	+	0.717919i
$118$	−1.66461	+	0.243277i	−0.153239	+	0.0223954i
$119$	8.79227	−	12.1015i	0.805986	−	1.10934i
$120$	−1.86076	+	3.66601i	−0.169863	+	0.334659i
$121$	−0.479811	−	10.9895i	−0.0436192	−	0.999048i
$122$	12.4493	−	6.15681i	1.12711	−	0.557412i
$123$	3.56907	+	2.59308i	0.321812	+	0.233810i
$124$	−4.69686	−	6.80101i	−0.421790	−	0.610748i
$125$	−2.97548	−	10.7771i	−0.266135	−	0.963936i
$126$	4.42387	−	8.43150i	0.394110	−	0.751137i
$127$	−1.11068	+	7.01253i	−0.0985565	+	0.622261i	0.888126	+	0.459601i	$0.152008\pi$
$127$	−1.11068	+	7.01253i	−0.0985565	+	0.622261i	−0.986682	+	0.162660i	$0.947992\pi$
$128$	−4.38368	+	10.4299i	−0.387466	+	0.921884i
$129$	−1.68970	−	0.549016i	−0.148769	−	0.0483381i
$130$	9.03886	+	4.31916i	0.792760	+	0.378815i
$131$	10.6115	−	10.6115i	0.927134	−	0.927134i	−0.0703858	−	0.997520i	$-0.522423\pi$
$131$	10.6115	−	10.6115i	0.927134	−	0.927134i	0.997520	+	0.0703858i	$0.0224230\pi$
$132$	−0.665563	−	4.26020i	−0.0579298	−	0.370803i
$133$			12.3577i			1.07155i
$134$	16.5121	−	11.6976i	1.42643	−	1.01052i
$135$	1.56700	+	7.95412i	0.134866	+	0.684582i
$136$	1.95820	+	16.0777i	0.167914	+	1.37865i
$137$	1.24068	−	7.83332i	0.105998	−	0.669245i	−0.876278	−	0.481806i	$-0.839981\pi$
$137$	1.24068	−	7.83332i	0.105998	−	0.669245i	0.982276	−	0.187440i	$-0.0600189\pi$
$138$	−0.998222	+	1.90252i	−0.0849743	+	0.161953i
$139$	9.74921	+	4.96747i	0.826917	+	0.421335i	0.815611	−	0.578601i	$-0.196401\pi$
$139$	9.74921	+	4.96747i	0.826917	+	0.421335i	0.0113060	+	0.999936i	$0.496401\pi$
$140$	−3.75976	−	11.0605i	−0.317758	−	0.934784i
$141$	−0.317290	−	2.00329i	−0.0267207	−	0.168708i
$142$	−3.42139	+	10.1166i	−0.287117	+	0.848969i
$143$	−10.3391	+	1.86961i	−0.864596	+	0.156344i
$144$	2.71334	+	9.94634i	0.226112	+	0.828862i
$145$	1.32414	+	1.68602i	0.109964	+	0.140017i
$146$	−3.05880	−	20.9296i	−0.253148	−	1.73215i
$147$	0.0354472	+	0.109095i	0.00292363	+	0.00899802i
$148$	−14.7706	−	0.353390i	−1.21413	−	0.0290485i
$149$	−10.5730	−	1.67460i	−0.866174	−	0.137189i	−0.292494	−	0.956267i	$-0.594485\pi$
$149$	−10.5730	−	1.67460i	−0.866174	−	0.137189i	−0.573681	+	0.819079i	$0.694485\pi$
$150$	3.88112	+	2.46262i	0.316892	+	0.201072i
$151$	−1.54389	+	4.75160i	−0.125640	+	0.386680i	−0.994017	−	0.109224i	$-0.965163\pi$
$151$	−1.54389	+	4.75160i	−0.125640	+	0.386680i	0.868377	+	0.495904i	$0.165163\pi$
$152$	−9.11608	−	9.79492i	−0.739412	−	0.794473i
$153$	10.4364	+	10.4364i	0.843737	+	0.843737i
$154$	9.98278	+	7.10365i	0.804435	+	0.572428i
$155$	−8.07085	+	4.50045i	−0.648266	+	0.361485i
$156$	−3.94627	+	1.17864i	−0.315954	+	0.0943669i
$157$	21.0061	+	6.82529i	1.67647	+	0.544717i	0.984221	−	0.176945i	$-0.0566214\pi$
$157$	21.0061	+	6.82529i	1.67647	+	0.544717i	0.692246	+	0.721662i	$0.256621\pi$
$158$	7.33037	+	0.0876778i	0.583173	+	0.00697527i
$159$	−3.65084	+	2.65249i	−0.289530	+	0.210356i
$160$	11.1392	+	5.99321i	0.880630	+	0.473805i
$161$	−1.88654	−	5.80618i	−0.148680	−	0.457591i
$162$	6.09645	+	4.54172i	0.478982	+	0.356831i
$163$	5.62774	−	7.74592i	0.440798	−	0.606707i	−0.529591	−	0.848253i	$-0.677655\pi$
$163$	5.62774	−	7.74592i	0.440798	−	0.606707i	0.970389	+	0.241546i	$0.0776545\pi$
$164$	8.23859	−	10.7871i	0.643326	−	0.842332i
$165$	−4.81236	+	0.285469i	−0.374642	+	0.0222237i
$166$	11.3369	+	3.83410i	0.879918	+	0.297584i
$167$	−2.17831	−	13.7533i	−0.168563	−	1.06426i	−0.916366	−	0.400342i	$-0.868891\pi$
$167$	−2.17831	−	13.7533i	−0.168563	−	1.06426i	0.747803	−	0.663920i	$-0.231109\pi$
$168$	4.19830	+	2.33251i	0.323906	+	0.179957i
$169$	−0.916047	−	2.81930i	−0.0704652	−	0.216869i
$170$	18.1024	−	0.461233i	1.38839	−	0.0353750i
$171$	−12.0433	−	1.90746i	−0.920971	−	0.145867i
$172$	−1.81304	+	5.15686i	−0.138243	+	0.393207i
$173$	−3.78439	+	11.6472i	−0.287722	+	0.885518i	0.697847	+	0.716247i	$0.254141\pi$
$173$	−3.78439	+	11.6472i	−0.287722	+	0.885518i	−0.985569	+	0.169271i	$0.945859\pi$
$174$	−0.868813	−	0.148279i	−0.0658646	−	0.0112410i
$175$	−12.7112	+	3.00236i	−0.960875	+	0.226957i
$176$	−13.1527	+	1.73367i	−0.991425	+	0.130680i
$177$	−0.546777	−	0.546777i	−0.0410983	−	0.0410983i
$178$	−3.45357	+	2.44659i	−0.258856	+	0.183380i
$179$	−0.156503	+	0.0797421i	−0.0116976	+	0.00596020i	−0.459829	−	0.888007i	$-0.652089\pi$
$179$	−0.156503	+	0.0797421i	−0.0116976	+	0.00596020i	0.448132	+	0.893967i	$0.352089\pi$
$180$	11.3594	−	1.95685i	0.846678	−	0.145855i
$181$	−3.00487	+	18.9720i	−0.223350	+	1.41018i	0.579973	+	0.814636i	$0.303063\pi$
$181$	−3.00487	+	18.9720i	−0.223350	+	1.41018i	−0.803323	+	0.595543i	$0.796937\pi$
$182$	5.43731	−	10.3630i	0.403040	−	0.768159i
$183$	5.68804	+	2.89820i	0.420472	+	0.214241i
$184$	5.77842	+	3.21040i	0.425991	+	0.236674i
$185$	−1.97168	+	16.4007i	−0.144961	+	1.20580i
$186$	1.21711	−	3.59885i	0.0892431	−	0.263881i
$187$	−15.1178	+	11.4958i	−1.10552	+	0.840658i
$188$	−6.18519	+	0.828516i	−0.451101	+	0.0604257i
$189$	9.35405	−	1.48154i	0.680407	−	0.107766i
$190$	−11.8751	+	9.09874i	−0.861508	+	0.660092i
$191$	−5.19916	+	1.68931i	−0.376198	+	0.122234i	−0.491012	−	0.871153i	$-0.663373\pi$
$191$	−5.19916	+	1.68931i	−0.376198	+	0.122234i	0.114814	+	0.993387i	$0.463373\pi$
$192$	−5.04829	+	1.24823i	−0.364329	+	0.0900835i
$193$	0.580803	−	3.66705i	0.0418071	−	0.263960i	−0.957927	−	0.287011i	$-0.907338\pi$
$193$	0.580803	−	3.66705i	0.0418071	−	0.263960i	0.999734	+	0.0230517i	$0.00733823\pi$
$194$	−17.4742	−	17.8972i	−1.25457	−	1.28495i
$195$	0.890029	+	4.51781i	0.0637363	+	0.323527i
$196$	0.338170	−	0.101002i	0.0241550	−	0.00721443i
$197$	7.92706			0.564780			0.282390	−	0.959300i	$-0.408873\pi$
$197$	7.92706			0.564780			0.282390	+	0.959300i	$0.408873\pi$
$198$	−8.46376	+	8.63227i	−0.601493	+	0.613469i
$199$		−	19.2478i		−	1.36444i	−0.731148	−	0.682219i	$-0.761015\pi$
$199$		−	19.2478i		−	1.36444i	0.731148	−	0.682219i	$-0.238985\pi$
$200$	7.86028	−	11.7565i	0.555806	−	0.831312i
$201$	8.84606	+	2.87426i	0.623953	+	0.202735i
$202$	13.4583	−	13.1401i	0.946921	−	0.924536i
$203$	2.02614	−	1.47207i	0.142207	−	0.103319i
$204$	−5.38860	+	5.13678i	−0.377278	+	0.359647i
$205$	−11.1248	−	10.3216i	−0.776987	−	0.720890i
$206$	−12.6546	+	1.84942i	−0.881686	+	0.128856i
$207$	5.94963	−	0.942328i	0.413528	−	0.0654963i
$208$	3.33493	+	12.2249i	0.231236	+	0.847644i
$209$	4.52188	−	15.0246i	0.312785	−	1.03927i
$210$	3.04452	−	4.42310i	0.210092	−	0.305223i
$211$	−18.3820	+	2.91142i	−1.26547	+	0.200430i	−0.752853	−	0.658189i	$-0.771323\pi$
$211$	−18.3820	+	2.91142i	−1.26547	+	0.200430i	−0.512614	+	0.858619i	$0.671323\pi$
$212$	7.89001	+	11.4247i	0.541888	+	0.784648i
$213$	−4.66856	+	1.51691i	−0.319884	+	0.103937i
$214$	−22.2779	+	6.94507i	−1.52288	+	0.474755i
$215$	5.54541	+	2.56882i	0.378194	+	0.175192i
$216$	−6.32126	+	8.07461i	−0.430107	+	0.549408i
$217$	4.90091	+	9.61858i	0.332696	+	0.652952i
$218$	−1.29630	+	7.59543i	−0.0877967	+	0.514428i
$219$	6.87480	−	6.87480i	0.464556	−	0.464556i
$220$	0.523916	+	14.8231i	0.0353224	+	0.999376i
$221$	12.8273	+	12.8273i	0.862856	+	0.862856i
$222$	−3.92577	−	5.54155i	−0.263481	−	0.371924i
$223$	−15.3145	+	7.80315i	−1.02554	+	0.522538i	−0.884045	−	0.467402i	$-0.845190\pi$
$223$	−15.3145	+	7.80315i	−1.02554	+	0.522538i	−0.141493	+	0.989939i	$0.545190\pi$
$224$	7.48342	−	12.7417i	0.500007	−	0.851342i
$225$	−0.963939	−	12.8511i	−0.0642626	−	0.856743i
$226$	5.50204	+	2.88683i	0.365990	+	0.192029i
$227$	−6.69670	−	20.6103i	−0.444475	−	1.36795i	−0.883058	−	0.469264i	$-0.844519\pi$
$227$	−6.69670	−	20.6103i	−0.444475	−	1.36795i	0.438583	−	0.898691i	$-0.355481\pi$
$228$	1.10716	−	6.04993i	0.0733232	−	0.400667i
$229$	−0.389219	−	2.45743i	−0.0257203	−	0.162392i	0.971485	−	0.237101i	$-0.0761972\pi$
$229$	−0.389219	−	2.45743i	−0.0257203	−	0.162392i	−0.997205	+	0.0747090i	$0.976197\pi$
$230$	4.19038	−	6.08783i	0.276306	−	0.401420i
$231$	0.122855	+	5.63038i	0.00808324	+	0.370452i
$232$	−0.520022	+	2.66143i	−0.0341411	+	0.174732i
$233$	4.23231	+	26.7218i	0.277268	+	1.75060i	0.596212	+	0.802827i	$0.296672\pi$
$233$	4.23231	+	26.7218i	0.277268	+	1.75060i	−0.318944	+	0.947774i	$0.603328\pi$
$234$	9.26004	+	6.89852i	0.605348	+	0.450970i
$235$	0.261116	+	6.97212i	0.0170333	+	0.454811i
$236$	−1.72205	+	1.64157i	−0.112096	+	0.106857i
$237$	1.98062	+	2.72608i	0.128655	+	0.177078i
$238$	0.253006	−	21.1527i	0.0163999	−	1.37113i
$239$	3.27449	−	10.0778i	0.211809	−	0.651882i	−0.787556	−	0.616244i	$-0.788654\pi$
$239$	3.27449	−	10.0778i	0.211809	−	0.651882i	0.999365	−	0.0356380i	$-0.0113463\pi$
$240$	0.849717	+	5.75170i	0.0548490	+	0.371271i
$241$	4.15786			0.267832			0.133916	−	0.990993i	$-0.457245\pi$
$241$	4.15786			0.267832			0.133916	+	0.990993i	$0.457245\pi$
$242$	−9.53775	−	12.2895i	−0.613110	−	0.789998i
$243$			14.3710i			0.921902i
$244$	9.33303	−	17.2823i	0.597486	−	1.10639i
$245$	−0.0762697	−	0.387147i	−0.00487269	−	0.0247339i
$246$	6.23851	+	0.0746182i	0.397753	+	0.00475749i
$247$	−14.8022	−	2.34444i	−0.941841	−	0.149173i
$248$	−10.9800	−	4.00851i	−0.697230	−	0.254541i
$249$	1.69988	+	5.23170i	0.107726	+	0.331546i
$250$	−12.2441	−	10.0041i	−0.774383	−	0.632717i
$251$	−3.93408	−	24.8388i	−0.248317	−	1.56781i	−0.725007	−	0.688741i	$-0.758164\pi$
$251$	−3.93408	−	24.8388i	−0.248317	−	1.56781i	0.476690	−	0.879071i	$-0.341836\pi$
$252$	−1.78777	−	13.3464i	−0.112619	−	0.840742i
$253$	0.169093	+	7.74948i	0.0106308	+	0.487206i
$254$	4.45112	+	9.00033i	0.279288	+	0.564731i
$255$	5.14097	+	6.54598i	0.321940	+	0.409925i
$256$	3.46788	+	15.6197i	0.216743	+	0.976229i
$257$	0.467375	−	0.917276i	0.0291541	−	0.0572181i	−0.875970	−	0.482365i	$-0.839778\pi$
$257$	0.467375	−	0.917276i	0.0291541	−	0.0572181i	0.905124	+	0.425147i	$0.139778\pi$
$258$	−2.39871	+	0.747790i	−0.149337	+	0.0465554i
$259$	19.0597	+	3.01876i	1.18431	+	0.187577i
$260$	13.9616	−	2.40513i	0.865864	−	0.149160i
$261$	1.12187	+	2.20180i	0.0694421	+	0.136288i
$262$	3.57049	−	20.9206i	0.220585	−	1.29248i
$263$	15.2743	−	15.2743i	0.941856	−	0.941856i	−0.0565443	−	0.998400i	$-0.518008\pi$
$263$	15.2743	−	15.2743i	0.941856	−	0.941856i	0.998400	+	0.0565443i	$0.0180082\pi$
$264$	−4.25080	−	4.37209i	−0.261619	−	0.269084i
$265$	13.5578	−	7.56007i	0.832849	−	0.464411i
$266$	10.1026	+	14.2606i	0.619429	+	0.874374i
$267$	−1.85018	−	0.601161i	−0.113229	−	0.0367904i
$268$	9.49180	−	26.9977i	0.579804	−	1.64915i
$269$	−3.74880	+	23.6690i	−0.228569	+	1.44312i	0.560161	+	0.828384i	$0.310739\pi$
$269$	−3.74880	+	23.6690i	−0.228569	+	1.44312i	−0.788729	+	0.614741i	$0.789261\pi$
$270$	8.31086	+	7.89788i	0.505783	+	0.480650i
$271$	25.7243	−	8.35834i	1.56264	−	0.507733i	0.605129	−	0.796127i	$-0.293121\pi$
$271$	25.7243	−	8.35834i	1.56264	−	0.507733i	0.957512	+	0.288395i	$0.0931215\pi$
$272$	15.4034	+	16.9526i	0.933971	+	1.02790i
$273$	5.31296	−	0.841490i	0.321555	−	0.0509293i
$274$	−4.97210	−	10.0538i	−0.300376	−	0.607371i
$275$	16.5529	+	1.00093i	0.998177	+	0.0603586i
$276$	0.403400	+	3.01153i	0.0242818	+	0.181273i
$277$	−2.37108	−	1.72269i	−0.142464	−	0.103506i	0.514270	−	0.857628i	$-0.328063\pi$
$277$	−2.37108	−	1.72269i	−0.142464	−	0.103506i	−0.656735	+	0.754122i	$0.728063\pi$
$278$	15.3114	−	2.23771i	0.918315	−	0.134209i
$279$	−10.1303	+	3.29153i	−0.606484	+	0.197059i
$280$	−13.3808	−	9.69000i	−0.799655	−	0.579088i
$281$	−13.1280	−	18.0691i	−0.783151	−	1.07791i	−0.994927	−	0.100596i	$-0.967925\pi$
$281$	−13.1280	−	18.0691i	−0.783151	−	1.07791i	0.211777	−	0.977318i	$-0.432075\pi$
$282$	−2.00386	−	2.05238i	−0.119328	−	0.122217i
$283$	−2.38306	+	7.33429i	−0.141658	+	0.435978i	−0.996566	−	0.0828010i	$-0.973613\pi$
$283$	−2.38306	+	7.33429i	−0.141658	+	0.435978i	0.854908	+	0.518779i	$0.173613\pi$
$284$	4.32223	+	14.4714i	0.256477	+	0.858722i
$285$	−6.61475	−	1.87867i	−0.391824	−	0.111283i
$286$	−10.4027	+	10.6098i	−0.615123	+	0.627370i
$287$	−12.5357	+	12.5357i	−0.739956	+	0.739956i
$288$	11.2624	+	9.25972i	0.663643	+	0.545634i
$289$	15.0182	+	4.87970i	0.883421	+	0.287041i
$290$	2.90638	+	0.863143i	0.170669	+	0.0506855i
$291$	1.79856	−	11.3557i	0.105434	−	0.665681i
$292$	−20.6400	−	21.6518i	−1.20786	−	1.26708i
$293$	7.01802	−	2.28029i	0.409997	−	0.133216i	−0.0967545	−	0.995308i	$-0.530846\pi$
$293$	7.01802	−	2.28029i	0.409997	−	0.133216i	0.506751	+	0.862092i	$0.330846\pi$
$294$	0.130092	+	0.0969155i	0.00758711	+	0.00565223i
$295$	1.64291	+	2.09191i	0.0956539	+	0.121796i
$296$	−17.3339	+	11.6673i	−1.00751	+	0.678148i
$297$	−11.9148	−	1.62153i	−0.691366	−	0.0940909i
$298$	−13.5701	+	6.71109i	−0.786093	+	0.388763i
$299$	7.31260	−	1.15820i	0.422898	−	0.0669805i
$300$	6.49196	−	0.331033i	0.374813	−	0.0191122i
$301$	3.24126	−	6.36133i	0.186823	−	0.366661i
$302$	2.10286	+	6.74541i	0.121006	+	0.388155i
$303$	8.53918	+	1.35247i	0.490563	+	0.0776976i
$304$	−18.5272	−	3.85067i	−1.06261	−	0.220851i
$305$	−18.2364	−	12.2337i	−1.04421	−	0.700498i
$306$	20.5754	+	3.51157i	1.17622	+	0.200743i
$307$	24.5310			1.40006			0.700030	−	0.714114i	$-0.253170\pi$
$307$	24.5310			1.40006			0.700030	+	0.714114i	$0.253170\pi$
$308$	17.3273	+	0.0364595i	0.987313	+	0.00207747i
$309$	−4.15668	−	4.15668i	−0.236465	−	0.236465i
$310$	−5.63446	+	11.7914i	−0.320016	+	0.669709i
$311$	4.39622	−	13.5302i	0.249286	−	0.767225i	−0.745615	−	0.666377i	$-0.767844\pi$
$311$	4.39622	−	13.5302i	0.249286	−	0.767225i	0.994902	−	0.100848i	$-0.0321557\pi$
$312$	−3.59037	+	4.58625i	−0.203265	+	0.259645i
$313$	−13.0780	−	2.07136i	−0.739214	−	0.117080i	−0.224539	−	0.974465i	$-0.572088\pi$
$313$	−13.0780	−	2.07136i	−0.739214	−	0.117080i	−0.514675	+	0.857385i	$0.672088\pi$
$314$	29.8204	−	9.29642i	1.68286	−	0.524627i
$315$	−15.0444	+	0.563435i	−0.847657	+	0.0317459i
$316$	8.53080	−	5.89147i	0.479895	−	0.331421i
$317$	−6.32596	+	8.70694i	−0.355301	+	0.489030i	−0.948832	−	0.315781i	$-0.897734\pi$
$317$	−6.32596	+	8.70694i	−0.355301	+	0.489030i	0.593531	+	0.804811i	$0.297734\pi$
$318$	−2.04457	+	6.04553i	−0.114654	+	0.339016i
$319$	−3.00203	+	1.04836i	−0.168082	+	0.0586967i
$320$	17.7539	−	2.19034i	0.992475	−	0.122444i
$321$	−8.67754	−	6.30460i	−0.484333	−	0.351888i
$322$	−6.92366	−	5.15797i	−0.385840	−	0.287442i
$323$	−25.7643	+	8.37132i	−1.43356	+	0.465793i
$324$	10.7481	+	0.257151i	0.597117	+	0.0142862i
$325$	−1.18476	−	15.7951i	−0.0657188	−	0.876157i
$326$	0.161943	−	13.5394i	0.00896921	−	0.749878i
$327$	−3.15568	+	1.60790i	−0.174509	+	0.0889170i
$328$	0.688611	−	19.1833i	0.0380222	−	1.05922i
$329$	8.15059			0.449357
$330$	−5.32001	+	4.26358i	−0.292857	+	0.234703i
$331$	−0.367838	−	0.367838i	−0.0202182	−	0.0202182i	0.696925	−	0.717144i	$-0.254551\pi$
$331$	−0.367838	−	0.367838i	−0.0202182	−	0.0202182i	−0.717144	+	0.696925i	$0.754551\pi$
$332$	16.2171	−	4.84359i	0.890026	−	0.265827i
$333$	−5.88389	+	18.1087i	−0.322435	+	0.992353i
$334$	−13.7572	−	14.0903i	−0.752760	−	0.770986i
$335$	−29.0319	−	13.4486i	−1.58618	−	0.734773i
$336$	6.75162	−	0.740483i	0.368331	−	0.0403967i
$337$	−3.76709	+	7.39332i	−0.205206	+	0.402740i	−0.970556	−	0.240874i	$-0.922566\pi$
$337$	−3.76709	+	7.39332i	−0.205206	+	0.402740i	0.765350	+	0.643614i	$0.222566\pi$
$338$	−3.36191	−	2.50455i	−0.182864	−	0.136229i
$339$	0.446772	+	2.82081i	0.0242653	+	0.153205i
$340$	20.5128	−	15.3312i	1.11246	−	0.831450i
$341$	−2.43895	−	13.4876i	−0.132077	−	0.730395i
$342$	−15.4571	+	7.64431i	−0.835824	+	0.413357i
$343$	−18.5155	+	2.93257i	−0.999743	+	0.158344i
$344$	2.12357	+	7.43311i	0.114495	+	0.400766i
$345$	3.39469	−	0.127136i	0.182764	−	0.00684477i
$346$	5.15456	+	16.5344i	0.277111	+	0.888896i
$347$	−2.90738	−	4.00167i	−0.156076	−	0.214821i	0.723817	−	0.689992i	$-0.242386\pi$
$347$	−2.90738	−	4.00167i	−0.156076	−	0.214821i	−0.879893	+	0.475171i	$0.842386\pi$
$348$	−1.12382	+	0.539152i	−0.0602428	+	0.0289016i
$349$	2.05342	+	4.03006i	0.109917	+	0.215724i	0.939412	−	0.342790i	$-0.111372\pi$
$349$	2.05342	+	4.03006i	0.109917	+	0.215724i	−0.829495	+	0.558514i	$0.811372\pi$
$350$	−12.2140	+	13.8562i	−0.652867	+	0.740645i
$351$			11.4854i			0.613047i
$352$	−13.7607	+	12.7531i	−0.733450	+	0.679744i
$353$	−18.5581	+	18.5581i	−0.987749	+	0.987749i	−0.999926	−	0.0121771i	$-0.996124\pi$
$353$	−18.5581	+	18.5581i	−0.987749	+	0.987749i	0.0121771	+	0.999926i	$0.496124\pi$
$354$	−1.07797	−	0.183975i	−0.0572933	−	0.00977817i
$355$	16.5674	−	3.26385i	0.879305	−	0.173227i
$356$	−1.98524	+	5.64666i	−0.105218	+	0.299272i
$357$	7.86646	−	5.71532i	0.416337	−	0.302487i
$358$	−0.115411	+	0.219964i	−0.00609968	+	0.0116254i
$359$	5.50543	−	1.78882i	0.290565	−	0.0944104i	−0.160107	−	0.987100i	$-0.551184\pi$
$359$	5.50543	−	1.78882i	0.290565	−	0.0944104i	0.450673	+	0.892689i	$0.351184\pi$
$360$	11.5088	−	11.5446i	0.606566	−	0.608453i
$361$	1.98696	−	2.73481i	0.104577	−	0.143937i
$362$	12.0423	+	24.3499i	0.632927	+	1.27980i
$363$	1.91087	−	6.89038i	0.100295	−	0.361651i
$364$	−2.19732	−	16.4038i	−0.115171	−	0.859793i
$365$	−26.3023	+	20.6568i	−1.37672	+	1.08123i
$366$	8.93320	−	1.30556i	0.466946	−	0.0682426i
$367$	−13.6056	−	6.93240i	−0.710206	−	0.361868i	0.0612744	−	0.998121i	$-0.480484\pi$
$367$	−13.6056	−	6.93240i	−0.710206	−	0.361868i	−0.771481	+	0.636253i	$0.780484\pi$
$368$	9.29273	−	1.01918i	0.484417	−	0.0531284i
$369$	−10.2817	−	14.1516i	−0.535245	−	0.736702i
$370$	11.1324	+	20.5379i	0.578747	+	1.06772i
$371$	−8.23278	−	16.1577i	−0.427425	−	0.838868i
$372$	−1.53757	−	5.14802i	−0.0797194	−	0.266912i
$373$		−	24.1126i		−	1.24850i	−0.781224	−	0.624251i	$-0.785404\pi$
$373$		−	24.1126i		−	1.24850i	0.781224	−	0.624251i	$-0.214596\pi$
$374$	−8.04770	+	25.6249i	−0.416137	+	1.32503i
$375$	0.325322	−	7.26038i	0.0167995	−	0.374924i
$376$	−6.46028	+	6.01255i	−0.333163	+	0.310073i
$377$	1.37888	+	2.70620i	0.0710157	+	0.139376i
$378$	9.58325	−	9.35671i	0.492909	−	0.481257i
$379$	−4.79213	+	30.2563i	−0.246155	+	1.55416i	0.486571	+	0.873641i	$0.338247\pi$
$379$	−4.79213	+	30.2563i	−0.246155	+	1.55416i	−0.732727	+	0.680523i	$0.761753\pi$
$380$	−6.26530	+	20.2078i	−0.321403	+	1.03664i
$381$	−2.09528	+	4.11221i	−0.107344	+	0.210675i
$382$	−4.61872	+	6.19981i	−0.236314	+	0.317210i
$383$	0.176143	+	1.11212i	0.00900048	+	0.0568268i	0.991780	−	0.127956i	$-0.0408417\pi$
$383$	0.176143	+	1.11212i	0.00900048	+	0.0568268i	−0.982779	+	0.184783i	$0.940842\pi$
$384$	−4.80519	+	5.56747i	−0.245214	+	0.284114i
$385$	1.89218	−	19.2799i	0.0964342	−	0.982594i
$386$	−2.32761	−	4.70652i	−0.118472	−	0.239556i
$387$	5.69915	+	4.14068i	0.289704	+	0.210482i
$388$	−34.7961	−	6.36779i	−1.76650	−	0.323276i
$389$	6.49792	−	12.7529i	0.329458	−	0.646597i	−0.665555	−	0.746349i	$-0.731805\pi$
$389$	6.49792	−	12.7529i	0.329458	−	0.646597i	0.995012	+	0.0997519i	$0.0318049\pi$
$390$	4.72044	+	4.48587i	0.239029	+	0.227151i
$391$	10.8272	−	7.86640i	0.547553	−	0.397821i
$392$	0.307672	−	0.393012i	0.0155398	−	0.0198501i
$393$	8.69188	−	4.42873i	0.438447	−	0.223400i
$394$	9.14769	−	6.48045i	0.460854	−	0.326481i
$395$	−5.64511	−	10.1236i	−0.284036	−	0.509375i
$396$	−2.71006	+	16.8807i	−0.136186	+	0.848287i
$397$			16.3434i			0.820253i	0.912029	+	0.410127i	$0.134515\pi$
$397$			16.3434i			0.820253i	−0.912029	+	0.410127i	$0.865485\pi$
$398$	−15.7352	−	22.2116i	−0.788737	−	1.11337i
$399$	−2.48234	+	7.63985i	−0.124272	+	0.382471i
$400$	−0.540464	−	19.9927i	−0.0270232	−	0.999635i
$401$	−26.0729	+	18.9431i	−1.30202	+	0.945972i	−0.999973	−	0.00732209i	$-0.997669\pi$
$401$	−26.0729	+	18.9431i	−1.30202	+	0.945972i	−0.302045	+	0.953294i	$0.597669\pi$
$402$	12.5579	−	3.91490i	0.626333	−	0.195258i
$403$	−12.4510	+	4.04557i	−0.620228	+	0.201524i
$404$	4.78842	−	26.1658i	0.238233	−	1.30180i
$405$	1.43473	−	11.9342i	0.0712925	−	0.593018i
$406$	1.13469	−	3.35514i	0.0563137	−	0.166513i
$407$	−22.0682	−	10.6445i	−1.09388	−	0.527626i
$408$	−2.01898	+	10.3330i	−0.0999545	+	0.511560i
$409$	30.2329	+	21.9655i	1.49492	+	1.08613i	0.972349	+	0.233531i	$0.0750281\pi$
$409$	30.2329	+	21.9655i	1.49492	+	1.08613i	0.522574	+	0.852594i	$0.324972\pi$
$410$	−21.2758	−	2.81630i	−1.05074	−	0.139087i
$411$	2.34052	−	4.59353i	0.115449	−	0.226582i
$412$	−13.0912	+	12.4795i	−0.644959	+	0.614819i
$413$	2.51390	−	1.82645i	0.123701	−	0.0898740i
$414$	6.09540	−	5.95131i	0.299573	−	0.292491i
$415$	−3.65754	−	18.5658i	−0.179542	−	0.911359i
$416$	13.8424	+	11.3810i	0.678681	+	0.557998i
$417$	5.02936	+	5.02936i	0.246289	+	0.246289i
$418$	−7.06456	−	21.0348i	−0.345539	−	1.02884i
$419$	17.8489	+	17.8489i	0.871976	+	0.871976i	0.992688	−	0.120711i	$-0.0385175\pi$
$419$	17.8489	+	17.8489i	0.871976	+	0.871976i	−0.120711	+	0.992688i	$0.538518\pi$
$420$	−0.102614	−	7.59311i	−0.00500704	−	0.370506i
$421$	−11.6918	−	22.9465i	−0.569824	−	1.11834i	−0.978612	−	0.205714i	$-0.934048\pi$
$421$	−11.6918	−	22.9465i	−0.569824	−	1.11834i	0.408788	−	0.912629i	$-0.365952\pi$
$422$	−18.8324	+	18.3872i	−0.916745	+	0.895074i
$423$	−1.25808	+	7.94318i	−0.0611698	+	0.386211i
$424$	18.4447	+	6.73369i	0.895754	+	0.327017i
$425$	−14.8703	−	24.4673i	−0.721315	−	1.18684i
$426$	−4.14735	+	5.56708i	−0.200940	+	0.269726i
$427$	−15.0787	+	20.7541i	−0.729712	+	1.00436i
$428$	−20.0306	+	26.2269i	−0.968217	+	1.26772i
$429$	−6.76741	−	0.921006i	−0.326734	−	0.0444666i
$430$	8.49935	−	1.56905i	0.409875	−	0.0756664i
$431$	−15.8029	+	21.7508i	−0.761199	+	1.04770i	0.235914	+	0.971774i	$0.424192\pi$
$431$	−15.8029	+	21.7508i	−0.761199	+	1.04770i	−0.997113	+	0.0759268i	$0.975808\pi$
$432$	−0.693542	+	14.4857i	−0.0333681	+	0.696941i
$433$	6.84272	+	3.48654i	0.328840	+	0.167552i	0.610614	−	0.791928i	$-0.290923\pi$
$433$	6.84272	+	3.48654i	0.328840	+	0.167552i	−0.281774	+	0.959481i	$0.590923\pi$
$434$	13.5189	+	7.09313i	0.648926	+	0.340481i
$435$	0.479940	+	1.30833i	0.0230113	+	0.0627294i
$436$	4.71344	+	9.82474i	0.225733	+	0.470520i
$437$	−3.41662	+	10.5153i	−0.163439	+	0.503013i
$438$	2.31318	−	13.5536i	0.110528	−	0.647618i
$439$			5.32777i			0.254281i	0.991885	+	0.127140i	$0.0405798\pi$
$439$			5.32777i			0.254281i	−0.991885	+	0.127140i	$0.959420\pi$
$440$	12.7227	+	16.6773i	0.606529	+	0.795061i
$441$		−	0.454830i		−	0.0216586i
$442$	25.2889	+	4.31602i	1.20287	+	0.205292i
$443$	−5.50867	+	16.9539i	−0.261725	+	0.805506i	0.730705	+	0.682693i	$0.239191\pi$
$443$	−5.50867	+	16.9539i	−0.261725	+	0.805506i	−0.992430	+	0.122813i	$0.960809\pi$
$444$	−9.06055	−	3.18549i	−0.429995	−	0.151177i
$445$	6.07211	+	2.81281i	0.287845	+	0.133340i
$446$	−11.2936	+	21.5245i	−0.534766	+	1.01921i
$447$	−6.20011	−	3.15911i	−0.293255	−	0.149421i
$448$	−1.78076	−	20.8215i	−0.0841332	−	0.983724i
$449$	−2.43432	+	3.35055i	−0.114882	+	0.158122i	−0.862586	−	0.505911i	$-0.831157\pi$
$449$	−2.43432	+	3.35055i	−0.114882	+	0.158122i	0.747703	+	0.664033i	$0.231157\pi$
$450$	−11.6183	−	14.0420i	−0.547693	−	0.661945i
$451$	19.8279	−	10.6539i	0.933657	−	0.501672i
$452$	8.70928	−	1.16662i	0.409650	−	0.0548733i
$453$	−1.90894	+	2.62743i	−0.0896898	+	0.123447i
$454$	−24.5770	−	18.3093i	−1.15346	−	0.859299i
$455$	−18.4909	+	0.692509i	−0.866865	+	0.0324653i
$456$	−3.66824	−	7.88663i	−0.171781	−	0.369325i
$457$	1.13957	−	7.19494i	0.0533067	−	0.336565i	−0.946593	−	0.322430i	$-0.895500\pi$
$457$	1.13957	−	7.19494i	0.0533067	−	0.336565i	0.999900	−	0.0141355i	$-0.00449961\pi$
$458$	−2.45813	−	2.51765i	−0.114861	−	0.117642i
$459$	9.42540	+	18.4984i	0.439940	+	0.863430i
$460$	−0.141235	−	10.4509i	−0.00658510	−	0.487277i
$461$	−7.92561	−	7.92561i	−0.369132	−	0.369132i	0.498028	−	0.867161i	$-0.334058\pi$
$461$	−7.92561	−	7.92561i	−0.369132	−	0.369132i	−0.867161	+	0.498028i	$0.834058\pi$
$462$	4.74466	+	6.39692i	0.220742	+	0.297612i
$463$	−11.0663	−	11.0663i	−0.514296	−	0.514296i	0.401544	−	0.915840i	$-0.368474\pi$
$463$	−11.0663	−	11.0663i	−0.514296	−	0.514296i	−0.915840	+	0.401544i	$0.868474\pi$
$464$	1.57565	+	3.49637i	0.0731479	+	0.162315i
$465$	−5.89362	+	1.16107i	−0.273310	+	0.0538433i
$466$	26.7293	+	27.3765i	1.23821	+	1.26819i
$467$	−25.3284	+	18.4022i	−1.17206	+	0.851551i	−0.991254	−	0.131968i	$-0.957870\pi$
$467$	−25.3284	+	18.4022i	−1.17206	+	0.851551i	−0.180805	+	0.983519i	$0.557870\pi$
$468$	16.3255	+	0.390592i	0.754649	+	0.0180551i
$469$	−16.9690	+	33.3035i	−0.783554	+	1.53781i
$470$	6.00111	+	7.83225i	0.276811	+	0.361275i
$471$	11.6154	+	8.43911i	0.535211	+	0.388854i
$472$	−0.645210	+	3.30213i	−0.0296982	+	0.151993i
$473$	−6.26844	+	6.54810i	−0.288223	+	0.301082i
$474$	4.51420	+	1.52668i	0.207344	+	0.0701227i
$475$	21.8200	+	9.13217i	1.00117	+	0.419013i
$476$	−17.0006	−	24.6167i	−0.779222	−	1.12830i
$477$	17.0173	−	5.52927i	0.779170	−	0.253168i
$478$	−4.46004	−	14.3066i	−0.203998	−	0.654368i
$479$	8.63011	−	6.27014i	0.394320	−	0.286490i	−0.372904	−	0.927870i	$-0.621638\pi$
$479$	8.63011	−	6.27014i	0.394320	−	0.286490i	0.767223	+	0.641380i	$0.221638\pi$
$480$	5.68264	+	5.94271i	0.259376	+	0.271247i
$481$	−7.23180	+	22.2572i	−0.329742	+	1.01484i
$482$	4.79810	−	3.39910i	0.218548	−	0.154825i
$483$		−	3.96848i		−	0.180572i
$484$	−21.0532	−	6.38463i	−0.956963	−	0.290211i
$485$	−10.8051	+	38.0446i	−0.490636	+	1.72752i
$486$	11.7485	+	16.5839i	0.532921	+	0.752262i
$487$	−3.93863	+	2.00683i	−0.178476	+	0.0909383i	−0.540946	−	0.841057i	$-0.681934\pi$
$487$	−3.93863	+	2.00683i	−0.178476	+	0.0909383i	0.362470	+	0.931996i	$0.381934\pi$
$488$	−3.35831	−	27.5733i	−0.152024	−	1.24819i
$489$	5.03515	−	3.65825i	0.227697	−	0.165432i
$490$	−0.404511	−	0.384410i	−0.0182739	−	0.0173659i
$491$	13.2568	−	26.0179i	0.598271	−	1.17417i	−0.371105	−	0.928591i	$-0.621021\pi$
$491$	13.2568	−	26.0179i	0.598271	−	1.17417i	0.969376	−	0.245581i	$-0.0789788\pi$
$492$	7.26014	−	5.01394i	0.327312	−	0.226046i
$493$	4.44162	+	3.22703i	0.200041	+	0.145338i
$494$	−18.9981	+	9.39551i	−0.854764	+	0.422724i
$495$	18.4972	+	4.81995i	0.831387	+	0.216641i
$496$	−15.9477	+	4.35051i	−0.716074	+	0.195344i
$497$	−3.08584	−	19.4833i	−0.138419	−	0.873943i
$498$	6.23861	+	4.64762i	0.279559	+	0.208265i
$499$	−7.39379	+	14.5111i	−0.330991	+	0.649607i	−0.995192	−	0.0979477i	$-0.968772\pi$
$499$	−7.39379	+	14.5111i	−0.330991	+	0.649607i	0.664200	+	0.747555i	$0.268772\pi$
$500$	−22.3079	−	1.53494i	−0.997641	−	0.0686445i
$501$	1.41599	−	8.94019i	0.0632616	−	0.399418i
$502$	−24.8459	−	25.4474i	−1.10893	−	1.13577i
$503$	−8.41823	−	16.5217i	−0.375350	−	0.736667i	0.623634	−	0.781716i	$-0.285655\pi$
$503$	−8.41823	−	16.5217i	−0.375350	−	0.736667i	−0.998985	+	0.0450495i	$0.985655\pi$
$504$	−12.9738	−	13.9400i	−0.577901	−	0.620935i
$505$	−28.6086	−	8.12519i	−1.27307	−	0.361566i
$506$	6.53042	+	8.80453i	0.290312	+	0.391409i
$507$		−	1.92697i		−	0.0855798i
$508$	12.4944	+	6.74739i	0.554348	+	0.299367i
$509$	−14.2259	−	27.9198i	−0.630550	−	1.23752i	−0.956388	−	0.292099i	$-0.905646\pi$
$509$	−14.2259	−	27.9198i	−0.630550	−	1.23752i	0.325838	−	0.945426i	$-0.394354\pi$
$510$	11.2840	+	3.35115i	0.499664	+	0.148391i
$511$	22.9646	+	31.6081i	1.01589	+	1.39826i
$512$	16.7711	+	15.1898i	0.741186	+	0.671300i
$513$	−15.2824	−	7.78675i	−0.674732	−	0.343793i
$514$	−0.210540	−	1.44060i	−0.00928650	−	0.0635424i
$515$	12.4896	+	15.9030i	0.550360	+	0.700770i
$516$	−2.15674	+	2.82391i	−0.0949452	+	0.124315i
$517$	−9.90950	−	2.98242i	−0.435820	−	0.131167i
$518$	24.4625	−	12.0979i	1.07482	−	0.531552i
$519$	−4.67921	+	6.44038i	−0.205394	+	0.282701i
$520$	14.1453	−	14.1893i	0.620311	−	0.622241i
$521$	22.0445	−	7.16269i	0.965787	−	0.313803i	0.216673	−	0.976244i	$-0.430479\pi$
$521$	22.0445	−	7.16269i	0.965787	−	0.313803i	0.749114	+	0.662441i	$0.230479\pi$
$522$	3.09461	+	1.62369i	0.135448	+	0.0710672i
$523$	29.8395	−	21.6796i	1.30479	−	0.947985i	0.304799	−	0.952417i	$-0.401411\pi$
$523$	29.8395	−	21.6796i	1.30479	−	0.947985i	0.999990	+	0.00443188i	$0.00141072\pi$
$524$	−12.9825	−	27.0609i	−0.567144	−	1.18216i
$525$	−8.46146	−	0.697203i	−0.369288	−	0.0304284i
$526$	5.13939	−	30.1132i	0.224088	−	1.31300i
$527$	−16.7335	+	16.7335i	−0.728925	+	0.728925i
$528$	−8.47959	−	1.57024i	−0.369027	−	0.0683358i
$529$			17.5379i			0.762517i
$530$	9.46503	−	19.8078i	0.411135	−	0.860397i
$531$	1.39195	+	2.73185i	0.0604053	+	0.118552i
$532$	23.3164	+	8.19753i	1.01089	+	0.355408i
$533$	−12.6371	−	17.3935i	−0.547374	−	0.753396i
$534$	−2.62653	+	0.818815i	−0.113661	+	0.0354336i
$535$	27.0478	+	25.0950i	1.16938	+	1.08495i
$536$	−11.1175	−	38.9145i	−0.480204	−	1.68085i
$537$	−0.112772	+	0.0178613i	−0.00486646	+	0.000770772i
$538$	15.0236	+	30.3783i	0.647714	+	1.30970i
$539$	0.579923	+	0.0789242i	0.0249791	+	0.00339951i
$540$	16.0472	+	2.31980i	0.690561	+	0.0998282i
$541$	−4.36899	−	27.5847i	−0.187837	−	1.18596i	−0.883794	−	0.467875i	$-0.845020\pi$
$541$	−4.36899	−	27.5847i	−0.187837	−	1.18596i	0.695957	−	0.718083i	$-0.254980\pi$
$542$	22.8524	−	30.6753i	0.981594	−	1.31762i
$543$	−5.66865	+	11.1254i	−0.243265	+	0.477435i
$544$	31.6342	+	6.97051i	1.35631	+	0.298858i
$545$	11.4378	−	4.19578i	0.489941	−	0.179727i
$546$	5.44313	−	5.31446i	0.232945	−	0.227438i
$547$	1.70398	−	5.24432i	0.0728571	−	0.224231i	−0.907996	−	0.418978i	$-0.862389\pi$
$547$	1.70398	−	5.24432i	0.0728571	−	0.224231i	0.980854	+	0.194747i	$0.0623885\pi$
$548$	−13.9568	−	7.53714i	−0.596205	−	0.321971i
$549$	−17.8985	−	17.8985i	−0.763890	−	0.763890i
$550$	19.9200	−	12.3771i	0.849393	−	0.527761i
$551$	−4.53566			−0.193226
$552$	2.92748	+	3.14547i	0.124602	+	0.133880i
$553$	−12.0650	+	6.14743i	−0.513056	+	0.261415i
$554$	−4.14451	−	0.0495720i	−0.176083	−	0.00210611i
$555$	−4.51339	+	9.74322i	−0.191583	+	0.413577i
$556$	15.8397	−	15.0995i	0.671753	−	0.640361i
$557$	15.5717	−	5.05956i	0.659795	−	0.214380i	0.0400669	−	0.999197i	$-0.487243\pi$
$557$	15.5717	−	5.05956i	0.659795	−	0.214380i	0.619728	+	0.784817i	$0.287243\pi$
$558$	−8.99932	+	12.0800i	−0.380971	+	0.511387i
$559$	7.00474	+	5.08924i	0.296269	+	0.215252i
$560$	−23.3629	−	0.243156i	−0.987261	−	0.0102752i
$561$	−11.6554	+	4.07024i	−0.492091	+	0.171846i
$562$	−29.9212	−	10.1192i	−1.26215	−	0.426853i
$563$	2.71950	−	3.74308i	0.114613	−	0.157752i	−0.747856	−	0.663861i	$-0.768917\pi$
$563$	2.71950	−	3.74308i	0.114613	−	0.157752i	0.862469	+	0.506109i	$0.168917\pi$
$564$	−3.99026	−	0.730230i	−0.168020	−	0.0307482i
$565$	−0.367674	−	9.81736i	−0.0154682	−	0.413019i
$566$	3.24586	+	10.4118i	0.136434	+	0.437642i
$567$	−13.8692	−	2.19666i	−0.582451	−	0.0922511i
$568$	16.8183	+	13.1663i	0.705682	+	0.552447i
$569$	8.45995	−	26.0370i	0.354660	−	1.09153i	−0.601547	−	0.798837i	$-0.705449\pi$
$569$	8.45995	−	26.0370i	0.354660	−	1.09153i	0.956207	−	0.292692i	$-0.0945512\pi$
$570$	−9.16914	+	3.23968i	−0.384053	+	0.135695i
$571$	13.9687	+	13.9687i	0.584572	+	0.584572i	0.936156	−	0.351584i	$-0.114357\pi$
$571$	13.9687	+	13.9687i	0.584572	+	0.584572i	−0.351584	+	0.936156i	$0.614357\pi$
$572$	−3.33090	+	20.7478i	−0.139272	+	0.867510i
$573$	−3.55359			−0.148453
$574$	−4.21790	+	24.7140i	−0.176052	+	1.03154i
$575$	−11.6461	−	0.959610i	−0.485676	−	0.0400185i
$576$	20.5665	+	1.47843i	0.856938	+	0.0616014i
$577$	−6.68071	−	1.05812i	−0.278122	−	0.0440501i	0.0158154	−	0.999875i	$-0.494966\pi$
$577$	−6.68071	−	1.05812i	−0.278122	−	0.0440501i	−0.293937	+	0.955825i	$0.594966\pi$
$578$	21.3199	−	6.64642i	0.886791	−	0.276455i
$579$	1.09568	−	2.15039i	0.0455348	−	0.0893671i
$580$	4.05954	−	1.37994i	0.168563	−	0.0572991i
$581$	−21.8334	+	3.45807i	−0.905802	+	0.143465i
$582$	−7.20788	−	14.5746i	−0.298776	−	0.604136i
$583$	4.09707	+	22.6571i	0.169683	+	0.938362i
$584$	−41.5188	−	8.11243i	−1.71806	−	0.335695i
$585$	2.17925	−	18.1272i	0.0901010	−	0.749468i
$586$	6.23451	−	8.36872i	0.257545	−	0.345709i
$587$	−7.74222	+	2.51560i	−0.319556	+	0.103830i	−0.464403	−	0.885624i	$-0.653731\pi$
$587$	−7.74222	+	2.51560i	−0.319556	+	0.103830i	0.144847	+	0.989454i	$0.453731\pi$
$588$	0.229353	+	0.00548733i	0.00945837	+	0.000226294i
$589$	3.05838	−	19.3099i	0.126018	−	0.795649i
$590$	3.60605	+	1.07093i	0.148459	+	0.0440895i
$591$	4.90070	+	1.59233i	0.201588	+	0.0654999i
$592$	−10.4649	+	27.6345i	−0.430104	+	1.13577i
$593$	16.4374	−	16.4374i	0.675005	−	0.675005i	−0.283861	−	0.958865i	$-0.591615\pi$
$593$	16.4374	−	16.4374i	0.675005	−	0.675005i	0.958865	+	0.283861i	$0.0916154\pi$
$594$	−15.0751	+	7.86925i	−0.618538	+	0.322879i
$595$	−29.2130	+	16.2897i	−1.19762	+	0.667812i
$596$	−10.1732	+	18.8382i	−0.416712	+	0.771641i
$597$	3.86636	−	11.8994i	0.158240	−	0.487011i
$598$	7.49177	−	7.31467i	0.306361	−	0.299119i
$599$	−8.56255	−	11.7853i	−0.349856	−	0.481536i	0.597431	−	0.801920i	$-0.296188\pi$
$599$	−8.56255	−	11.7853i	−0.349856	−	0.481536i	−0.947288	+	0.320384i	$0.896188\pi$
$600$	7.22099	−	5.68925i	0.294796	−	0.232263i
$601$	−30.5746	+	9.93428i	−1.24716	+	0.405228i	−0.856903	−	0.515477i	$-0.827615\pi$
$601$	−30.5746	+	9.93428i	−1.24716	+	0.405228i	−0.390259	+	0.920705i	$0.627615\pi$
$602$	−1.46010	−	9.99064i	−0.0595092	−	0.407188i
$603$	−29.8368	−	21.6777i	−1.21505	−	0.882783i
$604$	7.94112	+	6.06498i	0.323119	+	0.246780i
$605$	−9.35531	+	22.7481i	−0.380347	+	0.924844i
$606$	10.9597	−	5.42014i	0.445209	−	0.220178i
$607$	3.14846	−	0.498667i	0.127792	−	0.0202403i	−0.0922107	−	0.995740i	$-0.529393\pi$
$607$	3.14846	−	0.498667i	0.127792	−	0.0202403i	0.220003	+	0.975499i	$0.429393\pi$
$608$	−24.5281	+	10.7026i	−0.994745	+	0.434048i
$609$	1.54831	−	0.503076i	0.0627406	−	0.0203856i
$610$	−31.0457	+	0.791015i	−1.25700	+	0.0320273i
$611$	−1.54628	+	9.76284i	−0.0625559	+	0.394962i
$612$	26.6144	−	12.7683i	1.07582	−	0.516128i
$613$	23.2861	+	7.56610i	0.940515	+	0.305592i	0.738856	−	0.673864i	$-0.235367\pi$
$613$	23.2861	+	7.56610i	0.940515	+	0.305592i	0.201660	+	0.979456i	$0.435367\pi$
$614$	28.3084	−	20.0544i	1.14243	−	0.809329i
$615$	−4.80427	−	8.61571i	−0.193727	−	0.347419i
$616$	20.0252	−	14.1232i	0.806837	−	0.569038i
$617$	7.14027	−	7.14027i	0.287456	−	0.287456i	−0.548617	−	0.836074i	$-0.684846\pi$
$617$	7.14027	−	7.14027i	0.287456	−	0.287456i	0.836074	+	0.548617i	$0.184846\pi$
$618$	−8.19487	−	1.39861i	−0.329646	−	0.0562602i
$619$	−1.82187	−	3.57562i	−0.0732270	−	0.143716i	0.851491	−	0.524370i	$-0.175699\pi$
$619$	−1.82187	−	3.57562i	−0.0732270	−	0.143716i	−0.924718	+	0.380654i	$0.875699\pi$
$620$	3.13757	+	18.2134i	0.126008	+	0.731466i
$621$	8.36903	+	1.32552i	0.335837	+	0.0531914i
$622$	−5.98789	−	19.2075i	−0.240093	−	0.770152i
$623$	3.54911	−	6.96553i	0.142192	−	0.279068i
$624$	−0.393921	+	8.22762i	−0.0157695	+	0.329369i
$625$	−4.09209	+	24.6628i	−0.163684	+	0.986513i
$626$	−16.7852	+	8.30112i	−0.670871	+	0.331780i
$627$	5.81357	−	8.38022i	0.232171	−	0.334674i
$628$	26.8123	−	35.1064i	1.06993	−	1.40090i
$629$	6.61762	+	41.7820i	0.263862	+	1.66596i
$630$	−16.9004	+	12.9492i	−0.673327	+	0.515907i
$631$	−13.9158	−	42.8284i	−0.553979	−	1.70497i	−0.698624	−	0.715489i	$-0.746204\pi$
$631$	−13.9158	−	42.8284i	−0.553979	−	1.70497i	0.144644	−	0.989484i	$-0.453796\pi$
$632$	5.02805	−	13.7727i	0.200005	−	0.547848i
$633$	−11.9490	−	1.89254i	−0.474930	−	0.0752216i
$634$	−0.182035	+	15.2192i	−0.00722955	+	0.604432i
$635$	8.84443	−	13.1842i	0.350980	−	0.523197i
$636$	2.58289	+	8.64789i	0.102418	+	0.342911i
$637$		−	0.559025i		−	0.0221494i
$638$	−2.60725	+	3.66398i	−0.103222	+	0.145058i
$639$	19.4638			0.769975
$640$	18.6971	−	17.0416i	0.739069	−	0.673630i
$641$	−7.64209	+	23.5199i	−0.301844	+	0.928981i	0.678992	+	0.734146i	$0.262417\pi$
$641$	−7.64209	+	23.5199i	−0.301844	+	0.928981i	−0.980836	+	0.194835i	$0.937583\pi$
$642$	−15.1678	−	0.181421i	−0.598625	−	0.00716010i
$643$	9.68439	+	13.3294i	0.381915	+	0.525661i	0.956091	−	0.293071i	$-0.0946773\pi$
$643$	9.68439	+	13.3294i	0.381915	+	0.525661i	−0.574176	+	0.818732i	$0.694677\pi$
$644$	−12.2065	−	0.292043i	−0.481002	−	0.0115081i
$645$	2.91230	+	2.70203i	0.114672	+	0.106392i
$646$	−22.8879	+	30.7229i	−0.900512	+	1.20878i
$647$	3.49348	+	22.0570i	0.137343	+	0.867150i	0.956107	+	0.293019i	$0.0946599\pi$
$647$	3.49348	+	22.0570i	0.137343	+	0.867150i	−0.818764	+	0.574131i	$0.805340\pi$
$648$	12.6133	−	8.48994i	0.495499	−	0.333516i
$649$	−3.72473	+	1.30073i	−0.146208	+	0.0510583i
$650$	−14.2799	−	17.2588i	−0.560104	−	0.676945i
$651$	1.09775	+	6.93090i	0.0430241	+	0.271643i
$652$	−10.8817	−	15.7566i	−0.426161	−	0.617077i
$653$	9.47209	+	29.1521i	0.370671	+	1.14081i	0.946353	+	0.323135i	$0.104737\pi$
$653$	9.47209	+	29.1521i	0.370671	+	1.14081i	−0.575681	+	0.817674i	$0.695263\pi$
$654$	−2.32712	+	4.43529i	−0.0909978	+	0.173433i
$655$	−31.5038	+	11.5567i	−1.23096	+	0.451558i
$656$	−14.8879	−	22.7001i	−0.581274	−	0.886291i
$657$	−34.3484	+	17.5014i	−1.34006	+	0.682794i
$658$	9.40564	−	6.66320i	0.366670	−	0.259758i
$659$	−25.4490	−	25.4490i	−0.991351	−	0.991351i	0.00861234	−	0.999963i	$-0.497259\pi$
$659$	−25.4490	−	25.4490i	−0.991351	−	0.991351i	−0.999963	+	0.00861234i	$0.997259\pi$
$660$	−2.65367	+	9.26927i	−0.103294	+	0.360806i
$661$	−13.3978	+	13.3978i	−0.521116	+	0.521116i	−0.917908	−	0.396793i	$-0.870123\pi$
$661$	−13.3978	+	13.3978i	−0.521116	+	0.521116i	0.396793	+	0.917908i	$0.370123\pi$
$662$	−0.725190	−	0.123767i	−0.0281853	−	0.00481035i
$663$	5.35348	+	10.5068i	0.207912	+	0.408050i
$664$	14.7545	−	18.8470i	0.572586	−	0.731407i
$665$	11.6148	−	25.0732i	0.450401	−	0.972297i
$666$	8.01419	+	25.7073i	0.310543	+	0.996138i
$667$	2.13104	−	0.692418i	0.0825144	−	0.0268105i
$668$	−27.3945	−	5.01328i	−1.05993	−	0.193970i
$669$	−11.0353	+	1.74781i	−0.426648	+	0.0675744i
$670$	−44.4966	+	8.21445i	−1.71905	+	0.317352i
$671$	25.9270	−	19.7153i	1.00090	−	0.761102i
$672$	7.18590	−	6.37403i	0.277202	−	0.245883i
$673$	20.2476	−	3.20690i	0.780488	−	0.123617i	0.246538	−	0.969133i	$-0.420707\pi$
$673$	20.2476	−	3.20690i	0.780488	−	0.123617i	0.533950	+	0.845516i	$0.320707\pi$
$674$	1.69697	+	11.6114i	0.0653648	+	0.447254i
$675$	4.29655	−	17.6113i	0.165374	−	0.677858i
$676$	−5.92708	−	0.141807i	−0.227965	−	0.00545411i
$677$	30.6371	−	22.2591i	1.17748	−	0.855488i	0.185593	−	0.982627i	$-0.440579\pi$
$677$	30.6371	−	22.2591i	1.17748	−	0.855488i	0.991885	+	0.127139i	$0.0405793\pi$
$678$	2.82161	+	2.88992i	0.108363	+	0.110987i
$679$	43.9404	+	14.2771i	1.68628	+	0.547905i
$680$	11.1380	−	34.4614i	0.427124	−	1.32153i
$681$		−	14.0870i		−	0.539814i
$682$	−13.8408	−	13.5706i	−0.529991	−	0.519645i
$683$	43.4754			1.66354			0.831770	−	0.555120i	$-0.187328\pi$
$683$	43.4754			1.66354			0.831770	+	0.555120i	$0.187328\pi$
$684$	−11.5879	+	21.4577i	−0.443075	+	0.820457i
$685$	−9.87963	+	14.7273i	−0.377481	+	0.562701i
$686$	−18.9692	+	18.5207i	−0.724246	+	0.707125i
$687$	0.253008	−	1.59743i	0.00965286	−	0.0609457i
$688$	8.52721	+	6.84163i	0.325097	+	0.260835i
$689$	20.9157	−	6.79594i	0.796827	−	0.258905i
$690$	3.81348	−	2.92191i	0.145177	−	0.111235i
$691$	19.8604	−	3.14559i	0.755527	−	0.119664i	0.233223	−	0.972423i	$-0.425073\pi$
$691$	19.8604	−	3.14559i	0.755527	−	0.119664i	0.522304	+	0.852760i	$0.325073\pi$
$692$	19.4653	+	14.8665i	0.739961	+	0.565141i
$693$	6.43546	−	21.3827i	0.244463	−	0.812261i
$694$	−6.62647	−	2.24104i	−0.251538	−	0.0850687i
$695$	−15.1118	−	19.2418i	−0.573224	−	0.729883i
$696$	−0.856101	+	1.54090i	−0.0324504	+	0.0584078i
$697$	−34.6271	−	17.6434i	−1.31159	−	0.668291i
$698$	5.66422	+	2.97193i	0.214394	+	0.112489i
$699$	−2.75117	+	17.3702i	−0.104059	+	0.657001i
$700$	−2.76718	+	25.9749i	−0.104590	+	0.981759i
$701$	−21.9468	+	11.1825i	−0.828920	+	0.422356i	−0.816345	−	0.577565i	$-0.804003\pi$
$701$	−21.9468	+	11.1825i	−0.828920	+	0.422356i	−0.0125757	+	0.999921i	$0.504003\pi$
$702$	9.38946	+	13.2540i	0.354382	+	0.500239i
$703$	−24.7122	−	24.7122i	−0.932037	−	0.932037i
$704$	−5.45384	+	25.9664i	−0.205549	+	0.978647i
$705$	−1.23908	+	4.36279i	−0.0466666	+	0.164312i
$706$	−6.24429	+	36.5872i	−0.235007	+	1.37698i
$707$	−10.7360	+	33.0421i	−0.403770	+	1.24268i
$708$	−1.39436	+	0.668946i	−0.0524032	+	0.0251405i
$709$	15.6769	+	2.48297i	0.588757	+	0.0932499i	0.443703	−	0.896174i	$-0.353665\pi$
$709$	15.6769	+	2.48297i	0.588757	+	0.0932499i	0.145054	+	0.989424i	$0.453665\pi$
$710$	16.4502	−	17.3104i	0.617366	−	0.649649i
$711$	−4.12871	−	12.7069i	−0.154839	−	0.476544i
$712$	2.32527	+	8.13910i	0.0871431	+	0.305026i
$713$	1.51091	+	9.53949i	0.0565839	+	0.357257i
$714$	4.40543	−	13.0263i	0.164869	−	0.487497i
$715$	22.7346	+	5.92413i	0.850227	+	0.221550i
$716$	0.0466398	+	0.348184i	0.00174301	+	0.0130123i
$717$	4.04874	−	5.57261i	0.151203	−	0.208113i
$718$	4.89079	−	6.56502i	0.182523	−	0.245004i
$719$	−10.9426	−	33.6777i	−0.408088	−	1.25597i	−0.918289	−	0.395911i	$-0.870429\pi$
$719$	−10.9426	−	33.6777i	−0.408088	−	1.25597i	0.510200	−	0.860056i	$-0.329571\pi$
$720$	3.84312	−	22.7308i	0.143225	−	0.847127i
$721$	19.1110	−	13.8850i	0.711732	−	0.517104i
$722$	0.0571765	−	4.78028i	0.00212789	−	0.177904i
$723$	2.57049	+	0.835204i	0.0955976	+	0.0310616i
$724$	33.8029	+	18.2547i	1.25627	+	0.678430i
$725$	−1.10196	−	4.66539i	−0.0409257	−	0.173268i
$726$	−3.42784	−	9.51353i	−0.127219	−	0.353080i
$727$	−1.67696	−	1.67696i	−0.0621951	−	0.0621951i	0.675325	−	0.737520i	$-0.264003\pi$
$727$	−1.67696	−	1.67696i	−0.0621951	−	0.0621951i	−0.737520	+	0.675325i	$0.764003\pi$
$728$	−15.9460	−	17.1334i	−0.590997	−	0.635006i
$729$	2.09669	−	6.45295i	0.0776552	−	0.238998i
$730$	−13.4652	+	45.3400i	−0.498368	+	1.67811i
$731$	15.4582	+	2.44834i	0.571744	+	0.0905553i
$732$	9.24146	−	8.80958i	0.341574	−	0.325611i
$733$	10.4792	+	32.2518i	0.387060	+	1.19125i	0.934975	+	0.354713i	$0.115421\pi$
$733$	10.4792	+	32.2518i	0.387060	+	1.19125i	−0.547916	+	0.836534i	$0.684579\pi$
$734$	−21.3679	+	3.12285i	−0.788705	+	0.115267i
$735$	0.0306157	−	0.254664i	0.00112928	−	0.00939344i
$736$	9.89046	−	8.77302i	0.364567	−	0.323378i
$737$	32.8171	−	34.2812i	1.20883	−	1.26277i
$738$	−23.4340	−	7.92526i	−0.862618	−	0.291733i
$739$	−1.69695	−	10.7141i	−0.0624233	−	0.394125i	−0.999041	−	0.0437736i	$-0.986062\pi$
$739$	−1.69695	−	10.7141i	−0.0624233	−	0.394125i	0.936618	−	0.350352i	$-0.113938\pi$
$740$	29.6366	+	14.5996i	1.08946	+	0.536691i
$741$	−8.68014	−	4.42275i	−0.318873	−	0.162474i
$742$	−22.7096	−	11.9154i	−0.833696	−	0.437427i
$743$	3.97807	−	25.1165i	0.145941	−	0.921437i	−0.800681	−	0.599091i	$-0.795529\pi$
$743$	3.97807	−	25.1165i	0.145941	−	0.921437i	0.946622	−	0.322346i	$-0.104471\pi$
$744$	−5.98289	−	4.68374i	−0.219344	−	0.171714i
$745$	19.8782	+	13.3350i	0.728279	+	0.488557i
$746$	−19.7123	−	27.8255i	−0.721718	−	1.01876i
$747$		−	21.8116i		−	0.798044i
$748$	11.6617	+	36.1498i	0.426396	+	1.32177i
$749$	30.4782	−	30.4782i	1.11365	−	1.11365i
$750$	−5.56002	−	8.64430i	−0.203023	−	0.315645i
$751$	51.5118	+	16.7372i	1.87969	+	0.610749i	0.987153	+	0.159777i	$0.0510774\pi$
$751$	51.5118	+	16.7372i	1.87969	+	0.610749i	0.892538	+	0.450972i	$0.148923\pi$
$752$	−2.53973	+	12.2197i	−0.0926143	+	0.445607i
$753$	2.55731	−	16.1462i	0.0931935	−	0.588401i
$754$	3.80354	+	1.99566i	0.138517	+	0.0726776i
$755$	7.59840	−	8.18969i	0.276534	−	0.298053i
$756$	3.40969	−	18.6319i	0.124009	−	0.677635i
$757$	−7.02376	−	5.10306i	−0.255283	−	0.185474i	0.452782	−	0.891621i	$-0.350432\pi$
$757$	−7.02376	−	5.10306i	−0.255283	−	0.185474i	−0.708065	+	0.706147i	$0.750432\pi$
$758$	19.2048	+	38.8329i	0.697551	+	1.41048i
$759$	−1.45213	+	4.82488i	−0.0527088	+	0.175132i
$760$	9.29002	+	28.4414i	0.336984	+	1.03168i
$761$	−5.80985	+	7.99658i	−0.210607	+	0.289876i	−0.901232	−	0.433338i	$-0.857336\pi$
$761$	−5.80985	+	7.99658i	−0.210607	+	0.289876i	0.690625	+	0.723213i	$0.257336\pi$
$762$	0.943863	+	6.45833i	0.0341926	+	0.233961i
$763$	−4.39804	−	13.5358i	−0.159220	−	0.490028i
$764$	−0.261510	+	10.9303i	−0.00946112	+	0.395445i
$765$	−11.3660	−	30.9840i	−0.410939	−	1.12023i
$766$	1.11244	+	1.13937i	0.0401940	+	0.0411672i
$767$	1.71082	+	3.35767i	0.0617741	+	0.121239i
$768$	−0.993642	+	10.3531i	−0.0358550	+	0.373584i
$769$		−	7.22602i		−	0.260577i	−0.991476	−	0.130289i	$-0.958410\pi$
$769$		−	7.22602i		−	0.260577i	0.991476	−	0.130289i	$-0.0415904\pi$
$770$	−13.5780	−	23.7955i	−0.489316	−	0.857532i
$771$	0.473199	−	0.473199i	0.0170418	−	0.0170418i
$772$	−6.53365	−	3.52840i	−0.235151	−	0.126990i
$773$	38.0364	+	12.3588i	1.36807	+	0.444514i	0.898730	−	0.438502i	$-0.144491\pi$
$773$	38.0364	+	12.3588i	1.36807	+	0.444514i	0.469343	+	0.883016i	$0.344491\pi$
$774$	9.96177	+	0.119152i	0.358068	+	0.00428282i
$775$	20.6052	−	1.54556i	0.740161	−	0.0555180i
$776$	−45.3598	+	21.0978i	−1.62832	+	0.757368i
$777$	11.1768	+	5.69486i	0.400965	+	0.204302i
$778$	−2.92713	−	20.0287i	−0.104943	−	0.718065i
$779$	31.7111	−	5.02255i	1.13617	−	0.179951i
$780$	9.11455	+	1.31761i	0.326353	+	0.0471780i
$781$	−3.37744	+	24.8169i	−0.120854	+	0.888020i
$782$	6.06350	−	17.9290i	0.216830	−	0.641140i
$783$	0.543769	+	3.43322i	0.0194327	+	0.122693i
$784$	0.0337565	−	0.705054i	0.00120559	−	0.0251805i
$785$	−36.2053	−	33.5913i	−1.29222	−	1.19892i
$786$	6.40974	−	12.2164i	0.228628	−	0.435744i
$787$	23.2250	−	16.8740i	0.827882	−	0.601491i	−0.0910774	−	0.995844i	$-0.529031\pi$
$787$	23.2250	−	16.8740i	0.827882	−	0.601491i	0.918959	+	0.394352i	$0.129031\pi$
$788$	5.25844	−	14.9567i	0.187324	−	0.532809i
$789$	12.5112	−	6.37476i	0.445409	−	0.226947i
$790$	−14.7905	−	7.06755i	−0.526223	−	0.251452i
$791$	−11.4767			−0.408066
$792$	10.6728	+	21.6955i	0.379241	+	0.770918i
$793$	−21.9988	−	21.9988i	−0.781200	−	0.781200i
$794$	13.3609	+	18.8600i	0.474161	+	0.669318i
$795$	9.90038	−	1.95042i	0.351130	−	0.0691742i
$796$	−36.3164	−	12.7681i	−1.28720	−	0.452552i
$797$	11.2908	+	15.5405i	0.399941	+	0.550472i	0.960729	−	0.277488i	$-0.0895018\pi$
$797$	11.2908	+	15.5405i	0.399941	+	0.550472i	−0.560788	+	0.827959i	$0.689502\pi$
$798$	3.38108	+	10.8456i	0.119689	+	0.383930i
$799$	5.52134	+	16.9929i	0.195331	+	0.601167i
$800$	−16.9679	−	22.6294i	−0.599907	−	0.800070i
$801$	6.24045	+	4.53396i	0.220496	+	0.160199i
$802$	−14.6015	+	43.1748i	−0.515597	+	1.52456i
$803$	−16.3545	−	46.8322i	−0.577139	−	1.65267i
$804$	11.2912	−	14.7840i	0.398209	−	0.521391i
$805$	−1.62941	+	13.5536i	−0.0574291	+	0.477700i
$806$	−11.0609	+	14.8473i	−0.389604	+	0.522975i
$807$	−7.07207	+	13.8797i	−0.248949	+	0.488589i
$808$	−15.8650	−	34.1094i	−0.558130	−	1.19997i
$809$	−13.8740	+	10.0801i	−0.487785	+	0.354396i	−0.804332	−	0.594181i	$-0.797476\pi$
$809$	−13.8740	+	10.0801i	−0.487785	+	0.354396i	0.316547	+	0.948577i	$0.397476\pi$
$810$	−8.10072	−	14.9448i	−0.284630	−	0.525108i
$811$	−5.35381	+	2.72790i	−0.187998	+	0.0957896i	−0.545456	−	0.838140i	$-0.683643\pi$
$811$	−5.35381	+	2.72790i	−0.187998	+	0.0957896i	0.357458	+	0.933929i	$0.383643\pi$
$812$	−1.43345	−	4.79939i	−0.0503041	−	0.168426i
$813$	17.5824			0.616640
$814$	−34.1683	+	5.75750i	−1.19760	+	0.201800i
$815$	−18.6986	+	10.4267i	−0.654984	+	0.365230i
$816$	6.11746	+	13.5746i	0.214154	+	0.475207i
$817$	−11.5207	+	5.87007i	−0.403057	+	0.205368i
$818$	52.8454	+	0.632078i	1.84769	+	0.0221001i
$819$	−21.0662	−	3.33656i	−0.736113	−	0.116589i
$820$	−26.8542	+	14.1432i	−0.937791	+	0.493902i
$821$	25.6475	+	13.0680i	0.895103	+	0.456078i	0.840114	−	0.542409i	$-0.182488\pi$
$821$	25.6475	+	13.0680i	0.895103	+	0.456078i	0.0549886	+	0.998487i	$0.482488\pi$
$822$	−1.05434	−	7.21425i	−0.0367743	−	0.251626i
$823$	−2.42175	+	0.383567i	−0.0844169	+	0.0133703i	−0.198500	−	0.980101i	$-0.563607\pi$
$823$	−2.42175	+	0.383567i	−0.0844169	+	0.0133703i	0.114083	+	0.993471i	$0.463607\pi$
$824$	−4.90498	+	25.1033i	−0.170873	+	0.874515i
$825$	10.0323	+	3.94383i	0.349281	+	0.137307i
$826$	1.40785	−	4.16284i	0.0489854	−	0.144844i
$827$	−4.18832	+	5.76472i	−0.145642	+	0.200459i	−0.875605	−	0.483027i	$-0.839537\pi$
$827$	−4.18832	+	5.76472i	−0.145642	+	0.200459i	0.729963	+	0.683486i	$0.239537\pi$
$828$	2.16873	−	11.8508i	0.0753685	−	0.411843i
$829$	−17.2748	−	8.80196i	−0.599979	−	0.305705i	0.127495	−	0.991839i	$-0.459306\pi$
$829$	−17.2748	−	8.80196i	−0.599979	−	0.305705i	−0.727475	+	0.686134i	$0.759306\pi$
$830$	−19.3985	−	18.4345i	−0.673331	−	0.639872i
$831$	−1.11982	−	1.54130i	−0.0388460	−	0.0534670i
$832$	25.2780	+	1.81712i	0.876357	+	0.0629973i
$833$	−0.458758	−	0.900364i	−0.0158950	−	0.0311957i
$834$	9.91536	+	1.69224i	0.343341	+	0.0585975i
$835$	−8.50675	+	29.9521i	−0.294388	+	1.03653i
$836$	−25.3485	−	18.4984i	−0.876697	−	0.639780i
$837$	−14.9831			−0.517890
$838$	35.1890	+	6.00566i	1.21558	+	0.207462i
$839$	−3.12992	−	1.01697i	−0.108057	−	0.0351098i	0.254489	−	0.967076i	$-0.418093\pi$
$839$	−3.12992	−	1.01697i	−0.108057	−	0.0351098i	−0.362546	+	0.931966i	$0.618093\pi$
$840$	−6.32586	−	8.67843i	−0.218263	−	0.299434i
$841$	−16.5055	−	22.7178i	−0.569154	−	0.783374i
$842$	−32.2511	−	16.9217i	−1.11145	−	0.583159i
$843$	−4.48644	−	13.8078i	−0.154521	−	0.475567i
$844$	−6.70051	+	36.6142i	−0.230641	+	1.26031i
$845$	−0.791190	+	6.58119i	−0.0272178	+	0.226400i
$846$	5.04184	+	10.1948i	0.173342	+	0.350504i
$847$	26.1469	+	11.9158i	0.898418	+	0.409433i
$848$	26.7897	−	7.30819i	0.919963	−	0.250964i
$849$	−2.94653	+	4.05555i	−0.101125	+	0.139186i
$850$	−37.1624	−	16.0783i	−1.27466	−	0.551480i
$851$	15.3834	+	7.83824i	0.527337	+	0.268691i
$852$	−0.234822	+	9.81482i	−0.00804486	+	0.336250i
$853$	24.5411	+	33.7780i	0.840272	+	1.15654i	0.985923	+	0.167200i	$0.0534725\pi$
$853$	24.5411	+	33.7780i	0.840272	+	1.15654i	−0.145651	+	0.989336i	$0.546528\pi$
$854$	−0.433905	+	36.2769i	−0.0148479	+	1.24137i
$855$	22.6424	+	15.1893i	0.774352	+	0.519465i
$856$	−1.67423	+	46.6406i	−0.0572240	+	1.59414i
$857$	5.32372	−	5.32372i	0.181855	−	0.181855i	−0.610309	−	0.792164i	$-0.708955\pi$
$857$	5.32372	−	5.32372i	0.181855	−	0.181855i	0.792164	+	0.610309i	$0.208955\pi$
$858$	−8.56241	+	4.46961i	−0.292316	+	0.152590i
$859$	0.455854	−	0.455854i	0.0155535	−	0.0155535i	−0.699287	−	0.714841i	$-0.746499\pi$
$859$	0.455854	−	0.455854i	0.0155535	−	0.0155535i	0.714841	+	0.699287i	$0.246499\pi$
$860$	8.52538	−	8.75896i	0.290713	−	0.298678i
$861$	−10.2679	+	5.23177i	−0.349930	+	0.178298i
$862$	−0.454743	+	38.0191i	−0.0154886	+	1.29494i
$863$	41.3360	+	6.54698i	1.40709	+	0.222862i	0.813342	−	0.581786i	$-0.197646\pi$
$863$	41.3360	+	6.54698i	1.40709	+	0.222862i	0.593753	+	0.804648i	$0.297646\pi$
$864$	11.0418	+	17.2832i	0.375651	+	0.587985i
$865$	18.6253	−	20.0746i	0.633278	−	0.682558i
$866$	10.7467	−	1.57059i	0.365187	−	0.0533708i
$867$	8.30439	+	6.03349i	0.282032	+	0.204908i
$868$	21.3992	−	2.86646i	0.726338	−	0.0972941i
$869$	16.9181	−	3.05929i	0.573907	−	0.103779i
$870$	1.62341	+	1.11743i	0.0550388	+	0.0378844i
$871$	−36.6719	−	26.6437i	−1.24258	−	0.902787i
$872$	13.4711	+	7.48430i	0.456187	+	0.253450i
$873$	−20.6962	+	40.6185i	−0.700459	+	1.37473i
$874$	4.65362	+	14.9276i	0.157411	+	0.504932i
$875$	28.6122	+	5.85533i	0.967268	+	0.197946i
$876$	−8.41087	−	17.5317i	−0.284177	−	0.592342i
$877$	48.5637	+	15.7793i	1.63988	+	0.532829i	0.976512	−	0.215463i	$-0.0691262\pi$
$877$	48.5637	+	15.7793i	1.63988	+	0.532829i	0.663369	+	0.748293i	$0.269126\pi$
$878$	4.35551	+	6.14815i	0.146991	+	0.207490i
$879$	4.79676			0.161791
$880$	28.3156	+	8.84445i	0.954520	+	0.298146i
$881$	−19.0860			−0.643024			−0.321512	−	0.946906i	$-0.604191\pi$
$881$	−19.0860			−0.643024			−0.321512	+	0.946906i	$0.604191\pi$
$882$	−0.371829	−	0.524866i	−0.0125201	−	0.0176732i
$883$	44.6392	+	14.5041i	1.50223	+	0.488103i	0.940667	−	0.339332i	$-0.110201\pi$
$883$	44.6392	+	14.5041i	1.50223	+	0.488103i	0.561561	+	0.827435i	$0.310201\pi$
$884$	32.7113	−	15.6933i	1.10020	−	0.527824i
$885$	0.595478	+	1.62329i	0.0200168	+	0.0545662i
$886$	7.50312	+	24.0679i	0.252072	+	0.808579i
$887$	−21.0503	+	41.3135i	−0.706800	+	1.38717i	0.205913	+	0.978570i	$0.433984\pi$
$887$	−21.0503	+	41.3135i	−0.706800	+	1.38717i	−0.912712	+	0.408602i	$0.866016\pi$
$888$	−13.0599	+	3.73109i	−0.438261	+	0.125207i
$889$	−15.0043	−	10.9013i	−0.503230	−	0.365618i
$890$	9.30661	−	1.71808i	0.311958	−	0.0575901i
$891$	16.0584	+	7.74564i	0.537976	+	0.259489i
$892$	4.56393	+	34.0715i	0.152812	+	1.14080i
$893$	−11.9420	−	8.67635i	−0.399623	−	0.290343i
$894$	−9.73742	+	1.42309i	−0.325668	+	0.0475953i
$895$	0.392484	−	0.0146991i	0.0131193	−	0.000491335i
$896$	−19.0768	−	22.5719i	−0.637310	−	0.754073i
$897$	4.75348	+	0.752877i	0.158714	+	0.0251378i
$898$	−0.0700497	+	5.85656i	−0.00233759	+	0.195436i
$899$	−3.53031	+	1.79878i	−0.117742	+	0.0599927i
$900$	−24.8868	−	6.70609i	−0.829560	−	0.223536i
$901$	28.1098	−	28.1098i	0.936473	−	0.936473i
$902$	14.1713	−	28.5039i	0.471854	−	0.949076i
$903$	3.28165	−	3.28165i	0.109206	−	0.109206i
$904$	9.09663	−	8.46619i	0.302549	−	0.281581i
$905$	23.9281	−	35.6690i	0.795397	−	1.18568i
$906$	−0.0549315	+	4.59259i	−0.00182498	+	0.152578i
$907$	16.1399	+	22.2147i	0.535918	+	0.737628i	0.988018	−	0.154339i	$-0.0493249\pi$
$907$	16.1399	+	22.2147i	0.535918	+	0.737628i	−0.452100	+	0.891967i	$0.649325\pi$
$908$	−43.3295	−	1.03667i	−1.43794	−	0.0344031i
$909$	−30.5441	−	15.5630i	−1.01308	−	0.516192i
$910$	−20.7720	+	15.9156i	−0.688585	+	0.527598i
$911$	−10.2464	+	14.1029i	−0.339477	+	0.467251i	−0.944289	−	0.329118i	$-0.893249\pi$
$911$	−10.2464	+	14.1029i	−0.339477	+	0.467251i	0.604811	+	0.796369i	$0.293249\pi$
$912$	−10.6805	−	6.10221i	−0.353667	−	0.202064i
$913$	27.8105	+	3.78484i	0.920392	+	0.125260i
$914$	−4.56690	−	9.23445i	−0.151060	−	0.305448i
$915$	−8.81677	−	11.2264i	−0.291474	−	0.371132i
$916$	−4.89484	−	0.895772i	−0.161730	−	0.0295971i
$917$	12.1138	+	37.2824i	0.400033	+	1.23117i
$918$	25.9994	+	13.6415i	0.858107	+	0.450235i
$919$	17.2008	+	23.6748i	0.567401	+	0.780961i	0.992244	−	0.124306i	$-0.0396706\pi$
$919$	17.2008	+	23.6748i	0.567401	+	0.780961i	−0.424843	+	0.905267i	$0.639671\pi$
$920$	−8.70673	−	11.9447i	−0.287052	−	0.393806i
$921$	15.1657	+	4.92763i	0.499726	+	0.162371i
$922$	−15.6253	−	2.66675i	−0.514591	−	0.0878246i
$923$	23.9226			0.787423
$924$	10.7048	+	3.50312i	0.352162	+	0.115244i
$925$	19.4151	−	31.4229i	0.638363	−	1.03318i
$926$	−21.8172	−	3.72351i	−0.716958	−	0.122362i
$927$	10.5818	+	20.7679i	0.347551	+	0.682108i
$928$	4.67660	+	2.74664i	0.153517	+	0.0901628i
$929$	23.8085	+	32.7696i	0.781132	+	1.07514i	0.995156	+	0.0983078i	$0.0313430\pi$
$929$	23.8085	+	32.7696i	0.781132	+	1.07514i	−0.214024	+	0.976828i	$0.568657\pi$
$930$	−5.85195	+	6.15795i	−0.191893	+	0.201927i
$931$	0.743831	+	0.379001i	0.0243781	+	0.0124213i
$932$	53.2258	+	9.74049i	1.74347	+	0.319060i
$933$	5.43569	−	7.48159i	0.177957	−	0.244936i
$934$	−14.1846	+	41.9420i	−0.464134	+	1.37239i
$935$	41.4779	−	9.11555i	1.35647	−	0.298110i
$936$	19.1587	−	12.8956i	0.626222	−	0.421505i
$937$	32.8956	−	5.21015i	1.07465	−	0.170208i	0.406066	−	0.913844i	$-0.366900\pi$
$937$	32.8956	−	5.21015i	1.07465	−	0.170208i	0.668585	+	0.743636i	$0.266900\pi$
$938$	7.64405	+	52.3039i	0.249587	+	1.70778i
$939$	−7.66908	−	3.90759i	−0.250271	−	0.127519i
$940$	13.3281	+	4.13231i	0.434715	+	0.134781i
$941$	−5.18352	−	0.820989i	−0.168978	−	0.0267635i	0.0713721	−	0.997450i	$-0.477262\pi$
$941$	−5.18352	−	0.820989i	−0.168978	−	0.0267635i	−0.240350	+	0.970686i	$0.577262\pi$
$942$	20.3031	+	0.242843i	0.661510	+	0.00791226i
$943$	−14.1325	+	7.20085i	−0.460216	+	0.234492i
$944$	1.95497	+	4.33807i	0.0636288	+	0.141192i
$945$	−20.3714	−	5.78571i	−0.662680	−	0.188209i
$946$	−1.88053	+	12.6809i	−0.0611414	+	0.412292i
$947$	52.7600			1.71447			0.857235	−	0.514925i	$-0.172180\pi$
$947$	52.7600			1.71447			0.857235	+	0.514925i	$0.172180\pi$
$948$	6.45738	−	1.92864i	0.209726	−	0.0626394i
$949$	−42.2171	+	21.5107i	−1.37043	+	0.698266i
$950$	32.6456	−	7.29975i	1.05916	−	0.236835i
$951$	−5.65985	+	4.11212i	−0.183533	+	0.133345i
$952$	−39.7428	−	14.5091i	−1.28807	−	0.470242i
$953$	1.45501	−	2.85562i	0.0471324	−	0.0925025i	−0.866239	−	0.499630i	$-0.833469\pi$
$953$	1.45501	−	2.85562i	0.0471324	−	0.0925025i	0.913371	+	0.407127i	$0.133469\pi$
$954$	15.1175	−	20.2925i	0.489446	−	0.656995i
$955$	12.1366	+	1.45906i	0.392730	+	0.0472140i
$956$	−16.8426	−	12.8634i	−0.544729	−	0.416033i
$957$	−2.06652	+	0.0450913i	−0.0668010	+	0.00145760i
$958$	4.83309	−	14.2908i	0.156150	−	0.461716i
$959$	16.7605	+	12.1772i	0.541226	+	0.393224i
$960$	11.4159	+	2.21217i	0.368446	+	0.0713976i
$961$	4.30197	+	13.2401i	0.138773	+	0.427100i
$962$	9.85011	+	31.5965i	0.317580	+	1.01871i
$963$	24.9981	+	34.4070i	0.805554	+	1.10875i
$964$	2.75813	−	7.84500i	0.0888334	−	0.252670i
$965$	−4.62500	+	6.89436i	−0.148884	+	0.221937i
$966$	−3.24427	−	4.57956i	−0.104383	−	0.147345i
$967$	40.7331	+	40.7331i	1.30989	+	1.30989i	0.921494	+	0.388393i	$0.126970\pi$
$967$	40.7331	+	40.7331i	1.30989	+	1.30989i	0.388393	+	0.921494i	$0.373030\pi$
$968$	−29.5145	+	9.84344i	−0.948632	+	0.316380i
$969$	−17.6097			−0.565704
$970$	18.6329	+	52.7361i	0.598268	+	1.69326i
$971$	−33.8481	+	17.2465i	−1.08624	+	0.553466i	−0.903017	−	0.429606i	$-0.858653\pi$
$971$	−33.8481	+	17.2465i	−1.08624	+	0.553466i	−0.183222	+	0.983072i	$0.558653\pi$
$972$	27.1151	+	9.53306i	0.869716	+	0.305773i
$973$	−23.1233	+	16.8001i	−0.741300	+	0.538586i
$974$	−2.90451	+	5.53572i	−0.0930664	+	0.177376i
$975$	2.44037	−	10.0029i	0.0781545	−	0.320350i
$976$	−26.4169	−	29.0737i	−0.845585	−	0.930626i
$977$	2.29280	+	14.4762i	0.0733533	+	0.463134i	0.996835	+	0.0794930i	$0.0253301\pi$
$977$	2.29280	+	14.4762i	0.0733533	+	0.463134i	−0.923482	+	0.383641i	$0.874670\pi$
$978$	2.81982	−	8.33785i	0.0901679	−	0.266615i
$979$	−6.86381	+	7.17003i	−0.219368	+	0.229155i
$980$	−0.781058	−	0.112910i	−0.0249500	−	0.00360679i
$981$	13.8702	−	2.19682i	0.442841	−	0.0701391i
$982$	−5.97181	−	40.8618i	−0.190568	−	1.30395i
$983$	−9.91698	−	5.05295i	−0.316303	−	0.161164i	0.288630	−	0.957441i	$-0.406800\pi$
$983$	−9.91698	−	5.05295i	−0.316303	−	0.161164i	−0.604933	+	0.796276i	$0.706800\pi$
$984$	4.27912	−	11.7212i	0.136413	−	0.373660i
$985$	−16.0836	−	7.45047i	−0.512466	−	0.237392i
$986$	7.76368	+	0.0928607i	0.247246	+	0.00295729i
$987$	5.03889	+	1.63724i	0.160390	+	0.0521138i
$988$	−14.2425	+	26.3734i	−0.453115	+	0.839049i
$989$	4.51676	−	4.51676i	0.143625	−	0.143625i
$990$	25.2858	−	9.55951i	0.803636	−	0.303821i
$991$		−	16.3295i		−	0.518722i	−0.965780	−	0.259361i	$-0.916488\pi$
$991$		−	16.3295i		−	0.518722i	0.965780	−	0.259361i	$-0.0835120\pi$
$992$	−14.8468	+	18.0578i	−0.471387	+	0.573337i
$993$	−0.153517	−	0.301295i	−0.00487173	−	0.00956130i
$994$	−19.4888	−	19.9606i	−0.618147	−	0.633113i
$995$	−18.0906	+	39.0527i	−0.573509	+	1.23805i
$996$	10.9987	+	0.263147i	0.348508	+	0.00833813i
$997$	−15.4301	−	47.4890i	−0.488677	−	1.50399i	−0.826584	−	0.562814i	$-0.809719\pi$
$997$	−15.4301	−	47.4890i	−0.488677	−	1.50399i	0.337907	−	0.941180i	$-0.390281\pi$
$998$	3.33069	+	22.7901i	0.105431	+	0.721407i
$999$	−15.7429	+	21.6683i	−0.498085	+	0.685555i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	880.2.cz.a.147.113	yes	1120
5.3	odd	4		880.2.ch.a.323.45	yes	1120
11.3	even	5	inner	880.2.cz.a.707.58	yes	1120
16.11	odd	4		880.2.ch.a.587.14	yes	1120
55.3	odd	20		880.2.ch.a.3.14	✓	1120
80.43	even	4	inner	880.2.cz.a.763.58	yes	1120
176.91	odd	20		880.2.ch.a.267.45	yes	1120
880.443	even	20	inner	880.2.cz.a.443.113	yes	1120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
880.2.ch.a.3.14	✓	1120	55.3	odd	20
880.2.ch.a.267.45	yes	1120	176.91	odd	20
880.2.ch.a.323.45	yes	1120	5.3	odd	4
880.2.ch.a.587.14	yes	1120	16.11	odd	4
880.2.cz.a.147.113	yes	1120	1.1	even	1	trivial
880.2.cz.a.443.113	yes	1120	880.443	even	20	inner
880.2.cz.a.707.58	yes	1120	11.3	even	5	inner
880.2.cz.a.763.58	yes	1120	80.43	even	4	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:	\( N \)	\(=\)	\( 880 = 2^{4} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	880.cz (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.15398 - 0.817511i) q^{2} +(0.618224 + 0.200873i) q^{3} +(0.663353 - 1.88679i) q^{4} +(-2.02895 - 0.939878i) q^{5} +(0.877636 - 0.273601i) q^{6} +(-1.18591 + 2.32748i) q^{7} +(-0.776970 - 2.71962i) q^{8} +(-2.08520 - 1.51499i) q^{9} +O(q^{10})\)	\(q+(1.15398 - 0.817511i) q^{2} +(0.618224 + 0.200873i) q^{3} +(0.663353 - 1.88679i) q^{4} +(-2.02895 - 0.939878i) q^{5} +(0.877636 - 0.273601i) q^{6} +(-1.18591 + 2.32748i) q^{7} +(-0.776970 - 2.71962i) q^{8} +(-2.08520 - 1.51499i) q^{9} +(-3.10973 + 0.574083i) q^{10} +(2.29349 - 2.39581i) q^{11} +(0.789106 - 1.03321i) q^{12} +(-2.56289 - 1.86205i) q^{13} +(0.534219 + 3.65536i) q^{14} +(-1.06555 - 0.988617i) q^{15} +(-3.11993 - 2.50321i) q^{16} +(-5.65584 - 0.895798i) q^{17} +(-3.64480 - 0.0435951i) q^{18} +(4.21517 - 2.14774i) q^{19} +(-3.11926 + 3.20472i) q^{20} +(-1.20069 + 1.20069i) q^{21} +(0.688047 - 4.63968i) q^{22} +(-1.65259 + 1.65259i) q^{23} +(0.0659563 - 1.83741i) q^{24} +(3.23326 + 3.81393i) q^{25} +(-4.47977 - 0.0535821i) q^{26} +(-2.13105 - 2.93314i) q^{27} +(3.60478 + 3.78150i) q^{28} +(-0.854255 - 0.435264i) q^{29} +(-2.03783 - 0.269750i) q^{30} +(2.42909 - 3.34336i) q^{31} +(-5.64674 - 0.338088i) q^{32} +(1.89914 - 1.02045i) q^{33} +(-7.25907 + 3.58998i) q^{34} +(4.59369 - 3.60772i) q^{35} +(-4.24168 + 2.92936i) q^{36} +(-2.28283 - 7.02584i) q^{37} +(3.10844 - 5.92440i) q^{38} +(-1.21040 - 1.66598i) q^{39} +(-0.979677 + 6.24822i) q^{40} +(6.45452 + 2.09720i) q^{41} +(-0.403997 + 2.36714i) q^{42} -2.73314 q^{43} +(-2.99899 - 5.91659i) q^{44} +(2.80686 + 5.03366i) q^{45} +(-0.556050 + 3.25807i) q^{46} +(-1.41655 - 2.78013i) q^{47} +(-1.42599 - 2.17425i) q^{48} +(0.103724 + 0.142763i) q^{49} +(6.84905 + 1.75798i) q^{50} +(-3.31664 - 1.68991i) q^{51} +(-5.21338 + 3.60043i) q^{52} +(-4.08050 + 5.61633i) q^{53} +(-4.85707 - 1.64264i) q^{54} +(-6.90514 + 2.70537i) q^{55} +(7.25127 + 1.41684i) q^{56} +(3.03734 - 0.481068i) q^{57} +(-1.34163 + 0.196075i) q^{58} +(-1.05990 - 0.540048i) q^{59} +(-2.57214 + 1.35466i) q^{60} +(9.69978 + 1.53629i) q^{61} +(0.0698994 - 5.84399i) q^{62} +(5.99896 - 3.05662i) q^{63} +(-6.79263 + 4.22612i) q^{64} +(3.44987 + 6.18680i) q^{65} +(1.35735 - 2.73015i) q^{66} +14.3088 q^{67} +(-5.44200 + 10.0771i) q^{68} +(-1.35363 + 0.689710i) q^{69} +(2.35169 - 7.91864i) q^{70} +(-6.10934 + 4.43870i) q^{71} +(-2.50004 + 6.84804i) q^{72} +(6.79020 - 13.3265i) q^{73} +(-8.37805 - 6.24146i) q^{74} +(1.23276 + 3.00734i) q^{75} +(-1.25618 - 9.37783i) q^{76} +(2.85632 + 8.17926i) q^{77} +(-2.75874 - 0.932992i) q^{78} +(4.19372 + 3.04692i) q^{79} +(3.97746 + 8.01123i) q^{80} +(1.66115 + 5.11249i) q^{81} +(9.16288 - 2.85650i) q^{82} +(4.97411 + 6.84628i) q^{83} +(1.46896 + 3.06192i) q^{84} +(10.6335 + 7.13333i) q^{85} +(-3.15400 + 2.23437i) q^{86} +(-0.440688 - 0.440688i) q^{87} +(-8.29766 - 4.37594i) q^{88} -2.99274 q^{89} +(7.35414 + 3.51412i) q^{90} +(7.37322 - 3.75685i) q^{91} +(2.02183 + 4.21433i) q^{92} +(2.17332 - 1.57901i) q^{93} +(-3.90746 - 2.05018i) q^{94} +(-10.5710 + 0.395898i) q^{95} +(-3.42304 - 1.34329i) q^{96} +(-2.76685 - 17.4692i) q^{97} +(0.236406 + 0.0799513i) q^{98} +(-8.41200 + 1.52114i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1120 q - 6 q^{2} - 6 q^{5} - 12 q^{6} - 12 q^{7} - 6 q^{8} + 264 q^{9}+O(q^{10}) \) 1120 * q - 6 * q^2 - 6 * q^5 - 12 * q^6 - 12 * q^7 - 6 * q^8 + 264 * q^9	\( 1120 q - 6 q^{2} - 6 q^{5} - 12 q^{6} - 12 q^{7} - 6 q^{8} + 264 q^{9} - 8 q^{10} - 16 q^{11} - 44 q^{12} - 12 q^{13} - 24 q^{15} - 12 q^{16} - 12 q^{17} - 10 q^{18} - 6 q^{20} - 32 q^{21} - 10 q^{22} - 32 q^{23} - 24 q^{24} + 20 q^{26} - 22 q^{28} + 36 q^{30} - 36 q^{32} - 16 q^{33} - 32 q^{34} + 14 q^{35} + 20 q^{36} - 12 q^{37} - 26 q^{38} - 88 q^{40} - 6 q^{42} + 32 q^{43} + 80 q^{44} - 8 q^{45} - 12 q^{46} - 18 q^{48} + 16 q^{50} - 12 q^{51} + 34 q^{52} - 168 q^{54} - 16 q^{55} - 80 q^{56} - 24 q^{57} + 38 q^{58} + 16 q^{59} - 32 q^{60} - 12 q^{61} + 96 q^{62} + 36 q^{63} - 32 q^{65} - 24 q^{66} - 32 q^{67} - 38 q^{68} + 36 q^{69} - 42 q^{70} - 56 q^{71} - 76 q^{72} + 100 q^{74} + 30 q^{75} - 32 q^{76} - 108 q^{78} + 102 q^{80} - 240 q^{81} - 18 q^{82} + 24 q^{84} + 14 q^{85} - 4 q^{86} - 32 q^{87} - 98 q^{88} - 44 q^{90} - 28 q^{91} - 48 q^{92} - 36 q^{93} - 48 q^{94} - 120 q^{95} + 20 q^{96} - 12 q^{97} - 284 q^{98} + 20 q^{99}+O(q^{100}) \) 1120 * q - 6 * q^2 - 6 * q^5 - 12 * q^6 - 12 * q^7 - 6 * q^8 + 264 * q^9 - 8 * q^10 - 16 * q^11 - 44 * q^12 - 12 * q^13 - 24 * q^15 - 12 * q^16 - 12 * q^17 - 10 * q^18 - 6 * q^20 - 32 * q^21 - 10 * q^22 - 32 * q^23 - 24 * q^24 + 20 * q^26 - 22 * q^28 + 36 * q^30 - 36 * q^32 - 16 * q^33 - 32 * q^34 + 14 * q^35 + 20 * q^36 - 12 * q^37 - 26 * q^38 - 88 * q^40 - 6 * q^42 + 32 * q^43 + 80 * q^44 - 8 * q^45 - 12 * q^46 - 18 * q^48 + 16 * q^50 - 12 * q^51 + 34 * q^52 - 168 * q^54 - 16 * q^55 - 80 * q^56 - 24 * q^57 + 38 * q^58 + 16 * q^59 - 32 * q^60 - 12 * q^61 + 96 * q^62 + 36 * q^63 - 32 * q^65 - 24 * q^66 - 32 * q^67 - 38 * q^68 + 36 * q^69 - 42 * q^70 - 56 * q^71 - 76 * q^72 + 100 * q^74 + 30 * q^75 - 32 * q^76 - 108 * q^78 + 102 * q^80 - 240 * q^81 - 18 * q^82 + 24 * q^84 + 14 * q^85 - 4 * q^86 - 32 * q^87 - 98 * q^88 - 44 * q^90 - 28 * q^91 - 48 * q^92 - 36 * q^93 - 48 * q^94 - 120 * q^95 + 20 * q^96 - 12 * q^97 - 284 * q^98 + 20 * q^99

Introduction

L-functions

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