LMFDB - Embedded newform 966.2.q.h.169.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(85,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("966.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.q (of order $11$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			169.1
Character	$\chi$	$=$	966.169
Dual form			966.2.q.h.463.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 - 0.989821i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-0.257442 - 0.297104i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(0.841254 + 0.540641i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(0.142315 - 0.989821i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-0.257442 - 0.297104i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(0.841254 + 0.540641i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(-0.330718 + 0.212539i) q^{10} +(0.869049 + 6.04437i) q^{11} +(0.142315 + 0.989821i) q^{12} +(2.02990 - 1.30454i) q^{13} +(0.654861 - 0.755750i) q^{14} +(-0.163310 + 0.357599i) q^{15} +(0.841254 + 0.540641i) q^{16} +(6.39260 - 1.87704i) q^{17} +(0.654861 + 0.755750i) q^{18} +(-0.509719 - 0.149667i) q^{19} +(0.163310 + 0.357599i) q^{20} +(0.142315 - 0.989821i) q^{21} +6.10653 q^{22} +(4.11493 - 2.46319i) q^{23} +1.00000 q^{24} +(0.689580 - 4.79613i) q^{25} +(-1.00238 - 2.19490i) q^{26} +(0.959493 + 0.281733i) q^{27} +(-0.654861 - 0.755750i) q^{28} +(4.21223 - 1.23682i) q^{29} +(0.330718 + 0.212539i) q^{30} +(-1.82886 + 4.00464i) q^{31} +(0.654861 - 0.755750i) q^{32} +(5.13714 - 3.30144i) q^{33} +(-0.948169 - 6.59466i) q^{34} +(-0.0559475 - 0.389124i) q^{35} +(0.841254 - 0.540641i) q^{36} +(-6.36314 + 7.34345i) q^{37} +(-0.220684 + 0.483231i) q^{38} +(-2.02990 - 1.30454i) q^{39} +(0.377201 - 0.110756i) q^{40} +(-8.27342 - 9.54803i) q^{41} +(-0.959493 - 0.281733i) q^{42} +(2.31202 + 5.06262i) q^{43} +(0.869049 - 6.04437i) q^{44} +0.393125 q^{45} +(-1.85251 - 4.42360i) q^{46} +6.17551 q^{47} +(0.142315 - 0.989821i) q^{48} +(0.415415 + 0.909632i) q^{49} +(-4.64918 - 1.36512i) q^{50} +(-4.36299 - 5.03516i) q^{51} +(-2.31521 + 0.679807i) q^{52} +(0.220875 + 0.141948i) q^{53} +(0.415415 - 0.909632i) q^{54} +(1.57208 - 1.81427i) q^{55} +(-0.841254 + 0.540641i) q^{56} +(0.0756030 + 0.525830i) q^{57} +(-0.624771 - 4.34538i) q^{58} +(5.61794 - 3.61043i) q^{59} +(0.257442 - 0.297104i) q^{60} +(-2.24548 + 4.91690i) q^{61} +(3.70360 + 2.38016i) q^{62} +(-0.959493 + 0.281733i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-0.910167 - 0.267249i) q^{65} +(-2.53674 - 5.55469i) q^{66} +(-0.0133892 + 0.0931237i) q^{67} -6.66247 q^{68} +(-3.95001 - 2.71983i) q^{69} -0.393125 q^{70} +(1.54439 - 10.7414i) q^{71} +(-0.415415 - 0.909632i) q^{72} +(8.38666 + 2.46254i) q^{73} +(6.36314 + 7.34345i) q^{74} +(-4.64918 + 1.36512i) q^{75} +(0.446905 + 0.287209i) q^{76} +(-2.53674 + 5.55469i) q^{77} +(-1.58015 + 1.82359i) q^{78} +(3.48125 - 2.23727i) q^{79} +(-0.0559475 - 0.389124i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-10.6283 + 6.83038i) q^{82} +(6.62049 - 7.64045i) q^{83} +(-0.415415 + 0.909632i) q^{84} +(-2.20340 - 1.41604i) q^{85} +(5.34012 - 1.56800i) q^{86} +(-2.87488 - 3.31779i) q^{87} +(-5.85917 - 1.72041i) q^{88} +(0.210281 + 0.460451i) q^{89} +(0.0559475 - 0.389124i) q^{90} +2.41295 q^{91} +(-4.64221 + 1.20411i) q^{92} +4.40248 q^{93} +(0.878867 - 6.11265i) q^{94} +(0.0867565 + 0.189970i) q^{95} +(-0.959493 - 0.281733i) q^{96} +(4.23061 + 4.88239i) q^{97} +(0.959493 - 0.281733i) q^{98} +(-5.13714 - 3.30144i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 10 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) $ 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 10 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 10 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} - 3 q^{9} + 12 q^{10} + 9 q^{11} + 3 q^{12} - 12 q^{13} + 3 q^{14} + q^{15} - 3 q^{16} + 13 q^{17} + 3 q^{18} - 18 q^{19} - q^{20} + 3 q^{21} + 24 q^{22} + 21 q^{23} + 30 q^{24} - 3 q^{25} + 34 q^{26} + 3 q^{27} - 3 q^{28} - 11 q^{29} - 12 q^{30} + 7 q^{31} + 3 q^{32} + 2 q^{33} - 13 q^{34} - q^{35} - 3 q^{36} + 3 q^{37} - 15 q^{38} + 12 q^{39} + q^{40} + 15 q^{41} - 3 q^{42} + 42 q^{43} + 9 q^{44} + 10 q^{45} + q^{46} + 12 q^{47} + 3 q^{48} - 3 q^{49} - 30 q^{50} + 9 q^{51} - q^{52} - 28 q^{53} - 3 q^{54} + 4 q^{55} + 3 q^{56} - 4 q^{57} - 11 q^{58} + 3 q^{59} - 10 q^{60} - 2 q^{61} + 26 q^{62} - 3 q^{63} - 3 q^{64} - 70 q^{65} - 2 q^{66} + 24 q^{67} + 2 q^{68} + q^{69} - 10 q^{70} - 3 q^{71} + 3 q^{72} - 7 q^{73} - 3 q^{74} - 30 q^{75} - 18 q^{76} - 2 q^{77} + 10 q^{78} - 32 q^{79} - q^{80} - 3 q^{81} - 26 q^{82} + 8 q^{83} + 3 q^{84} - 39 q^{85} + 35 q^{86} - 11 q^{87} + 13 q^{88} + 50 q^{89} + q^{90} + 32 q^{91} - 12 q^{92} + 4 q^{93} + 10 q^{94} + 73 q^{95} - 3 q^{96} + 24 q^{97} + 3 q^{98} - 2 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 10 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 - 3 * q^9 + 12 * q^10 + 9 * q^11 + 3 * q^12 - 12 * q^13 + 3 * q^14 + q^15 - 3 * q^16 + 13 * q^17 + 3 * q^18 - 18 * q^19 - q^20 + 3 * q^21 + 24 * q^22 + 21 * q^23 + 30 * q^24 - 3 * q^25 + 34 * q^26 + 3 * q^27 - 3 * q^28 - 11 * q^29 - 12 * q^30 + 7 * q^31 + 3 * q^32 + 2 * q^33 - 13 * q^34 - q^35 - 3 * q^36 + 3 * q^37 - 15 * q^38 + 12 * q^39 + q^40 + 15 * q^41 - 3 * q^42 + 42 * q^43 + 9 * q^44 + 10 * q^45 + q^46 + 12 * q^47 + 3 * q^48 - 3 * q^49 - 30 * q^50 + 9 * q^51 - q^52 - 28 * q^53 - 3 * q^54 + 4 * q^55 + 3 * q^56 - 4 * q^57 - 11 * q^58 + 3 * q^59 - 10 * q^60 - 2 * q^61 + 26 * q^62 - 3 * q^63 - 3 * q^64 - 70 * q^65 - 2 * q^66 + 24 * q^67 + 2 * q^68 + q^69 - 10 * q^70 - 3 * q^71 + 3 * q^72 - 7 * q^73 - 3 * q^74 - 30 * q^75 - 18 * q^76 - 2 * q^77 + 10 * q^78 - 32 * q^79 - q^80 - 3 * q^81 - 26 * q^82 + 8 * q^83 + 3 * q^84 - 39 * q^85 + 35 * q^86 - 11 * q^87 + 13 * q^88 + 50 * q^89 + q^90 + 32 * q^91 - 12 * q^92 + 4 * q^93 + 10 * q^94 + 73 * q^95 - 3 * q^96 + 24 * q^97 + 3 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{11}\right)$

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 $

$2$	0.142315	−	0.989821i	0.100632	−	0.699909i
$2$	0.142315	−	0.989821i	0.100632	−	0.699909i
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$3$	−0.415415	−	0.909632i	−0.239840	−	0.525176i
$4$	−0.959493	−	0.281733i	−0.479746	−	0.140866i
$5$	−0.257442	−	0.297104i	−0.115132	−	0.132869i	0.695258	−	0.718760i	$-0.255290\pi$
$5$	−0.257442	−	0.297104i	−0.115132	−	0.132869i	−0.810390	+	0.585891i	$0.800745\pi$
$6$	−0.959493	+	0.281733i	−0.391711	+	0.115017i
$7$	0.841254	+	0.540641i	0.317964	+	0.204343i
$7$	0.841254	+	0.540641i	0.317964	+	0.204343i
$8$	−0.415415	+	0.909632i	−0.146871	+	0.321603i
$9$	−0.654861	+	0.755750i	−0.218287	+	0.251917i
$10$	−0.330718	+	0.212539i	−0.104582	+	0.0672109i
$11$	0.869049	+	6.04437i	0.262028	+	1.82245i	0.517561	+	0.855646i	$0.326840\pi$
$11$	0.869049	+	6.04437i	0.262028	+	1.82245i	−0.255533	+	0.966800i	$0.582251\pi$
$12$	0.142315	+	0.989821i	0.0410828	+	0.285737i
$13$	2.02990	−	1.30454i	0.562994	−	0.361814i	−0.227978	−	0.973666i	$-0.573212\pi$
$13$	2.02990	−	1.30454i	0.562994	−	0.361814i	0.790972	+	0.611852i	$0.209575\pi$
$14$	0.654861	−	0.755750i	0.175019	−	0.201983i
$15$	−0.163310	+	0.357599i	−0.0421665	+	0.0923317i
$16$	0.841254	+	0.540641i	0.210313	+	0.135160i
$17$	6.39260	−	1.87704i	1.55043	−	0.455248i	0.609203	−	0.793015i	$-0.291490\pi$
$17$	6.39260	−	1.87704i	1.55043	−	0.455248i	0.941230	+	0.337766i	$0.109671\pi$
$18$	0.654861	+	0.755750i	0.154352	+	0.178132i
$19$	−0.509719	−	0.149667i	−0.116937	−	0.0343359i	0.222740	−	0.974878i	$-0.428500\pi$
$19$	−0.509719	−	0.149667i	−0.116937	−	0.0343359i	−0.339678	+	0.940542i	$0.610318\pi$
$20$	0.163310	+	0.357599i	0.0365172	+	0.0799616i
$21$	0.142315	−	0.989821i	0.0310556	−	0.215997i
$22$	6.10653			1.30192
$23$	4.11493	−	2.46319i	0.858023	−	0.513611i
$23$	4.11493	−	2.46319i	0.858023	−	0.513611i
$24$	1.00000			0.204124
$25$	0.689580	−	4.79613i	0.137916	−	0.959227i
$26$	−1.00238	−	2.19490i	−0.196582	−	0.430455i
$27$	0.959493	+	0.281733i	0.184655	+	0.0542195i
$28$	−0.654861	−	0.755750i	−0.123757	−	0.142823i
$29$	4.21223	−	1.23682i	0.782192	−	0.229672i	0.133830	−	0.991004i	$-0.457272\pi$
$29$	4.21223	−	1.23682i	0.782192	−	0.229672i	0.648362	+	0.761332i	$0.275454\pi$
$30$	0.330718	+	0.212539i	0.0603806	+	0.0388042i
$31$	−1.82886	+	4.00464i	−0.328473	+	0.719255i	−0.999759	−	0.0219433i	$-0.993015\pi$
$31$	−1.82886	+	4.00464i	−0.328473	+	0.719255i	0.671287	+	0.741198i	$0.265742\pi$
$32$	0.654861	−	0.755750i	0.115764	−	0.133599i
$33$	5.13714	−	3.30144i	0.894261	−	0.574707i
$34$	−0.948169	−	6.59466i	−0.162610	−	1.13097i
$35$	−0.0559475	−	0.389124i	−0.00945686	−	0.0657739i
$36$	0.841254	−	0.540641i	0.140209	−	0.0901068i
$37$	−6.36314	+	7.34345i	−1.04609	+	1.20726i	−0.0683047	+	0.997665i	$0.521759\pi$
$37$	−6.36314	+	7.34345i	−1.04609	+	1.20726i	−0.977789	+	0.209592i	$0.932786\pi$
$38$	−0.220684	+	0.483231i	−0.0357997	+	0.0783904i
$39$	−2.02990	−	1.30454i	−0.325045	−	0.208894i
$40$	0.377201	−	0.110756i	0.0596407	−	0.0175121i
$41$	−8.27342	−	9.54803i	−1.29209	−	1.49115i	−0.769633	−	0.638486i	$-0.779561\pi$
$41$	−8.27342	−	9.54803i	−1.29209	−	1.49115i	−0.522457	−	0.852666i	$-0.674984\pi$
$42$	−0.959493	−	0.281733i	−0.148053	−	0.0434723i
$43$	2.31202	+	5.06262i	0.352580	+	0.772042i	0.999951	+	0.00986733i	$0.00314092\pi$
$43$	2.31202	+	5.06262i	0.352580	+	0.772042i	−0.647372	+	0.762175i	$0.724132\pi$
$44$	0.869049	−	6.04437i	0.131014	−	0.911223i
$45$	0.393125			0.0586036
$46$	−1.85251	−	4.42360i	−0.273137	−	0.652224i
$47$	6.17551			0.900791			0.450396	−	0.892829i	$-0.351283\pi$
$47$	6.17551			0.900791			0.450396	+	0.892829i	$0.351283\pi$
$48$	0.142315	−	0.989821i	0.0205414	−	0.142868i
$49$	0.415415	+	0.909632i	0.0593450	+	0.129947i
$50$	−4.64918	−	1.36512i	−0.657493	−	0.193057i
$51$	−4.36299	−	5.03516i	−0.610941	−	0.705064i
$52$	−2.31521	+	0.679807i	−0.321062	+	0.0942722i
$53$	0.220875	+	0.141948i	0.0303396	+	0.0194981i	0.555723	−	0.831368i	$-0.312442\pi$
$53$	0.220875	+	0.141948i	0.0303396	+	0.0194981i	−0.525383	+	0.850866i	$0.676078\pi$
$54$	0.415415	−	0.909632i	0.0565308	−	0.123785i
$55$	1.57208	−	1.81427i	0.211979	−	0.244637i
$56$	−0.841254	+	0.540641i	−0.112417	+	0.0722462i
$57$	0.0756030	+	0.525830i	0.0100139	+	0.0696479i
$58$	−0.624771	−	4.34538i	−0.0820364	−	0.570576i
$59$	5.61794	−	3.61043i	0.731394	−	0.470038i	−0.121189	−	0.992629i	$-0.538671\pi$
$59$	5.61794	−	3.61043i	0.731394	−	0.470038i	0.852584	+	0.522591i	$0.175034\pi$
$60$	0.257442	−	0.297104i	0.0332356	−	0.0383560i
$61$	−2.24548	+	4.91690i	−0.287504	+	0.629545i	−0.997185	−	0.0749774i	$-0.976112\pi$
$61$	−2.24548	+	4.91690i	−0.287504	+	0.629545i	0.709682	+	0.704523i	$0.248839\pi$
$62$	3.70360	+	2.38016i	0.470358	+	0.302281i
$63$	−0.959493	+	0.281733i	−0.120885	+	0.0354950i
$64$	−0.654861	−	0.755750i	−0.0818576	−	0.0944687i
$65$	−0.910167	−	0.267249i	−0.112892	−	0.0331482i
$66$	−2.53674	−	5.55469i	−0.312251	−	0.683735i
$67$	−0.0133892	+	0.0931237i	−0.00163575	+	0.0113769i	−0.990623	−	0.136624i	$-0.956375\pi$
$67$	−0.0133892	+	0.0931237i	−0.00163575	+	0.0113769i	0.988987	+	0.148001i	$0.0472839\pi$
$68$	−6.66247			−0.807944
$69$	−3.95001	−	2.71983i	−0.475525	−	0.327429i
$70$	−0.393125			−0.0469874
$71$	1.54439	−	10.7414i	0.183285	−	1.27477i	−0.665645	−	0.746269i	$-0.731843\pi$
$71$	1.54439	−	10.7414i	0.183285	−	1.27477i	0.848930	−	0.528506i	$-0.177247\pi$
$72$	−0.415415	−	0.909632i	−0.0489571	−	0.107201i
$73$	8.38666	+	2.46254i	0.981584	+	0.288219i	0.732878	−	0.680360i	$-0.238177\pi$
$73$	8.38666	+	2.46254i	0.981584	+	0.288219i	0.248706	+	0.968579i	$0.419995\pi$
$74$	6.36314	+	7.34345i	0.739700	+	0.853659i
$75$	−4.64918	+	1.36512i	−0.536841	+	0.157631i
$76$	0.446905	+	0.287209i	0.0512636	+	0.0329451i
$77$	−2.53674	+	5.55469i	−0.289089	+	0.633016i
$78$	−1.58015	+	1.82359i	−0.178916	+	0.206481i
$79$	3.48125	−	2.23727i	0.391672	−	0.251712i	−0.329952	−	0.943998i	$-0.607033\pi$
$79$	3.48125	−	2.23727i	0.391672	−	0.251712i	0.721624	+	0.692286i	$0.243396\pi$
$80$	−0.0559475	−	0.389124i	−0.00625513	−	0.0435054i
$81$	−0.142315	−	0.989821i	−0.0158128	−	0.109980i
$82$	−10.6283	+	6.83038i	−1.17370	+	0.754289i
$83$	6.62049	−	7.64045i	0.726693	−	0.838649i	−0.265402	−	0.964138i	$-0.585505\pi$
$83$	6.62049	−	7.64045i	0.726693	−	0.838649i	0.992095	+	0.125489i	$0.0400501\pi$
$84$	−0.415415	+	0.909632i	−0.0453255	+	0.0992490i
$85$	−2.20340	−	1.41604i	−0.238992	−	0.153591i
$86$	5.34012	−	1.56800i	0.575840	−	0.169082i
$87$	−2.87488	−	3.31779i	−0.308219	−	0.355704i
$88$	−5.85917	−	1.72041i	−0.624590	−	0.183396i
$89$	0.210281	+	0.460451i	0.0222897	+	0.0488077i	0.920449	−	0.390862i	$-0.127823\pi$
$89$	0.210281	+	0.460451i	0.0222897	+	0.0488077i	−0.898160	+	0.439669i	$0.855096\pi$
$90$	0.0559475	−	0.389124i	0.00589739	−	0.0410172i
$91$	2.41295			0.252946
$92$	−4.64221	+	1.20411i	−0.483984	+	0.125537i
$93$	4.40248			0.456516
$94$	0.878867	−	6.11265i	0.0906482	−	0.630472i
$95$	0.0867565	+	0.189970i	0.00890102	+	0.0194905i
$96$	−0.959493	−	0.281733i	−0.0979278	−	0.0287542i
$97$	4.23061	+	4.88239i	0.429553	+	0.495731i	0.928724	−	0.370773i	$-0.120907\pi$
$97$	4.23061	+	4.88239i	0.429553	+	0.495731i	−0.499170	+	0.866504i	$0.666362\pi$
$98$	0.959493	−	0.281733i	0.0969234	−	0.0284593i
$99$	−5.13714	−	3.30144i	−0.516302	−	0.331807i
$100$	−2.01287	+	4.40758i	−0.201287	+	0.440758i
$101$	9.99139	−	11.5307i	0.994181	−	1.14735i	0.00509775	−	0.999987i	$-0.498377\pi$
$101$	9.99139	−	11.5307i	0.994181	−	1.14735i	0.989083	−	0.147359i	$-0.0470772\pi$
$102$	−5.60483	+	3.60201i	−0.554961	+	0.356652i
$103$	1.47843	+	10.2827i	0.145674	+	1.01318i	0.923196	+	0.384328i	$0.125567\pi$
$103$	1.47843	+	10.2827i	0.145674	+	1.01318i	−0.777523	+	0.628855i	$0.783524\pi$
$104$	0.343399	+	2.38839i	0.0336730	+	0.234201i
$105$	−0.330718	+	0.212539i	−0.0322748	+	0.0207417i
$106$	0.171937	−	0.198426i	0.0167000	−	0.0192728i
$107$	−4.66120	+	10.2066i	−0.450615	+	0.986710i	0.538912	+	0.842362i	$0.318836\pi$
$107$	−4.66120	+	10.2066i	−0.450615	+	0.986710i	−0.989527	+	0.144347i	$0.953892\pi$
$108$	−0.841254	−	0.540641i	−0.0809497	−	0.0520232i
$109$	6.35476	−	1.86592i	0.608675	−	0.178723i	0.0371528	−	0.999310i	$-0.488171\pi$
$109$	6.35476	−	1.86592i	0.608675	−	0.178723i	0.571522	+	0.820586i	$0.306353\pi$
$110$	−1.57208	−	1.81427i	−0.149892	−	0.172984i
$111$	9.32318	+	2.73753i	0.884918	+	0.259835i
$112$	0.415415	+	0.909632i	0.0392530	+	0.0859521i
$113$	−0.0493028	+	0.342909i	−0.00463802	+	0.0322581i	−0.992009	−	0.126167i	$-0.959733\pi$
$113$	−0.0493028	+	0.342909i	−0.00463802	+	0.0322581i	0.987371	+	0.158425i	$0.0506416\pi$
$114$	0.531238			0.0497550
$115$	−1.79118	−	0.588434i	−0.167029	−	0.0548717i
$116$	−4.39006			−0.407607
$117$	−0.343399	+	2.38839i	−0.0317472	+	0.220807i
$118$	−2.77417	−	6.07458i	−0.255383	−	0.559210i
$119$	6.39260	+	1.87704i	0.586008	+	0.172068i
$120$	−0.257442	−	0.297104i	−0.0235012	−	0.0271218i
$121$	−25.2248	+	7.40666i	−2.29316	+	0.673332i
$122$	4.54729	+	2.92237i	0.411693	+	0.264579i
$123$	−5.24829	+	11.4922i	−0.473223	+	1.03621i
$124$	2.88301	−	3.32718i	0.258902	−	0.298789i
$125$	−3.25607	+	2.09255i	−0.291232	+	0.187163i
$126$	0.142315	+	0.989821i	0.0126784	+	0.0881803i
$127$	−2.29381	−	15.9538i	−0.203543	−	1.41567i	−0.793663	−	0.608357i	$-0.791829\pi$
$127$	−2.29381	−	15.9538i	−0.203543	−	1.41567i	0.590120	−	0.807315i	$-0.299080\pi$
$128$	−0.841254	+	0.540641i	−0.0743570	+	0.0477863i
$129$	3.64467	−	4.20617i	0.320895	−	0.370333i
$130$	−0.394059	+	0.862869i	−0.0345613	+	0.0756786i
$131$	8.68118	+	5.57906i	0.758478	+	0.487444i	0.861828	−	0.507201i	$-0.169320\pi$
$131$	8.68118	+	5.57906i	0.758478	+	0.487444i	−0.103350	+	0.994645i	$0.532956\pi$
$132$	−5.85917	+	1.72041i	−0.509975	+	0.149742i
$133$	−0.347887	−	0.401483i	−0.0301656	−	0.0348130i
$134$	0.0902703	+	0.0265058i	0.00779817	+	0.00228975i
$135$	−0.163310	−	0.357599i	−0.0140555	−	0.0307772i
$136$	−0.948169	+	6.59466i	−0.0813048	+	0.565487i
$137$	−21.4776			−1.83496			−0.917479	−	0.397783i	$-0.869780\pi$
$137$	−21.4776			−1.83496			−0.917479	+	0.397783i	$0.869780\pi$
$138$	−3.25429	+	3.52273i	−0.277023	+	0.299875i
$139$	9.26336			0.785708			0.392854	−	0.919601i	$-0.371488\pi$
$139$	9.26336			0.785708			0.392854	+	0.919601i	$0.371488\pi$
$140$	−0.0559475	+	0.389124i	−0.00472843	+	0.0328870i
$141$	−2.56540	−	5.61744i	−0.216046	−	0.473074i
$142$	−10.4123	−	3.05733i	−0.873782	−	0.256566i
$143$	9.64921	+	11.1358i	0.806907	+	0.931221i
$144$	−0.959493	+	0.281733i	−0.0799577	+	0.0234777i
$145$	−1.45187	−	0.933061i	−0.120571	−	0.0774865i
$146$	3.63102	−	7.95083i	0.300506	−	0.658016i
$147$	0.654861	−	0.755750i	0.0540120	−	0.0623332i
$148$	8.17428	−	5.25329i	0.671921	−	0.431818i
$149$	1.34160	+	9.33104i	0.109908	+	0.764428i	0.968003	+	0.250937i	$0.0807389\pi$
$149$	1.34160	+	9.33104i	0.109908	+	0.764428i	−0.858095	+	0.513491i	$0.828352\pi$
$150$	0.689580	+	4.79613i	0.0563040	+	0.391603i
$151$	−13.8807	+	8.92059i	−1.12960	+	0.725947i	−0.965476	−	0.260493i	$-0.916115\pi$
$151$	−13.8807	+	8.92059i	−1.12960	+	0.725947i	−0.164120	+	0.986440i	$0.552479\pi$
$152$	0.347887	−	0.401483i	0.0282173	−	0.0325645i
$153$	−2.76769	+	6.06040i	−0.223755	+	0.489954i
$154$	5.13714	+	3.30144i	0.413962	+	0.266037i
$155$	1.66062	−	0.487602i	0.133384	−	0.0391651i
$156$	1.58015	+	1.82359i	0.126513	+	0.146004i
$157$	−5.01423	−	1.47231i	−0.400179	−	0.117503i	0.0754491	−	0.997150i	$-0.475961\pi$
$157$	−5.01423	−	1.47231i	−0.400179	−	0.117503i	−0.475628	+	0.879647i	$0.657779\pi$
$158$	−1.71906	−	3.76421i	−0.136761	−	0.299465i
$159$	0.0373655	−	0.259883i	0.00296328	−	0.0206100i
$160$	−0.393125			−0.0310793
$161$	4.79341	+	0.152530i	0.377773	+	0.0120210i
$162$	−1.00000			−0.0785674
$163$	1.52887	−	10.6335i	0.119750	−	0.832879i	−0.838081	−	0.545546i	$-0.816322\pi$
$163$	1.52887	−	10.6335i	0.119750	−	0.832879i	0.957831	−	0.287333i	$-0.0927687\pi$
$164$	5.24829	+	11.4922i	0.409823	+	0.897387i
$165$	−2.30339	−	0.676335i	−0.179318	−	0.0526526i
$166$	−6.62049	−	7.64045i	−0.513850	−	0.593014i
$167$	3.34656	−	0.982637i	0.258964	−	0.0760388i	−0.149673	−	0.988736i	$-0.547822\pi$
$167$	3.34656	−	0.982637i	0.258964	−	0.0760388i	0.408638	+	0.912697i	$0.366004\pi$
$168$	0.841254	+	0.540641i	0.0649041	+	0.0417113i
$169$	−2.98171	+	6.52904i	−0.229362	+	0.502234i
$170$	−1.71520	+	1.97945i	−0.131550	+	0.151817i
$171$	0.446905	−	0.287209i	0.0341757	−	0.0219634i
$172$	−0.792063	−	5.50892i	−0.0603942	−	0.420051i
$173$	2.78516	+	19.3712i	0.211752	+	1.47277i	0.767302	+	0.641285i	$0.221599\pi$
$173$	2.78516	+	19.3712i	0.211752	+	1.47277i	−0.555550	+	0.831483i	$0.687492\pi$
$174$	−3.69315	+	2.37345i	−0.279977	+	0.179931i
$175$	3.17310	−	3.66195i	0.239864	−	0.276817i
$176$	−2.53674	+	5.55469i	−0.191214	+	0.418701i
$177$	−5.61794	−	3.61043i	−0.422271	−	0.271377i
$178$	0.485691	−	0.142612i	0.0364041	−	0.0106892i
$179$	3.17211	+	3.66081i	0.237094	+	0.273621i	0.861810	−	0.507231i	$-0.169331\pi$
$179$	3.17211	+	3.66081i	0.237094	+	0.273621i	−0.624716	+	0.780852i	$0.714785\pi$
$180$	−0.377201	−	0.110756i	−0.0281149	−	0.00825528i
$181$	−3.81832	−	8.36095i	−0.283813	−	0.621465i	0.713006	−	0.701158i	$-0.247333\pi$
$181$	−3.81832	−	8.36095i	−0.283813	−	0.621465i	−0.996819	+	0.0796932i	$0.974606\pi$
$182$	0.343399	−	2.38839i	0.0254544	−	0.177039i
$183$	5.40538			0.399577
$184$	0.531195	+	4.76632i	0.0391602	+	0.351378i
$185$	3.81991			0.280845
$186$	0.626539	−	4.35767i	0.0459400	−	0.319520i
$187$	16.9010	+	37.0080i	1.23592	+	2.70629i
$188$	−5.92536	−	1.73984i	−0.432151	−	0.126891i
$189$	0.654861	+	0.755750i	0.0476341	+	0.0549727i
$190$	0.200383	−	0.0588378i	0.0145373	−	0.00426854i
$191$	11.4087	+	7.33195i	0.825508	+	0.530521i	0.883847	−	0.467775i	$-0.154944\pi$
$191$	11.4087	+	7.33195i	0.825508	+	0.530521i	−0.0583399	+	0.998297i	$0.518581\pi$
$192$	−0.415415	+	0.909632i	−0.0299800	+	0.0656470i
$193$	−13.4452	+	15.5166i	−0.967808	+	1.11691i	0.0252972	+	0.999680i	$0.491947\pi$
$193$	−13.4452	+	15.5166i	−0.967808	+	1.11691i	−0.993105	+	0.117230i	$0.962599\pi$
$194$	5.43477	−	3.49271i	0.390194	−	0.250762i
$195$	0.134999	+	0.938936i	0.00966745	+	0.0672386i
$196$	−0.142315	−	0.989821i	−0.0101653	−	0.0707015i
$197$	20.2931	−	13.0416i	1.44582	−	0.929174i	0.446412	−	0.894827i	$-0.352701\pi$
$197$	20.2931	−	13.0416i	1.44582	−	0.929174i	0.999410	−	0.0343464i	$-0.0109349\pi$
$198$	−3.99892	+	4.61501i	−0.284191	+	0.327974i
$199$	0.353676	−	0.774442i	0.0250714	−	0.0548987i	−0.896682	−	0.442675i	$-0.854029\pi$
$199$	0.353676	−	0.774442i	0.0250714	−	0.0548987i	0.921753	+	0.387776i	$0.126757\pi$
$200$	4.07625	+	2.61965i	0.288235	+	0.185237i
$201$	0.0902703	−	0.0265058i	0.00636718	−	0.00186957i
$202$	−9.99139	−	11.5307i	−0.702992	−	0.811296i
$203$	4.21223	+	1.23682i	0.295641	+	0.0868080i
$204$	2.76769	+	6.06040i	0.193777	+	0.424313i
$205$	−0.706833	+	4.91613i	−0.0493674	+	0.343358i
$206$	10.3884			0.723796
$207$	−0.833150	+	4.72291i	−0.0579079	+	0.328265i
$208$	2.41295			0.167308
$209$	0.461672	−	3.21100i	0.0319345	−	0.222109i
$210$	0.163310	+	0.357599i	0.0112695	+	0.0246767i
$211$	−8.96093	−	2.63117i	−0.616896	−	0.181137i	−0.0416697	−	0.999131i	$-0.513268\pi$
$211$	−8.96093	−	2.63117i	−0.616896	−	0.181137i	−0.575226	+	0.817995i	$0.695086\pi$
$212$	−0.171937	−	0.198426i	−0.0118087	−	0.0136279i
$213$	−10.4123	+	3.05733i	−0.713440	+	0.209485i
$214$	9.43936	+	6.06631i	0.645261	+	0.414684i
$215$	0.908913	−	1.99024i	0.0619874	−	0.135733i
$216$	−0.654861	+	0.755750i	−0.0445576	+	0.0514222i
$217$	−3.70360	+	2.38016i	−0.251417	+	0.161576i
$218$	−0.942556	−	6.55562i	−0.0638380	−	0.444003i
$219$	−1.24393	−	8.65175i	−0.0840572	−	0.584631i
$220$	−2.01954	+	1.29788i	−0.136157	+	0.0875029i
$221$	10.5277	−	12.1496i	0.708169	−	0.817270i
$222$	4.03650	−	8.83870i	0.270912	−	0.593214i
$223$	9.83209	+	6.31870i	0.658405	+	0.423131i	0.826729	−	0.562600i	$-0.190199\pi$
$223$	9.83209	+	6.31870i	0.658405	+	0.423131i	−0.168324	+	0.985732i	$0.553835\pi$
$224$	0.959493	−	0.281733i	0.0641088	−	0.0188240i
$225$	3.17310	+	3.66195i	0.211540	+	0.244130i
$226$	0.332402	+	0.0976020i	0.0221110	+	0.00649239i
$227$	0.840608	+	1.84067i	0.0557931	+	0.122170i	0.935475	−	0.353392i	$-0.114972\pi$
$227$	0.840608	+	1.84067i	0.0557931	+	0.122170i	−0.879682	+	0.475562i	$0.842245\pi$
$228$	0.0756030	−	0.525830i	0.00500693	−	0.0348240i
$229$	−10.2600			−0.677998			−0.338999	−	0.940787i	$-0.610088\pi$
$229$	−10.2600			−0.677998			−0.338999	+	0.940787i	$0.610088\pi$
$230$	−0.837356	+	1.68921i	−0.0552136	+	0.111383i
$231$	6.10653			0.401780
$232$	−0.624771	+	4.34538i	−0.0410182	+	0.285288i
$233$	−11.5425	−	25.2746i	−0.756177	−	1.65580i	−0.754936	−	0.655798i	$-0.772332\pi$
$233$	−11.5425	−	25.2746i	−0.756177	−	1.65580i	−0.00124074	−	0.999999i	$-0.500395\pi$
$234$	2.31521	+	0.679807i	0.151350	+	0.0444404i
$235$	−1.58984	−	1.83477i	−0.103710	−	0.119687i
$236$	−6.40755	+	1.88143i	−0.417096	+	0.122471i
$237$	−3.48125	−	2.23727i	−0.226132	−	0.145326i
$238$	2.76769	−	6.06040i	0.179403	−	0.392837i
$239$	−5.19840	+	5.99927i	−0.336256	+	0.388060i	−0.898546	−	0.438880i	$-0.855375\pi$
$239$	−5.19840	+	5.99927i	−0.336256	+	0.388060i	0.562289	+	0.826941i	$0.309921\pi$
$240$	−0.330718	+	0.212539i	−0.0213477	+	0.0137194i
$241$	−1.67005	−	11.6154i	−0.107577	−	0.748215i	−0.970189	−	0.242349i	$-0.922082\pi$
$241$	−1.67005	−	11.6154i	−0.107577	−	0.748215i	0.862612	−	0.505866i	$-0.168827\pi$
$242$	3.74141	+	26.0221i	0.240507	+	1.67276i
$243$	−0.841254	+	0.540641i	−0.0539664	+	0.0346821i
$244$	3.53977	−	4.08511i	0.226611	−	0.261522i
$245$	0.163310	−	0.357599i	0.0104335	−	0.0228462i
$246$	10.6283	+	6.83038i	0.677634	+	0.435489i
$247$	−1.22993	+	0.361139i	−0.0782583	+	0.0229787i
$248$	−2.88301	−	3.32718i	−0.183072	−	0.211276i
$249$	−9.70025	−	2.84825i	−0.614728	−	0.180501i
$250$	1.60786	+	3.52073i	0.101690	+	0.222670i
$251$	−3.37327	+	23.4616i	−0.212919	+	1.48089i	0.550420	+	0.834888i	$0.314468\pi$
$251$	−3.37327	+	23.4616i	−0.212919	+	1.48089i	−0.763339	+	0.645998i	$0.776442\pi$
$252$	1.00000			0.0629941
$253$	18.4645	+	22.7315i	1.16086	+	1.42912i
$254$	−16.1179			−1.01133
$255$	−0.372749	+	2.59253i	−0.0233425	+	0.162350i
$256$	0.415415	+	0.909632i	0.0259634	+	0.0568520i
$257$	−28.2176	−	8.28543i	−1.76017	−	0.516831i	−0.767857	−	0.640621i	$-0.778677\pi$
$257$	−28.2176	−	8.28543i	−1.76017	−	0.516831i	−0.992308	+	0.123790i	$0.960495\pi$
$258$	−3.64467	−	4.20617i	−0.226907	−	0.261865i
$259$	−9.32318	+	2.73753i	−0.579315	+	0.170102i
$260$	0.798006	+	0.512847i	0.0494902	+	0.0318054i
$261$	−1.82370	+	3.99334i	−0.112884	+	0.247182i
$262$	6.75773	−	7.79883i	0.417494	−	0.481814i
$263$	−15.2832	+	9.82189i	−0.942400	+	0.605644i	−0.919074	−	0.394084i	$-0.871062\pi$
$263$	−15.2832	+	9.82189i	−0.942400	+	0.605644i	−0.0233258	+	0.999728i	$0.507426\pi$
$264$	0.869049	+	6.04437i	0.0534863	+	0.372005i
$265$	−0.0146893	−	0.102166i	−0.000902357	−	0.00627603i
$266$	−0.446905	+	0.287209i	−0.0274015	+	0.0176099i
$267$	0.331487	−	0.382557i	0.0202867	−	0.0234121i
$268$	0.0390828	−	0.0855794i	0.00238736	−	0.00522759i
$269$	−11.3799	−	7.31339i	−0.693842	−	0.445905i	0.145608	−	0.989342i	$-0.453486\pi$
$269$	−11.3799	−	7.31339i	−0.693842	−	0.445905i	−0.839450	+	0.543437i	$0.817123\pi$
$270$	−0.377201	+	0.110756i	−0.0229557	+	0.00674040i
$271$	−4.69393	−	5.41709i	−0.285136	−	0.329065i	0.595054	−	0.803686i	$-0.297131\pi$
$271$	−4.69393	−	5.41709i	−0.285136	−	0.329065i	−0.880190	+	0.474621i	$0.842585\pi$
$272$	6.39260	+	1.87704i	0.387608	+	0.113812i
$273$	−1.00238	−	2.19490i	−0.0606666	−	0.132841i
$274$	−3.05659	+	21.2590i	−0.184655	+	1.28431i
$275$	29.5889			1.78428
$276$	3.02374	+	3.72250i	0.182008	+	0.224068i
$277$	−18.0003			−1.08153			−0.540766	−	0.841173i	$-0.681866\pi$
$277$	−18.0003			−1.08153			−0.540766	+	0.841173i	$0.681866\pi$
$278$	1.31831	−	9.16907i	0.0790672	−	0.549924i
$279$	−1.82886	−	4.00464i	−0.109491	−	0.239752i
$280$	0.377201	+	0.110756i	0.0225421	+	0.00661895i
$281$	−1.16209	−	1.34112i	−0.0693244	−	0.0800046i	0.720028	−	0.693945i	$-0.244129\pi$
$281$	−1.16209	−	1.34112i	−0.0693244	−	0.0800046i	−0.789352	+	0.613940i	$0.789583\pi$
$282$	−5.92536	+	1.73984i	−0.352850	+	0.103606i
$283$	−8.88722	−	5.71147i	−0.528290	−	0.339511i	0.249154	−	0.968464i	$-0.419848\pi$
$283$	−8.88722	−	5.71147i	−0.528290	−	0.339511i	−0.777444	+	0.628953i	$0.783484\pi$
$284$	−4.50804	+	9.87123i	−0.267503	+	0.585750i
$285$	0.136763	−	0.157833i	0.00810114	−	0.00934921i
$286$	12.3957	−	7.96621i	0.732971	−	0.471052i
$287$	−1.79798	−	12.5053i	−0.106132	−	0.738162i
$288$	0.142315	+	0.989821i	0.00838598	+	0.0583258i
$289$	23.0407	−	14.8074i	1.35534	−	0.871022i
$290$	−1.13019	+	1.30431i	−0.0663669	+	0.0765915i
$291$	2.68371	−	5.87652i	0.157322	−	0.344487i
$292$	−7.35316	−	4.72559i	−0.430311	−	0.276544i
$293$	21.5800	−	6.33646i	1.26072	−	0.370180i	0.417955	−	0.908468i	$-0.362747\pi$
$293$	21.5800	−	6.33646i	1.26072	−	0.370180i	0.842761	+	0.538288i	$0.180929\pi$
$294$	−0.654861	−	0.755750i	−0.0381923	−	0.0440762i
$295$	−2.51897	−	0.739637i	−0.146660	−	0.0430633i
$296$	−4.03650	−	8.83870i	−0.234617	−	0.513739i
$297$	−0.869049	+	6.04437i	−0.0504274	+	0.350730i
$298$	9.42699			0.546091
$299$	5.13958	−	10.3681i	0.297230	−	0.599605i
$300$	4.84545			0.279752
$301$	−0.792063	+	5.50892i	−0.0456537	+	0.317529i
$302$	6.85436	+	15.0090i	0.394424	+	0.863668i
$303$	−14.6393	−	4.29847i	−0.841003	−	0.246941i
$304$	−0.347887	−	0.401483i	−0.0199527	−	0.0230266i
$305$	2.03891	−	0.598679i	0.116748	−	0.0342803i
$306$	5.60483	+	3.60201i	0.320407	+	0.205913i
$307$	5.44043	−	11.9129i	0.310502	−	0.679904i	−0.688469	−	0.725266i	$-0.741717\pi$
$307$	5.44043	−	11.9129i	0.310502	−	0.679904i	0.998971	+	0.0453619i	$0.0144441\pi$
$308$	3.99892	−	4.61501i	0.227860	−	0.262964i
$309$	8.73930	−	5.61641i	0.497161	−	0.319506i
$310$	−0.246308	−	1.71311i	−0.0139894	−	0.0972981i
$311$	4.65489	+	32.3755i	0.263955	+	1.83584i	0.502335	+	0.864673i	$0.332474\pi$
$311$	4.65489	+	32.3755i	0.263955	+	1.83584i	−0.238381	+	0.971172i	$0.576617\pi$
$312$	2.02990	−	1.30454i	0.114921	−	0.0738550i
$313$	−5.09896	+	5.88451i	−0.288210	+	0.332612i	−0.881329	−	0.472502i	$-0.843351\pi$
$313$	−5.09896	+	5.88451i	−0.288210	+	0.332612i	0.593119	+	0.805115i	$0.297896\pi$
$314$	−2.17092	+	4.75366i	−0.122512	+	0.268264i
$315$	0.330718	+	0.212539i	0.0186338	+	0.0119752i
$316$	−3.97055	+	1.16586i	−0.223361	+	0.0655846i
$317$	6.08634	+	7.02401i	0.341843	+	0.394508i	0.900475	−	0.434908i	$-0.143219\pi$
$317$	6.08634	+	7.02401i	0.341843	+	0.394508i	−0.558632	+	0.829416i	$0.688674\pi$
$318$	−0.251920	−	0.0739703i	−0.0141270	−	0.00414805i
$319$	11.1365	+	24.3854i	0.623522	+	1.36532i
$320$	−0.0559475	+	0.389124i	−0.00312756	+	0.0217527i
$321$	11.2206			0.626272
$322$	0.833150	−	4.72291i	0.0464296	−	0.263197i
$323$	−3.53936			−0.196935
$324$	−0.142315	+	0.989821i	−0.00790638	+	0.0549901i
$325$	−4.85697	−	10.6353i	−0.269416	−	0.589939i
$326$	−10.3077	−	3.02661i	−0.570890	−	0.167628i
$327$	−4.33717	−	5.00536i	−0.239846	−	0.276797i
$328$	12.1221	−	3.55937i	0.669331	−	0.196533i
$329$	5.19517	+	3.33873i	0.286419	+	0.184070i
$330$	−0.997257	+	2.18369i	−0.0548972	+	0.120208i
$331$	−18.0946	+	20.8823i	−0.994569	+	1.14779i	−0.00555286	+	0.999985i	$0.501768\pi$
$331$	−18.0946	+	20.8823i	−0.994569	+	1.14779i	−0.989016	+	0.147809i	$0.952778\pi$
$332$	−8.50488	+	5.46575i	−0.466766	+	0.299972i
$333$	−1.38284	−	9.61788i	−0.0757793	−	0.527057i
$334$	−0.496371	−	3.45234i	−0.0271602	−	0.188903i
$335$	0.0311144	−	0.0199960i	0.00169996	−	0.00109250i
$336$	0.654861	−	0.755750i	0.0357256	−	0.0412295i
$337$	3.46372	−	7.58449i	0.188681	−	0.413154i	−0.791524	−	0.611138i	$-0.790712\pi$
$337$	3.46372	−	7.58449i	0.188681	−	0.413154i	0.980205	+	0.197984i	$0.0634394\pi$
$338$	6.03824	+	3.88054i	0.328437	+	0.211074i
$339$	0.332402	−	0.0976020i	0.0180536	−	0.00530101i
$340$	1.71520	+	1.97945i	0.0930199	+	0.107351i
$341$	−25.7949	−	7.57407i	−1.39687	−	0.410159i
$342$	−0.220684	−	0.483231i	−0.0119332	−	0.0261301i
$343$	−0.142315	+	0.989821i	−0.00768428	+	0.0534453i
$344$	−5.56557			−0.300075
$345$	0.208826	+	1.87376i	0.0112428	+	0.100880i
$346$	19.5704			1.05211
$347$	1.99626	−	13.8843i	0.107165	−	0.745348i	−0.863402	−	0.504517i	$-0.831671\pi$
$347$	1.99626	−	13.8843i	0.107165	−	0.745348i	0.970567	−	0.240832i	$-0.0774202\pi$
$348$	1.82370	+	3.99334i	0.0977604	+	0.214066i
$349$	−23.7637	−	6.97767i	−1.27204	−	0.373506i	−0.425080	−	0.905156i	$-0.639754\pi$
$349$	−23.7637	−	6.97767i	−1.27204	−	0.373506i	−0.846964	+	0.531650i	$0.821572\pi$
$350$	−3.17310	−	3.66195i	−0.169609	−	0.195739i
$351$	2.31521	−	0.679807i	0.123577	−	0.0362854i
$352$	5.13714	+	3.30144i	0.273810	+	0.175967i
$353$	−2.80310	+	6.13793i	−0.149194	+	0.326689i	−0.969443	−	0.245318i	$-0.921108\pi$
$353$	−2.80310	+	6.13793i	−0.149194	+	0.326689i	0.820249	+	0.572007i	$0.193835\pi$
$354$	−4.37320	+	5.04694i	−0.232433	+	0.268242i
$355$	−3.58892	+	2.30646i	−0.190480	+	0.122414i
$356$	−0.0720391	−	0.501043i	−0.00381806	−	0.0265552i
$357$	−0.948169	−	6.59466i	−0.0501824	−	0.349026i
$358$	4.07498	−	2.61883i	0.215369	−	0.138410i
$359$	−12.0888	+	13.9512i	−0.638022	+	0.736316i	−0.979024	−	0.203746i	$-0.934688\pi$
$359$	−12.0888	+	13.9512i	−0.638022	+	0.736316i	0.341002	+	0.940063i	$0.389234\pi$
$360$	−0.163310	+	0.357599i	−0.00860720	+	0.0188471i
$361$	−15.7464	−	10.1196i	−0.828758	−	0.532610i
$362$	−8.81925	+	2.58957i	−0.463530	+	0.136105i
$363$	17.2161	+	19.8684i	0.903610	+	1.04282i
$364$	−2.31521	−	0.679807i	−0.121350	−	0.0356316i
$365$	−1.42745	−	3.12567i	−0.0747160	−	0.163605i
$366$	0.769265	−	5.35036i	0.0402102	−	0.279668i
$367$	−2.30370			−0.120252			−0.0601261	−	0.998191i	$-0.519150\pi$
$367$	−2.30370			−0.120252			−0.0601261	+	0.998191i	$0.519150\pi$
$368$	4.79341	+	0.152530i	0.249874	+	0.00795117i
$369$	12.6339			0.657692
$370$	0.543630	−	3.78103i	0.0282620	−	0.196566i
$371$	0.109069	+	0.238829i	0.00566260	+	0.0123994i
$372$	−4.22415	−	1.24032i	−0.219012	−	0.0643077i
$373$	−19.6238	−	22.6471i	−1.01608	−	1.17262i	−0.984903	−	0.173106i	$-0.944620\pi$
$373$	−19.6238	−	22.6471i	−1.01608	−	1.17262i	−0.0311779	−	0.999514i	$-0.509926\pi$
$374$	39.0366	−	11.4622i	2.01853	−	0.592695i
$375$	3.25607	+	2.09255i	0.168143	+	0.108059i
$376$	−2.56540	+	5.61744i	−0.132300	+	0.289698i
$377$	6.93694	−	8.00566i	0.357271	−	0.412312i
$378$	0.841254	−	0.540641i	0.0432694	−	0.0278076i
$379$	0.855960	+	5.95334i	0.0439677	+	0.305802i	0.999924	+	0.0122945i	$0.00391357\pi$
$379$	0.855960	+	5.95334i	0.0439677	+	0.305802i	−0.955957	+	0.293508i	$0.905177\pi$
$380$	−0.0297214	−	0.206717i	−0.00152468	−	0.0106044i
$381$	−13.5592	+	8.71398i	−0.694660	+	0.446431i
$382$	8.88096	−	10.2492i	0.454389	−	0.524393i
$383$	−7.57383	+	16.5844i	−0.387005	+	0.847422i	0.611420	+	0.791306i	$0.290599\pi$
$383$	−7.57383	+	16.5844i	−0.387005	+	0.847422i	−0.998424	+	0.0561153i	$0.982129\pi$
$384$	0.841254	+	0.540641i	0.0429300	+	0.0275895i
$385$	2.30339	−	0.676335i	0.117391	−	0.0344692i
$386$	13.4452	+	15.5166i	0.684343	+	0.789774i
$387$	−5.34012	−	1.56800i	−0.271454	−	0.0797060i
$388$	−2.68371	−	5.87652i	−0.136245	−	0.298335i
$389$	−3.44726	+	23.9762i	−0.174783	+	1.21564i	0.693826	+	0.720143i	$0.255924\pi$
$389$	−3.44726	+	23.9762i	−0.174783	+	1.21564i	−0.868609	+	0.495499i	$0.834985\pi$
$390$	0.948592			0.0480338
$391$	21.6816	−	23.4701i	1.09649	−	1.18693i
$392$	−1.00000			−0.0505076
$393$	1.46859	−	10.2143i	0.0740808	−	0.515243i
$394$	−10.0208	−	21.9425i	−0.504842	−	1.10545i
$395$	−1.56092	−	0.458328i	−0.0785385	−	0.0230610i
$396$	3.99892	+	4.61501i	0.200954	+	0.231913i
$397$	27.4172	−	8.05042i	1.37603	−	0.404039i	0.491645	−	0.870796i	$-0.336396\pi$
$397$	27.4172	−	8.05042i	1.37603	−	0.404039i	0.884386	+	0.466756i	$0.154577\pi$
$398$	−0.716226	−	0.460290i	−0.0359011	−	0.0230723i
$399$	−0.220684	+	0.483231i	−0.0110480	+	0.0241918i
$400$	3.17310	−	3.66195i	0.158655	−	0.183097i
$401$	7.77917	−	4.99937i	0.388473	−	0.249657i	−0.331796	−	0.943351i	$-0.607655\pi$
$401$	7.77917	−	4.99937i	0.388473	−	0.249657i	0.720269	+	0.693695i	$0.244018\pi$
$402$	−0.0133892	−	0.0931237i	−0.000667791	−	0.00464459i
$403$	1.51181	+	10.5148i	0.0753085	+	0.523782i
$404$	−12.8352	+	8.24871i	−0.638577	+	0.410389i
$405$	−0.257442	+	0.297104i	−0.0127924	+	0.0147632i
$406$	1.82370	−	3.99334i	0.0905086	−	0.198186i
$407$	−49.9164	−	32.0794i	−2.47427	−	1.59011i
$408$	6.39260	−	1.87704i	0.316481	−	0.0929271i
$409$	8.21757	+	9.48358i	0.406333	+	0.468933i	0.921625	−	0.388082i	$-0.126862\pi$
$409$	8.21757	+	9.48358i	0.406333	+	0.468933i	−0.515292	+	0.857014i	$0.672317\pi$
$410$	4.76550	+	1.39928i	0.235351	+	0.0691054i
$411$	8.92214	+	19.5368i	0.440097	+	0.963677i
$412$	1.47843	−	10.2827i	0.0728369	−	0.506592i
$413$	6.67806			0.328606
$414$	4.55627	+	1.49681i	0.223928	+	0.0735642i
$415$	−3.97440			−0.195096
$416$	0.343399	−	2.38839i	0.0168365	−	0.117100i
$417$	−3.84814	−	8.42625i	−0.188444	−	0.412635i
$418$	−3.11261	−	0.913945i	−0.152243	−	0.0447025i
$419$	−4.50831	−	5.20287i	−0.220246	−	0.254177i	0.634864	−	0.772624i	$-0.281056\pi$
$419$	−4.50831	−	5.20287i	−0.220246	−	0.254177i	−0.855110	+	0.518447i	$0.826510\pi$
$420$	0.377201	−	0.110756i	0.0184055	−	0.00540435i
$421$	−20.2732	−	13.0288i	−0.988055	−	0.634985i	−0.0564307	−	0.998407i	$-0.517972\pi$
$421$	−20.2732	−	13.0288i	−0.988055	−	0.634985i	−0.931625	+	0.363422i	$0.881608\pi$
$422$	−3.87966	+	8.49526i	−0.188859	+	0.413543i
$423$	−4.04410	+	4.66714i	−0.196631	+	0.226924i
$424$	−0.220875	+	0.141948i	−0.0107267	+	0.00689361i
$425$	−4.59431	−	31.9541i	−0.222857	−	1.55000i
$426$	1.54439	+	10.7414i	0.0748257	+	0.520424i
$427$	−4.54729	+	2.92237i	−0.220059	+	0.141423i
$428$	7.34792	−	8.47995i	0.355175	−	0.409894i
$429$	6.12104	−	13.4032i	0.295526	−	0.647113i
$430$	−1.84063	−	1.18290i	−0.0887632	−	0.0570446i
$431$	−14.4363	+	4.23889i	−0.695373	+	0.204180i	−0.610272	−	0.792192i	$-0.708940\pi$
$431$	−14.4363	+	4.23889i	−0.695373	+	0.204180i	−0.0851017	+	0.996372i	$0.527122\pi$
$432$	0.654861	+	0.755750i	0.0315070	+	0.0363610i
$433$	−0.348094	−	0.102210i	−0.0167284	−	0.00491189i	0.273358	−	0.961912i	$-0.411866\pi$
$433$	−0.348094	−	0.102210i	−0.0167284	−	0.00491189i	−0.290086	+	0.957001i	$0.593684\pi$
$434$	1.82886	+	4.00464i	0.0877880	+	0.192229i
$435$	−0.245613	+	1.70828i	−0.0117762	+	0.0819056i
$436$	−6.62304			−0.317186
$437$	−2.46612	+	0.639667i	−0.117970	+	0.0305994i
$438$	−8.74072			−0.417648
$439$	4.92737	−	34.2706i	0.235171	−	1.63565i	−0.440008	−	0.897994i	$-0.645024\pi$
$439$	4.92737	−	34.2706i	0.235171	−	1.63565i	0.675179	−	0.737654i	$-0.264066\pi$
$440$	0.997257	+	2.18369i	0.0475424	+	0.104103i
$441$	−0.959493	−	0.281733i	−0.0456901	−	0.0134158i
$442$	−10.5277	−	12.1496i	−0.500751	−	0.577897i
$443$	−17.4214	+	5.11538i	−0.827715	+	0.243039i	−0.668035	−	0.744130i	$-0.732864\pi$
$443$	−17.4214	+	5.11538i	−0.827715	+	0.243039i	−0.159680	+	0.987169i	$0.551046\pi$
$444$	−8.17428	−	5.25329i	−0.387934	−	0.249310i
$445$	0.0826668	−	0.181015i	0.00391878	−	0.00858093i
$446$	7.65363	−	8.83277i	0.362410	−	0.418244i
$447$	7.93049	−	5.09662i	0.375099	−	0.241062i
$448$	−0.142315	−	0.989821i	−0.00672374	−	0.0467647i
$449$	−1.01513	−	7.06037i	−0.0479069	−	0.333200i	−0.999654	−	0.0263153i	$-0.991623\pi$
$449$	−1.01513	−	7.06037i	−0.0479069	−	0.333200i	0.951747	−	0.306884i	$-0.0992865\pi$
$450$	4.07625	−	2.61965i	0.192156	−	0.123491i
$451$	50.5218	−	58.3053i	2.37898	−	2.74549i
$452$	0.143914	−	0.315128i	0.00676916	−	0.0148224i
$453$	13.8807	+	8.92059i	0.652173	+	0.419126i
$454$	1.94157	−	0.570096i	0.0911224	−	0.0267559i
$455$	−0.621195	−	0.716898i	−0.0291221	−	0.0336087i
$456$	−0.509719	−	0.149667i	−0.0238698	−	0.00700880i
$457$	4.13714	+	9.05906i	0.193527	+	0.423765i	0.981374	−	0.192106i	$-0.0615316\pi$
$457$	4.13714	+	9.05906i	0.193527	+	0.423765i	−0.787847	+	0.615871i	$0.788804\pi$
$458$	−1.46015	+	10.1555i	−0.0682282	+	0.474537i
$459$	6.66247			0.310978
$460$	1.55285	+	1.06923i	0.0724018	+	0.0498532i
$461$	7.73104			0.360070			0.180035	−	0.983660i	$-0.442379\pi$
$461$	7.73104			0.360070			0.180035	+	0.983660i	$0.442379\pi$
$462$	0.869049	−	6.04437i	0.0404318	−	0.281210i
$463$	6.19334	+	13.5615i	0.287829	+	0.630258i	0.997216	−	0.0745612i	$-0.0237556\pi$
$463$	6.19334	+	13.5615i	0.287829	+	0.630258i	−0.709387	+	0.704819i	$0.751028\pi$
$464$	4.21223	+	1.23682i	0.195548	+	0.0574181i
$465$	−1.13339	−	1.30800i	−0.0525595	−	0.0606569i
$466$	−26.6601	+	7.82810i	−1.23500	+	0.362630i
$467$	−32.2190	−	20.7059i	−1.49092	−	0.958154i	−0.996013	−	0.0892070i	$-0.971567\pi$
$467$	−32.2190	−	20.7059i	−1.49092	−	0.958154i	−0.494904	−	0.868947i	$-0.664797\pi$
$468$	1.00238	−	2.19490i	0.0463348	−	0.101459i
$469$	−0.0616101	+	0.0711019i	−0.00284489	+	0.00328318i
$470$	−2.04235	+	1.31254i	−0.0942067	+	0.0605430i
$471$	0.743725	+	5.17272i	0.0342690	+	0.238346i
$472$	0.950388	+	6.61009i	0.0437451	+	0.304254i
$473$	−28.5911	+	18.3744i	−1.31462	+	0.844854i
$474$	−2.70993	+	3.12742i	−0.124471	+	0.143647i
$475$	−1.06931	+	2.34147i	−0.0490635	+	0.107434i
$476$	−5.60483	−	3.60201i	−0.256897	−	0.165098i
$477$	−0.251920	+	0.0739703i	−0.0115346	+	0.00338687i
$478$	5.19840	+	5.99927i	0.237769	+	0.274400i
$479$	−35.4377	−	10.4054i	−1.61919	−	0.475437i	−0.658389	−	0.752678i	$-0.728762\pi$
$479$	−35.4377	−	10.4054i	−1.61919	−	0.475437i	−0.960800	+	0.277241i	$0.910580\pi$
$480$	0.163310	+	0.357599i	0.00745405	+	0.0163221i
$481$	−3.33673	+	23.2075i	−0.152142	+	1.05817i
$482$	−11.7349			−0.534508
$483$	−1.85251	−	4.42360i	−0.0842920	−	0.201281i
$484$	26.2897			1.19499
$485$	0.361439	−	2.51386i	0.0164121	−	0.114149i
$486$	0.415415	+	0.909632i	0.0188436	+	0.0412617i
$487$	−27.2236	−	7.99358i	−1.23362	−	0.362223i	−0.401005	−	0.916076i	$-0.631339\pi$
$487$	−27.2236	−	7.99358i	−1.23362	−	0.362223i	−0.832615	+	0.553852i	$0.813157\pi$
$488$	−3.53977	−	4.08511i	−0.160238	−	0.184924i
$489$	−10.3077	+	3.02661i	−0.466129	+	0.136868i
$490$	−0.330718	−	0.212539i	−0.0149403	−	0.00960156i
$491$	8.03263	−	17.5890i	0.362508	−	0.793781i	−0.637225	−	0.770677i	$-0.719918\pi$
$491$	8.03263	−	17.5890i	0.362508	−	0.793781i	0.999733	−	0.0231035i	$-0.00735472\pi$
$492$	8.27342	−	9.54803i	0.372994	−	0.430458i
$493$	24.6055	−	15.8130i	1.10818	−	0.712183i
$494$	0.182426	+	1.26880i	0.00820775	+	0.0570861i
$495$	0.341645	+	2.37619i	0.0153558	+	0.106802i
$496$	−3.70360	+	2.38016i	−0.166297	+	0.106872i
$497$	7.10648	−	8.20132i	0.318769	−	0.367879i
$498$	−4.19975	+	9.19617i	−0.188195	+	0.412090i
$499$	24.0611	+	15.4632i	1.07712	+	0.692226i	0.953892	−	0.300152i	$-0.0970373\pi$
$499$	24.0611	+	15.4632i	1.07712	+	0.692226i	0.123233	+	0.992378i	$0.460674\pi$
$500$	3.71371	−	1.09044i	0.166082	−	0.0487662i
$501$	−2.28405	−	2.63593i	−0.102044	−	0.117765i
$502$	22.7428	+	6.67788i	1.01506	+	0.298048i
$503$	0.580577	+	1.27129i	0.0258866	+	0.0566839i	0.922134	−	0.386871i	$-0.126444\pi$
$503$	0.580577	+	1.27129i	0.0258866	+	0.0566839i	−0.896247	+	0.443555i	$0.853717\pi$
$504$	0.142315	−	0.989821i	0.00633921	−	0.0440902i
$505$	−5.99802			−0.266908
$506$	25.1280	−	15.0416i	1.11707	−	0.668679i
$507$	7.17767			0.318771
$508$	−2.29381	+	15.9538i	−0.101772	+	0.707836i
$509$	8.76123	+	19.1844i	0.388335	+	0.850334i	0.998321	+	0.0579225i	$0.0184476\pi$
$509$	8.76123	+	19.1844i	0.388335	+	0.850334i	−0.609986	+	0.792412i	$0.708825\pi$
$510$	2.51309	+	0.737910i	0.111282	+	0.0326752i
$511$	5.72395	+	6.60579i	0.253213	+	0.292223i
$512$	0.959493	−	0.281733i	0.0424040	−	0.0124509i
$513$	−0.446905	−	0.287209i	−0.0197314	−	0.0126806i
$514$	−12.2169	+	26.7512i	−0.538864	+	1.17995i
$515$	2.67442	−	3.08644i	0.117849	−	0.136005i
$516$	−4.68205	+	3.00897i	−0.206116	+	0.132463i
$517$	5.36683	+	37.3271i	0.236033	+	1.64164i
$518$	1.38284	+	9.61788i	0.0607586	+	0.422585i
$519$	16.4637	−	10.5806i	0.722676	−	0.464436i
$520$	0.621195	−	0.716898i	0.0272412	−	0.0314380i
$521$	16.3939	−	35.8977i	0.718232	−	1.57271i	−0.0981344	−	0.995173i	$-0.531288\pi$
$521$	16.3939	−	35.8977i	0.718232	−	1.57271i	0.816366	−	0.577535i	$-0.195985\pi$
$522$	3.69315	+	2.37345i	0.161645	+	0.103883i
$523$	15.9234	−	4.67554i	0.696284	−	0.204447i	0.0856088	−	0.996329i	$-0.472716\pi$
$523$	15.9234	−	4.67554i	0.696284	−	0.204447i	0.610675	+	0.791882i	$0.290898\pi$
$524$	−6.75773	−	7.79883i	−0.295213	−	0.340694i
$525$	−4.64918	−	1.36512i	−0.202907	−	0.0595788i
$526$	7.54690	+	16.5254i	0.329060	+	0.720542i
$527$	−4.17430	+	29.0329i	−0.181835	+	1.26469i
$528$	6.10653			0.265752
$529$	10.8653	−	20.2718i	0.472406	−	0.881381i
$530$	−0.103217			−0.00448346
$531$	−0.950388	+	6.61009i	−0.0412433	+	0.286853i
$532$	0.220684	+	0.483231i	0.00956787	+	0.0209507i
$533$	−29.2500	−	8.58858i	−1.26696	−	0.372013i
$534$	−0.331487	−	0.382557i	−0.0143449	−	0.0165549i
$535$	4.23241	−	1.24275i	0.182983	−	0.0537287i
$536$	−0.0791462	−	0.0508642i	−0.00341860	−	0.00219700i
$537$	2.01225	−	4.40620i	0.0868348	−	0.190142i
$538$	−8.85847	+	10.2232i	−0.381916	+	0.440754i
$539$	−5.13714	+	3.30144i	−0.221272	+	0.142203i
$540$	0.0559475	+	0.389124i	0.00240760	+	0.0167452i
$541$	1.04254	+	7.25099i	0.0448221	+	0.311744i	0.999882	+	0.0153330i	$0.00488085\pi$
$541$	1.04254	+	7.25099i	0.0448221	+	0.311744i	−0.955060	+	0.296411i	$0.904210\pi$
$542$	−6.02996	+	3.87522i	−0.259009	+	0.166455i
$543$	−6.01920	+	6.94653i	−0.258309	+	0.298104i
$544$	2.76769	−	6.06040i	0.118664	−	0.259838i
$545$	−2.19036	−	1.40766i	−0.0938246	−	0.0602974i
$546$	−2.31521	+	0.679807i	−0.0990818	+	0.0290930i
$547$	−2.31486	−	2.67149i	−0.0989764	−	0.114225i	0.704100	−	0.710101i	$-0.251351\pi$
$547$	−2.31486	−	2.67149i	−0.0989764	−	0.114225i	−0.803077	+	0.595876i	$0.796805\pi$
$548$	20.6076	+	6.05095i	0.880315	+	0.258484i
$549$	−2.24548	−	4.91690i	−0.0958345	−	0.209848i
$550$	4.21094	−	29.2877i	0.179555	−	1.24883i
$551$	−2.33217			−0.0993536
$552$	4.11493	−	2.46319i	0.175143	−	0.104841i
$553$	4.13817			0.175973
$554$	−2.56171	+	17.8171i	−0.108837	+	0.756975i
$555$	−1.58685	−	3.47471i	−0.0673580	−	0.147493i
$556$	−8.88813	−	2.60979i	−0.376941	−	0.110680i
$557$	27.5151	+	31.7542i	1.16585	+	1.34547i	0.927292	+	0.374340i	$0.122131\pi$
$557$	27.5151	+	31.7542i	1.16585	+	1.34547i	0.238562	+	0.971127i	$0.423324\pi$
$558$	−4.22415	+	1.24032i	−0.178823	+	0.0525071i
$559$	11.2976	+	7.26050i	0.477836	+	0.307086i
$560$	0.163310	−	0.357599i	0.00690111	−	0.0151113i
$561$	26.6427	−	30.7474i	1.12486	−	1.29815i
$562$	−1.49285	+	0.959398i	−0.0629722	+	0.0404698i
$563$	−2.76258	−	19.2142i	−0.116429	−	0.809780i	−0.961437	−	0.275026i	$-0.911313\pi$
$563$	−2.76258	−	19.2142i	−0.116429	−	0.809780i	0.845008	−	0.534754i	$-0.179596\pi$
$564$	0.878867	+	6.11265i	0.0370070	+	0.257389i
$565$	0.114572	−	0.0736311i	0.00482009	−	0.00309768i
$566$	−6.91812	+	7.98393i	−0.290790	+	0.335590i
$567$	0.415415	−	0.909632i	0.0174458	−	0.0382010i
$568$	9.12920	+	5.86698i	0.383053	+	0.246173i
$569$	37.5935	−	11.0384i	1.57600	−	0.462755i	0.627259	−	0.778811i	$-0.284177\pi$
$569$	37.5935	−	11.0384i	1.57600	−	0.462755i	0.948741	+	0.316056i	$0.102359\pi$
$570$	−0.136763	−	0.157833i	−0.00572837	−	0.00661089i
$571$	−26.1615	−	7.68170i	−1.09482	−	0.321469i	−0.316029	−	0.948749i	$-0.602350\pi$
$571$	−26.1615	−	7.68170i	−1.09482	−	0.321469i	−0.778793	+	0.627280i	$0.784168\pi$
$572$	−6.12104	−	13.4032i	−0.255933	−	0.560416i
$573$	1.93002	−	13.4236i	0.0806276	−	0.560777i
$574$	−12.6339			−0.527327
$575$	−8.97623	−	21.4343i	−0.374335	−	0.893874i
$576$	1.00000			0.0416667
$577$	−0.110732	+	0.770160i	−0.00460985	+	0.0320622i	−0.991997	−	0.126265i	$-0.959701\pi$
$577$	−0.110732	+	0.770160i	−0.00460985	+	0.0320622i	0.987387	+	0.158327i	$0.0506101\pi$
$578$	−11.3776	−	24.9135i	−0.473247	−	1.03627i
$579$	19.6997	+	5.78437i	0.818693	+	0.240390i
$580$	1.13019	+	1.30431i	0.0469285	+	0.0541583i
$581$	9.70025	−	2.84825i	0.402434	−	0.118165i
$582$	−5.43477	−	3.49271i	−0.225278	−	0.144778i
$583$	−0.666035	+	1.45841i	−0.0275843	+	0.0604013i
$584$	−5.72395	+	6.60579i	−0.236859	+	0.273350i
$585$	0.798006	−	0.512847i	0.0329935	−	0.0212036i
$586$	−3.20081	−	22.2621i	−0.132224	−	0.919639i
$587$	−4.24491	−	29.5240i	−0.175206	−	1.21858i	−0.867673	−	0.497135i	$-0.834385\pi$
$587$	−4.24491	−	29.5240i	−0.175206	−	1.21858i	0.692467	−	0.721449i	$-0.256524\pi$
$588$	−0.841254	+	0.540641i	−0.0346927	+	0.0222957i
$589$	1.53157	−	1.76752i	0.0631070	−	0.0728294i
$590$	−1.09060	+	2.38807i	−0.0448991	+	0.0983153i
$591$	−20.2931	−	13.0416i	−0.834746	−	0.536459i
$592$	−9.32318	+	2.73753i	−0.383181	+	0.112512i
$593$	−29.4893	−	34.0324i	−1.21098	−	1.39754i	−0.893370	−	0.449323i	$-0.851665\pi$
$593$	−29.4893	−	34.0324i	−1.21098	−	1.39754i	−0.317609	−	0.948222i	$-0.602880\pi$
$594$	5.85917	+	1.72041i	0.240405	+	0.0705892i
$595$	−1.08805	−	2.38250i	−0.0446057	−	0.0976728i
$596$	1.34160	−	9.33104i	0.0549541	−	0.382214i
$597$	−0.851379			−0.0348446
$598$	−9.53117	−	6.56281i	−0.389758	−	0.268373i
$599$	37.7694			1.54322			0.771608	−	0.636099i	$-0.219453\pi$
$599$	37.7694			1.54322			0.771608	+	0.636099i	$0.219453\pi$
$600$	0.689580	−	4.79613i	0.0281520	−	0.195801i
$601$	0.562033	+	1.23068i	0.0229258	+	0.0502005i	0.920749	−	0.390157i	$-0.127579\pi$
$601$	0.562033	+	1.23068i	0.0229258	+	0.0502005i	−0.897823	+	0.440357i	$0.854852\pi$
$602$	5.34012	+	1.56800i	0.217647	+	0.0639070i
$603$	−0.0616101	−	0.0711019i	−0.00250896	−	0.00289549i
$604$	15.8317	−	4.64860i	0.644181	−	0.189149i
$605$	8.69447	+	5.58759i	0.353480	+	0.227168i
$606$	−6.33810	+	13.8785i	−0.257468	+	0.563776i
$607$	−15.0731	+	17.3953i	−0.611797	+	0.706052i	−0.974128	−	0.225998i	$-0.927436\pi$
$607$	−15.0731	+	17.3953i	−0.611797	+	0.706052i	0.362331	+	0.932050i	$0.381981\pi$
$608$	−0.446905	+	0.287209i	−0.0181244	+	0.0116479i
$609$	−0.624771	−	4.34538i	−0.0253170	−	0.176084i
$610$	−0.302418	−	2.10336i	−0.0122445	−	0.0851626i
$611$	12.5357	−	8.05620i	0.507140	−	0.325919i
$612$	4.36299	−	5.03516i	0.176364	−	0.203534i
$613$	−4.64497	+	10.1711i	−0.187609	+	0.410806i	−0.979942	−	0.199283i	$-0.936139\pi$
$613$	−4.64497	+	10.1711i	−0.187609	+	0.410806i	0.792333	+	0.610088i	$0.208866\pi$
$614$	−11.0174	−	7.08043i	−0.444625	−	0.285743i
$615$	4.76550	−	1.39928i	0.192164	−	0.0564243i
$616$	−3.99892	−	4.61501i	−0.161121	−	0.185944i
$617$	−7.90378	−	2.32076i	−0.318194	−	0.0934303i	0.118735	−	0.992926i	$-0.462116\pi$
$617$	−7.90378	−	2.32076i	−0.318194	−	0.0934303i	−0.436930	+	0.899496i	$0.643934\pi$
$618$	−4.31551	−	9.44965i	−0.173595	−	0.380120i
$619$	2.68078	−	18.6452i	0.107750	−	0.749415i	−0.862281	−	0.506431i	$-0.830965\pi$
$619$	2.68078	−	18.6452i	0.107750	−	0.749415i	0.970030	−	0.242984i	$-0.0781264\pi$
$620$	−1.73073			−0.0695077
$621$	4.64221	−	1.20411i	0.186286	−	0.0483191i
$622$	32.7084			1.31149
$623$	−0.0720391	+	0.501043i	−0.00288618	+	0.0200739i
$624$	−1.00238	−	2.19490i	−0.0401272	−	0.0878662i
$625$	−21.7859	−	6.39693i	−0.871437	−	0.255877i
$626$	5.09896	+	5.88451i	0.203795	+	0.235192i
$627$	−3.11261	+	0.913945i	−0.124306	+	0.0364995i
$628$	4.39632	+	2.82534i	0.175432	+	0.112743i
$629$	−26.8931	+	58.8876i	−1.07230	+	2.34800i
$630$	0.257442	−	0.297104i	0.0102567	−	0.0118369i
$631$	14.8079	−	9.51649i	0.589495	−	0.378845i	−0.211623	−	0.977351i	$-0.567875\pi$
$631$	14.8079	−	9.51649i	0.589495	−	0.378845i	0.801118	+	0.598506i	$0.204239\pi$
$632$	0.588923	+	4.09605i	0.0234261	+	0.162932i
$633$	1.32911	+	9.24417i	0.0528274	+	0.367423i
$634$	7.81870	−	5.02477i	0.310520	−	0.199559i
$635$	−4.14942	+	4.78869i	−0.164665	+	0.190033i
$636$	−0.109069	+	0.238829i	−0.00432488	+	0.00947017i
$637$	2.02990	+	1.30454i	0.0804277	+	0.0516877i
$638$	25.7221	−	7.55270i	1.01835	−	0.299014i
$639$	7.10648	+	8.20132i	0.281128	+	0.324439i
$640$	0.377201	+	0.110756i	0.0149102	+	0.00437802i
$641$	−19.5063	−	42.7128i	−0.770452	−	1.68706i	−0.725654	−	0.688059i	$-0.758463\pi$
$641$	−19.5063	−	42.7128i	−0.770452	−	1.68706i	−0.0447982	−	0.998996i	$-0.514264\pi$
$642$	1.59686	−	11.1064i	0.0630229	−	0.438334i
$643$	32.2185			1.27057			0.635287	−	0.772276i	$-0.280882\pi$
$643$	32.2185			1.27057			0.635287	+	0.772276i	$0.280882\pi$
$644$	−4.55627	−	1.49681i	−0.179542	−	0.0589826i
$645$	−2.18796			−0.0861510
$646$	−0.503703	+	3.50333i	−0.0198179	+	0.137837i
$647$	1.52355	+	3.33611i	0.0598969	+	0.131156i	0.937214	−	0.348756i	$-0.113396\pi$
$647$	1.52355	+	3.33611i	0.0598969	+	0.131156i	−0.877317	+	0.479912i	$0.840669\pi$
$648$	0.959493	+	0.281733i	0.0376924	+	0.0110675i
$649$	26.7051	+	30.8193i	1.04827	+	1.20976i
$650$	−11.2182	+	3.29397i	−0.440015	+	0.129200i
$651$	3.70360	+	2.38016i	0.145156	+	0.0932859i
$652$	−4.46274	+	9.77203i	−0.174774	+	0.382702i
$653$	−22.9930	+	26.5353i	−0.899784	+	1.03841i	0.0992764	+	0.995060i	$0.468347\pi$
$653$	−22.9930	+	26.5353i	−0.899784	+	1.03841i	−0.999060	+	0.0433458i	$0.986198\pi$
$654$	−5.57165	+	3.58068i	−0.217869	+	0.140016i
$655$	−0.577342	−	4.01550i	−0.0225586	−	0.156899i
$656$	−1.79798	−	12.5053i	−0.0701995	−	0.488248i
$657$	−7.35316	+	4.72559i	−0.286874	+	0.184363i
$658$	4.04410	−	4.66714i	0.157655	−	0.181944i
$659$	−2.79287	+	6.11554i	−0.108795	+	0.238228i	−0.956197	−	0.292724i	$-0.905438\pi$
$659$	−2.79287	+	6.11554i	−0.108795	+	0.238228i	0.847402	+	0.530952i	$0.178165\pi$
$660$	2.01954	+	1.29788i	0.0786104	+	0.0505198i
$661$	−37.4036	+	10.9827i	−1.45483	+	0.427177i	−0.911136	−	0.412105i	$-0.864794\pi$
$661$	−37.4036	+	10.9827i	−1.45483	+	0.427177i	−0.543696	+	0.839282i	$0.682976\pi$
$662$	18.0946	+	20.8823i	0.703266	+	0.811613i
$663$	−15.4250	−	4.52920i	−0.599058	−	0.175899i
$664$	4.19975	+	9.19617i	0.162982	+	0.356881i
$665$	−0.0297214	+	0.206717i	−0.00115255	+	0.00801615i
$666$	−9.71678			−0.376518
$667$	14.2865	−	15.4650i	0.553176	−	0.598807i
$668$	−3.48784			−0.134948
$669$	1.66329	−	11.5685i	0.0643067	−	0.447263i
$670$	−0.0153644	−	0.0336434i	−0.000593579	−	0.00129976i
$671$	−31.6710	−	9.29945i	−1.22265	−	0.359001i
$672$	−0.654861	−	0.755750i	−0.0252618	−	0.0291537i
$673$	−24.3676	+	7.15496i	−0.939301	+	0.275804i	−0.715326	−	0.698791i	$-0.753722\pi$
$673$	−24.3676	+	7.15496i	−0.939301	+	0.275804i	−0.223975	+	0.974595i	$0.571903\pi$
$674$	−7.01436	−	4.50785i	−0.270183	−	0.173636i
$675$	2.01287	−	4.40758i	0.0774755	−	0.169648i
$676$	4.70037	−	5.42452i	0.180784	−	0.208635i
$677$	18.4618	−	11.8647i	0.709544	−	0.455996i	−0.135441	−	0.990785i	$-0.543245\pi$
$677$	18.4618	−	11.8647i	0.709544	−	0.455996i	0.844986	+	0.534789i	$0.179609\pi$
$678$	−0.0493028	−	0.342909i	−0.00189346	−	0.0131693i
$679$	0.919400	+	6.39456i	0.0352833	+	0.245401i
$680$	2.20340	−	1.41604i	0.0844965	−	0.0543026i
$681$	1.32514	−	1.52929i	0.0507793	−	0.0586024i
$682$	−11.1680	+	24.4544i	−0.427644	+	0.936409i
$683$	43.6692	+	28.0645i	1.67096	+	1.07386i	0.898721	+	0.438522i	$0.144498\pi$
$683$	43.6692	+	28.0645i	1.67096	+	1.07386i	0.772235	+	0.635336i	$0.219139\pi$
$684$	−0.509719	+	0.149667i	−0.0194896	+	0.00572266i
$685$	5.52925	+	6.38110i	0.211262	+	0.243809i
$686$	0.959493	+	0.281733i	0.0366336	+	0.0107566i
$687$	4.26215	+	9.33280i	0.162611	+	0.356069i
$688$	−0.792063	+	5.50892i	−0.0301971	+	0.210025i
$689$	0.633533			0.0241357
$690$	1.88441	+	0.0599634i	0.0717382	+	0.00228277i
$691$	−19.2555			−0.732514			−0.366257	−	0.930514i	$-0.619361\pi$
$691$	−19.2555			−0.732514			−0.366257	+	0.930514i	$0.619361\pi$
$692$	2.78516	−	19.3712i	0.105876	−	0.736384i
$693$	−2.53674	−	5.55469i	−0.0963629	−	0.211005i
$694$	−13.4589	−	3.95188i	−0.510892	−	0.150011i
$695$	−2.38478	−	2.75218i	−0.0904599	−	0.104396i
$696$	4.21223	−	1.23682i	0.159664	−	0.0468817i
$697$	−70.8106	−	45.5072i	−2.68214	−	1.72371i
$698$	−10.2886	+	22.5288i	−0.389428	+	0.852729i
$699$	−18.1957	+	20.9989i	−0.688224	+	0.794253i
$700$	−4.07625	+	2.61965i	−0.154068	+	0.0990134i
$701$	−5.94215	−	41.3286i	−0.224432	−	1.56096i	−0.720984	−	0.692952i	$-0.756310\pi$
$701$	−5.94215	−	41.3286i	−0.224432	−	1.56096i	0.496551	−	0.868007i	$-0.334599\pi$
$702$	−0.343399	−	2.38839i	−0.0129607	−	0.0901440i
$703$	4.34248	−	2.79074i	0.163780	−	0.105255i
$704$	3.99892	−	4.61501i	0.150715	−	0.173935i
$705$	−1.00852	+	2.20836i	−0.0379832	+	0.0831716i
$706$	5.67653	+	3.64809i	0.213639	+	0.137298i
$707$	14.6393	−	4.29847i	0.550566	−	0.161661i
$708$	4.37320	+	5.04694i	0.164355	+	0.189676i
$709$	33.1433	+	9.73176i	1.24472	+	0.365484i	0.836788	−	0.547527i	$-0.184431\pi$
$709$	33.1433	+	9.73176i	1.24472	+	0.365484i	0.407935	+	0.913011i	$0.366249\pi$
$710$	1.77222	+	3.88063i	0.0665104	+	0.145637i
$711$	−0.588923	+	4.09605i	−0.0220864	+	0.153614i
$712$	−0.506195			−0.0189705
$713$	2.33858	+	20.9837i	0.0875805	+	0.785844i
$714$	−6.66247			−0.249337
$715$	0.824373	−	5.73364i	0.0308298	−	0.214426i
$716$	−2.01225	−	4.40620i	−0.0752011	−	0.164668i
$717$	7.61662	+	2.23644i	0.284448	+	0.0835214i
$718$	12.0888	+	13.9512i	0.451149	+	0.520654i
$719$	−3.76542	+	1.10563i	−0.140427	+	0.0412330i	−0.351191	−	0.936304i	$-0.614223\pi$
$719$	−3.76542	+	1.10563i	−0.140427	+	0.0412330i	0.210764	+	0.977537i	$0.432405\pi$
$720$	0.330718	+	0.212539i	0.0123251	+	0.00792088i
$721$	−4.31551	+	9.44965i	−0.160718	+	0.351923i
$722$	−12.2575	+	14.1460i	−0.456179	+	0.526458i
$723$	−9.87200	+	6.34435i	−0.367143	+	0.235949i
$724$	1.30810	+	9.09802i	0.0486151	+	0.338125i
$725$	−3.02730	−	21.0553i	−0.112431	−	0.781975i
$726$	22.1163	−	14.2133i	0.820812	−	0.527504i
$727$	−8.57157	+	9.89212i	−0.317902	+	0.366878i	−0.892100	−	0.451838i	$-0.850768\pi$
$727$	−8.57157	+	9.89212i	−0.317902	+	0.366878i	0.574198	+	0.818716i	$0.305314\pi$
$728$	−1.00238	+	2.19490i	−0.0371505	+	0.0813483i
$729$	0.841254	+	0.540641i	0.0311575	+	0.0200237i
$730$	−3.29701	+	0.968088i	−0.122028	+	0.0358305i
$731$	24.2825	+	28.0235i	0.898122	+	1.03649i
$732$	−5.18642	−	1.52287i	−0.191696	−	0.0562869i
$733$	6.94450	+	15.2063i	0.256501	+	0.561659i	0.993447	−	0.114293i	$-0.0364601\pi$
$733$	6.94450	+	15.2063i	0.256501	+	0.561659i	−0.736946	+	0.675952i	$0.763733\pi$
$734$	−0.327851	+	2.28025i	−0.0121012	+	0.0841657i
$735$	−0.393125			−0.0145006
$736$	0.833150	−	4.72291i	0.0307103	−	0.174089i
$737$	−0.574510			−0.0211623
$738$	1.79798	−	12.5053i	0.0661847	−	0.460325i
$739$	11.0024	+	24.0918i	0.404728	+	0.886231i	0.996769	+	0.0803232i	$0.0255952\pi$
$739$	11.0024	+	24.0918i	0.404728	+	0.886231i	−0.592041	+	0.805908i	$0.701677\pi$
$740$	−3.66518	−	1.07619i	−0.134735	−	0.0395617i
$741$	0.839433	+	0.968758i	0.0308374	+	0.0355882i
$742$	0.251920	−	0.0739703i	0.00924827	−	0.00271554i
$743$	20.3482	+	13.0770i	0.746501	+	0.479747i	0.857764	−	0.514044i	$-0.171853\pi$
$743$	20.3482	+	13.0770i	0.746501	+	0.479747i	−0.111263	+	0.993791i	$0.535489\pi$
$744$	−1.82886	+	4.00464i	−0.0670492	+	0.146817i
$745$	2.42691	−	2.80080i	0.0889149	−	0.102613i
$746$	−25.2093	+	16.2010i	−0.922978	+	0.593162i
$747$	1.43877	+	10.0069i	0.0526418	+	0.366132i
$748$	−5.79002	−	40.2705i	−0.211704	−	1.47243i
$749$	−9.43936	+	6.06631i	−0.344907	+	0.221658i
$750$	2.53464	−	2.92512i	0.0925518	−	0.106810i
$751$	−14.8844	+	32.5923i	−0.543140	+	1.18931i	0.416773	+	0.909011i	$0.363161\pi$
$751$	−14.8844	+	32.5923i	−0.543140	+	1.18931i	−0.959913	+	0.280299i	$0.909566\pi$
$752$	5.19517	+	3.33873i	0.189448	+	0.121751i
$753$	22.7428	−	6.67788i	0.828792	−	0.243355i
$754$	−6.93694	−	8.00566i	−0.252628	−	0.291549i
$755$	6.22382	+	1.82748i	0.226508	+	0.0665088i
$756$	−0.415415	−	0.909632i	−0.0151085	−	0.0330830i
$757$	−1.64340	+	11.4301i	−0.0597303	+	0.415433i	0.937916	+	0.346863i	$0.112753\pi$
$757$	−1.64340	+	11.4301i	−0.0597303	+	0.415433i	−0.997646	+	0.0685708i	$0.978156\pi$
$758$	6.01456			0.218458
$759$	13.0069	−	26.2390i	0.472120	−	0.952414i
$760$	−0.208843			−0.00757553
$761$	3.12166	−	21.7116i	0.113160	−	0.787045i	−0.851653	−	0.524106i	$-0.824399\pi$
$761$	3.12166	−	21.7116i	0.113160	−	0.787045i	0.964813	−	0.262938i	$-0.0846915\pi$
$762$	6.69561	+	14.6613i	0.242556	+	0.531124i
$763$	6.35476	+	1.86592i	0.230058	+	0.0675510i
$764$	−8.88096	−	10.2492i	−0.321302	−	0.370802i
$765$	2.51309	−	0.737910i	0.0908610	−	0.0266792i
$766$	15.3377	+	9.85694i	0.554174	+	0.356146i
$767$	6.69393	−	14.6577i	0.241704	−	0.529258i
$768$	0.654861	−	0.755750i	0.0236303	−	0.0272708i
$769$	14.0561	−	9.03331i	0.506876	−	0.325750i	−0.262085	−	0.965045i	$-0.584410\pi$
$769$	14.0561	−	9.03331i	0.506876	−	0.325750i	0.768961	+	0.639295i	$0.220774\pi$
$770$	−0.341645	−	2.37619i	−0.0123120	−	0.0856321i
$771$	4.18532	+	29.1095i	0.150731	+	1.04835i
$772$	17.2721	−	11.1001i	0.621637	−	0.399502i
$773$	5.80103	−	6.69475i	0.208649	−	0.240793i	−0.641774	−	0.766894i	$-0.721801\pi$
$773$	5.80103	−	6.69475i	0.208649	−	0.240793i	0.850422	+	0.526101i	$0.176347\pi$
$774$	−2.31202	+	5.06262i	−0.0831038	+	0.181972i
$775$	17.9456	+	11.5330i	0.644626	+	0.414276i
$776$	−6.19863	+	1.82008i	−0.222518	+	0.0653372i
$777$	6.36314	+	7.34345i	0.228276	+	0.263445i
$778$	23.2416	+	6.82434i	0.833251	+	0.244664i
$779$	2.78809	+	6.10507i	0.0998937	+	0.218737i
$780$	0.134999	−	0.938936i	0.00483373	−	0.0336193i
$781$	66.2674			2.37123
$782$	−20.1456	−	24.8011i	−0.720404	−	0.886884i
$783$	4.39006			0.156888
$784$	−0.142315	+	0.989821i	−0.00508267	+	0.0353508i
$785$	0.853444	+	1.86878i	0.0304607	+	0.0666997i
$786$	−9.90133	−	2.90729i	−0.353169	−	0.103700i
$787$	−14.6367	−	16.8916i	−0.521742	−	0.602122i	0.432324	−	0.901718i	$-0.357694\pi$
$787$	−14.6367	−	16.8916i	−0.521742	−	0.602122i	−0.954066	+	0.299596i	$0.903148\pi$
$788$	−23.1453	+	6.79608i	−0.824517	+	0.242100i
$789$	15.2832	+	9.82189i	0.544095	+	0.349669i
$790$	−0.675805	+	1.47981i	−0.0240441	+	0.0526492i
$791$	−0.226867	+	0.261818i	−0.00806645	+	0.00930918i
$792$	5.13714	−	3.30144i	0.182540	−	0.117311i
$793$	1.85620	+	12.9102i	0.0659156	+	0.458453i
$794$	−4.06660	−	28.2839i	−0.144318	−	1.00376i
$795$	−0.0868317	+	0.0558033i	−0.00307960	+	0.00197914i
$796$	−0.557535	+	0.643429i	−0.0197613	+	0.0228058i
$797$	−1.02023	+	2.23400i	−0.0361384	+	0.0791322i	−0.926840	−	0.375456i	$-0.877486\pi$
$797$	−1.02023	+	2.23400i	−0.0361384	+	0.0791322i	0.890702	+	0.454588i	$0.150213\pi$
$798$	0.446905	+	0.287209i	0.0158203	+	0.0101671i
$799$	39.4776	−	11.5917i	1.39662	−	0.410083i
$800$	−3.17310	−	3.66195i	−0.112186	−	0.129469i
$801$	−0.485691	−	0.142612i	−0.0171610	−	0.00503894i
$802$	−3.84139	−	8.41147i	−0.135644	−	0.297019i
$803$	−7.59611	+	52.8321i	−0.268061	+	1.86441i
$804$	−0.0940813			−0.00331799
$805$	−1.18871	−	1.46341i	−0.0418964	−	0.0515784i
$806$	10.6230			0.374178
$807$	−1.92513	+	13.3896i	−0.0677678	+	0.471335i
$808$	6.33810	+	13.8785i	0.222974	+	0.488244i
$809$	−3.04017	−	0.892675i	−0.106887	−	0.0313848i	0.227852	−	0.973696i	$-0.426830\pi$
$809$	−3.04017	−	0.892675i	−0.106887	−	0.0313848i	−0.334739	+	0.942311i	$0.608648\pi$
$810$	0.257442	+	0.297104i	0.00904560	+	0.0104392i
$811$	22.1232	−	6.49596i	0.776851	−	0.228104i	0.130811	−	0.991407i	$-0.458242\pi$
$811$	22.1232	−	6.49596i	0.776851	−	0.228104i	0.646040	+	0.763303i	$0.276424\pi$
$812$	−3.69315	−	2.37345i	−0.129604	−	0.0832916i
$813$	−2.97763	+	6.52009i	−0.104430	+	0.228670i
$814$	−38.8567	+	44.8430i	−1.36193	+	1.57175i
$815$	−3.55285	+	2.28328i	−0.124451	+	0.0799797i
$816$	−0.948169	−	6.59466i	−0.0331926	−	0.230859i
$817$	−0.420773	−	2.92654i	−0.0147210	−	0.102387i
$818$	10.5565	−	6.78427i	0.369101	−	0.237206i
$819$	−1.58015	+	1.82359i	−0.0552148	+	0.0637213i
$820$	2.06324	−	4.51786i	0.0720513	−	0.157770i
$821$	−19.6793	−	12.6471i	−0.686811	−	0.441387i	0.150140	−	0.988665i	$-0.452028\pi$
$821$	−19.6793	−	12.6471i	−0.686811	−	0.441387i	−0.836951	+	0.547278i	$0.815664\pi$
$822$	20.6076	−	6.05095i	0.718774	−	0.211051i
$823$	−0.682567	−	0.787724i	−0.0237928	−	0.0274583i	0.743728	−	0.668482i	$-0.233056\pi$
$823$	−0.682567	−	0.787724i	−0.0237928	−	0.0274583i	−0.767521	+	0.641024i	$0.778510\pi$
$824$	−9.96762	−	2.92676i	−0.347239	−	0.101958i
$825$	−12.2917	−	26.9150i	−0.427941	−	0.937060i
$826$	0.950388	−	6.61009i	0.0330682	−	0.229994i
$827$	−29.4329			−1.02348			−0.511741	−	0.859140i	$-0.670999\pi$
$827$	−29.4329			−1.02348			−0.511741	+	0.859140i	$0.670999\pi$
$828$	2.13000	−	4.29687i	0.0740226	−	0.149327i
$829$	−19.6802			−0.683520			−0.341760	−	0.939787i	$-0.611023\pi$
$829$	−19.6802			−0.683520			−0.341760	+	0.939787i	$0.611023\pi$
$830$	−0.565617	+	3.93395i	−0.0196328	+	0.136549i
$831$	7.47759	+	16.3736i	0.259395	+	0.567995i
$832$	−2.31521	−	0.679807i	−0.0802654	−	0.0235681i
$833$	4.36299	+	5.03516i	0.151169	+	0.174458i
$834$	−8.88813	+	2.60979i	−0.307771	+	0.0903696i
$835$	−1.15349	−	0.741303i	−0.0399182	−	0.0256539i
$836$	−1.34761	+	2.95086i	−0.0466082	+	0.102058i
$837$	−2.88301	+	3.32718i	−0.0996515	+	0.115004i
$838$	−5.79151	+	3.72198i	−0.200065	+	0.128574i
$839$	7.68986	+	53.4841i	0.265483	+	1.84648i	0.489641	+	0.871924i	$0.337128\pi$
$839$	7.68986	+	53.4841i	0.265483	+	1.84648i	−0.224157	+	0.974553i	$0.571963\pi$
$840$	−0.0559475	−	0.389124i	−0.00193037	−	0.0134260i
$841$	−8.18317	+	5.25901i	−0.282178	+	0.181345i
$842$	−15.7814	+	18.2127i	−0.543862	+	0.627650i
$843$	−0.737178	+	1.61419i	−0.0253898	+	0.0555958i
$844$	7.85666	+	5.04917i	0.270437	+	0.173800i
$845$	2.70742	−	0.794971i	0.0931382	−	0.0273478i
$846$	4.04410	+	4.66714i	0.139039	+	0.160460i
$847$	−25.2248	−	7.40666i	−0.866733	−	0.254496i
$848$	0.109069	+	0.238829i	0.00374546	+	0.00820141i
$849$	−1.50345	+	10.4567i	−0.0515983	+	0.358874i
$850$	−32.2827			−1.10729
$851$	−8.09554	+	45.8915i	−0.277511	+	1.57314i
$852$	10.8519			0.371780
$853$	−0.780030	+	5.42523i	−0.0267077	+	0.185756i	−0.998808	−	0.0488088i	$-0.984458\pi$
$853$	−0.780030	+	5.42523i	−0.0267077	+	0.185756i	0.972100	+	0.234565i	$0.0753666\pi$
$854$	2.24548	+	4.91690i	0.0768386	+	0.168253i
$855$	−0.200383	−	0.0588378i	−0.00685296	−	0.00201221i
$856$	−7.34792	−	8.47995i	−0.251147	−	0.289839i
$857$	−54.9147	+	16.1244i	−1.87585	+	0.550800i	−0.878528	+	0.477692i	$0.841474\pi$
$857$	−54.9147	+	16.1244i	−1.87585	+	0.550800i	−0.997324	+	0.0731080i	$0.976708\pi$
$858$	−12.3957	−	7.96621i	−0.423181	−	0.271962i
$859$	7.00589	−	15.3408i	0.239038	−	0.523420i	−0.751652	−	0.659560i	$-0.770743\pi$
$859$	7.00589	−	15.3408i	0.239038	−	0.523420i	0.990690	+	0.136140i	$0.0434698\pi$
$860$	−1.43281	+	1.65355i	−0.0488585	+	0.0563857i
$861$	−10.6283	+	6.83038i	−0.362211	+	0.232779i
$862$	2.14124	+	14.8926i	0.0729309	+	0.507245i
$863$	−3.32362	−	23.1163i	−0.113137	−	0.786887i	−0.964835	−	0.262854i	$-0.915336\pi$
$863$	−3.32362	−	23.1163i	−0.113137	−	0.786887i	0.851698	−	0.524033i	$-0.175573\pi$
$864$	0.841254	−	0.540641i	0.0286200	−	0.0183930i
$865$	5.03826	−	5.81446i	0.171306	−	0.197698i
$866$	−0.150708	+	0.330005i	−0.00512128	+	0.0112140i
$867$	−23.0407	−	14.8074i	−0.782504	−	0.502885i
$868$	4.22415	−	1.24032i	0.143377	−	0.0420993i
$869$	16.5482	+	19.0977i	0.561361	+	0.647845i
$870$	1.65593	+	0.486226i	0.0561414	+	0.0164846i
$871$	0.0943048	+	0.206499i	0.00319540	+	0.00699694i
$872$	−0.942556	+	6.55562i	−0.0319190	+	0.222001i
$873$	−6.46032			−0.218649
$874$	0.282191	+	2.53205i	0.00954525	+	0.0856479i
$875$	−3.87049			−0.130847
$876$	−1.24393	+	8.65175i	−0.0420286	+	0.292315i
$877$	11.7496	+	25.7281i	0.396756	+	0.868775i	0.997589	+	0.0694002i	$0.0221085\pi$
$877$	11.7496	+	25.7281i	0.396756	+	0.868775i	−0.600833	+	0.799375i	$0.705164\pi$
$878$	−33.2206	−	9.75444i	−1.12114	−	0.329196i
$879$	−14.7285	−	16.9976i	−0.496780	−	0.573315i
$880$	2.30339	−	0.676335i	0.0776472	−	0.0227993i
$881$	40.9002	+	26.2850i	1.37796	+	0.885563i	0.999202	−	0.0399320i	$-0.0127141\pi$
$881$	40.9002	+	26.2850i	1.37796	+	0.885563i	0.378760	+	0.925495i	$0.376351\pi$
$882$	−0.415415	+	0.909632i	−0.0139878	+	0.0306289i
$883$	−8.54344	+	9.85965i	−0.287510	+	0.331804i	−0.881070	−	0.472986i	$-0.843176\pi$
$883$	−8.54344	+	9.85965i	−0.287510	+	0.331804i	0.593561	+	0.804789i	$0.297722\pi$
$884$	−13.5242	+	8.69146i	−0.454867	+	0.292325i
$885$	0.373621	+	2.59859i	0.0125591	+	0.0873507i
$886$	2.58399	+	17.9721i	0.0868109	+	0.603783i
$887$	−39.9747	+	25.6902i	−1.34222	+	0.862592i	−0.997110	−	0.0759701i	$-0.975795\pi$
$887$	−39.9747	+	25.6902i	−1.34222	+	0.862592i	−0.345110	+	0.938562i	$0.612158\pi$
$888$	−6.36314	+	7.34345i	−0.213533	+	0.246430i
$889$	6.69561	−	14.6613i	0.224564	−	0.491726i
$890$	−0.167408	−	0.107586i	−0.00561152	−	0.00360631i
$891$	5.85917	−	1.72041i	0.196290	−	0.0576358i
$892$	−7.65363	−	8.83277i	−0.256263	−	0.295743i
$893$	−3.14777	−	0.924270i	−0.105336	−	0.0309295i
$894$	−3.91611	−	8.57509i	−0.130974	−	0.286794i
$895$	0.271006	−	1.88489i	0.00905875	−	0.0630050i
$896$	−1.00000			−0.0334077
$897$	−11.5663	−	0.368047i	−0.386186	−	0.0122887i
$898$	−7.13298			−0.238031
$899$	−2.75054	+	19.1305i	−0.0917358	+	0.638036i
$900$	−2.01287	−	4.40758i	−0.0670958	−	0.146919i
$901$	1.67841	+	0.492825i	0.0559159	+	0.0164184i
$902$	−50.5218	−	58.3053i	−1.68219	−	1.94135i
$903$	5.34012	−	1.56800i	0.177708	−	0.0521798i
$904$	−0.291440	−	0.187297i	−0.00969314	−	0.00622940i
$905$	−1.50108	+	3.28690i	−0.0498975	+	0.109260i
$906$	10.8052	−	12.4699i	0.358979	−	0.414284i
$907$	6.74218	−	4.33294i	0.223871	−	0.143873i	−0.423898	−	0.905710i	$-0.639339\pi$
$907$	6.74218	−	4.33294i	0.223871	−	0.143873i	0.647769	+	0.761837i	$0.275702\pi$
$908$	−0.287979	−	2.00294i	−0.00955693	−	0.0664699i
$909$	2.17134	+	15.1020i	0.0720187	+	0.500901i
$910$	−0.798006	+	0.512847i	−0.0264536	+	0.0170007i
$911$	4.39063	−	5.06705i	0.145468	−	0.167879i	−0.678340	−	0.734748i	$-0.737300\pi$
$911$	4.39063	−	5.06705i	0.145468	−	0.167879i	0.823808	+	0.566870i	$0.191846\pi$
$912$	−0.220684	+	0.483231i	−0.00730758	+	0.0160014i
$913$	51.9353	+	33.3768i	1.71881	+	1.10461i
$914$	9.55563	−	2.80579i	0.316072	−	0.0928072i
$915$	−1.39157	−	1.60596i	−0.0460040	−	0.0530914i
$916$	9.84437	+	2.89057i	0.325267	+	0.0955071i
$917$	4.28681	+	9.38680i	0.141563	+	0.309979i
$918$	0.948169	−	6.59466i	0.0312942	−	0.217656i
$919$	−32.6662			−1.07756			−0.538779	−	0.842447i	$-0.681114\pi$
$919$	−32.6662			−1.07756			−0.538779	+	0.842447i	$0.681114\pi$
$920$	1.27934	−	1.38487i	0.0421787	−	0.0456579i
$921$	−13.0964			−0.431540
$922$	1.10024	−	7.65235i	0.0362345	−	0.252017i
$923$	−10.8777	−	23.8188i	−0.358043	−	0.784005i
$924$	−5.85917	−	1.72041i	−0.192753	−	0.0565973i
$925$	30.8323	+	35.5824i	1.01376	+	1.16994i
$926$	14.3049	−	4.20030i	0.470088	−	0.138030i
$927$	−8.73930	−	5.61641i	−0.287036	−	0.184467i
$928$	1.82370	−	3.99334i	0.0598658	−	0.131088i
$929$	15.6403	−	18.0498i	0.513140	−	0.592195i	−0.438760	−	0.898604i	$-0.644582\pi$
$929$	15.6403	−	18.0498i	0.513140	−	0.592195i	0.951900	+	0.306409i	$0.0991275\pi$
$930$	−1.45598	+	0.935702i	−0.0477435	+	0.0306829i
$931$	−0.0756030	−	0.525830i	−0.00247779	−	0.0172334i
$932$	3.95430	+	27.5028i	0.129527	+	0.900883i
$933$	27.5161	−	17.6835i	0.900835	−	0.578932i
$934$	−25.0804	+	28.9443i	−0.820655	+	0.947086i
$935$	6.64420	−	14.5488i	0.217289	−	0.475796i
$936$	−2.02990	−	1.30454i	−0.0663495	−	0.0426402i
$937$	−3.67701	+	1.07967i	−0.120123	+	0.0352712i	−0.341241	−	0.939976i	$-0.610847\pi$
$937$	−3.67701	+	1.07967i	−0.120123	+	0.0352712i	0.221119	+	0.975247i	$0.429029\pi$
$938$	0.0616101	+	0.0711019i	0.00201164	+	0.00232156i
$939$	7.47092	+	2.19366i	0.243804	+	0.0715874i
$940$	1.00852	+	2.20836i	0.0328944	+	0.0720287i
$941$	1.50739	−	10.4841i	0.0491395	−	0.341773i	−0.950389	−	0.311064i	$-0.899315\pi$
$941$	1.50739	−	10.4841i	0.0491395	−	0.341773i	0.999528	−	0.0307084i	$-0.00977632\pi$
$942$	5.22591			0.170269
$943$	−57.5632	−	18.9105i	−1.87452	−	0.615810i
$944$	6.67806			0.217352
$945$	0.0559475	−	0.389124i	0.00181997	−	0.0126582i
$946$	14.1184	+	30.9150i	0.459029	+	1.00513i
$947$	22.6169	+	6.64092i	0.734950	+	0.215801i	0.627726	−	0.778434i	$-0.283986\pi$
$947$	22.6169	+	6.64092i	0.734950	+	0.215801i	0.107224	+	0.994235i	$0.465804\pi$
$948$	2.70993	+	3.12742i	0.0880143	+	0.101574i
$949$	20.2366	−	5.94200i	0.656907	−	0.192885i
$950$	2.16546	+	1.39166i	0.0702568	+	0.0451513i
$951$	3.86091	−	8.45421i	0.125199	−	0.274147i
$952$	−4.36299	+	5.03516i	−0.141405	+	0.163191i
$953$	10.8024	−	6.94230i	0.349925	−	0.224883i	−0.353856	−	0.935300i	$-0.615130\pi$
$953$	10.8024	−	6.94230i	0.349925	−	0.224883i	0.703781	+	0.710417i	$0.251494\pi$
$954$	0.0373655	+	0.259883i	0.00120975	+	0.00841401i
$955$	−0.758738	−	5.27714i	−0.0245522	−	0.170764i
$956$	6.67801	−	4.29170i	0.215982	−	0.138803i
$957$	17.5555	−	20.2602i	0.567490	−	0.654918i
$958$	−15.3428	+	33.5961i	−0.495705	+	1.08544i
$959$	−18.0681	−	11.6117i	−0.583451	−	0.374961i
$960$	0.377201	−	0.110756i	0.0121741	−	0.00357464i
$961$	7.60826	+	8.78040i	0.245428	+	0.283239i
$962$	22.4964	+	6.60553i	0.725313	+	0.212971i
$963$	−4.66120	−	10.2066i	−0.150205	−	0.328903i
$964$	−1.67005	+	11.6154i	−0.0537885	+	0.374107i
$965$	8.07141			0.259828
$966$	−4.64221	+	1.20411i	−0.149361	+	0.0387415i
$967$	−22.4345			−0.721444			−0.360722	−	0.932673i	$-0.617470\pi$
$967$	−22.4345			−0.721444			−0.360722	+	0.932673i	$0.617470\pi$
$968$	3.74141	−	26.0221i	0.120253	−	0.836381i
$969$	1.47030	+	3.21951i	0.0472329	+	0.103426i
$970$	−2.43684	−	0.715520i	−0.0782422	−	0.0229740i
$971$	−30.3748	−	35.0544i	−0.974773	−	1.12495i	−0.992144	−	0.125099i	$-0.960075\pi$
$971$	−30.3748	−	35.0544i	−0.974773	−	1.12495i	0.0173709	−	0.999849i	$-0.494470\pi$
$972$	0.959493	−	0.281733i	0.0307758	−	0.00903658i
$973$	7.79283	+	5.00815i	0.249827	+	0.160554i
$974$	−11.7865	+	25.8089i	−0.377665	+	0.826971i
$975$	−7.65653	+	8.83610i	−0.245205	+	0.282982i
$976$	−4.54729	+	2.92237i	−0.145555	+	0.0935427i
$977$	−2.47103	−	17.1864i	−0.0790552	−	0.549841i	−0.990404	−	0.138205i	$-0.955867\pi$
$977$	−2.47103	−	17.1864i	−0.0790552	−	0.549841i	0.911348	−	0.411636i	$-0.135042\pi$
$978$	1.52887	+	10.6335i	0.0488877	+	0.340022i
$979$	−2.60039	+	1.67117i	−0.0831090	+	0.0534109i
$980$	−0.257442	+	0.297104i	−0.00822369	+	0.00949064i
$981$	−2.75131	+	6.02452i	−0.0878425	+	0.192348i
$982$	−16.2668	−	10.4540i	−0.519095	−	0.333602i
$983$	36.5902	−	10.7439i	1.16705	−	0.342676i	0.359880	−	0.932999i	$-0.382818\pi$
$983$	36.5902	−	10.7439i	1.16705	−	0.342676i	0.807167	+	0.590322i	$0.200999\pi$
$984$	−8.27342	−	9.54803i	−0.263747	−	0.304380i
$985$	−9.09900	−	2.67171i	−0.289918	−	0.0851277i
$986$	−12.1503	−	26.6055i	−0.386946	−	0.847293i
$987$	0.878867	−	6.11265i	0.0279746	−	0.194568i
$988$	1.28185			0.0407811
$989$	21.9840	+	15.1374i	0.699051	+	0.481341i
$990$	2.40063			0.0762970
$991$	−0.0319445	+	0.222179i	−0.00101475	+	0.00705774i	−0.990323	−	0.138785i	$-0.955680\pi$
$991$	−0.0319445	+	0.222179i	−0.00101475	+	0.00705774i	0.989308	+	0.145843i	$0.0465894\pi$
$992$	1.82886	+	4.00464i	0.0580663	+	0.127147i
$993$	26.5119	+	7.78461i	0.841331	+	0.247037i
$994$	−7.10648	−	8.20132i	−0.225404	−	0.260130i
$995$	−0.321141	+	0.0942955i	−0.0101809	+	0.00298937i
$996$	8.50488	+	5.46575i	0.269487	+	0.173189i
$997$	−19.3583	+	42.3887i	−0.613082	+	1.34246i	0.307364	+	0.951592i	$0.400553\pi$
$997$	−19.3583	+	42.3887i	−0.613082	+	1.34246i	−0.920446	+	0.390870i	$0.872174\pi$
$998$	18.7300	−	21.6156i	0.592889	−	0.684230i
$999$	−8.17428	+	5.25329i	−0.258623	+	0.166207i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.h.169.1	✓	30
23.3	even	11	inner	966.2.q.h.463.1	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.h.169.1	✓	30	1.1	even	1	trivial
966.2.q.h.463.1	yes	30	23.3	even	11	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 - 0.989821i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-0.257442 - 0.297104i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(0.841254 + 0.540641i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.142315 - 0.989821i) q^{2} +(-0.415415 - 0.909632i) q^{3} +(-0.959493 - 0.281733i) q^{4} +(-0.257442 - 0.297104i) q^{5} +(-0.959493 + 0.281733i) q^{6} +(0.841254 + 0.540641i) q^{7} +(-0.415415 + 0.909632i) q^{8} +(-0.654861 + 0.755750i) q^{9} +(-0.330718 + 0.212539i) q^{10} +(0.869049 + 6.04437i) q^{11} +(0.142315 + 0.989821i) q^{12} +(2.02990 - 1.30454i) q^{13} +(0.654861 - 0.755750i) q^{14} +(-0.163310 + 0.357599i) q^{15} +(0.841254 + 0.540641i) q^{16} +(6.39260 - 1.87704i) q^{17} +(0.654861 + 0.755750i) q^{18} +(-0.509719 - 0.149667i) q^{19} +(0.163310 + 0.357599i) q^{20} +(0.142315 - 0.989821i) q^{21} +6.10653 q^{22} +(4.11493 - 2.46319i) q^{23} +1.00000 q^{24} +(0.689580 - 4.79613i) q^{25} +(-1.00238 - 2.19490i) q^{26} +(0.959493 + 0.281733i) q^{27} +(-0.654861 - 0.755750i) q^{28} +(4.21223 - 1.23682i) q^{29} +(0.330718 + 0.212539i) q^{30} +(-1.82886 + 4.00464i) q^{31} +(0.654861 - 0.755750i) q^{32} +(5.13714 - 3.30144i) q^{33} +(-0.948169 - 6.59466i) q^{34} +(-0.0559475 - 0.389124i) q^{35} +(0.841254 - 0.540641i) q^{36} +(-6.36314 + 7.34345i) q^{37} +(-0.220684 + 0.483231i) q^{38} +(-2.02990 - 1.30454i) q^{39} +(0.377201 - 0.110756i) q^{40} +(-8.27342 - 9.54803i) q^{41} +(-0.959493 - 0.281733i) q^{42} +(2.31202 + 5.06262i) q^{43} +(0.869049 - 6.04437i) q^{44} +0.393125 q^{45} +(-1.85251 - 4.42360i) q^{46} +6.17551 q^{47} +(0.142315 - 0.989821i) q^{48} +(0.415415 + 0.909632i) q^{49} +(-4.64918 - 1.36512i) q^{50} +(-4.36299 - 5.03516i) q^{51} +(-2.31521 + 0.679807i) q^{52} +(0.220875 + 0.141948i) q^{53} +(0.415415 - 0.909632i) q^{54} +(1.57208 - 1.81427i) q^{55} +(-0.841254 + 0.540641i) q^{56} +(0.0756030 + 0.525830i) q^{57} +(-0.624771 - 4.34538i) q^{58} +(5.61794 - 3.61043i) q^{59} +(0.257442 - 0.297104i) q^{60} +(-2.24548 + 4.91690i) q^{61} +(3.70360 + 2.38016i) q^{62} +(-0.959493 + 0.281733i) q^{63} +(-0.654861 - 0.755750i) q^{64} +(-0.910167 - 0.267249i) q^{65} +(-2.53674 - 5.55469i) q^{66} +(-0.0133892 + 0.0931237i) q^{67} -6.66247 q^{68} +(-3.95001 - 2.71983i) q^{69} -0.393125 q^{70} +(1.54439 - 10.7414i) q^{71} +(-0.415415 - 0.909632i) q^{72} +(8.38666 + 2.46254i) q^{73} +(6.36314 + 7.34345i) q^{74} +(-4.64918 + 1.36512i) q^{75} +(0.446905 + 0.287209i) q^{76} +(-2.53674 + 5.55469i) q^{77} +(-1.58015 + 1.82359i) q^{78} +(3.48125 - 2.23727i) q^{79} +(-0.0559475 - 0.389124i) q^{80} +(-0.142315 - 0.989821i) q^{81} +(-10.6283 + 6.83038i) q^{82} +(6.62049 - 7.64045i) q^{83} +(-0.415415 + 0.909632i) q^{84} +(-2.20340 - 1.41604i) q^{85} +(5.34012 - 1.56800i) q^{86} +(-2.87488 - 3.31779i) q^{87} +(-5.85917 - 1.72041i) q^{88} +(0.210281 + 0.460451i) q^{89} +(0.0559475 - 0.389124i) q^{90} +2.41295 q^{91} +(-4.64221 + 1.20411i) q^{92} +4.40248 q^{93} +(0.878867 - 6.11265i) q^{94} +(0.0867565 + 0.189970i) q^{95} +(-0.959493 - 0.281733i) q^{96} +(4.23061 + 4.88239i) q^{97} +(0.959493 - 0.281733i) q^{98} +(-5.13714 - 3.30144i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 10 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} - 3 q^{9}+O(q^{10}) \) 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 10 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 - 3 * q^9	\( 30 q + 3 q^{2} + 3 q^{3} - 3 q^{4} + 10 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} - 3 q^{9} + 12 q^{10} + 9 q^{11} + 3 q^{12} - 12 q^{13} + 3 q^{14} + q^{15} - 3 q^{16} + 13 q^{17} + 3 q^{18} - 18 q^{19} - q^{20} + 3 q^{21} + 24 q^{22} + 21 q^{23} + 30 q^{24} - 3 q^{25} + 34 q^{26} + 3 q^{27} - 3 q^{28} - 11 q^{29} - 12 q^{30} + 7 q^{31} + 3 q^{32} + 2 q^{33} - 13 q^{34} - q^{35} - 3 q^{36} + 3 q^{37} - 15 q^{38} + 12 q^{39} + q^{40} + 15 q^{41} - 3 q^{42} + 42 q^{43} + 9 q^{44} + 10 q^{45} + q^{46} + 12 q^{47} + 3 q^{48} - 3 q^{49} - 30 q^{50} + 9 q^{51} - q^{52} - 28 q^{53} - 3 q^{54} + 4 q^{55} + 3 q^{56} - 4 q^{57} - 11 q^{58} + 3 q^{59} - 10 q^{60} - 2 q^{61} + 26 q^{62} - 3 q^{63} - 3 q^{64} - 70 q^{65} - 2 q^{66} + 24 q^{67} + 2 q^{68} + q^{69} - 10 q^{70} - 3 q^{71} + 3 q^{72} - 7 q^{73} - 3 q^{74} - 30 q^{75} - 18 q^{76} - 2 q^{77} + 10 q^{78} - 32 q^{79} - q^{80} - 3 q^{81} - 26 q^{82} + 8 q^{83} + 3 q^{84} - 39 q^{85} + 35 q^{86} - 11 q^{87} + 13 q^{88} + 50 q^{89} + q^{90} + 32 q^{91} - 12 q^{92} + 4 q^{93} + 10 q^{94} + 73 q^{95} - 3 q^{96} + 24 q^{97} + 3 q^{98} - 2 q^{99}+O(q^{100}) \) 30 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 + 10 * q^5 - 3 * q^6 - 3 * q^7 + 3 * q^8 - 3 * q^9 + 12 * q^10 + 9 * q^11 + 3 * q^12 - 12 * q^13 + 3 * q^14 + q^15 - 3 * q^16 + 13 * q^17 + 3 * q^18 - 18 * q^19 - q^20 + 3 * q^21 + 24 * q^22 + 21 * q^23 + 30 * q^24 - 3 * q^25 + 34 * q^26 + 3 * q^27 - 3 * q^28 - 11 * q^29 - 12 * q^30 + 7 * q^31 + 3 * q^32 + 2 * q^33 - 13 * q^34 - q^35 - 3 * q^36 + 3 * q^37 - 15 * q^38 + 12 * q^39 + q^40 + 15 * q^41 - 3 * q^42 + 42 * q^43 + 9 * q^44 + 10 * q^45 + q^46 + 12 * q^47 + 3 * q^48 - 3 * q^49 - 30 * q^50 + 9 * q^51 - q^52 - 28 * q^53 - 3 * q^54 + 4 * q^55 + 3 * q^56 - 4 * q^57 - 11 * q^58 + 3 * q^59 - 10 * q^60 - 2 * q^61 + 26 * q^62 - 3 * q^63 - 3 * q^64 - 70 * q^65 - 2 * q^66 + 24 * q^67 + 2 * q^68 + q^69 - 10 * q^70 - 3 * q^71 + 3 * q^72 - 7 * q^73 - 3 * q^74 - 30 * q^75 - 18 * q^76 - 2 * q^77 + 10 * q^78 - 32 * q^79 - q^80 - 3 * q^81 - 26 * q^82 + 8 * q^83 + 3 * q^84 - 39 * q^85 + 35 * q^86 - 11 * q^87 + 13 * q^88 + 50 * q^89 + q^90 + 32 * q^91 - 12 * q^92 + 4 * q^93 + 10 * q^94 + 73 * q^95 - 3 * q^96 + 24 * q^97 + 3 * q^98 - 2 * q^99

Introduction

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