LMFDB - Embedded newform 588.2.ba.b.187.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [588,2,Mod(103,588)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(588, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 0, 29]))

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

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

chi := DirichletCharacter("588.103");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 588 = 2^{2} \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	588.ba (of order $42$, degree $12$, 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:	$4.69520363885$
Analytic rank:	$0$
Dimension:	$336$
Relative dimension:	$28$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			187.4
Character	$\chi$	$=$	588.187
Dual form			588.2.ba.b.283.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.30318 + 0.549285i) q^{2} +(-0.988831 - 0.149042i) q^{3} +(1.39657 - 1.43164i) q^{4} +(-2.67539 + 1.05002i) q^{5} +(1.37049 - 0.348920i) q^{6} +(-0.927902 - 2.47770i) q^{7} +(-1.03361 + 2.63280i) q^{8} +(0.955573 + 0.294755i) q^{9} +O(q^{10})$	\(q+(-1.30318 + 0.549285i) q^{2} +(-0.988831 - 0.149042i) q^{3} +(1.39657 - 1.43164i) q^{4} +(-2.67539 + 1.05002i) q^{5} +(1.37049 - 0.348920i) q^{6} +(-0.927902 - 2.47770i) q^{7} +(-1.03361 + 2.63280i) q^{8} +(0.955573 + 0.294755i) q^{9} +(2.90977 - 2.83792i) q^{10} +(-1.21319 - 3.93306i) q^{11} +(-1.59435 + 1.20750i) q^{12} +(4.15433 + 0.948198i) q^{13} +(2.57019 + 2.71921i) q^{14} +(2.80201 - 0.639540i) q^{15} +(-0.0991714 - 3.99877i) q^{16} +(-1.41274 + 2.07211i) q^{17} +(-1.40719 + 0.140762i) q^{18} +(-1.77717 + 3.07815i) q^{19} +(-2.23314 + 5.29662i) q^{20} +(0.548256 + 2.58832i) q^{21} +(3.74138 + 4.45911i) q^{22} +(-0.0806465 - 0.118287i) q^{23} +(1.41447 - 2.44934i) q^{24} +(2.38995 - 2.21755i) q^{25} +(-5.93468 + 1.04623i) q^{26} +(-0.900969 - 0.433884i) q^{27} +(-4.84305 - 2.13187i) q^{28} +(-1.88067 + 0.905681i) q^{29} +(-3.30024 + 2.37254i) q^{30} +(2.09249 + 3.62430i) q^{31} +(2.32570 + 5.15666i) q^{32} +(0.613446 + 4.06995i) q^{33} +(0.702881 - 3.47633i) q^{34} +(5.08413 + 5.65451i) q^{35} +(1.75651 - 0.956387i) q^{36} +(-0.213032 + 2.84272i) q^{37} +(0.625198 - 4.98757i) q^{38} +(-3.96660 - 1.55678i) q^{39} +(0.000840595 - 8.12909i) q^{40} +(5.74932 + 4.58493i) q^{41} +(-2.13620 - 3.07191i) q^{42} +(0.530190 - 0.422812i) q^{43} +(-7.32502 - 3.75596i) q^{44} +(-2.86603 + 0.214779i) q^{45} +(0.170070 + 0.109851i) q^{46} +(4.03381 + 3.74283i) q^{47} +(-0.497922 + 3.96889i) q^{48} +(-5.27800 + 4.59813i) q^{49} +(-1.89647 + 4.20263i) q^{50} +(1.70579 - 1.83841i) q^{51} +(7.15929 - 4.62326i) q^{52} +(0.987714 + 13.1801i) q^{53} +(1.41245 + 0.0705414i) q^{54} +(7.37553 + 9.24862i) q^{55} +(7.48238 + 0.118000i) q^{56} +(2.21610 - 2.77890i) q^{57} +(1.95338 - 2.21329i) q^{58} +(-0.259487 + 0.661162i) q^{59} +(2.99762 - 4.90463i) q^{60} +(-8.24273 - 0.617707i) q^{61} +(-4.71767 - 3.57376i) q^{62} +(-0.156363 - 2.64113i) q^{63} +(-5.86329 - 5.44259i) q^{64} +(-12.1101 + 1.82530i) q^{65} +(-3.03499 - 4.96693i) q^{66} +(-13.2691 + 7.66092i) q^{67} +(0.993515 + 4.91638i) q^{68} +(0.0621160 + 0.128985i) q^{69} +(-9.73149 - 4.57623i) q^{70} +(6.00357 - 12.4665i) q^{71} +(-1.76372 + 2.21117i) q^{72} +(8.63806 + 9.30962i) q^{73} +(-1.28384 - 3.82160i) q^{74} +(-2.69376 + 1.83657i) q^{75} +(1.92485 + 6.84313i) q^{76} +(-8.61922 + 6.65541i) q^{77} +(6.02433 - 0.150030i) q^{78} +(0.803099 + 0.463670i) q^{79} +(4.46409 + 10.5942i) q^{80} +(0.826239 + 0.563320i) q^{81} +(-10.0108 - 2.81699i) q^{82} +(3.42570 + 15.0090i) q^{83} +(4.47122 + 2.82988i) q^{84} +(1.60389 - 7.02711i) q^{85} +(-0.458690 + 0.842227i) q^{86} +(1.99465 - 0.615267i) q^{87} +(11.6089 + 0.871176i) q^{88} +(4.14664 - 13.4431i) q^{89} +(3.61699 - 1.85416i) q^{90} +(-1.50546 - 11.1730i) q^{91} +(-0.281972 - 0.0497394i) q^{92} +(-1.52895 - 3.89569i) q^{93} +(-7.31267 - 2.66188i) q^{94} +(1.52253 - 10.1013i) q^{95} +(-1.53117 - 5.44569i) q^{96} -1.93928i q^{97} +(4.35251 - 8.89132i) q^{98} -4.11592i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 336 q + 28 q^{3} - 2 q^{7} - 6 q^{8} + 28 q^{9}+O(q^{10}) $ 336 * q + 28 * q^3 - 2 * q^7 - 6 * q^8 + 28 * q^9	$ 336 q + 28 q^{3} - 2 q^{7} - 6 q^{8} + 28 q^{9} - 23 q^{10} - 6 q^{11} - 30 q^{14} - 12 q^{16} + 6 q^{19} + 25 q^{20} + 4 q^{21} + 6 q^{22} + 15 q^{24} - 26 q^{25} - 12 q^{26} - 56 q^{27} + 36 q^{28} - 13 q^{30} - 2 q^{31} - 25 q^{32} + 6 q^{33} + 68 q^{34} + 12 q^{35} + 16 q^{37} + 82 q^{38} - 8 q^{39} - 19 q^{40} - 9 q^{42} - 11 q^{44} + 10 q^{46} - 4 q^{47} - 8 q^{48} - 4 q^{49} - 114 q^{50} - 8 q^{52} - 4 q^{53} - 41 q^{56} - 12 q^{57} - 33 q^{58} + 10 q^{59} + 17 q^{60} + 2 q^{61} + 16 q^{62} + 12 q^{63} + 84 q^{64} - 4 q^{65} + 15 q^{66} - 42 q^{67} + 10 q^{68} - 38 q^{70} - 28 q^{71} + 33 q^{72} + 18 q^{73} + 2 q^{74} - 54 q^{75} - 7 q^{76} - 8 q^{77} - 6 q^{78} + 6 q^{79} - 14 q^{80} + 28 q^{81} - 87 q^{82} - 10 q^{83} - 14 q^{84} + 24 q^{85} + 126 q^{86} - 244 q^{88} - 20 q^{90} + 34 q^{91} + 14 q^{92} - 2 q^{93} - 184 q^{94} + 24 q^{95} - 20 q^{96} - 122 q^{98}+O(q^{100}) $ 336 * q + 28 * q^3 - 2 * q^7 - 6 * q^8 + 28 * q^9 - 23 * q^10 - 6 * q^11 - 30 * q^14 - 12 * q^16 + 6 * q^19 + 25 * q^20 + 4 * q^21 + 6 * q^22 + 15 * q^24 - 26 * q^25 - 12 * q^26 - 56 * q^27 + 36 * q^28 - 13 * q^30 - 2 * q^31 - 25 * q^32 + 6 * q^33 + 68 * q^34 + 12 * q^35 + 16 * q^37 + 82 * q^38 - 8 * q^39 - 19 * q^40 - 9 * q^42 - 11 * q^44 + 10 * q^46 - 4 * q^47 - 8 * q^48 - 4 * q^49 - 114 * q^50 - 8 * q^52 - 4 * q^53 - 41 * q^56 - 12 * q^57 - 33 * q^58 + 10 * q^59 + 17 * q^60 + 2 * q^61 + 16 * q^62 + 12 * q^63 + 84 * q^64 - 4 * q^65 + 15 * q^66 - 42 * q^67 + 10 * q^68 - 38 * q^70 - 28 * q^71 + 33 * q^72 + 18 * q^73 + 2 * q^74 - 54 * q^75 - 7 * q^76 - 8 * q^77 - 6 * q^78 + 6 * q^79 - 14 * q^80 + 28 * q^81 - 87 * q^82 - 10 * q^83 - 14 * q^84 + 24 * q^85 + 126 * q^86 - 244 * q^88 - 20 * q^90 + 34 * q^91 + 14 * q^92 - 2 * q^93 - 184 * q^94 + 24 * q^95 - 20 * q^96 - 122 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/588\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$493$
$\chi(n)$	$1$	$-1$	$e\left(\frac{23}{42}\right)$

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 $

$2$	−1.30318	+	0.549285i	−0.921490	+	0.388403i
$2$	−1.30318	+	0.549285i	−0.921490	+	0.388403i
$3$	−0.988831	−	0.149042i	−0.570902	−	0.0860496i
$3$	−0.988831	−	0.149042i	−0.570902	−	0.0860496i
$4$	1.39657	−	1.43164i	0.698286	−	0.715819i
$5$	−2.67539	+	1.05002i	−1.19647	+	0.469581i	−0.878143	−	0.478399i	$-0.841217\pi$
$5$	−2.67539	+	1.05002i	−1.19647	+	0.469581i	−0.318330	+	0.947980i	$0.603122\pi$
$6$	1.37049	−	0.348920i	0.559502	−	0.142446i
$7$	−0.927902	−	2.47770i	−0.350714	−	0.936483i
$7$	−0.927902	−	2.47770i	−0.350714	−	0.936483i
$8$	−1.03361	+	2.63280i	−0.365437	+	0.930836i
$9$	0.955573	+	0.294755i	0.318524	+	0.0982517i
$10$	2.90977	−	2.83792i	0.920151	−	0.897428i
$11$	−1.21319	−	3.93306i	−0.365790	−	1.18586i	−0.932263	−	0.361782i	$-0.882169\pi$
$11$	−1.21319	−	3.93306i	−0.365790	−	1.18586i	0.566473	−	0.824080i	$-0.308308\pi$
$12$	−1.59435	+	1.20750i	−0.460249	+	0.348575i
$13$	4.15433	+	0.948198i	1.15220	+	0.262983i	0.755616	−	0.655015i	$-0.227338\pi$
$13$	4.15433	+	0.948198i	1.15220	+	0.262983i	0.396587	+	0.917997i	$0.370195\pi$
$14$	2.57019	+	2.71921i	0.686912	+	0.726741i
$15$	2.80201	−	0.639540i	0.723476	−	0.165129i
$16$	−0.0991714	−	3.99877i	−0.0247929	−	0.999693i
$17$	−1.41274	+	2.07211i	−0.342640	+	0.502560i	−0.958421	−	0.285357i	$-0.907888\pi$
$17$	−1.41274	+	2.07211i	−0.342640	+	0.502560i	0.615782	+	0.787917i	$0.288840\pi$
$18$	−1.40719	+	0.140762i	−0.331678	+	0.0331778i
$19$	−1.77717	+	3.07815i	−0.407711	+	0.706176i	−0.994633	−	0.103467i	$-0.967006\pi$
$19$	−1.77717	+	3.07815i	−0.407711	+	0.706176i	0.586922	+	0.809644i	$0.300340\pi$
$20$	−2.23314	+	5.29662i	−0.499346	+	1.18436i
$21$	0.548256	+	2.58832i	0.119639	+	0.564818i
$22$	3.74138	+	4.45911i	0.797664	+	0.950686i
$23$	−0.0806465	−	0.118287i	−0.0168160	−	0.0246645i	0.817739	−	0.575590i	$-0.195227\pi$
$23$	−0.0806465	−	0.118287i	−0.0168160	−	0.0246645i	−0.834555	+	0.550925i	$0.814275\pi$
$24$	1.41447	−	2.44934i	0.288727	−	0.499970i
$25$	2.38995	−	2.21755i	0.477989	−	0.443509i
$26$	−5.93468	+	1.04623i	−1.16389	+	0.205183i
$27$	−0.900969	−	0.433884i	−0.173392	−	0.0835010i
$28$	−4.84305	−	2.13187i	−0.915251	−	0.402885i
$29$	−1.88067	+	0.905681i	−0.349231	+	0.168181i	−0.600273	−	0.799796i	$-0.704941\pi$
$29$	−1.88067	+	0.905681i	−0.349231	+	0.168181i	0.251042	+	0.967976i	$0.419227\pi$
$30$	−3.30024	+	2.37254i	−0.602539	+	0.433164i
$31$	2.09249	+	3.62430i	0.375823	+	0.650944i	0.990450	−	0.137874i	$-0.0440268\pi$
$31$	2.09249	+	3.62430i	0.375823	+	0.650944i	−0.614627	+	0.788818i	$0.710694\pi$
$32$	2.32570	+	5.15666i	0.411130	+	0.911577i
$33$	0.613446	+	4.06995i	0.106787	+	0.708487i
$34$	0.702881	−	3.47633i	0.120543	−	0.596186i
$35$	5.08413	+	5.65451i	0.859374	+	0.955787i
$36$	1.75651	−	0.956387i	0.292752	−	0.159398i
$37$	−0.213032	+	2.84272i	−0.0350223	+	0.467340i	0.951929	+	0.306319i	$0.0990975\pi$
$37$	−0.213032	+	2.84272i	−0.0350223	+	0.467340i	−0.986951	+	0.161020i	$0.948522\pi$
$38$	0.625198	−	4.98757i	0.101420	−	0.809090i
$39$	−3.96660	−	1.55678i	−0.635165	−	0.249284i
$40$	0.000840595	−	8.12909i	0.000132910	−	1.28532i
$41$	5.74932	+	4.58493i	0.897893	+	0.716045i	0.959396	−	0.282061i	$-0.0910182\pi$
$41$	5.74932	+	4.58493i	0.897893	+	0.716045i	−0.0615037	+	0.998107i	$0.519590\pi$
$42$	−2.13620	−	3.07191i	−0.329624	−	0.474006i
$43$	0.530190	−	0.422812i	0.0808532	−	0.0644783i	−0.582229	−	0.813025i	$-0.697819\pi$
$43$	0.530190	−	0.422812i	0.0808532	−	0.0644783i	0.663082	+	0.748546i	$0.269248\pi$
$44$	−7.32502	−	3.75596i	−1.10429	−	0.566232i
$45$	−2.86603	+	0.214779i	−0.427243	+	0.0320174i
$46$	0.170070	+	0.109851i	0.0250755	+	0.0161967i
$47$	4.03381	+	3.74283i	0.588392	+	0.545948i	0.917189	−	0.398453i	$-0.130453\pi$
$47$	4.03381	+	3.74283i	0.588392	+	0.545948i	−0.328797	+	0.944401i	$0.606643\pi$
$48$	−0.497922	+	3.96889i	−0.0718689	+	0.572860i
$49$	−5.27800	+	4.59813i	−0.753999	+	0.656875i
$50$	−1.89647	+	4.20263i	−0.268202	+	0.594342i
$51$	1.70579	−	1.83841i	0.238859	−	0.257429i
$52$	7.15929	−	4.62326i	0.992815	−	0.641131i
$53$	0.987714	+	13.1801i	0.135673	+	1.81043i	0.486168	+	0.873865i	$0.338394\pi$
$53$	0.987714	+	13.1801i	0.135673	+	1.81043i	−0.350495	+	0.936564i	$0.613987\pi$
$54$	1.41245	+	0.0705414i	0.192211	+	0.00959947i
$55$	7.37553	+	9.24862i	0.994516	+	1.24708i
$56$	7.48238	+	0.118000i	0.999876	+	0.0157685i
$57$	2.21610	−	2.77890i	0.293529	−	0.368074i
$58$	1.95338	−	2.21329i	0.256491	−	0.290619i
$59$	−0.259487	+	0.661162i	−0.0337823	+	0.0860759i	−0.946769	−	0.321912i	$-0.895674\pi$
$59$	−0.259487	+	0.661162i	−0.0337823	+	0.0860759i	0.912987	+	0.407988i	$0.133770\pi$
$60$	2.99762	−	4.90463i	0.386991	−	0.633184i
$61$	−8.24273	−	0.617707i	−1.05537	−	0.0790893i	−0.464277	−	0.885690i	$-0.653686\pi$
$61$	−8.24273	−	0.617707i	−1.05537	−	0.0790893i	−0.591096	+	0.806601i	$0.701305\pi$
$62$	−4.71767	−	3.57376i	−0.599145	−	0.453867i
$63$	−0.156363	−	2.64113i	−0.0196999	−	0.332751i
$64$	−5.86329	−	5.44259i	−0.732911	−	0.680324i
$65$	−12.1101	+	1.82530i	−1.50207	+	0.226401i
$66$	−3.03499	−	4.96693i	−0.373582	−	0.611387i
$67$	−13.2691	+	7.66092i	−1.62108	+	0.935930i	−0.634446	+	0.772967i	$0.718772\pi$
$67$	−13.2691	+	7.66092i	−1.62108	+	0.935930i	−0.986632	+	0.162963i	$0.947895\pi$
$68$	0.993515	+	4.91638i	0.120481	+	0.596199i
$69$	0.0621160	+	0.128985i	0.00747789	+	0.0155280i
$70$	−9.73149	−	4.57623i	−1.16314	−	0.546965i
$71$	6.00357	−	12.4665i	0.712493	−	1.47951i	−0.158059	−	0.987430i	$-0.550524\pi$
$71$	6.00357	−	12.4665i	0.712493	−	1.47951i	0.870552	−	0.492077i	$-0.163762\pi$
$72$	−1.76372	+	2.21117i	−0.207857	+	0.260589i
$73$	8.63806	+	9.30962i	1.01101	+	1.08961i	0.995967	+	0.0897213i	$0.0285976\pi$
$73$	8.63806	+	9.30962i	1.01101	+	1.08961i	0.0150417	+	0.999887i	$0.495212\pi$
$74$	−1.28384	−	3.82160i	−0.149243	−	0.444251i
$75$	−2.69376	+	1.83657i	−0.311049	+	0.212069i
$76$	1.92485	+	6.84313i	0.220795	+	0.784960i
$77$	−8.61922	+	6.65541i	−0.982251	+	0.758454i
$78$	6.02433	−	0.150030i	0.682121	−	0.0169875i
$79$	0.803099	+	0.463670i	0.0903557	+	0.0521669i	0.544497	−	0.838763i	$-0.316721\pi$
$79$	0.803099	+	0.463670i	0.0903557	+	0.0521669i	−0.454141	+	0.890930i	$0.650054\pi$
$80$	4.46409	+	10.5942i	0.499101	+	1.18446i
$81$	0.826239	+	0.563320i	0.0918043	+	0.0625911i
$82$	−10.0108	−	2.81699i	−1.10551	−	0.311084i
$83$	3.42570	+	15.0090i	0.376020	+	1.64745i	0.709509	+	0.704697i	$0.248917\pi$
$83$	3.42570	+	15.0090i	0.376020	+	1.64745i	−0.333489	+	0.942754i	$0.608226\pi$
$84$	4.47122	+	2.82988i	0.487850	+	0.308765i
$85$	1.60389	−	7.02711i	0.173966	−	0.762197i
$86$	−0.458690	+	0.842227i	−0.0494618	+	0.0908197i
$87$	1.99465	−	0.615267i	0.213848	−	0.0659635i
$88$	11.6089	+	0.871176i	1.23752	+	0.0928677i
$89$	4.14664	−	13.4431i	0.439543	−	1.42496i	−0.417008	−	0.908903i	$-0.636921\pi$
$89$	4.14664	−	13.4431i	0.439543	−	1.42496i	0.856551	−	0.516062i	$-0.172603\pi$
$90$	3.61699	−	1.85416i	0.381264	−	0.195446i
$91$	−1.50546	−	11.1730i	−0.157815	−	1.17125i
$92$	−0.281972	−	0.0497394i	−0.0293977	−	0.00518569i
$93$	−1.52895	−	3.89569i	−0.158544	−	0.403964i
$94$	−7.31267	−	2.66188i	−0.754244	−	0.274552i
$95$	1.52253	−	10.1013i	0.156208	−	1.03637i
$96$	−1.53117	−	5.44569i	−0.156274	−	0.555798i
$97$		−	1.93928i		−	0.196904i	−0.995142	−	0.0984521i	$-0.968611\pi$
$97$		−	1.93928i		−	0.196904i	0.995142	−	0.0984521i	$-0.0313891\pi$
$98$	4.35251	−	8.89132i	0.439670	−	0.898159i
$99$		−	4.11592i		−	0.413665i
$100$	0.163011	−	6.51850i	0.0163011	−	0.651850i
$101$	0.392703	−	2.60541i	0.0390754	−	0.259248i	−0.960760	−	0.277380i	$-0.910534\pi$
$101$	0.392703	−	2.60541i	0.0390754	−	0.259248i	0.999836	+	0.0181320i	$0.00577192\pi$
$102$	−1.21315	+	3.33275i	−0.120120	+	0.329991i
$103$	4.20845	+	10.7230i	0.414671	+	1.05656i	0.973784	+	0.227473i	$0.0730463\pi$
$103$	4.20845	+	10.7230i	0.414671	+	1.05656i	−0.559114	+	0.829091i	$0.688858\pi$
$104$	−6.79038	+	9.95745i	−0.665852	+	0.976408i
$105$	−4.18458	−	6.34911i	−0.408373	−	0.619610i
$106$	−8.52682	−	16.6336i	−0.828198	−	1.61560i
$107$	−2.68408	+	8.70158i	−0.259480	+	0.841214i	0.728286	+	0.685273i	$0.240317\pi$
$107$	−2.68408	+	8.70158i	−0.259480	+	0.841214i	−0.987766	+	0.155941i	$0.950159\pi$
$108$	−1.87943	+	0.683911i	−0.180848	+	0.0658093i
$109$	17.3397	−	5.34858i	1.66084	−	0.512301i	0.684585	−	0.728933i	$-0.259983\pi$
$109$	17.3397	−	5.34858i	1.66084	−	0.512301i	0.976253	+	0.216632i	$0.0695073\pi$
$110$	−14.6918	−	8.00138i	−1.40081	−	0.762902i
$111$	0.634338	−	2.77921i	0.0602087	−	0.263791i
$112$	−9.81573	+	3.95618i	−0.927500	+	0.373824i
$113$	−0.609792	−	2.67167i	−0.0573644	−	0.251330i	0.938113	−	0.346330i	$-0.112572\pi$
$113$	−0.609792	−	2.67167i	−0.0573644	−	0.251330i	−0.995477	+	0.0949997i	$0.969715\pi$
$114$	−1.36157	+	4.83868i	−0.127523	+	0.453184i
$115$	0.339964	+	0.231784i	0.0317018	+	0.0216139i
$116$	−1.32988	+	3.95728i	−0.123476	+	0.367424i
$117$	3.69028	+	2.13058i	0.341166	+	0.196972i
$118$	−0.0250072	−	1.00415i	−0.00230210	−	0.0924392i
$119$	6.44495	+	1.57763i	0.590808	+	0.144621i
$120$	−1.21241	+	8.03817i	−0.110677	+	0.733781i
$121$	−4.90850	+	3.34656i	−0.446228	+	0.304233i
$122$	11.0811	−	3.72262i	1.00323	−	0.337030i
$123$	−5.00175	−	5.39061i	−0.450993	−	0.486055i
$124$	8.11100	+	2.06591i	0.728390	+	0.185524i
$125$	2.16947	−	4.50494i	0.194043	−	0.402934i
$126$	1.65450	+	3.35598i	0.147395	+	0.298975i
$127$	−5.93348	−	12.3210i	−0.526512	−	1.09331i	−0.979434	−	0.201763i	$-0.935333\pi$
$127$	−5.93348	−	12.3210i	−0.526512	−	1.09331i	0.452923	−	0.891550i	$-0.350381\pi$
$128$	10.6305	+	3.87208i	0.939610	+	0.342247i
$129$	−0.587285	+	0.339069i	−0.0517076	+	0.0298534i
$130$	14.7790	−	9.03059i	1.29621	−	0.792035i
$131$	−1.97708	+	0.297996i	−0.172738	+	0.0260361i	−0.234842	−	0.972034i	$-0.575457\pi$
$131$	−1.97708	+	0.297996i	−0.172738	+	0.0260361i	0.0621036	+	0.998070i	$0.480219\pi$
$132$	6.68341	+	4.80574i	0.581716	+	0.418286i
$133$	9.27578	+	1.54708i	0.804312	+	0.134148i
$134$	13.0840	−	17.2721i	1.13029	−	1.49208i
$135$	2.86603	+	0.214779i	0.246669	+	0.0184853i
$136$	−3.99523	−	5.86122i	−0.342588	−	0.502596i
$137$	−1.39354	+	3.55068i	−0.119058	+	0.303355i	−0.977962	−	0.208781i	$-0.933050\pi$
$137$	−1.39354	+	3.55068i	−0.119058	+	0.303355i	0.858904	+	0.512136i	$0.171146\pi$
$138$	−0.151798	−	0.133972i	−0.0129219	−	0.0114045i
$139$	−10.6582	+	13.3649i	−0.904016	+	1.13360i	0.0865073	+	0.996251i	$0.472429\pi$
$139$	−10.6582	+	13.3649i	−0.904016	+	1.13360i	−0.990523	+	0.137348i	$0.956142\pi$
$140$	15.1956	+	0.618313i	1.28426	+	0.0522570i
$141$	−3.43092	−	4.30223i	−0.288935	−	0.362313i
$142$	−0.976069	+	19.5439i	−0.0819099	+	1.64008i
$143$	−1.31066	−	17.4896i	−0.109603	−	1.46255i
$144$	1.08389	−	3.85035i	0.0903244	−	0.320862i
$145$	4.08055	−	4.39778i	0.338871	−	0.365216i
$146$	−16.3706	−	7.38738i	−1.35484	−	0.611384i
$147$	5.90436	−	3.76012i	0.486983	−	0.310130i
$148$	3.77222	+	4.27504i	0.310075	+	0.351406i
$149$	−9.68614	−	8.98743i	−0.793520	−	0.736279i	0.175174	−	0.984537i	$-0.443951\pi$
$149$	−9.68614	−	8.98743i	−0.793520	−	0.736279i	−0.968694	+	0.248259i	$0.920142\pi$
$150$	2.50166	−	3.87303i	0.204260	−	0.316232i
$151$	23.6961	−	1.77577i	1.92836	−	0.144511i	0.945107	−	0.326762i	$-0.105957\pi$
$151$	23.6961	−	1.77577i	1.92836	−	0.144511i	0.983252	+	0.182251i	$0.0583384\pi$
$152$	−6.26725	−	7.86056i	−0.508341	−	0.637575i
$153$	−1.96074	+	1.56364i	−0.158517	+	0.126413i
$154$	7.57671	−	13.4076i	0.610549	−	1.08042i
$155$	−9.40381	−	7.49929i	−0.755333	−	0.602358i
$156$	−7.76839	+	3.50459i	−0.621969	+	0.280592i
$157$	12.6579	+	4.96787i	1.01021	+	0.396479i	0.811986	−	0.583677i	$-0.198387\pi$
$157$	12.6579	+	4.96787i	1.01021	+	0.396479i	0.198226	+	0.980156i	$0.436482\pi$
$158$	−1.30127	−	0.163116i	−0.103524	−	0.0129768i
$159$	0.987714	−	13.1801i	0.0783308	−	1.04525i
$160$	−11.6367	−	11.3541i	−0.919965	−	0.897618i
$161$	−0.218247	+	0.309576i	−0.0172003	+	0.0243980i
$162$	−1.38616	−	0.280269i	−0.108907	−	0.0220200i
$163$	−0.871221	−	5.78017i	−0.0682393	−	0.452738i	−0.996691	−	0.0812847i	$-0.974098\pi$
$163$	−0.871221	−	5.78017i	−0.0682393	−	0.452738i	0.928452	−	0.371453i	$-0.121140\pi$
$164$	14.5933	−	1.82776i	1.13954	−	0.142724i
$165$	−5.91471	−	10.2446i	−0.460460	−	0.797540i
$166$	−12.7085	−	17.6778i	−0.986373	−	1.37206i
$167$	11.3638	−	5.47252i	0.879358	−	0.423476i	0.0609680	−	0.998140i	$-0.480581\pi$
$167$	11.3638	−	5.47252i	0.879358	−	0.423476i	0.818390	+	0.574663i	$0.194867\pi$
$168$	−7.38123	−	1.23187i	−0.569474	−	0.0950411i
$169$	4.64675	+	2.23776i	0.357443	+	0.172135i
$170$	1.76972	+	10.0386i	0.135731	+	0.769926i
$171$	−2.60552	+	2.41757i	−0.199249	+	0.184876i
$172$	0.135135	−	1.34953i	0.0103039	−	0.102901i
$173$	−12.9438	−	18.9851i	−0.984099	−	1.44341i	−0.894310	−	0.447448i	$-0.852333\pi$
$173$	−12.9438	−	18.9851i	−0.984099	−	1.44341i	−0.0897890	−	0.995961i	$-0.528619\pi$
$174$	−2.26143	+	1.89743i	−0.171439	+	0.143844i
$175$	−7.71205	−	3.86390i	−0.582976	−	0.292084i
$176$	−15.6071	+	5.24131i	−1.17643	+	0.395078i
$177$	0.355130	−	0.615102i	0.0266932	−	0.0462339i
$178$	1.98025	+	19.7965i	0.148426	+	1.48381i
$179$	−11.2925	+	16.5630i	−0.844040	+	1.23798i	0.125266	+	0.992123i	$0.460021\pi$
$179$	−11.2925	+	16.5630i	−0.844040	+	1.23798i	−0.969306	+	0.245856i	$0.920931\pi$
$180$	−3.69513	+	4.40307i	−0.275419	+	0.328186i
$181$	−13.5612	+	3.09526i	−1.00800	+	0.230069i	−0.694479	−	0.719513i	$-0.744365\pi$
$181$	−13.5612	+	3.09526i	−1.00800	+	0.230069i	−0.313519	+	0.949582i	$0.601508\pi$
$182$	8.09905	+	13.7336i	0.600342	+	1.01800i
$183$	8.05860	+	1.83932i	0.595709	+	0.135967i
$184$	0.394783	−	0.0900636i	0.0291038	−	0.00663958i
$185$	−2.41495	−	7.82908i	−0.177551	−	0.575605i
$186$	4.13234	+	4.23697i	0.302998	+	0.310670i
$187$	9.86365	+	3.04253i	0.721301	+	0.222492i
$188$	10.9919	−	0.547822i	0.801665	−	0.0399540i
$189$	−0.239023	+	2.63493i	−0.0173864	+	0.191663i
$190$	3.56437	+	14.0002i	0.258587	+	1.01568i
$191$	−0.507490	+	0.199175i	−0.0367207	+	0.0144118i	−0.383630	−	0.923487i	$-0.625326\pi$
$191$	−0.507490	+	0.199175i	−0.0367207	+	0.0144118i	0.346910	+	0.937899i	$0.387231\pi$
$192$	4.98662	+	6.25568i	0.359879	+	0.451465i
$193$	−9.01835	−	1.35930i	−0.649155	−	0.0978444i	−0.183793	−	0.982965i	$-0.558838\pi$
$193$	−9.01835	−	1.35930i	−0.649155	−	0.0978444i	−0.465362	+	0.885121i	$0.654076\pi$
$194$	1.06522	+	2.52724i	0.0764782	+	0.181445i
$195$	12.2469			0.877017
$196$	−0.788254	+	13.9778i	−0.0563039	+	0.998414i
$197$	11.5293			0.821432			0.410716	−	0.911763i	$-0.365279\pi$
$197$	11.5293			0.821432			0.410716	+	0.911763i	$0.365279\pi$
$198$	2.26081	+	5.36379i	0.160669	+	0.381188i
$199$	1.12543	+	0.169632i	0.0797798	+	0.0120249i	0.188811	−	0.982013i	$-0.439537\pi$
$199$	1.12543	+	0.169632i	0.0797798	+	0.0120249i	−0.109031	+	0.994038i	$0.534775\pi$
$200$	3.36808	+	8.58434i	0.238159	+	0.607004i
$201$	14.2627	−	5.59770i	1.00601	−	0.394831i
$202$	0.919350	+	3.61104i	0.0646852	+	0.254072i
$203$	3.98908	+	3.81934i	0.279979	+	0.268065i
$204$	−0.249670	−	5.00955i	−0.0174804	−	0.350738i
$205$	−20.1959	−	6.22962i	−1.41055	−	0.435096i
$206$	−11.3743	−	11.6623i	−0.792487	−	0.812553i
$207$	−0.0421980	−	0.136803i	−0.00293296	−	0.00950843i
$208$	3.37964	−	16.7062i	0.234336	−	1.15837i
$209$	14.2626	+	3.25534i	0.986564	+	0.225177i
$210$	8.94074	+	5.97552i	0.616970	+	0.412350i
$211$	−11.6188	+	2.65192i	−0.799873	+	0.182566i	−0.602873	−	0.797838i	$-0.705977\pi$
$211$	−11.6188	+	2.65192i	−0.799873	+	0.182566i	−0.197001	+	0.980403i	$0.563120\pi$
$212$	20.2486	+	16.9930i	1.39068	+	1.16708i
$213$	−7.79456	+	11.4325i	−0.534074	+	0.783343i
$214$	−1.28180	−	12.8141i	−0.0876218	−	0.875953i
$215$	−0.974508	+	1.68790i	−0.0664609	+	0.115114i
$216$	2.07358	−	1.92360i	0.141089	−	0.130885i
$217$	7.03831	−	8.54757i	0.477791	−	0.580247i
$218$	−19.6589	+	16.4946i	−1.33147	+	1.11715i
$219$	−7.15406	−	10.4931i	−0.483426	−	0.709056i
$220$	23.5411	+	2.35728i	1.58714	+	0.158928i
$221$	−7.83375	+	7.26866i	−0.526955	+	0.488943i
$222$	0.699922	+	3.97026i	0.0469757	+	0.266466i
$223$	5.10130	+	2.45666i	0.341608	+	0.164510i	0.596820	−	0.802375i	$-0.296431\pi$
$223$	5.10130	+	2.45666i	0.341608	+	0.164510i	−0.255211	+	0.966885i	$0.582145\pi$
$224$	10.6186	−	10.5473i	0.709487	−	0.704719i
$225$	2.93740	−	1.41458i	0.195827	−	0.0943052i
$226$	2.26218	+	3.14673i	0.150478	+	0.209317i
$227$	0.863063	+	1.49487i	0.0572835	+	0.0992179i	0.893245	−	0.449570i	$-0.148423\pi$
$227$	0.863063	+	1.49487i	0.0572835	+	0.0992179i	−0.835962	+	0.548788i	$0.815089\pi$
$228$	−0.883434	−	7.05358i	−0.0585068	−	0.467135i
$229$	3.42237	+	22.7059i	0.226156	+	1.50045i	0.757244	+	0.653133i	$0.226546\pi$
$229$	3.42237	+	22.7059i	0.226156	+	1.50045i	−0.531087	+	0.847317i	$0.678216\pi$
$230$	−0.570351	−	0.115319i	−0.0376078	−	0.00760393i
$231$	9.51489	−	5.29645i	0.626034	−	0.348481i
$232$	−0.440598	−	5.88754i	−0.0289267	−	0.386536i
$233$	−1.71738	+	22.9168i	−0.112509	+	1.50133i	0.600187	+	0.799860i	$0.295093\pi$
$233$	−1.71738	+	22.9168i	−0.112509	+	1.50133i	−0.712697	+	0.701472i	$0.752526\pi$
$234$	−5.97940	−	0.749525i	−0.390886	−	0.0489980i
$235$	−14.7221	−	5.77798i	−0.960361	−	0.376914i
$236$	0.584152	+	1.29485i	0.0380250	+	0.0842876i
$237$	−0.725023	−	0.578187i	−0.0470953	−	0.0375573i
$238$	−9.26552	+	1.48417i	−0.600594	+	0.0962044i
$239$	−6.13325	+	4.89111i	−0.396727	+	0.316379i	−0.801452	−	0.598059i	$-0.795939\pi$
$239$	−6.13325	+	4.89111i	−0.396727	+	0.316379i	0.404725	+	0.914439i	$0.367367\pi$
$240$	−2.83525	−	11.1412i	−0.183015	−	0.719159i
$241$	−12.6967	+	0.951489i	−0.817869	+	0.0612908i	−0.477092	−	0.878853i	$-0.658309\pi$
$241$	−12.6967	+	0.951489i	−0.817869	+	0.0612908i	−0.340777	+	0.940144i	$0.610690\pi$
$242$	4.55846	−	7.05735i	0.293029	−	0.453664i
$243$	−0.733052	−	0.680173i	−0.0470253	−	0.0436331i
$244$	−12.3959	+	10.9379i	−0.793566	+	0.700229i
$245$	9.29262	−	17.8438i	0.593684	−	1.14000i
$246$	9.47918	+	4.27756i	0.604371	+	0.272727i
$247$	−10.3016	+	11.1025i	−0.655478	+	0.706437i
$248$	−11.7049	+	1.76299i	−0.743262	+	0.111950i
$249$	−1.15047	−	15.3519i	−0.0729079	−	0.972889i
$250$	−0.352715	+	7.06242i	−0.0223076	+	0.446666i
$251$	−1.60515	−	2.01279i	−0.101316	−	0.127046i	0.728589	−	0.684952i	$-0.240177\pi$
$251$	−1.60515	−	2.01279i	−0.101316	−	0.127046i	−0.829905	+	0.557905i	$0.811605\pi$
$252$	−3.99951	−	3.46467i	−0.251945	−	0.218254i
$253$	−0.367389	+	0.460692i	−0.0230976	+	0.0289634i
$254$	14.5002	+	12.7974i	0.909821	+	0.802978i
$255$	−2.63331	+	6.70957i	−0.164904	+	0.420170i
$256$	−15.9803	+	0.793128i	−0.998771	+	0.0495705i
$257$	−3.03096	−	0.227139i	−0.189066	−	0.0141686i	−0.0201396	−	0.999797i	$-0.506411\pi$
$257$	−3.03096	−	0.227139i	−0.189066	−	0.0141686i	−0.168927	+	0.985629i	$0.554030\pi$
$258$	0.579094	−	0.764456i	0.0360528	−	0.0475929i
$259$	7.24107	−	2.10993i	0.449938	−	0.131105i
$260$	−14.2994	+	19.8864i	−0.886814	+	1.23330i
$261$	−2.06407	+	0.311108i	−0.127763	+	0.0192571i
$262$	2.41281	−	1.47432i	0.149064	−	0.0910839i
$263$	−24.3576	+	14.0629i	−1.50196	+	0.867155i	−0.501959	+	0.864891i	$0.667387\pi$
$263$	−24.3576	+	14.0629i	−1.50196	+	0.867155i	−0.999997	+	0.00226372i	$0.999279\pi$
$264$	−11.3494	−	2.59167i	−0.698509	−	0.159506i
$265$	−16.4819	−	34.2249i	−1.01247	−	2.10242i
$266$	−12.9378	+	3.07892i	−0.793269	+	0.188781i
$267$	−6.10392	+	12.6749i	−0.373554	+	0.775692i
$268$	−7.56360	+	29.6956i	−0.462020	+	1.81395i
$269$	10.8483	+	11.6916i	0.661429	+	0.712851i	0.971281	−	0.237933i	$-0.0764700\pi$
$269$	10.8483	+	11.6916i	0.661429	+	0.712851i	−0.309852	+	0.950785i	$0.600280\pi$
$270$	−3.85294	+	1.29437i	−0.234482	+	0.0787729i
$271$	−25.5515	+	17.4207i	−1.55214	+	1.05823i	−0.582771	+	0.812636i	$0.698032\pi$
$271$	−25.5515	+	17.4207i	−1.55214	+	1.05823i	−0.969372	+	0.245597i	$0.921016\pi$
$272$	8.42599	+	5.44373i	0.510901	+	0.330075i
$273$	−0.176608	+	11.2726i	−0.0106888	+	0.682248i
$274$	−0.134298	−	5.39263i	−0.00811323	−	0.325781i
$275$	−11.6212	−	6.70950i	−0.700784	−	0.404598i
$276$	0.271410	+	0.0912096i	0.0163369	+	0.00549017i
$277$	7.78210	+	5.30575i	0.467581	+	0.318792i	0.774089	−	0.633077i	$-0.218208\pi$
$277$	7.78210	+	5.30575i	0.467581	+	0.318792i	−0.306508	+	0.951868i	$0.599161\pi$
$278$	6.54841	−	23.2713i	0.392747	−	1.39572i
$279$	0.931247	+	4.08006i	0.0557523	+	0.244267i
$280$	−20.1422	+	7.54092i	−1.20373	+	0.450656i
$281$	4.56950	−	20.0203i	0.272594	−	1.19431i	−0.634346	−	0.773050i	$-0.718730\pi$
$281$	4.56950	−	20.0203i	0.272594	−	1.19431i	0.906939	−	0.421261i	$-0.138413\pi$
$282$	6.83426	+	3.72205i	0.406974	+	0.221645i
$283$	−6.06198	+	1.86987i	−0.360347	+	0.111152i	−0.469642	−	0.882857i	$-0.655617\pi$
$283$	−6.06198	+	1.86987i	−0.360347	+	0.111152i	0.109295	+	0.994009i	$0.465141\pi$
$284$	−9.46315	−	26.0054i	−0.561535	−	1.54313i
$285$	−3.01105	+	9.76158i	−0.178359	+	0.578226i
$286$	11.3148	+	22.0722i	0.669057	+	1.30515i
$287$	6.02527	−	18.4994i	0.355661	−	1.09199i
$288$	0.702427	+	5.61307i	0.0413909	+	0.330754i
$289$	3.91300	+	9.97015i	0.230176	+	0.586479i
$290$	−2.90206	+	7.97250i	−0.170415	+	0.468161i
$291$	−0.289035	+	1.91762i	−0.0169435	+	0.112413i
$292$	25.3917	+	0.634980i	1.48594	+	0.0371594i
$293$			23.3709i			1.36534i	0.730726	+	0.682670i	$0.239181\pi$
$293$			23.3709i			1.36534i	−0.730726	+	0.682670i	$0.760819\pi$
$294$	−5.62908	+	8.14331i	−0.328295	+	0.474927i
$295$		−	2.04133i		−	0.118851i
$296$	−7.26412	−	3.49914i	−0.422218	−	0.203383i
$297$	−0.613446	+	4.06995i	−0.0355957	+	0.236162i
$298$	17.5595	+	6.39181i	1.01719	+	0.370268i
$299$	−0.222873	−	0.567870i	−0.0128891	−	0.0328408i
$300$	−1.13272	+	6.42140i	−0.0653977	+	0.370740i
$301$	−1.53957	−	0.921323i	−0.0887391	−	0.0531042i
$302$	−29.9049	+	15.3301i	−1.72083	+	0.882145i
$303$	−0.776633	+	2.51778i	−0.0446164	+	0.144643i
$304$	12.4851	+	6.80124i	0.716068	+	0.390078i
$305$	22.7012	−	7.00238i	1.29986	−	0.400955i
$306$	1.69632	−	3.11471i	0.0969722	−	0.178056i
$307$	−1.20464	+	5.27789i	−0.0687527	+	0.301225i	−0.997600	−	0.0692370i	$-0.977944\pi$
$307$	−1.20464	+	5.27789i	−0.0687527	+	0.301225i	0.928848	+	0.370462i	$0.120801\pi$
$308$	−2.50923	+	21.6344i	−0.142977	+	1.23273i
$309$	−2.56327	−	11.2304i	−0.145819	−	0.638876i
$310$	16.3741	+	4.60758i	0.929989	+	0.261693i
$311$	−19.7913	−	13.4935i	−1.12226	−	0.765145i	−0.147648	−	0.989040i	$-0.547170\pi$
$311$	−19.7913	−	13.4935i	−1.12226	−	0.765145i	−0.974613	+	0.223895i	$0.928123\pi$
$312$	8.19862	−	8.83418i	0.464155	−	0.500137i
$313$	3.09305	+	1.78578i	0.174830	+	0.100938i	0.584861	−	0.811133i	$-0.301149\pi$
$313$	3.09305	+	1.78578i	0.174830	+	0.100938i	−0.410031	+	0.912071i	$0.634482\pi$
$314$	−19.2244	+	0.478763i	−1.08489	+	0.0270181i
$315$	3.19156	+	6.90187i	0.179824	+	0.388876i
$316$	1.78539	−	0.502199i	0.100436	−	0.0282509i
$317$	17.7190	−	12.0806i	0.995197	−	0.678514i	0.0478937	−	0.998852i	$-0.484749\pi$
$317$	17.7190	−	12.0806i	0.995197	−	0.678514i	0.947303	+	0.320339i	$0.103797\pi$
$318$	5.95247	+	17.7187i	0.333798	+	0.993613i
$319$	5.84370	+	6.29801i	0.327184	+	0.352621i
$320$	21.4014	+	8.40455i	1.19638	+	0.469828i
$321$	3.95101	−	8.20435i	0.220524	−	0.457922i
$322$	0.114370	−	0.523314i	0.00637360	−	0.0291632i
$323$	−3.86758	−	8.03112i	−0.215198	−	0.446863i
$324$	1.96037	−	0.396157i	0.108910	−	0.0220087i
$325$	12.0313	−	6.94627i	0.667376	−	0.385310i
$326$	4.31032	+	7.05407i	0.238727	+	0.390689i
$327$	−17.9432	+	2.70450i	−0.992259	+	0.149559i
$328$	−18.0138	+	10.3978i	−0.994644	+	0.574121i
$329$	5.53063	−	13.4675i	0.304913	−	0.742490i
$330$	13.3352	+	10.1017i	0.734076	+	0.556081i
$331$	−12.4387	−	0.932155i	−0.683695	−	0.0512359i	−0.271646	−	0.962397i	$-0.587568\pi$
$331$	−12.4387	−	0.932155i	−0.683695	−	0.0512359i	−0.412050	+	0.911161i	$0.635187\pi$
$332$	26.2717	+	16.0568i	1.44185	+	0.881230i
$333$	−1.04147	+	2.65363i	−0.0570724	+	0.145418i
$334$	−11.8031	+	13.3737i	−0.645840	+	0.731774i
$335$	27.4560	−	34.4287i	1.50008	−	1.88104i
$336$	10.2957	−	2.44904i	0.561679	−	0.133606i
$337$	6.95615	+	8.72274i	0.378926	+	0.475158i	0.934323	−	0.356427i	$-0.116005\pi$
$337$	6.95615	+	8.72274i	0.378926	+	0.475158i	−0.555397	+	0.831585i	$0.687434\pi$
$338$	−7.28474	−	0.363818i	−0.396238	−	0.0197891i
$339$	0.204789	+	2.73272i	0.0111226	+	0.148421i
$340$	−7.82032	−	12.1101i	−0.424116	−	0.656760i
$341$	11.7160	−	12.6269i	0.634458	−	0.683783i
$342$	2.06753	−	4.58170i	0.111799	−	0.247750i
$343$	16.2902	+	8.81068i	0.879590	+	0.475732i
$344$	0.565170	+	1.83291i	0.0304719	+	0.0988238i
$345$	−0.301621	−	0.279864i	−0.0162388	−	0.0150674i
$346$	27.2964	+	17.6312i	1.46746	+	0.947859i
$347$	2.03847	−	0.152762i	0.109431	−	0.00820069i	−0.0199022	−	0.999802i	$-0.506335\pi$
$347$	2.03847	−	0.152762i	0.109431	−	0.00820069i	0.129333	+	0.991601i	$0.458716\pi$
$348$	1.90483	−	3.71487i	0.102109	−	0.199138i
$349$	13.1086	−	10.4538i	0.701687	−	0.559577i	−0.206344	−	0.978480i	$-0.566157\pi$
$349$	13.1086	−	10.4538i	0.701687	−	0.559577i	0.908031	+	0.418902i	$0.137585\pi$
$350$	12.1726	+	0.799263i	0.650653	+	0.0427224i
$351$	−3.33151	−	2.65679i	−0.177823	−	0.141809i
$352$	17.4599	−	15.4031i	0.930617	−	0.820989i
$353$	−18.3996	−	7.22129i	−0.979309	−	0.384351i	−0.178941	−	0.983860i	$-0.557267\pi$
$353$	−18.3996	−	7.22129i	−0.979309	−	0.384351i	−0.800368	+	0.599509i	$0.795362\pi$
$354$	−0.124932	+	0.996658i	−0.00664008	+	0.0529718i
$355$	−2.97186	+	39.6568i	−0.157730	+	2.10476i
$356$	−13.4545	−	24.7107i	−0.713089	−	1.30967i
$357$	−6.13783	−	2.52058i	−0.324848	−	0.133403i
$358$	5.61835	−	27.7875i	0.296939	−	1.46861i
$359$	1.68139	+	11.1553i	0.0887403	+	0.588754i	0.988366	+	0.152092i	$0.0486011\pi$
$359$	1.68139	+	11.1553i	0.0887403	+	0.588754i	−0.899626	+	0.436661i	$0.856161\pi$
$360$	2.39690	−	7.76769i	0.126327	−	0.409393i
$361$	3.18332	+	5.51368i	0.167543	+	0.290194i
$362$	15.9726	−	11.4827i	0.839500	−	0.603515i
$363$	5.35246	−	2.57761i	0.280931	−	0.135289i
$364$	−18.0982	−	13.4486i	−0.948602	−	0.704901i
$365$	−32.8855	−	15.8368i	−1.72130	−	0.828936i
$366$	−11.5121	+	2.02949i	−0.601749	+	0.106083i
$367$	−14.0298	+	13.0178i	−0.732351	+	0.679522i	−0.955410	−	0.295283i	$-0.904586\pi$
$367$	−14.0298	+	13.0178i	−0.732351	+	0.679522i	0.223059	+	0.974805i	$0.428396\pi$
$368$	−0.465004	+	0.334218i	−0.0242400	+	0.0174223i
$369$	4.14246	+	6.07587i	0.215648	+	0.316297i
$370$	7.44751	+	8.87622i	0.387178	+	0.461453i
$371$	31.7399	−	14.6771i	1.64785	−	0.761998i
$372$	−7.71250	−	3.25172i	−0.399875	−	0.168594i
$373$	17.0959	−	29.6109i	0.885190	−	1.53319i	0.0396947	−	0.999212i	$-0.487361\pi$
$373$	17.0959	−	29.6109i	0.885190	−	1.53319i	0.845495	−	0.533983i	$-0.179305\pi$
$374$	−14.5254	+	1.45298i	−0.751088	+	0.0751316i
$375$	−2.81666	+	4.13128i	−0.145452	+	0.213338i
$376$	−14.0235	+	6.75159i	−0.723208	+	0.348186i
$377$	−8.67167	+	1.97925i	−0.446614	+	0.101937i
$378$	−1.13584	−	3.56509i	−0.0584212	−	0.183368i
$379$	25.3759	+	5.79189i	1.30347	+	0.297509i	0.817229	−	0.576314i	$-0.195509\pi$
$379$	25.3759	+	5.79189i	1.30347	+	0.297509i	0.486244	+	0.873823i	$0.338367\pi$
$380$	−12.3351	−	16.2869i	−0.632778	−	0.835503i
$381$	4.03086	+	13.0677i	0.206507	+	0.669480i
$382$	0.551949	−	0.538319i	0.0282402	−	0.0275428i
$383$	−8.16656	−	2.51905i	−0.417292	−	0.128717i	0.0789973	−	0.996875i	$-0.474828\pi$
$383$	−8.16656	−	2.51905i	−0.417292	−	0.128717i	−0.496289	+	0.868157i	$0.665304\pi$
$384$	−9.93464	−	5.41322i	−0.506975	−	0.276242i
$385$	16.0715	−	26.8562i	0.819082	−	1.36872i
$386$	12.4992	−	3.18223i	0.636193	−	0.161971i
$387$	0.631261	−	0.247752i	0.0320888	−	0.0125939i
$388$	−2.77635	−	2.70835i	−0.140948	−	0.137495i
$389$	19.8996	+	2.99938i	1.00895	+	0.152074i	0.632661	−	0.774429i	$-0.281963\pi$
$389$	19.8996	+	2.99938i	1.00895	+	0.152074i	0.376287	+	0.926503i	$0.377201\pi$
$390$	−15.9599	+	6.72702i	−0.808162	+	0.340636i
$391$	0.359036			0.0181572
$392$	−6.65055	−	18.6486i	−0.335903	−	0.941896i
$393$	1.99941			0.100857
$394$	−15.0249	+	6.33290i	−0.756941	+	0.319047i
$395$	−2.63547	−	0.397233i	−0.132605	−	0.0199870i
$396$	−5.89250	−	5.74818i	−0.296109	−	0.288857i
$397$	−6.66837	+	2.61714i	−0.334676	+	0.131351i	−0.526728	−	0.850034i	$-0.676581\pi$
$397$	−6.66837	+	2.61714i	−0.334676	+	0.131351i	0.192052	+	0.981385i	$0.438486\pi$
$398$	−1.55982	+	0.397122i	−0.0781868	+	0.0199059i
$399$	−8.94159	−	2.91228i	−0.447640	−	0.145796i
$400$	−9.10447	−	9.33693i	−0.455224	−	0.466846i
$401$	11.7544	+	3.62574i	0.586985	+	0.181061i	0.574001	−	0.818855i	$-0.305391\pi$
$401$	11.7544	+	3.62574i	0.586985	+	0.181061i	0.0129846	+	0.999916i	$0.495867\pi$
$402$	−15.5122	+	15.1291i	−0.773677	+	0.754571i
$403$	5.25634	+	17.0406i	0.261837	+	0.848854i
$404$	−3.18157	−	4.20085i	−0.158289	−	0.209000i
$405$	−2.80201	−	0.639540i	−0.139233	−	0.0317790i
$406$	−7.29641	−	2.78616i	−0.362115	−	0.138275i
$407$	11.4390	−	2.61088i	0.567011	−	0.129417i
$408$	3.07703	+	6.39122i	0.152336	+	0.316412i
$409$	−16.5254	+	24.2383i	−0.817129	+	1.19851i	0.160264	+	0.987074i	$0.448766\pi$
$409$	−16.5254	+	24.2383i	−0.817129	+	1.19851i	−0.977392	+	0.211434i	$0.932187\pi$
$410$	29.7408	−	2.97498i	1.46880	−	0.146924i
$411$	1.90717	−	3.30332i	0.0940739	−	0.162941i
$412$	21.2288	+	8.95041i	1.04587	+	0.440955i
$413$	1.87894	+	0.0294373i	0.0924565	+	0.00144852i
$414$	0.130135	+	0.155100i	0.00639580	+	0.00762275i
$415$	−24.9248	−	36.5579i	−1.22351	−	1.79456i
$416$	4.77220	+	23.6277i	0.233976	+	1.15844i
$417$	12.5311	−	11.6271i	0.613650	−	0.569384i
$418$	−20.3749	+	3.59192i	−0.996568	+	0.175686i
$419$	−16.6493	−	8.01786i	−0.813370	−	0.391698i	−0.0195179	−	0.999810i	$-0.506213\pi$
$419$	−16.6493	−	8.01786i	−0.813370	−	0.391698i	−0.793852	+	0.608111i	$0.791927\pi$
$420$	−14.9337	−	2.87619i	−0.728689	−	0.140344i
$421$	−22.7977	+	10.9788i	−1.11109	+	0.535075i	−0.897130	−	0.441767i	$-0.854352\pi$
$421$	−22.7977	+	10.9788i	−1.11109	+	0.535075i	−0.213964	+	0.976842i	$0.568638\pi$
$422$	13.6848	−	9.83799i	0.666166	−	0.478906i
$423$	2.75138	+	4.76553i	0.133777	+	0.231708i
$424$	−35.7216	−	11.0227i	−1.73479	−	0.535309i
$425$	1.21862	+	8.08504i	0.0591120	+	0.392182i
$426$	3.87803	−	19.1801i	0.187891	−	0.929279i
$427$	6.11795	+	20.9962i	0.296068	+	1.01608i
$428$	8.70900	+	15.9950i	0.420965	+	0.773149i
$429$	−1.31066	+	17.4896i	−0.0632793	+	0.844404i
$430$	0.342826	−	2.73492i	0.0165325	−	0.131890i
$431$	−1.98869	−	0.780502i	−0.0957917	−	0.0375955i	0.316961	−	0.948438i	$-0.397337\pi$
$431$	−1.98869	−	0.780502i	−0.0957917	−	0.0375955i	−0.412753	+	0.910843i	$0.635433\pi$
$432$	−1.64565	+	3.64580i	−0.0791764	+	0.175408i
$433$	−16.7918	−	13.3910i	−0.806963	−	0.643531i	0.130566	−	0.991440i	$-0.458321\pi$
$433$	−16.7918	−	13.3910i	−0.806963	−	0.643531i	−0.937529	+	0.347908i	$0.886892\pi$
$434$	−4.47716	+	15.0051i	−0.214910	+	0.720267i
$435$	−4.69042	+	3.74049i	−0.224889	+	0.179343i
$436$	16.5589	−	32.2938i	0.793026	−	1.54659i
$437$	0.507427	−	0.0380264i	0.0242735	−	0.00181905i
$438$	15.0867	+	9.74478i	0.720872	+	0.465624i
$439$	7.72380	+	7.16664i	0.368637	+	0.342045i	0.842639	−	0.538478i	$-0.181001\pi$
$439$	7.72380	+	7.16664i	0.368637	+	0.342045i	−0.474002	+	0.880524i	$0.657191\pi$
$440$	−31.9732	+	9.85881i	−1.52426	+	0.470000i
$441$	−6.39883	+	2.83813i	−0.304706	+	0.135149i
$442$	6.21625	−	13.7754i	0.295677	−	0.655227i
$443$	8.17189	−	8.80721i	0.388258	−	0.418443i	−0.508431	−	0.861102i	$-0.669774\pi$
$443$	8.17189	−	8.80721i	0.388258	−	0.418443i	0.896690	+	0.442659i	$0.145965\pi$
$444$	−3.09293	−	4.78952i	−0.146784	−	0.227300i
$445$	3.02154	+	40.3196i	0.143235	+	1.91133i
$446$	−7.99733	−	0.399406i	−0.378685	−	0.0189124i
$447$	8.23845	+	10.3307i	0.389665	+	0.488625i
$448$	−8.04456	+	19.5777i	−0.380070	+	0.924958i
$449$	−10.9082	+	13.6784i	−0.514789	+	0.645524i	−0.969493	−	0.245118i	$-0.921173\pi$
$449$	−10.9082	+	13.6784i	−0.514789	+	0.645524i	0.454705	+	0.890642i	$0.349745\pi$
$450$	−3.05096	+	3.45692i	−0.143824	+	0.162961i
$451$	11.0578	−	28.1748i	0.520691	−	1.32670i
$452$	−4.67649	−	2.85818i	−0.219963	−	0.134438i
$453$	−23.6961	−	1.77577i	−1.11334	−	0.0834332i
$454$	−1.94584	−	1.47402i	−0.0913227	−	0.0691792i
$455$	15.7595	+	28.3115i	0.738818	+	1.32726i
$456$	5.02570	+	8.70685i	0.235350	+	0.407735i
$457$	−17.8452	+	2.68974i	−0.834766	+	0.125821i	−0.552497	−	0.833515i	$-0.686325\pi$
$457$	−17.8452	+	2.68974i	−0.834766	+	0.125821i	−0.282268	+	0.959335i	$0.591087\pi$
$458$	−16.9320	−	27.7101i	−0.791180	−	1.29481i
$459$	2.17189	−	1.25394i	0.101375	−	0.0585289i
$460$	0.806614	−	0.163003i	0.0376086	−	0.00760004i
$461$	3.36476	+	6.98699i	0.156712	+	0.325417i	0.964511	−	0.264041i	$-0.0850556\pi$
$461$	3.36476	+	6.98699i	0.156712	+	0.325417i	−0.807799	+	0.589458i	$0.799341\pi$
$462$	−9.49039	+	12.1286i	−0.441533	+	0.564275i
$463$	9.53941	−	19.8088i	0.443334	−	0.920592i	−0.552847	−	0.833283i	$-0.686459\pi$
$463$	9.53941	−	19.8088i	0.443334	−	0.920592i	0.996181	−	0.0873098i	$-0.0278270\pi$
$464$	3.80812	+	7.43054i	0.176788	+	0.344954i
$465$	8.18107	+	8.81710i	0.379388	+	0.408883i
$466$	−10.3498	−	30.8082i	−0.479446	−	1.42716i
$467$	−24.7068	+	16.8448i	−1.14329	+	0.779484i	−0.978378	−	0.206824i	$-0.933687\pi$
$467$	−24.7068	+	16.8448i	−1.14329	+	0.779484i	−0.164915	+	0.986308i	$0.552735\pi$
$468$	8.20396	−	2.30763i	0.379228	−	0.106670i
$469$	31.2939	+	25.7683i	1.44502	+	1.18987i
$470$	22.3593	−	0.556835i	1.03136	−	0.0256849i
$471$	−11.7761	−	6.79895i	−0.542615	−	0.313279i
$472$	−1.47250	−	1.36656i	−0.0677772	−	0.0629011i
$473$	−2.30617	−	1.57232i	−0.106038	−	0.0722952i
$474$	1.26243	+	0.355239i	0.0579852	+	0.0163167i
$475$	2.57860	+	11.2976i	0.118314	+	0.518368i
$476$	11.2594	−	7.02355i	0.516075	−	0.321924i
$477$	−2.94108	+	12.8857i	−0.134663	+	0.589996i
$478$	5.30614	−	9.74291i	0.242697	−	0.445630i
$479$	26.0234	−	8.02715i	1.18904	−	0.366770i	0.363759	−	0.931493i	$-0.381493\pi$
$479$	26.0234	−	8.02715i	1.18904	−	0.366770i	0.825280	+	0.564723i	$0.191017\pi$
$480$	9.81453	+	12.9616i	0.447970	+	0.591614i
$481$	−3.58046	+	11.6076i	−0.163255	+	0.529260i
$482$	16.0235	−	8.21409i	0.729852	−	0.374142i
$483$	0.261949	−	0.273591i	0.0119191	−	0.0124488i
$484$	−2.06402	+	11.7009i	−0.0938190	+	0.531860i
$485$	2.03627	+	5.18834i	0.0924625	+	0.235590i
$486$	1.32891	+	0.483735i	0.0602806	+	0.0219427i
$487$	2.78920	−	18.5051i	0.126391	−	0.838548i	−0.832347	−	0.554255i	$-0.813003\pi$
$487$	2.78920	−	18.5051i	0.126391	−	0.838548i	0.958738	−	0.284293i	$-0.0917588\pi$
$488$	10.1461	−	21.0630i	0.459292	−	0.953477i
$489$			5.84546i			0.264341i
$490$	−2.30867	+	28.3580i	−0.104295	+	1.28108i
$491$		−	27.2493i		−	1.22974i	−0.788627	−	0.614872i	$-0.789208\pi$
$491$		−	27.2493i		−	1.22974i	0.788627	−	0.614872i	$-0.210792\pi$
$492$	−14.7027	−	0.367677i	−0.662849	−	0.0165762i
$493$	0.780222	−	5.17644i	0.0351395	−	0.233135i
$494$	7.32648	−	20.1272i	0.329634	−	0.905564i
$495$	4.32178	+	11.0117i	0.194249	+	0.494939i
$496$	14.2852	−	8.72682i	0.641426	−	0.391846i
$497$	−36.4591	−	3.30732i	−1.63541	−	0.148354i
$498$	9.93185	+	19.3744i	0.445057	+	0.868189i
$499$	7.47292	−	24.2266i	0.334534	−	1.08453i	−0.619541	−	0.784964i	$-0.712681\pi$
$499$	7.47292	−	24.2266i	0.334534	−	1.08453i	0.954075	−	0.299568i	$-0.0968426\pi$
$500$	−3.41963	−	9.39736i	−0.152930	−	0.420263i
$501$	−12.0525	+	3.71771i	−0.538467	+	0.166095i
$502$	3.19740	+	1.74135i	0.142707	+	0.0777204i
$503$	−2.42338	+	10.6175i	−0.108053	+	0.473412i	0.891729	+	0.452569i	$0.149492\pi$
$503$	−2.42338	+	10.6175i	−0.108053	+	0.473412i	−0.999783	+	0.0208435i	$0.993365\pi$
$504$	7.11518	+	2.31823i	0.316935	+	0.103262i
$505$	1.68509	+	7.38285i	0.0749854	+	0.328533i
$506$	0.225725	−	0.802167i	0.0100347	−	0.0356607i
$507$	−4.26133	−	2.90533i	−0.189252	−	0.129030i
$508$	−25.9258	−	8.71258i	−1.15027	−	0.386558i
$509$	14.9562	+	8.63495i	0.662920	+	0.382737i	0.793389	−	0.608715i	$-0.208315\pi$
$509$	14.9562	+	8.63495i	0.662920	+	0.382737i	−0.130468	+	0.991452i	$0.541648\pi$
$510$	−0.253777	−	10.1902i	−0.0112374	−	0.451231i
$511$	15.0512	−	30.0409i	0.665824	−	1.32893i
$512$	20.3896	−	9.81134i	0.901103	−	0.433604i
$513$	2.93674	−	2.00223i	0.129660	−	0.0884007i
$514$	4.07466	−	1.36886i	0.179726	−	0.0603777i
$515$	−22.5185	−	24.2692i	−0.992285	−	1.06943i
$516$	−0.334762	+	1.31431i	−0.0147371	+	0.0578594i
$517$	9.82700	−	20.4060i	0.432191	−	0.897453i
$518$	−8.27749	+	6.72704i	−0.363692	+	0.295569i
$519$	9.96965	+	20.7022i	0.437619	+	0.908726i
$520$	7.71148	−	33.7701i	0.338171	−	1.48092i
$521$	−25.1685	+	14.5310i	−1.10265	+	0.636616i	−0.936916	−	0.349554i	$-0.886333\pi$
$521$	−25.1685	+	14.5310i	−1.10265	+	0.636616i	−0.165735	+	0.986170i	$0.553000\pi$
$522$	2.51897	−	1.53919i	0.110252	−	0.0673686i
$523$	−2.23559	+	0.336961i	−0.0977555	+	0.0147343i	−0.197738	−	0.980255i	$-0.563359\pi$
$523$	−2.23559	+	0.336961i	−0.0977555	+	0.0147343i	0.0999823	+	0.994989i	$0.468121\pi$
$524$	−2.33451	+	3.24663i	−0.101983	+	0.141830i
$525$	7.05003	+	4.97017i	0.307688	+	0.216916i
$526$	24.0179	−	31.7058i	1.04723	−	1.38244i
$527$	−10.4661	−	0.784326i	−0.455910	−	0.0341658i
$528$	16.2139	−	2.85665i	0.705621	−	0.124320i
$529$	8.39536	−	21.3910i	0.365015	−	0.930044i
$530$	40.2781	+	35.5481i	1.74957	+	1.54411i
$531$	−0.442839	+	0.555303i	−0.0192176	+	0.0240981i
$532$	15.1691	−	11.1189i	0.657666	−	0.482067i
$533$	19.5371	+	24.4988i	0.846247	+	1.06116i
$534$	0.992383	−	19.8705i	0.0429446	−	0.859882i
$535$	−1.95581	−	26.0985i	−0.0845571	−	1.12834i
$536$	−6.45457	−	42.8533i	−0.278795	−	1.85098i
$537$	13.6349	−	14.6950i	0.588391	−	0.634135i
$538$	−20.5593	−	9.27756i	−0.886374	−	0.399984i
$539$	24.4879	+	15.1803i	1.05477	+	0.653861i
$540$	4.31011	−	3.80316i	0.185477	−	0.163662i
$541$	−25.7150	−	23.8600i	−1.10557	−	1.02582i	−0.999505	−	0.0314630i	$-0.989983\pi$
$541$	−25.7150	−	23.8600i	−1.10557	−	1.02582i	−0.106068	−	0.994359i	$-0.533826\pi$
$542$	23.7293	−	36.7374i	1.01926	−	1.57801i
$543$	13.8711	−	1.03949i	0.595265	−	0.0446089i
$544$	−13.9708	−	2.46591i	−0.598992	−	0.105725i
$545$	−40.7743	+	32.5165i	−1.74658	+	1.39285i
$546$	−5.96171	−	14.7873i	−0.255138	−	0.632836i
$547$	−1.12437	−	0.896654i	−0.0480746	−	0.0383382i	0.599158	−	0.800631i	$-0.295502\pi$
$547$	−1.12437	−	0.896654i	−0.0480746	−	0.0383382i	−0.647232	+	0.762293i	$0.724074\pi$
$548$	3.13710	+	6.95382i	0.134010	+	0.297052i
$549$	−7.69445	−	3.01985i	−0.328391	−	0.128884i
$550$	18.8300	+	2.36036i	0.802913	+	0.100646i
$551$	0.554443	−	7.39853i	0.0236201	−	0.315188i
$552$	−0.403797	+	0.0302184i	−0.0171867	+	0.00128618i
$553$	0.403637	−	2.42008i	0.0171644	−	0.102912i
$554$	−13.0559	−	2.63977i	−0.554691	−	0.112153i
$555$	1.22111	+	8.10156i	0.0518334	+	0.343892i
$556$	4.24882	+	33.9238i	0.180190	+	1.43869i
$557$	−14.6146	−	25.3133i	−0.619241	−	1.07256i	−0.989624	−	0.143678i	$-0.954107\pi$
$557$	−14.6146	−	25.3133i	−0.619241	−	1.07256i	0.370383	−	0.928879i	$-0.379226\pi$
$558$	−3.45470	−	4.80554i	−0.146249	−	0.203435i
$559$	2.60349	−	1.25378i	0.110116	−	0.0530290i
$560$	22.1069	−	20.8910i	0.934187	−	0.882807i
$561$	−9.30001	−	4.47865i	−0.392647	−	0.189089i
$562$	5.04195	+	28.6001i	0.212682	+	1.20642i
$563$	−28.8114	+	26.7331i	−1.21426	+	1.12666i	−0.225957	+	0.974137i	$0.572551\pi$
$563$	−28.8114	+	26.7331i	−1.21426	+	1.12666i	−0.988299	+	0.152528i	$0.951259\pi$
$564$	−10.9508	−	1.09655i	−0.461110	−	0.0461731i
$565$	4.43673	+	6.50749i	0.186655	+	0.273772i
$566$	6.87278	−	5.76654i	0.288884	−	0.242386i
$567$	0.629070	−	2.56988i	0.0264184	−	0.107925i
$568$	26.6166	+	28.6918i	1.11681	+	1.20388i
$569$	0.983050	−	1.70269i	0.0412116	−	0.0713806i	−0.844684	−	0.535266i	$-0.820212\pi$
$569$	0.983050	−	1.70269i	0.0412116	−	0.0713806i	0.885895	+	0.463885i	$0.153545\pi$
$570$	−1.43794	−	14.3751i	−0.0602287	−	0.602105i
$571$	5.20661	−	7.63670i	0.217890	−	0.319586i	−0.701695	−	0.712478i	$-0.747573\pi$
$571$	5.20661	−	7.63670i	0.217890	−	0.319586i	0.919585	+	0.392892i	$0.128525\pi$
$572$	−26.8691	−	22.5490i	−1.12345	−	0.942823i
$573$	0.531508	−	0.121313i	0.0222041	−	0.00506793i
$574$	2.30943	+	27.4178i	0.0963939	+	1.14440i
$575$	−0.455047	−	0.103862i	−0.0189768	−	0.00433132i
$576$	−3.99857	−	6.92903i	−0.166607	−	0.288710i
$577$	−8.08136	−	26.1991i	−0.336431	−	1.09068i	−0.952895	−	0.303300i	$-0.901911\pi$
$577$	−8.08136	−	26.1991i	−0.336431	−	1.09068i	0.616464	−	0.787383i	$-0.288565\pi$
$578$	−10.5758	−	10.8436i	−0.439895	−	0.451034i
$579$	8.71503	+	2.68823i	0.362184	+	0.111719i
$580$	−0.597253	−	11.9837i	−0.0247996	−	0.497595i
$581$	34.0091	−	22.4147i	1.41093	−	0.929920i
$582$	−0.676655	−	2.65777i	−0.0280482	−	0.110168i
$583$	50.6399	−	19.8747i	2.09729	−	0.823126i
$584$	−33.4388	+	13.1198i	−1.38371	+	0.542900i
$585$	−12.1101	−	1.82530i	−0.500690	−	0.0754669i
$586$	−12.8373	−	30.4565i	−0.530302	−	1.25815i
$587$	−1.64453			−0.0678769			−0.0339384	−	0.999424i	$-0.510805\pi$
$587$	−1.64453			−0.0678769			−0.0339384	+	0.999424i	$0.510805\pi$
$588$	2.86273	−	13.7042i	0.118057	−	0.565151i
$589$	−14.8749			−0.612908
$590$	1.12127	+	2.66023i	0.0461621	+	0.109520i
$591$	−11.4006	−	1.71836i	−0.468957	−	0.0706839i
$592$	11.3885	+	0.569950i	0.468064	+	0.0234248i
$593$	37.5272	−	14.7283i	1.54106	−	0.604820i	0.565535	−	0.824724i	$-0.308670\pi$
$593$	37.5272	−	14.7283i	1.54106	−	0.604820i	0.975521	+	0.219904i	$0.0705745\pi$
$594$	−1.43613	−	5.64084i	−0.0589250	−	0.231447i
$595$	−18.8993	+	2.54651i	−0.774797	+	0.104397i
$596$	−26.3941	+	1.31545i	−1.08115	+	0.0538830i
$597$	−1.08758	−	0.335474i	−0.0445117	−	0.0137300i
$598$	0.602367	+	0.617619i	0.0246326	+	0.0252563i
$599$	9.62243	+	31.1952i	0.393162	+	1.27460i	0.908598	+	0.417671i	$0.137154\pi$
$599$	9.62243	+	31.1952i	0.393162	+	1.27460i	−0.515436	+	0.856928i	$0.672370\pi$
$600$	−2.05103	−	8.99044i	−0.0837330	−	0.367033i
$601$	34.2718	+	7.82231i	1.39797	+	0.319079i	0.854109	−	0.520094i	$-0.174103\pi$
$601$	34.2718	+	7.82231i	1.39797	+	0.319079i	0.543865	+	0.839172i	$0.316960\pi$
$602$	2.51241	+	0.354992i	0.102398	+	0.0144684i
$603$	−14.9377	+	3.40943i	−0.608310	+	0.138843i
$604$	30.5510	−	36.4042i	1.24310	−	1.48126i
$605$	9.61825	−	14.1074i	0.391037	−	0.573546i
$606$	−0.370885	−	3.70772i	−0.0150662	−	0.150616i
$607$	4.62803	−	8.01599i	0.187846	−	0.325359i	−0.756686	−	0.653779i	$-0.773183\pi$
$607$	4.62803	−	8.01599i	0.187846	−	0.325359i	0.944532	+	0.328420i	$0.106516\pi$
$608$	−20.0061	−	2.00540i	−0.811356	−	0.0813297i
$609$	−3.37528	−	4.37123i	−0.136773	−	0.177131i
$610$	−25.7375	+	21.5948i	−1.04208	+	0.874347i
$611$	13.2088	+	19.3738i	0.534372	+	0.783779i
$612$	−0.499753	+	4.99080i	−0.0202013	+	0.201741i
$613$	−13.6483	+	12.6638i	−0.551251	+	0.511486i	−0.905888	−	0.423518i	$-0.860795\pi$
$613$	−13.6483	+	12.6638i	−0.551251	+	0.511486i	0.354637	+	0.935004i	$0.384604\pi$
$614$	−1.32919	−	7.53975i	−0.0536419	−	0.304280i
$615$	19.0419	+	9.17009i	0.767843	+	0.369774i
$616$	−8.61344	−	29.5718i	−0.347045	−	1.19148i
$617$	−12.9670	+	6.24457i	−0.522031	+	0.251397i	−0.676293	−	0.736633i	$-0.736414\pi$
$617$	−12.9670	+	6.24457i	−0.522031	+	0.251397i	0.154261	+	0.988030i	$0.450700\pi$
$618$	9.50911	+	13.2273i	0.382513	+	0.532081i
$619$	−4.06071	−	7.03336i	−0.163214	−	0.282695i	0.772806	−	0.634643i	$-0.218853\pi$
$619$	−4.06071	−	7.03336i	−0.163214	−	0.282695i	−0.936020	+	0.351948i	$0.885519\pi$
$620$	−23.8694	+	2.98955i	−0.958617	+	0.120063i
$621$	0.0213373	+	0.141564i	0.000856237	+	0.00568076i
$622$	33.2034	+	6.71341i	1.33134	+	0.269183i
$623$	−37.1556	+	2.19973i	−1.48861	+	0.0881303i
$624$	−5.83182	+	16.0159i	−0.233460	+	0.641150i
$625$	−2.29212	+	30.5862i	−0.0916848	+	1.22345i
$626$	−5.01171	−	0.628225i	−0.200308	−	0.0251089i
$627$	−13.6181	−	5.34471i	−0.543855	−	0.213447i
$628$	24.7899	−	11.1836i	0.989224	−	0.446273i
$629$	−5.58946	−	4.45745i	−0.222866	−	0.177730i
$630$	−7.95028	−	7.24133i	−0.316747	−	0.288502i
$631$	23.4814	−	18.7258i	0.934778	−	0.745461i	−0.0324223	−	0.999474i	$-0.510322\pi$
$631$	23.4814	−	18.7258i	0.934778	−	0.745461i	0.967201	+	0.254013i	$0.0817507\pi$
$632$	−2.05084	+	1.63515i	−0.0815782	+	0.0650426i
$633$	11.8843	−	0.890606i	0.472359	−	0.0353984i
$634$	−16.4554	+	25.4760i	−0.653527	+	1.01178i
$635$	28.8117	+	26.7333i	1.14336	+	1.06088i
$636$	−17.4897	−	19.8210i	−0.693514	−	0.785956i
$637$	−26.2865	+	14.0975i	−1.04151	+	0.558565i
$638$	−11.0748	−	4.99761i	−0.438456	−	0.197857i
$639$	9.41143	−	10.1431i	0.372310	−	0.401255i
$640$	−32.5065	+	0.802812i	−1.28493	+	0.0317339i
$641$	1.89825	+	25.3304i	0.0749765	+	1.00049i	0.900141	+	0.435599i	$0.143463\pi$
$641$	1.89825	+	25.3304i	0.0749765	+	1.00049i	−0.825164	+	0.564893i	$0.808918\pi$
$642$	−0.642360	+	12.8620i	−0.0253519	+	0.507623i
$643$	20.0258	+	25.1115i	0.789739	+	0.990302i	0.999920	+	0.0126392i	$0.00402329\pi$
$643$	20.0258	+	25.1115i	0.789739	+	0.990302i	−0.210181	+	0.977663i	$0.567405\pi$
$644$	0.138403	+	0.744796i	0.00545386	+	0.0293491i
$645$	1.21519	−	1.52380i	0.0478481	−	0.0599996i
$646$	9.45154	+	8.34162i	0.371866	+	0.328196i
$647$	−4.12549	+	10.5116i	−0.162190	+	0.413253i	−0.988747	−	0.149601i	$-0.952201\pi$
$647$	−4.12549	+	10.5116i	−0.162190	+	0.413253i	0.826557	+	0.562853i	$0.190296\pi$
$648$	−2.33712	+	1.59307i	−0.0918108	+	0.0625816i
$649$	2.91519	+	0.218464i	0.114431	+	0.00857545i
$650$	−11.8635	+	15.6609i	−0.465324	+	0.614270i
$651$	−8.23364	+	7.40309i	−0.322702	+	0.290150i
$652$	−9.49183	−	6.82516i	−0.371729	−	0.267294i
$653$	23.5602	−	3.55113i	0.921983	−	0.138967i	0.329137	−	0.944282i	$-0.393242\pi$
$653$	23.5602	−	3.55113i	0.921983	−	0.138967i	0.592846	+	0.805316i	$0.298004\pi$
$654$	21.8977	−	13.3804i	0.856267	−	0.523213i
$655$	4.97656	−	2.87322i	0.194450	−	0.112266i
$656$	17.7639	−	23.4449i	0.693564	−	0.915369i
$657$	5.51024	+	11.4421i	0.214975	+	0.446400i
$658$	0.190101	+	20.5886i	0.00741093	+	0.802626i
$659$	13.8148	−	28.6868i	0.538150	−	1.11748i	−0.437717	−	0.899113i	$-0.644213\pi$
$659$	13.8148	−	28.6868i	0.538150	−	1.11748i	0.975867	−	0.218367i	$-0.0700730\pi$
$660$	−22.9269	−	5.83958i	−0.892427	−	0.227305i
$661$	−28.2128	−	30.4062i	−1.09735	−	1.18266i	−0.981910	−	0.189350i	$-0.939362\pi$
$661$	−28.2128	−	30.4062i	−1.09735	−	1.18266i	−0.115443	−	0.993314i	$-0.536829\pi$
$662$	16.7220	−	5.61765i	0.649918	−	0.218336i
$663$	8.82959	−	6.01992i	0.342913	−	0.233794i
$664$	−43.0565	−	6.49428i	−1.67092	−	0.252027i
$665$	−26.4408	+	5.60067i	−1.02533	+	0.217185i
$666$	−0.100369	−	4.03023i	−0.00388921	−	0.156168i
$667$	0.258799	+	0.149418i	0.0100207	+	0.00578548i
$668$	8.03571	−	23.9116i	0.310911	−	0.925169i
$669$	−4.67818	−	3.18953i	−0.180869	−	0.123314i
$670$	−16.8690	+	59.9481i	−0.651707	+	2.31600i
$671$	7.57050	+	33.1685i	0.292256	+	1.28046i
$672$	−12.0720	+	8.84684i	−0.465688	+	0.341274i
$673$	−2.56749	+	11.2489i	−0.0989695	+	0.433614i	−1.00000		0.000142149i	$-0.999955\pi$
$673$	−2.56749	+	11.2489i	−0.0989695	+	0.433614i	0.901031	+	0.433756i	$0.142812\pi$
$674$	−13.8564	−	7.54641i	−0.533729	−	0.290677i
$675$	−3.11542	+	0.960981i	−0.119913	+	0.0369882i
$676$	9.69319	−	3.52728i	0.372815	−	0.135664i
$677$	9.47494	−	30.7170i	0.364151	−	1.18055i	−0.569386	−	0.822070i	$-0.692819\pi$
$677$	9.47494	−	30.7170i	0.364151	−	1.18055i	0.933538	−	0.358480i	$-0.116705\pi$
$678$	−1.76792	−	3.44874i	−0.0678965	−	0.132448i
$679$	−4.80496	+	1.79946i	−0.184397	+	0.0690570i
$680$	16.8432	+	11.4860i	0.645906	+	0.440469i
$681$	−0.630625	−	1.60681i	−0.0241656	−	0.0615729i
$682$	−8.33237	+	22.8905i	−0.319063	+	0.876524i
$683$	−7.71238	+	51.1683i	−0.295106	+	1.95790i	−0.00811658	+	0.999967i	$0.502584\pi$
$683$	−7.71238	+	51.1683i	−0.295106	+	1.95790i	−0.286989	+	0.957934i	$0.592654\pi$
$684$	−0.177714	+	7.10646i	−0.00679508	+	0.271722i
$685$		−	10.9627i		−	0.418863i
$686$	−26.0687	−	2.53395i	−0.995309	−	0.0967466i
$687$		−	22.9624i		−	0.876070i
$688$	−1.74331	−	2.07818i	−0.0664630	−	0.0792297i
$689$	−8.39408	+	55.6911i	−0.319789	+	2.12166i
$690$	0.546793	+	0.199038i	0.0208160	+	0.00757723i
$691$	−13.7562	−	35.0503i	−0.523312	−	1.33338i	−0.911311	−	0.411718i	$-0.864929\pi$
$691$	−13.7562	−	35.0503i	−0.523312	−	1.33338i	0.387999	−	0.921660i	$-0.373166\pi$
$692$	−45.2567	−	7.98319i	−1.72040	−	0.303475i
$693$	−10.1980	+	3.81917i	−0.387390	+	0.145078i
$694$	−2.57258	+	1.31877i	−0.0976540	+	0.0500600i
$695$	14.4815	−	46.9478i	0.549313	−	1.78083i
$696$	−0.441816	+	5.88745i	−0.0167470	+	0.223163i
$697$	−17.6228	+	5.43590i	−0.667510	+	0.205899i
$698$	−11.3408	+	20.8235i	−0.429256	+	0.788182i
$699$	5.11378	−	22.4049i	0.193421	−	0.847432i
$700$	−16.3021	+	5.64464i	−0.616163	+	0.213347i
$701$	−2.53214	−	11.0940i	−0.0956376	−	0.419016i	0.904332	−	0.426830i	$-0.140370\pi$
$701$	−2.53214	−	11.0940i	−0.0956376	−	0.419016i	−0.999969	+	0.00781440i	$0.997513\pi$
$702$	5.80090	+	1.63234i	0.218941	+	0.0616086i
$703$	−8.37172	−	5.70774i	−0.315745	−	0.215271i
$704$	−14.2928	+	29.6636i	−0.538679	+	1.11799i
$705$	13.6965	+	7.90766i	0.515839	+	0.297820i
$706$	27.9445	−	0.695929i	1.05171	−	0.0261916i
$707$	−6.81982	+	1.44457i	−0.256486	+	0.0543286i
$708$	−0.384640	−	1.36745i	−0.0144556	−	0.0513920i
$709$	−10.7522	+	7.33072i	−0.403807	+	0.275311i	−0.748146	−	0.663535i	$-0.769056\pi$
$709$	−10.7522	+	7.33072i	−0.403807	+	0.275311i	0.344339	+	0.938845i	$0.388103\pi$
$710$	−17.9100	−	53.3124i	−0.672150	−	2.00078i
$711$	0.630751	+	0.679788i	0.0236550	+	0.0254940i
$712$	31.1070	+	24.8122i	1.16578	+	0.929878i
$713$	0.259955	−	0.539801i	0.00973538	−	0.0202157i
$714$	9.38323	−	0.0866387i	0.351159	−	0.00324237i
$715$	21.8708	+	45.4153i	0.817923	+	1.69843i
$716$	7.94149	+	39.2982i	0.296787	+	1.46864i
$717$	6.79373	−	3.92236i	0.253717	−	0.146483i
$718$	−8.31859	−	13.6138i	−0.310447	−	0.508063i
$719$	15.4682	−	2.33146i	0.576866	−	0.0869486i	0.145872	−	0.989303i	$-0.453401\pi$
$719$	15.4682	−	2.33146i	0.576866	−	0.0869486i	0.430994	+	0.902355i	$0.358163\pi$
$720$	1.14308	+	11.4393i	0.0426002	+	0.426318i
$721$	22.6632	−	20.3771i	0.844023	−	0.758884i
$722$	−7.17703	−	5.43678i	−0.267102	−	0.202336i
$723$	12.6967	+	0.951489i	0.472197	+	0.0353863i
$724$	−14.5079	+	23.7375i	−0.539183	+	0.882197i
$725$	−2.48630	+	6.33499i	−0.0923389	+	0.235276i
$726$	−5.55939	+	6.29912i	−0.206328	+	0.233782i
$727$	−7.28065	+	9.12965i	−0.270024	+	0.338600i	−0.898293	−	0.439396i	$-0.855192\pi$
$727$	−7.28065	+	9.12965i	−0.270024	+	0.338600i	0.628269	+	0.777996i	$0.283764\pi$
$728$	30.9724	+	7.58499i	1.14791	+	0.281119i
$729$	0.623490	+	0.781831i	0.0230922	+	0.0289567i
$730$	51.5547	+	2.57477i	1.90812	+	0.0952965i
$731$	0.127093	+	1.69594i	0.00470070	+	0.0627264i
$732$	13.8877	−	8.96825i	0.513303	−	0.331476i
$733$	−25.1100	+	27.0622i	−0.927461	+	0.999565i	0.0725369	+	0.997366i	$0.476890\pi$
$733$	−25.1100	+	27.0622i	−0.927461	+	0.999565i	−0.999998	+	0.00219913i	$0.999300\pi$
$734$	11.1330	−	24.6709i	0.410925	−	0.910620i
$735$	−11.8483	+	16.2595i	−0.437031	+	0.599740i
$736$	0.422404	−	0.690966i	0.0155700	−	0.0254693i
$737$	46.2288	+	42.8940i	1.70286	+	1.58002i
$738$	−8.73577	−	5.64259i	−0.321568	−	0.207706i
$739$	4.27755	−	0.320558i	0.157352	−	0.0117919i	0.00417895	−	0.999991i	$-0.498670\pi$
$739$	4.27755	−	0.320558i	0.157352	−	0.0117919i	0.153173	+	0.988199i	$0.451051\pi$
$740$	−14.5810	−	7.47654i	−0.536010	−	0.274843i
$741$	11.8413	−	9.44315i	0.435002	−	0.346903i
$742$	−33.3010	+	36.5612i	−1.22252	+	1.34220i
$743$	−6.44394	−	5.13887i	−0.236405	−	0.188527i	0.498120	−	0.867108i	$-0.334024\pi$
$743$	−6.44394	−	5.13887i	−0.236405	−	0.188527i	−0.734525	+	0.678581i	$0.762595\pi$
$744$	11.8369	+	0.00122401i	0.433963	+	4.48743e-5i
$745$	35.3512	+	13.8743i	1.29517	+	0.508316i
$746$	−6.01422	+	47.9789i	−0.220196	+	1.75663i
$747$	−1.15047	+	15.3519i	−0.0420934	+	0.561698i
$748$	18.1311	−	9.87205i	0.662939	−	0.360958i
$749$	24.0505	−	1.42386i	0.878786	−	0.0520269i
$750$	1.40137	−	6.93097i	0.0511709	−	0.253083i
$751$	−0.886640	−	5.88247i	−0.0323539	−	0.214654i	0.966812	−	0.255489i	$-0.0822364\pi$
$751$	−0.886640	−	5.88247i	−0.0323539	−	0.214654i	−0.999166	+	0.0408345i	$0.986998\pi$
$752$	14.5667	−	16.5015i	0.531192	−	0.601746i
$753$	1.28723	+	2.22955i	0.0469093	+	0.0812492i
$754$	10.2136	−	7.34254i	0.371957	−	0.267400i
$755$	−61.5317	+	29.6321i	−2.23937	+	1.07842i
$756$	3.43845	+	4.02207i	0.125055	+	0.146281i
$757$	−4.87083	−	2.34567i	−0.177033	−	0.0852548i	0.343268	−	0.939238i	$-0.388466\pi$
$757$	−4.87083	−	2.34567i	−0.177033	−	0.0852548i	−0.520301	+	0.853983i	$0.674180\pi$
$758$	−36.2508	+	6.39071i	−1.31669	+	0.232121i
$759$	0.431948	−	0.400789i	0.0156787	−	0.0145477i
$760$	25.0211	+	14.4494i	0.907610	+	0.524134i
$761$	27.9271	+	40.9616i	1.01236	+	1.48486i	0.868768	+	0.495219i	$0.164912\pi$
$761$	27.9271	+	40.9616i	1.01236	+	1.48486i	0.143590	+	0.989637i	$0.454135\pi$
$762$	−12.4309	−	14.8156i	−0.450322	−	0.536711i
$763$	−29.3417	−	37.9995i	−1.06224	−	1.37568i
$764$	−0.423600	+	1.00470i	−0.0153253	+	0.0363489i
$765$	3.60391	−	6.24216i	0.130300	−	0.225686i
$766$	12.0262	−	1.20298i	0.434524	−	0.0434656i
$767$	−1.70490	+	2.50064i	−0.0615605	+	0.0902927i
$768$	15.9201	+	1.59748i	0.574465	+	0.0576439i
$769$	−21.1135	+	4.81901i	−0.761371	+	0.173778i	−0.585541	−	0.810643i	$-0.699118\pi$
$769$	−21.1135	+	4.81901i	−0.761371	+	0.173778i	−0.175830	+	0.984421i	$0.556261\pi$
$770$	−6.19248	+	43.8263i	−0.223161	+	1.57939i
$771$	2.96326	+	0.676344i	0.106719	+	0.0243579i
$772$	−14.5408	+	11.0127i	−0.523335	+	0.396354i
$773$	−5.95288	−	19.2988i	−0.214110	−	0.694128i	−0.997373	−	0.0724373i	$-0.976922\pi$
$773$	−5.95288	−	19.2988i	−0.214110	−	0.694128i	0.783263	−	0.621691i	$-0.213554\pi$
$774$	−0.686563	+	0.669608i	−0.0246780	+	0.0240686i
$775$	13.0380	+	4.02169i	0.468339	+	0.144463i
$776$	5.10574	+	2.00447i	0.183285	+	0.0719561i
$777$	−7.47466	+	1.00714i	−0.268152	+	0.0361310i
$778$	−27.5803	+	7.02179i	−0.988801	+	0.251743i
$779$	−24.3306	+	9.54907i	−0.871735	+	0.342131i
$780$	17.1036	−	17.5331i	0.612409	−	0.627785i
$781$	−56.3151	−	8.48814i	−2.01511	−	0.303730i
$782$	−0.467889	+	0.197213i	−0.0167317	+	0.00705231i
$783$	2.08738			0.0745970
$784$	18.9103	+	20.6495i	0.675367	+	0.737482i
$785$	−39.0813			−1.39487
$786$	−2.60560	+	1.09824i	−0.0929385	+	0.0391731i
$787$	−30.3226	−	4.57039i	−1.08088	−	0.162917i	−0.415629	−	0.909534i	$-0.636439\pi$
$787$	−30.3226	−	4.57039i	−1.08088	−	0.162917i	−0.665254	+	0.746617i	$0.731677\pi$
$788$	16.1016	−	16.5058i	0.573595	−	0.587996i
$789$	26.1816	−	10.2755i	0.932088	−	0.365818i
$790$	3.65269	−	0.929955i	0.129957	−	0.0330863i
$791$	−6.05378	+	3.98993i	−0.215248	+	0.141866i
$792$	10.8364	+	4.25427i	0.385055	+	0.151169i
$793$	−33.6573	−	10.3819i	−1.19520	−	0.368672i
$794$	7.25255	−	7.07345i	0.257383	−	0.251027i
$795$	11.1968	+	36.2992i	0.397110	+	1.28740i
$796$	1.81460	−	1.37431i	0.0643168	−	0.0487111i
$797$	17.2312	+	3.93291i	0.610361	+	0.139311i	0.516518	−	0.856276i	$-0.327228\pi$
$797$	17.2312	+	3.93291i	0.610361	+	0.139311i	0.0938425	+	0.995587i	$0.470085\pi$
$798$	13.2522	−	1.11625i	0.469123	−	0.0395148i
$799$	−13.4543	+	3.07085i	−0.475978	+	0.108639i
$800$	16.9934	+	7.16678i	0.600808	+	0.253384i
$801$	7.92484	−	11.6236i	0.280010	−	0.410700i
$802$	−17.3097	+	1.73149i	−0.611226	+	0.0611411i
$803$	26.1357	−	45.2683i	0.922308	−	1.59748i
$804$	11.9050	−	28.2366i	0.419858	−	0.995828i
$805$	0.258837	−	1.05740i	0.00912280	−	0.0372685i
$806$	−16.2101	−	19.3198i	−0.570978	−	0.680512i
$807$	−8.98454	−	13.1779i	−0.316271	−	0.463884i
$808$	6.45363	+	3.72690i	0.227038	+	0.131112i
$809$	−3.17548	+	2.94642i	−0.111644	+	0.103591i	−0.734020	−	0.679128i	$-0.762358\pi$
$809$	−3.17548	+	2.94642i	−0.111644	+	0.103591i	0.622376	+	0.782719i	$0.286168\pi$
$810$	4.00282	−	0.705663i	0.140645	−	0.0247945i
$811$	3.83821	+	1.84838i	0.134778	+	0.0649056i	0.500057	−	0.865992i	$-0.333312\pi$
$811$	3.83821	+	1.84838i	0.134778	+	0.0649056i	−0.365279	+	0.930898i	$0.619027\pi$
$812$	11.0390	−	0.376927i	0.387391	−	0.0132275i
$813$	27.8625	−	13.4179i	0.977182	−	0.470586i
$814$	−13.4730	+	9.68574i	−0.472229	+	0.339485i
$815$	8.40013	+	14.5494i	0.294244	+	0.509645i
$816$	−7.52053	−	6.63876i	−0.263271	−	0.232403i
$817$	0.359242	+	2.38341i	0.0125683	+	0.0833851i
$818$	8.22189	−	40.6641i	0.287472	−	1.42179i
$819$	1.85473	−	11.1204i	0.0648094	−	0.388577i
$820$	−37.1236	+	20.2131i	−1.29641	+	0.705874i
$821$	−1.78475	+	23.8158i	−0.0622882	+	0.831179i	0.875333	+	0.483520i	$0.160642\pi$
$821$	−1.78475	+	23.8158i	−0.0622882	+	0.831179i	−0.937621	+	0.347658i	$0.886977\pi$
$822$	−0.670932	+	5.35242i	−0.0234014	+	0.186687i
$823$	−4.34906	−	1.70688i	−0.151599	−	0.0594981i	0.288328	−	0.957532i	$-0.406901\pi$
$823$	−4.34906	−	1.70688i	−0.151599	−	0.0594981i	−0.439927	+	0.898033i	$0.644996\pi$
$824$	−32.5813	−	0.00336910i	−1.13502	−	0.000117368i
$825$	10.4914	+	8.36661i	0.365264	+	0.291288i
$826$	−2.46477	+	0.993710i	−0.0857603	+	0.0345756i
$827$	−7.75065	+	6.18094i	−0.269517	+	0.214932i	−0.748917	−	0.662664i	$-0.769426\pi$
$827$	−7.75065	+	6.18094i	−0.269517	+	0.214932i	0.479400	+	0.877596i	$0.340854\pi$
$828$	−0.254784	−	0.130642i	−0.00885436	−	0.00454014i
$829$	47.9797	−	3.59558i	1.66641	−	0.124880i	0.792144	−	0.610335i	$-0.208965\pi$
$829$	47.9797	−	3.59558i	1.66641	−	0.124880i	0.874262	+	0.485455i	$0.161346\pi$
$830$	52.5623	+	33.9509i	1.82446	+	1.17845i
$831$	−6.90440	−	6.40635i	−0.239511	−	0.222234i
$832$	−19.1974	−	28.1699i	−0.665549	−	0.976615i
$833$	−2.07138	−	17.4325i	−0.0717691	−	0.604002i
$834$	−9.94368	+	22.0354i	−0.344322	+	0.763025i
$835$	−24.6564	+	26.5733i	−0.853271	+	0.919608i
$836$	24.5792	−	15.8725i	0.850090	−	0.548963i
$837$	−0.312744	−	4.17328i	−0.0108100	−	0.144250i
$838$	26.1011	+	1.30355i	0.901648	+	0.0450306i
$839$	8.98954	+	11.2725i	0.310354	+	0.389171i	0.912407	−	0.409285i	$-0.134222\pi$
$839$	8.98954	+	11.2725i	0.310354	+	0.389171i	−0.602053	+	0.798456i	$0.705650\pi$
$840$	21.0412	−	4.45465i	0.725990	−	0.153700i
$841$	−15.3646	+	19.2665i	−0.529812	+	0.664364i
$842$	23.6791	−	26.8299i	0.816037	−	0.924618i
$843$	−7.50234	+	19.1156i	−0.258394	+	0.658378i
$844$	−12.4299	+	20.3376i	−0.427856	+	0.700047i
$845$	−14.7816	−	1.10773i	−0.508502	−	0.0381070i
$846$	−6.20319	−	4.69907i	−0.213270	−	0.161557i
$847$	12.8464	+	9.05652i	0.441407	+	0.311186i
$848$	52.6063	−	5.25673i	1.80651	−	0.180517i
$849$	6.27296	−	0.945497i	0.215287	−	0.0324494i
$850$	−6.02908	−	9.86692i	−0.206796	−	0.338433i
$851$	0.353436	−	0.204056i	0.0121156	−	0.00699496i
$852$	5.48156	+	27.1253i	0.187795	+	0.929298i
$853$	7.63472	+	15.8537i	0.261408	+	0.542819i	0.989821	−	0.142319i	$-0.0454560\pi$
$853$	7.63472	+	15.8537i	0.261408	+	0.542819i	−0.728413	+	0.685138i	$0.759742\pi$
$854$	−19.5057	−	24.0014i	−0.667471	−	0.821310i
$855$	4.43231	−	9.20378i	0.151582	−	0.314763i
$856$	−20.1352	−	16.0607i	−0.688208	−	0.548944i
$857$	−35.2458	−	37.9859i	−1.20397	−	1.29757i	−0.943220	−	0.332168i	$-0.892220\pi$
$857$	−35.2458	−	37.9859i	−1.20397	−	1.29757i	−0.260752	−	0.965406i	$-0.583970\pi$
$858$	−7.89872	−	23.5120i	−0.269658	−	0.802687i
$859$	30.1645	−	20.5658i	1.02920	−	0.701696i	0.0738779	−	0.997267i	$-0.476462\pi$
$859$	30.1645	−	20.5658i	1.02920	−	0.701696i	0.955321	+	0.295572i	$0.0955101\pi$
$860$	1.05549	+	3.75241i	0.0359918	+	0.127956i
$861$	−8.71518	+	17.3948i	−0.297012	+	0.592813i
$862$	3.02034	−	0.0752184i	0.102873	−	0.00256195i
$863$	14.0816	+	8.13003i	0.479344	+	0.276750i	0.720143	−	0.693825i	$-0.244076\pi$
$863$	14.0816	+	8.13003i	0.479344	+	0.276750i	−0.240799	+	0.970575i	$0.577409\pi$
$864$	0.142004	−	5.65507i	0.00483107	−	0.192389i
$865$	54.5644	+	37.2014i	1.85525	+	1.26488i
$866$	29.2383	+	8.22746i	0.993557	+	0.279581i
$867$	−2.38332	−	10.4420i	−0.0809417	−	0.354629i
$868$	−2.40751	−	22.0136i	−0.0817162	−	0.747190i
$869$	0.849330	−	3.72116i	0.0288115	−	0.126232i
$870$	4.05789	−	7.45092i	0.137575	−	0.252610i
$871$	−62.3882	+	19.2442i	−2.11394	+	0.652066i
$872$	−3.84075	+	51.1802i	−0.130064	+	1.73318i
$873$	0.571613	−	1.85312i	0.0193462	−	0.0627188i
$874$	−0.640383	+	0.328277i	−0.0216613	+	0.0111041i
$875$	−13.1749	−	1.19514i	−0.445394	−	0.0404031i
$876$	−25.0134	−	4.41232i	−0.845125	−	0.149078i
$877$	−14.9613	−	38.1208i	−0.505208	−	1.28725i	−0.925117	−	0.379683i	$-0.876033\pi$
$877$	−14.9613	−	38.1208i	−0.505208	−	1.28725i	0.419909	−	0.907566i	$-0.362062\pi$
$878$	−14.0021	−	5.09688i	−0.472546	−	0.172011i
$879$	3.48325	−	23.1098i	0.117487	−	0.779475i
$880$	36.2517	−	30.4102i	1.22204	−	1.02513i
$881$			13.9830i			0.471098i	0.971862	+	0.235549i	$0.0756889\pi$
$881$			13.9830i			0.471098i	−0.971862	+	0.235549i	$0.924311\pi$
$882$	6.77991	−	7.21338i	0.228291	−	0.242887i
$883$		−	17.3174i		−	0.582777i	−0.956605	−	0.291388i	$-0.905883\pi$
$883$		−	17.3174i		−	0.582777i	0.956605	−	0.291388i	$-0.0941172\pi$
$884$	−0.534316	+	21.3663i	−0.0179710	+	0.718627i
$885$	−0.304245	+	2.01853i	−0.0102271	+	0.0678522i
$886$	−5.81181	+	15.9661i	−0.195252	+	0.536392i
$887$	4.12384	+	10.5074i	0.138465	+	0.352803i	0.983239	−	0.182320i	$-0.0583606\pi$
$887$	4.12384	+	10.5074i	0.138465	+	0.352803i	−0.844774	+	0.535123i	$0.820265\pi$
$888$	6.66146	+	4.54272i	0.223544	+	0.152444i
$889$	−25.0221	+	26.1341i	−0.839213	+	0.876509i
$890$	−26.0846	−	50.8842i	−0.874357	−	1.70564i
$891$	1.21319	−	3.93306i	0.0406433	−	0.131762i
$892$	10.6414	−	3.87231i	0.356300	−	0.129655i
$893$	−18.6898	+	5.76503i	−0.625429	+	0.192919i
$894$	−16.4107	−	8.93752i	−0.548856	−	0.298916i
$895$	12.8204	−	56.1699i	0.428539	−	1.87755i
$896$	−0.270182	−	29.9320i	−0.00902615	−	0.999959i
$897$	0.135747	+	0.594745i	0.00453245	+	0.0198580i
$898$	6.70200	−	23.8172i	0.223649	−	0.794789i
$899$	−7.21774	−	4.92097i	−0.240725	−	0.164124i
$900$	2.07713	−	6.18085i	0.0692377	−	0.206028i
$901$	−28.7060	−	16.5734i	−0.956337	−	0.552141i
$902$	1.06566	+	42.7908i	0.0354826	+	1.42478i
$903$	1.38505	+	1.14049i	0.0460917	+	0.0379532i
$904$	7.66427	+	1.15601i	0.254910	+	0.0384485i
$905$	33.0315	−	22.5205i	1.09801	−	0.748608i
$906$	31.8557	−	10.7017i	1.05834	−	0.355541i
$907$	19.2598	+	20.7571i	0.639510	+	0.689228i	0.966753	−	0.255712i	$-0.0823100\pi$
$907$	19.2598	+	20.7571i	0.639510	+	0.689228i	−0.327243	+	0.944940i	$0.606120\pi$
$908$	3.34544	+	0.852099i	0.111022	+	0.0282779i
$909$	1.14321	−	2.37391i	0.0379180	−	0.0787376i
$910$	−36.0886	−	28.2385i	−1.19633	−	0.936099i
$911$	14.3866	+	29.8740i	0.476648	+	0.989770i	0.991208	+	0.132315i	$0.0422411\pi$
$911$	14.3866	+	29.8740i	0.476648	+	0.989770i	−0.514560	+	0.857455i	$0.672045\pi$
$912$	−11.3319	−	8.58607i	−0.375238	−	0.284313i
$913$	54.8752	−	31.6822i	1.81610	−	1.04853i
$914$	21.7782	−	13.3073i	0.720359	−	0.440168i
$915$	−23.4913	+	3.54074i	−0.776597	+	0.117053i
$916$	37.2862	+	26.8109i	1.23197	+	0.885856i
$917$	2.57288	+	4.62209i	0.0849640	+	0.152635i
$918$	−2.14160	+	2.82710i	−0.0706833	+	0.0933082i
$919$	36.5736	+	2.74081i	1.20645	+	0.0904110i	0.662732	−	0.748856i	$-0.269397\pi$
$919$	36.5736	+	2.74081i	1.20645	+	0.0904110i	0.543719	+	0.839267i	$0.317016\pi$
$920$	−0.961631	+	0.655484i	−0.0317040	+	0.0216107i
$921$	1.97782	−	5.03940i	0.0651713	−	0.166054i
$922$	−8.22275	−	7.25712i	−0.270802	−	0.239001i
$923$	36.7616	−	46.0975i	1.21002	−	1.51732i
$924$	5.70564	−	21.0187i	0.187702	−	0.691466i
$925$	5.79472	+	7.26635i	0.190529	+	0.238916i
$926$	−1.55093	+	31.0543i	−0.0509667	+	1.02051i
$927$	0.860833	+	11.4870i	0.0282735	+	0.377283i
$928$	−9.04416	−	7.59161i	−0.296889	−	0.249207i
$929$	5.41976	−	5.84111i	0.177816	−	0.191641i	−0.637854	−	0.770157i	$-0.720178\pi$
$929$	5.41976	−	5.84111i	0.177816	−	0.191641i	0.815671	+	0.578517i	$0.196368\pi$
$930$	−15.5045	−	6.99655i	−0.508414	−	0.229426i
$931$	−4.77382	−	24.4181i	−0.156456	−	0.800272i
$932$	30.4102	+	34.4637i	0.996118	+	1.12890i
$933$	17.5591	+	16.2925i	0.574860	+	0.533393i
$934$	22.9449	−	35.5229i	0.750779	−	1.16234i
$935$	−29.5839	+	2.21700i	−0.967496	+	0.0725038i
$936$	−9.42371	+	7.51357i	−0.308024	+	0.245589i
$937$	21.3611	−	17.0349i	0.697835	−	0.556505i	−0.209038	−	0.977907i	$-0.567033\pi$
$937$	21.3611	−	17.0349i	0.697835	−	0.556505i	0.906874	+	0.421402i	$0.138462\pi$
$938$	−54.9358	−	16.3915i	−1.79372	−	0.535202i
$939$	−2.79235	−	2.22683i	−0.0911249	−	0.0726697i
$940$	−28.8324	+	13.0073i	−0.940409	+	0.424251i
$941$	−19.6429	−	7.70928i	−0.640341	−	0.251315i	0.0228806	−	0.999738i	$-0.492716\pi$
$941$	−19.6429	−	7.70928i	−0.640341	−	0.251315i	−0.663222	+	0.748423i	$0.730811\pi$
$942$	19.0810	+	2.39183i	0.621693	+	0.0779300i
$943$	0.0786736	−	1.04983i	0.00256197	−	0.0341870i
$944$	2.66957	+	0.972060i	0.0868870	+	0.0316379i
$945$	−2.12724	−	7.30046i	−0.0691990	−	0.237484i
$946$	3.86901	+	0.782275i	0.125792	+	0.0254340i
$947$	7.01991	+	46.5741i	0.228116	+	1.51345i	0.750573	+	0.660788i	$0.229778\pi$
$947$	7.01991	+	46.5741i	0.228116	+	1.51345i	−0.522456	+	0.852666i	$0.674984\pi$
$948$	−1.84030	+	0.230491i	−0.0597702	+	0.00748599i
$949$	27.0580	+	46.8658i	0.878339	+	1.52133i
$950$	−9.56597	−	13.3064i	−0.310361	−	0.431717i
$951$	−19.3216	+	9.30479i	−0.626545	+	0.301728i
$952$	−10.8152	+	15.3376i	−0.350522	+	0.497095i
$953$	−28.9274	−	13.9307i	−0.937049	−	0.451259i	−0.0979217	−	0.995194i	$-0.531219\pi$
$953$	−28.9274	−	13.9307i	−0.937049	−	0.451259i	−0.839127	+	0.543935i	$0.816934\pi$
$954$	−3.24516	−	18.4079i	−0.105066	−	0.595978i
$955$	1.14860	−	1.06575i	0.0371678	−	0.0344867i
$956$	−1.56324	+	15.6114i	−0.0505588	+	0.504908i
$957$	−4.83976	−	7.09863i	−0.156447	−	0.229466i
$958$	−29.5040	+	24.7551i	−0.953233	+	0.799801i
$959$	10.0906	+	0.158089i	0.325842	+	0.00510496i
$960$	−19.9098	−	11.5004i	−0.642584	−	0.371174i
$961$	6.74295	−	11.6791i	0.217515	−	0.376746i
$962$	−1.70987	−	17.0935i	−0.0551283	−	0.551116i
$963$	−5.12967	+	7.52385i	−0.165301	+	0.242453i
$964$	−16.3697	+	19.5060i	−0.527234	+	0.628245i
$965$	25.5549	−	5.83275i	0.822642	−	0.187763i
$966$	−0.191089	+	0.500423i	−0.00614818	+	0.0161009i
$967$	28.2573	+	6.44955i	0.908694	+	0.207404i	0.651227	−	0.758883i	$-0.274255\pi$
$967$	28.2573	+	6.44955i	0.908694	+	0.207404i	0.257468	+	0.966287i	$0.417112\pi$
$968$	−3.73734	−	16.3822i	−0.120123	−	0.526543i
$969$	2.62741	+	8.51785i	0.0844046	+	0.273633i
$970$	−5.50352	−	5.64287i	−0.176707	−	0.181181i
$971$	20.4848	+	6.31872i	0.657388	+	0.202777i	0.605463	−	0.795874i	$-0.292988\pi$
$971$	20.4848	+	6.31872i	0.657388	+	0.202777i	0.0519252	+	0.998651i	$0.483464\pi$
$972$	−1.99752	+	0.0995541i	−0.0640705	+	0.00319320i
$973$	43.0041	+	14.0064i	1.37865	+	0.449026i
$974$	6.52975	+	25.6477i	0.209227	+	0.821804i
$975$	−12.9322	+	5.07551i	−0.414162	+	0.162547i
$976$	−1.65263	+	33.0220i	−0.0528993	+	1.05701i
$977$	25.0417	+	3.77442i	0.801154	+	0.120754i	0.536842	−	0.843683i	$-0.319617\pi$
$977$	25.0417	+	3.77442i	0.801154	+	0.120754i	0.264312	+	0.964437i	$0.414855\pi$
$978$	−3.21082	−	7.61771i	−0.102671	−	0.243587i
$979$	−57.9031			−1.85059
$980$	−12.5680	−	38.2238i	−0.401470	−	1.22101i
$981$	18.1458			0.579352
$982$	14.9676	+	35.5108i	0.477636	+	1.13320i
$983$	39.4299	+	5.94310i	1.25762	+	0.189556i	0.743834	−	0.668364i	$-0.233005\pi$
$983$	39.4299	+	5.94310i	1.25762	+	0.189556i	0.513784	+	0.857919i	$0.328243\pi$
$984$	19.3623	−	7.59683i	0.617247	−	0.242178i
$985$	−30.8456	+	12.1060i	−0.982821	+	0.385729i
$986$	1.82657	+	7.17441i	0.0581697	+	0.228480i
$987$	−7.47609	+	12.4928i	−0.237967	+	0.397651i
$988$	1.50781	+	30.2537i	0.0479698	+	0.962499i
$989$	−0.0927710	−	0.0286161i	−0.00294995	−	0.000909938i
$990$	−11.6806	−	11.9764i	−0.371235	−	0.380634i
$991$	−14.5700	−	47.2347i	−0.462831	−	1.50046i	−0.823255	−	0.567672i	$-0.807844\pi$
$991$	−14.5700	−	47.2347i	−0.462831	−	1.50046i	0.360424	−	0.932789i	$-0.382632\pi$
$992$	−13.8228	+	19.2193i	−0.438873	+	0.610214i
$993$	12.1609	+	2.77564i	0.385914	+	0.0880824i
$994$	49.3295	−	15.7164i	1.56464	−	0.498493i
$995$	−3.18909	+	0.727890i	−0.101101	+	0.0230756i
$996$	−23.5851	−	19.7930i	−0.747323	−	0.627166i
$997$	6.02064	−	8.83066i	0.190676	−	0.279670i	−0.718982	−	0.695029i	$-0.755392\pi$
$997$	6.02064	−	8.83066i	0.190676	−	0.279670i	0.909658	+	0.415359i	$0.136344\pi$
$998$	3.56873	+	35.6765i	0.112966	+	1.12932i
$999$	1.42534	−	2.46877i	0.0450959	−	0.0781084i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	588.2.ba.b.187.4	yes	336
4.3	odd	2		588.2.ba.a.187.17	✓	336
49.38	odd	42		588.2.ba.a.283.17	yes	336
196.87	even	42	inner	588.2.ba.b.283.4	yes	336

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.ba.a.187.17	✓	336	4.3	odd	2
588.2.ba.a.283.17	yes	336	49.38	odd	42
588.2.ba.b.187.4	yes	336	1.1	even	1	trivial
588.2.ba.b.283.4	yes	336	196.87	even	42	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:	\( N \)	\(=\)	\( 588 = 2^{2} \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	588.ba (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.30318 + 0.549285i) q^{2} +(-0.988831 - 0.149042i) q^{3} +(1.39657 - 1.43164i) q^{4} +(-2.67539 + 1.05002i) q^{5} +(1.37049 - 0.348920i) q^{6} +(-0.927902 - 2.47770i) q^{7} +(-1.03361 + 2.63280i) q^{8} +(0.955573 + 0.294755i) q^{9} +O(q^{10})\)	\(q+(-1.30318 + 0.549285i) q^{2} +(-0.988831 - 0.149042i) q^{3} +(1.39657 - 1.43164i) q^{4} +(-2.67539 + 1.05002i) q^{5} +(1.37049 - 0.348920i) q^{6} +(-0.927902 - 2.47770i) q^{7} +(-1.03361 + 2.63280i) q^{8} +(0.955573 + 0.294755i) q^{9} +(2.90977 - 2.83792i) q^{10} +(-1.21319 - 3.93306i) q^{11} +(-1.59435 + 1.20750i) q^{12} +(4.15433 + 0.948198i) q^{13} +(2.57019 + 2.71921i) q^{14} +(2.80201 - 0.639540i) q^{15} +(-0.0991714 - 3.99877i) q^{16} +(-1.41274 + 2.07211i) q^{17} +(-1.40719 + 0.140762i) q^{18} +(-1.77717 + 3.07815i) q^{19} +(-2.23314 + 5.29662i) q^{20} +(0.548256 + 2.58832i) q^{21} +(3.74138 + 4.45911i) q^{22} +(-0.0806465 - 0.118287i) q^{23} +(1.41447 - 2.44934i) q^{24} +(2.38995 - 2.21755i) q^{25} +(-5.93468 + 1.04623i) q^{26} +(-0.900969 - 0.433884i) q^{27} +(-4.84305 - 2.13187i) q^{28} +(-1.88067 + 0.905681i) q^{29} +(-3.30024 + 2.37254i) q^{30} +(2.09249 + 3.62430i) q^{31} +(2.32570 + 5.15666i) q^{32} +(0.613446 + 4.06995i) q^{33} +(0.702881 - 3.47633i) q^{34} +(5.08413 + 5.65451i) q^{35} +(1.75651 - 0.956387i) q^{36} +(-0.213032 + 2.84272i) q^{37} +(0.625198 - 4.98757i) q^{38} +(-3.96660 - 1.55678i) q^{39} +(0.000840595 - 8.12909i) q^{40} +(5.74932 + 4.58493i) q^{41} +(-2.13620 - 3.07191i) q^{42} +(0.530190 - 0.422812i) q^{43} +(-7.32502 - 3.75596i) q^{44} +(-2.86603 + 0.214779i) q^{45} +(0.170070 + 0.109851i) q^{46} +(4.03381 + 3.74283i) q^{47} +(-0.497922 + 3.96889i) q^{48} +(-5.27800 + 4.59813i) q^{49} +(-1.89647 + 4.20263i) q^{50} +(1.70579 - 1.83841i) q^{51} +(7.15929 - 4.62326i) q^{52} +(0.987714 + 13.1801i) q^{53} +(1.41245 + 0.0705414i) q^{54} +(7.37553 + 9.24862i) q^{55} +(7.48238 + 0.118000i) q^{56} +(2.21610 - 2.77890i) q^{57} +(1.95338 - 2.21329i) q^{58} +(-0.259487 + 0.661162i) q^{59} +(2.99762 - 4.90463i) q^{60} +(-8.24273 - 0.617707i) q^{61} +(-4.71767 - 3.57376i) q^{62} +(-0.156363 - 2.64113i) q^{63} +(-5.86329 - 5.44259i) q^{64} +(-12.1101 + 1.82530i) q^{65} +(-3.03499 - 4.96693i) q^{66} +(-13.2691 + 7.66092i) q^{67} +(0.993515 + 4.91638i) q^{68} +(0.0621160 + 0.128985i) q^{69} +(-9.73149 - 4.57623i) q^{70} +(6.00357 - 12.4665i) q^{71} +(-1.76372 + 2.21117i) q^{72} +(8.63806 + 9.30962i) q^{73} +(-1.28384 - 3.82160i) q^{74} +(-2.69376 + 1.83657i) q^{75} +(1.92485 + 6.84313i) q^{76} +(-8.61922 + 6.65541i) q^{77} +(6.02433 - 0.150030i) q^{78} +(0.803099 + 0.463670i) q^{79} +(4.46409 + 10.5942i) q^{80} +(0.826239 + 0.563320i) q^{81} +(-10.0108 - 2.81699i) q^{82} +(3.42570 + 15.0090i) q^{83} +(4.47122 + 2.82988i) q^{84} +(1.60389 - 7.02711i) q^{85} +(-0.458690 + 0.842227i) q^{86} +(1.99465 - 0.615267i) q^{87} +(11.6089 + 0.871176i) q^{88} +(4.14664 - 13.4431i) q^{89} +(3.61699 - 1.85416i) q^{90} +(-1.50546 - 11.1730i) q^{91} +(-0.281972 - 0.0497394i) q^{92} +(-1.52895 - 3.89569i) q^{93} +(-7.31267 - 2.66188i) q^{94} +(1.52253 - 10.1013i) q^{95} +(-1.53117 - 5.44569i) q^{96} -1.93928i q^{97} +(4.35251 - 8.89132i) q^{98} -4.11592i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 336 q + 28 q^{3} - 2 q^{7} - 6 q^{8} + 28 q^{9}+O(q^{10}) \) 336 * q + 28 * q^3 - 2 * q^7 - 6 * q^8 + 28 * q^9	\( 336 q + 28 q^{3} - 2 q^{7} - 6 q^{8} + 28 q^{9} - 23 q^{10} - 6 q^{11} - 30 q^{14} - 12 q^{16} + 6 q^{19} + 25 q^{20} + 4 q^{21} + 6 q^{22} + 15 q^{24} - 26 q^{25} - 12 q^{26} - 56 q^{27} + 36 q^{28} - 13 q^{30} - 2 q^{31} - 25 q^{32} + 6 q^{33} + 68 q^{34} + 12 q^{35} + 16 q^{37} + 82 q^{38} - 8 q^{39} - 19 q^{40} - 9 q^{42} - 11 q^{44} + 10 q^{46} - 4 q^{47} - 8 q^{48} - 4 q^{49} - 114 q^{50} - 8 q^{52} - 4 q^{53} - 41 q^{56} - 12 q^{57} - 33 q^{58} + 10 q^{59} + 17 q^{60} + 2 q^{61} + 16 q^{62} + 12 q^{63} + 84 q^{64} - 4 q^{65} + 15 q^{66} - 42 q^{67} + 10 q^{68} - 38 q^{70} - 28 q^{71} + 33 q^{72} + 18 q^{73} + 2 q^{74} - 54 q^{75} - 7 q^{76} - 8 q^{77} - 6 q^{78} + 6 q^{79} - 14 q^{80} + 28 q^{81} - 87 q^{82} - 10 q^{83} - 14 q^{84} + 24 q^{85} + 126 q^{86} - 244 q^{88} - 20 q^{90} + 34 q^{91} + 14 q^{92} - 2 q^{93} - 184 q^{94} + 24 q^{95} - 20 q^{96} - 122 q^{98}+O(q^{100}) \) 336 * q + 28 * q^3 - 2 * q^7 - 6 * q^8 + 28 * q^9 - 23 * q^10 - 6 * q^11 - 30 * q^14 - 12 * q^16 + 6 * q^19 + 25 * q^20 + 4 * q^21 + 6 * q^22 + 15 * q^24 - 26 * q^25 - 12 * q^26 - 56 * q^27 + 36 * q^28 - 13 * q^30 - 2 * q^31 - 25 * q^32 + 6 * q^33 + 68 * q^34 + 12 * q^35 + 16 * q^37 + 82 * q^38 - 8 * q^39 - 19 * q^40 - 9 * q^42 - 11 * q^44 + 10 * q^46 - 4 * q^47 - 8 * q^48 - 4 * q^49 - 114 * q^50 - 8 * q^52 - 4 * q^53 - 41 * q^56 - 12 * q^57 - 33 * q^58 + 10 * q^59 + 17 * q^60 + 2 * q^61 + 16 * q^62 + 12 * q^63 + 84 * q^64 - 4 * q^65 + 15 * q^66 - 42 * q^67 + 10 * q^68 - 38 * q^70 - 28 * q^71 + 33 * q^72 + 18 * q^73 + 2 * q^74 - 54 * q^75 - 7 * q^76 - 8 * q^77 - 6 * q^78 + 6 * q^79 - 14 * q^80 + 28 * q^81 - 87 * q^82 - 10 * q^83 - 14 * q^84 + 24 * q^85 + 126 * q^86 - 244 * q^88 - 20 * q^90 + 34 * q^91 + 14 * q^92 - 2 * q^93 - 184 * q^94 + 24 * q^95 - 20 * q^96 - 122 * q^98

Introduction

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