LMFDB - Embedded newform 210.2.u.b.157.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,2,Mod(73,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 9, 2]))

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

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

chi := DirichletCharacter("210.73");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	210.u (of order $12$, degree $4$, 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:	$1.67685844245$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			157.2
Root			$-0.709944 - 0.925217i$ of defining polynomial
Character	$\chi$	$=$	210.157
Dual form			210.2.u.b.103.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.96047 + 1.07544i) q^{5} +1.00000i q^{6} +(-1.52856 + 2.15951i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.96047 + 1.07544i) q^{5} +1.00000i q^{6} +(-1.52856 + 2.15951i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-1.54620 + 1.61532i) q^{10} +(0.883028 - 1.52945i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(2.71395 + 2.71395i) q^{13} +(-1.69031 - 2.03540i) q^{14} +(2.17201 + 0.531389i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.574830 - 2.14529i) q^{17} +(0.258819 + 0.965926i) q^{18} +(0.886994 + 1.53632i) q^{19} +(-1.16009 - 1.91159i) q^{20} +(-0.917556 + 2.48155i) q^{21} +(1.24879 + 1.24879i) q^{22} +(-3.90900 - 1.04741i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.68686 + 4.21673i) q^{25} +(-3.32389 + 1.91905i) q^{26} +(0.707107 - 0.707107i) q^{27} +(2.40353 - 1.10591i) q^{28} -3.84628i q^{29} +(-1.07544 + 1.96047i) q^{30} +(-8.94554 - 5.16471i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(0.457089 - 1.70588i) q^{33} +2.22097 q^{34} +(-5.31912 + 2.58977i) q^{35} -1.00000 q^{36} +(-0.861499 + 3.21516i) q^{37} +(-1.71354 + 0.459142i) q^{38} +(3.32389 + 1.91905i) q^{39} +(2.14671 - 0.625808i) q^{40} -11.8993i q^{41} +(-2.15951 - 1.52856i) q^{42} +(3.46335 - 3.46335i) q^{43} +(-1.52945 + 0.883028i) q^{44} +(2.23553 - 0.0488750i) q^{45} +(2.02344 - 3.50471i) q^{46} +(5.93837 + 1.59118i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-2.32699 - 6.60190i) q^{49} +(-4.76846 + 1.50394i) q^{50} +(-1.11049 - 1.92342i) q^{51} +(-0.993373 - 3.70732i) q^{52} +(0.106258 + 0.396561i) q^{53} +(0.500000 + 0.866025i) q^{54} +(3.37598 - 2.04879i) q^{55} +(0.446149 + 2.60786i) q^{56} +(1.25440 + 1.25440i) q^{57} +(3.71522 + 0.995491i) q^{58} +(5.18379 - 8.97859i) q^{59} +(-1.61532 - 1.54620i) q^{60} +(-5.87936 + 3.39445i) q^{61} +(7.30401 - 7.30401i) q^{62} +(-0.244018 + 2.63447i) q^{63} -1.00000i q^{64} +(2.40191 + 8.23928i) q^{65} +(1.52945 + 0.883028i) q^{66} +(-7.37834 + 1.97702i) q^{67} +(-0.574830 + 2.14529i) q^{68} -4.04689 q^{69} +(-1.12484 - 5.80816i) q^{70} -10.7193 q^{71} +(0.258819 - 0.965926i) q^{72} +(10.2705 - 2.75198i) q^{73} +(-2.88263 - 1.66429i) q^{74} +(3.68668 + 3.37764i) q^{75} -1.77399i q^{76} +(1.95310 + 4.24477i) q^{77} +(-2.71395 + 2.71395i) q^{78} +(-10.9907 + 6.34546i) q^{79} +(0.0488750 + 2.23553i) q^{80} +(0.500000 - 0.866025i) q^{81} +(11.4939 + 3.07978i) q^{82} +(-1.94227 - 1.94227i) q^{83} +(2.03540 - 1.69031i) q^{84} +(1.18020 - 4.82397i) q^{85} +(2.44896 + 4.24172i) q^{86} +(-0.995491 - 3.71522i) q^{87} +(-0.457089 - 1.70588i) q^{88} +(-0.558127 - 0.966705i) q^{89} +(-0.531389 + 2.17201i) q^{90} +(-10.0092 + 1.71236i) q^{91} +(2.86158 + 2.86158i) q^{92} +(-9.97746 - 2.67345i) q^{93} +(-3.07393 + 5.32419i) q^{94} +(0.0867037 + 3.96581i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(-7.26720 + 7.26720i) q^{97} +(6.97922 - 0.539001i) q^{98} -1.76606i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{5} - 4 q^{7}+O(q^{10}) $ 16 * q + 12 * q^5 - 4 * q^7	$ 16 q + 12 q^{5} - 4 q^{7} + 4 q^{10} + 4 q^{11} + 16 q^{13} - 16 q^{14} + 4 q^{15} + 8 q^{16} + 12 q^{17} + 8 q^{19} + 8 q^{20} + 8 q^{21} + 4 q^{22} - 40 q^{23} + 8 q^{24} + 16 q^{25} - 12 q^{26} - 4 q^{28} - 4 q^{30} - 24 q^{31} + 4 q^{33} - 16 q^{34} - 44 q^{35} - 16 q^{36} - 8 q^{37} - 20 q^{38} + 12 q^{39} + 8 q^{42} - 24 q^{43} - 4 q^{45} - 4 q^{46} - 52 q^{49} + 8 q^{51} + 8 q^{52} - 28 q^{53} + 8 q^{54} + 56 q^{55} + 8 q^{56} - 8 q^{57} - 12 q^{58} - 8 q^{59} + 24 q^{61} - 8 q^{62} - 4 q^{63} + 16 q^{65} - 84 q^{67} + 12 q^{68} + 8 q^{69} + 4 q^{70} - 32 q^{71} + 16 q^{73} + 24 q^{74} - 24 q^{75} + 44 q^{77} - 16 q^{78} - 12 q^{79} + 12 q^{80} + 8 q^{81} + 36 q^{82} + 16 q^{83} - 4 q^{84} + 8 q^{85} - 8 q^{86} + 48 q^{87} - 4 q^{88} + 16 q^{89} + 8 q^{91} + 8 q^{92} - 32 q^{93} - 8 q^{94} + 72 q^{95} - 44 q^{97} + 24 q^{98}+O(q^{100}) $ 16 * q + 12 * q^5 - 4 * q^7 + 4 * q^10 + 4 * q^11 + 16 * q^13 - 16 * q^14 + 4 * q^15 + 8 * q^16 + 12 * q^17 + 8 * q^19 + 8 * q^20 + 8 * q^21 + 4 * q^22 - 40 * q^23 + 8 * q^24 + 16 * q^25 - 12 * q^26 - 4 * q^28 - 4 * q^30 - 24 * q^31 + 4 * q^33 - 16 * q^34 - 44 * q^35 - 16 * q^36 - 8 * q^37 - 20 * q^38 + 12 * q^39 + 8 * q^42 - 24 * q^43 - 4 * q^45 - 4 * q^46 - 52 * q^49 + 8 * q^51 + 8 * q^52 - 28 * q^53 + 8 * q^54 + 56 * q^55 + 8 * q^56 - 8 * q^57 - 12 * q^58 - 8 * q^59 + 24 * q^61 - 8 * q^62 - 4 * q^63 + 16 * q^65 - 84 * q^67 + 12 * q^68 + 8 * q^69 + 4 * q^70 - 32 * q^71 + 16 * q^73 + 24 * q^74 - 24 * q^75 + 44 * q^77 - 16 * q^78 - 12 * q^79 + 12 * q^80 + 8 * q^81 + 36 * q^82 + 16 * q^83 - 4 * q^84 + 8 * q^85 - 8 * q^86 + 48 * q^87 - 4 * q^88 + 16 * q^89 + 8 * q^91 + 8 * q^92 - 32 * q^93 - 8 * q^94 + 72 * q^95 - 44 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$2$	−0.258819	+	0.965926i	−0.183013	+	0.683013i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$3$	0.965926	−	0.258819i	0.557678	−	0.149429i
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	1.96047	+	1.07544i	0.876747	+	0.480951i
$5$	1.96047	+	1.07544i	0.876747	+	0.480951i
$6$			1.00000i			0.408248i
$7$	−1.52856	+	2.15951i	−0.577743	+	0.816219i
$7$	−1.52856	+	2.15951i	−0.577743	+	0.816219i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	−1.54620	+	1.61532i	−0.488952	+	0.510809i
$11$	0.883028	−	1.52945i	0.266243	−	0.461147i	−0.701645	−	0.712526i	$-0.747551\pi$
$11$	0.883028	−	1.52945i	0.266243	−	0.461147i	0.967889	+	0.251380i	$0.0808843\pi$
$12$	−0.965926	−	0.258819i	−0.278839	−	0.0747146i
$13$	2.71395	+	2.71395i	0.752713	+	0.752713i	0.974985	−	0.222272i	$-0.0713472\pi$
$13$	2.71395	+	2.71395i	0.752713	+	0.752713i	−0.222272	+	0.974985i	$0.571347\pi$
$14$	−1.69031	−	2.03540i	−0.451754	−	0.543984i
$15$	2.17201	+	0.531389i	0.560810	+	0.137204i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.574830	−	2.14529i	−0.139417	−	0.520310i	−0.999941	−	0.0109000i	$-0.996530\pi$
$17$	−0.574830	−	2.14529i	−0.139417	−	0.520310i	0.860524	−	0.509410i	$-0.170136\pi$
$18$	0.258819	+	0.965926i	0.0610042	+	0.227671i
$19$	0.886994	+	1.53632i	0.203490	+	0.352456i	0.949651	−	0.313311i	$-0.101438\pi$
$19$	0.886994	+	1.53632i	0.203490	+	0.352456i	−0.746160	+	0.665766i	$0.768105\pi$
$20$	−1.16009	−	1.91159i	−0.259405	−	0.427445i
$21$	−0.917556	+	2.48155i	−0.200227	+	0.541519i
$22$	1.24879	+	1.24879i	0.266243	+	0.266243i
$23$	−3.90900	−	1.04741i	−0.815082	−	0.218401i	−0.172887	−	0.984942i	$-0.555309\pi$
$23$	−3.90900	−	1.04741i	−0.815082	−	0.218401i	−0.642195	+	0.766541i	$0.721976\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	2.68686	+	4.21673i	0.537372	+	0.843346i
$26$	−3.32389	+	1.91905i	−0.651869	+	0.376356i
$27$	0.707107	−	0.707107i	0.136083	−	0.136083i
$28$	2.40353	−	1.10591i	0.454225	−	0.208998i
$29$		−	3.84628i		−	0.714236i	−0.934059	−	0.357118i	$-0.883759\pi$
$29$		−	3.84628i		−	0.714236i	0.934059	−	0.357118i	$-0.116241\pi$
$30$	−1.07544	+	1.96047i	−0.196348	+	0.357931i
$31$	−8.94554	−	5.16471i	−1.60667	−	0.927610i	−0.990109	−	0.140300i	$-0.955193\pi$
$31$	−8.94554	−	5.16471i	−1.60667	−	0.927610i	−0.616558	−	0.787310i	$-0.711473\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	0.457089	−	1.70588i	0.0795690	−	0.296956i
$34$	2.22097			0.380893
$35$	−5.31912	+	2.58977i	−0.899096	+	0.437752i
$36$	−1.00000			−0.166667
$37$	−0.861499	+	3.21516i	−0.141630	+	0.528569i	0.858253	+	0.513227i	$0.171550\pi$
$37$	−0.861499	+	3.21516i	−0.141630	+	0.528569i	−0.999882	+	0.0153416i	$0.995116\pi$
$38$	−1.71354	+	0.459142i	−0.277973	+	0.0744827i
$39$	3.32389	+	1.91905i	0.532248	+	0.307294i
$40$	2.14671	−	0.625808i	0.339425	−	0.0989490i
$41$		−	11.8993i		−	1.85836i	−0.369622	−	0.929182i	$-0.620513\pi$
$41$		−	11.8993i		−	1.85836i	0.369622	−	0.929182i	$-0.379487\pi$
$42$	−2.15951	−	1.52856i	−0.333220	−	0.235862i
$43$	3.46335	−	3.46335i	0.528155	−	0.528155i	−0.391867	−	0.920022i	$-0.628171\pi$
$43$	3.46335	−	3.46335i	0.528155	−	0.528155i	0.920022	+	0.391867i	$0.128171\pi$
$44$	−1.52945	+	0.883028i	−0.230573	+	0.133122i
$45$	2.23553	−	0.0488750i	0.333254	−	0.00728585i
$46$	2.02344	−	3.50471i	0.298341	−	0.516741i
$47$	5.93837	+	1.59118i	0.866200	+	0.232098i	0.664444	−	0.747338i	$-0.268668\pi$
$47$	5.93837	+	1.59118i	0.866200	+	0.232098i	0.201756	+	0.979436i	$0.435335\pi$
$48$	0.707107	+	0.707107i	0.102062	+	0.102062i
$49$	−2.32699	−	6.60190i	−0.332427	−	0.943129i
$50$	−4.76846	+	1.50394i	−0.674362	+	0.212689i
$51$	−1.11049	−	1.92342i	−0.155499	−	0.269332i
$52$	−0.993373	−	3.70732i	−0.137756	−	0.514113i
$53$	0.106258	+	0.396561i	0.0145957	+	0.0544719i	0.972840	−	0.231480i	$-0.0743569\pi$
$53$	0.106258	+	0.396561i	0.0145957	+	0.0544719i	−0.958244	+	0.285952i	$0.907690\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	3.37598	−	2.04879i	0.455217	−	0.276259i
$56$	0.446149	+	2.60786i	0.0596191	+	0.348490i
$57$	1.25440	+	1.25440i	0.166149	+	0.166149i
$58$	3.71522	+	0.995491i	0.487833	+	0.130714i
$59$	5.18379	−	8.97859i	0.674872	−	1.16891i	−0.301634	−	0.953424i	$-0.597532\pi$
$59$	5.18379	−	8.97859i	0.674872	−	1.16891i	0.976506	−	0.215489i	$-0.0691346\pi$
$60$	−1.61532	−	1.54620i	−0.208537	−	0.199614i
$61$	−5.87936	+	3.39445i	−0.752775	+	0.434615i	−0.826696	−	0.562649i	$-0.809782\pi$
$61$	−5.87936	+	3.39445i	−0.752775	+	0.434615i	0.0739204	+	0.997264i	$0.476449\pi$
$62$	7.30401	−	7.30401i	0.927610	−	0.927610i
$63$	−0.244018	+	2.63447i	−0.0307434	+	0.331913i
$64$		−	1.00000i		−	0.125000i
$65$	2.40191	+	8.23928i	0.297921	+	1.02196i
$66$	1.52945	+	0.883028i	0.188262	+	0.108693i
$67$	−7.37834	+	1.97702i	−0.901408	+	0.241532i	−0.679621	−	0.733563i	$-0.737856\pi$
$67$	−7.37834	+	1.97702i	−0.901408	+	0.241532i	−0.221787	+	0.975095i	$0.571189\pi$
$68$	−0.574830	+	2.14529i	−0.0697083	+	0.260155i
$69$	−4.04689			−0.487188
$70$	−1.12484	−	5.80816i	−0.134444	−	0.694208i
$71$	−10.7193			−1.27214			−0.636072	−	0.771629i	$-0.719442\pi$
$71$	−10.7193			−1.27214			−0.636072	+	0.771629i	$0.719442\pi$
$72$	0.258819	−	0.965926i	0.0305021	−	0.113835i
$73$	10.2705	−	2.75198i	1.20207	−	0.322095i	0.398426	−	0.917200i	$-0.369556\pi$
$73$	10.2705	−	2.75198i	1.20207	−	0.322095i	0.803647	+	0.595106i	$0.202890\pi$
$74$	−2.88263	−	1.66429i	−0.335099	−	0.193470i
$75$	3.68668	+	3.37764i	0.425701	+	0.390016i
$76$		−	1.77399i		−	0.203490i
$77$	1.95310	+	4.24477i	0.222577	+	0.483737i
$78$	−2.71395	+	2.71395i	−0.307294	+	0.307294i
$79$	−10.9907	+	6.34546i	−1.23655	+	0.713920i	−0.968386	−	0.249455i	$-0.919749\pi$
$79$	−10.9907	+	6.34546i	−1.23655	+	0.713920i	−0.268159	+	0.963375i	$0.586415\pi$
$80$	0.0488750	+	2.23553i	0.00546439	+	0.249940i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	11.4939	+	3.07978i	1.26929	+	0.340104i
$83$	−1.94227	−	1.94227i	−0.213191	−	0.213191i	0.592430	−	0.805622i	$-0.298169\pi$
$83$	−1.94227	−	1.94227i	−0.213191	−	0.213191i	−0.805622	+	0.592430i	$0.798169\pi$
$84$	2.03540	−	1.69031i	0.222081	−	0.184428i
$85$	1.18020	−	4.82397i	0.128011	−	0.523233i
$86$	2.44896	+	4.24172i	0.264078	+	0.457396i
$87$	−0.995491	−	3.71522i	−0.106728	−	0.398314i
$88$	−0.457089	−	1.70588i	−0.0487259	−	0.181847i
$89$	−0.558127	−	0.966705i	−0.0591614	−	0.102471i	0.834928	−	0.550359i	$-0.185509\pi$
$89$	−0.558127	−	0.966705i	−0.0591614	−	0.102471i	−0.894089	+	0.447889i	$0.852176\pi$
$90$	−0.531389	+	2.17201i	−0.0560133	+	0.228950i
$91$	−10.0092	+	1.71236i	−1.04925	+	0.179504i
$92$	2.86158	+	2.86158i	0.298341	+	0.298341i
$93$	−9.97746	−	2.67345i	−1.03461	−	0.277224i
$94$	−3.07393	+	5.32419i	−0.317051	+	0.549149i
$95$	0.0867037	+	3.96581i	0.00889561	+	0.406884i
$96$	−0.866025	+	0.500000i	−0.0883883	+	0.0510310i
$97$	−7.26720	+	7.26720i	−0.737872	+	0.737872i	−0.972166	−	0.234293i	$-0.924722\pi$
$97$	−7.26720	+	7.26720i	−0.737872	+	0.737872i	0.234293	+	0.972166i	$0.424722\pi$
$98$	6.97922	−	0.539001i	0.705007	−	0.0544473i
$99$		−	1.76606i		−	0.177495i
$100$	−0.218523	−	4.99522i	−0.0218523	−	0.499522i
$101$	15.8887	+	9.17333i	1.58098	+	0.912780i	0.994716	+	0.102661i	$0.0327358\pi$
$101$	15.8887	+	9.17333i	1.58098	+	0.912780i	0.586265	+	0.810119i	$0.300598\pi$
$102$	2.14529	−	0.574830i	0.212416	−	0.0569166i
$103$	2.36040	−	8.80911i	0.232577	−	0.867988i	−0.746650	−	0.665217i	$-0.768339\pi$
$103$	2.36040	−	8.80911i	0.232577	−	0.867988i	0.979226	−	0.202770i	$-0.0649945\pi$
$104$	3.83810			0.376356
$105$	−4.46760	+	3.87822i	−0.435993	+	0.378476i
$106$	−0.410550			−0.0398762
$107$	−3.81880	+	14.2519i	−0.369177	+	1.37779i	0.492492	+	0.870317i	$0.336086\pi$
$107$	−3.81880	+	14.2519i	−0.369177	+	1.37779i	−0.861669	+	0.507471i	$0.830581\pi$
$108$	−0.965926	+	0.258819i	−0.0929463	+	0.0249049i
$109$	17.4494	+	10.0744i	1.67135	+	0.964955i	0.966883	+	0.255218i	$0.0821474\pi$
$109$	17.4494	+	10.0744i	1.67135	+	0.964955i	0.704467	+	0.709736i	$0.251186\pi$
$110$	1.10521	+	3.79121i	0.105378	+	0.361478i
$111$			3.32858i			0.315935i
$112$	−2.63447	−	0.244018i	−0.248934	−	0.0230576i
$113$	−6.54677	+	6.54677i	−0.615869	+	0.615869i	−0.944469	−	0.328600i	$-0.893423\pi$
$113$	−6.54677	+	6.54677i	−0.615869	+	0.615869i	0.328600	+	0.944469i	$0.393423\pi$
$114$	−1.53632	+	0.886994i	−0.143889	+	0.0830746i
$115$	−6.53703	−	6.25731i	−0.609581	−	0.583497i
$116$	−1.92314	+	3.33098i	−0.178559	+	0.309273i
$117$	3.70732	+	0.993373i	0.342742	+	0.0918374i
$118$	7.33099	+	7.33099i	0.674872	+	0.674872i
$119$	5.51145	+	2.03786i	0.505234	+	0.186811i
$120$	1.91159	−	1.16009i	0.174504	−	0.105902i
$121$	3.94052	+	6.82518i	0.358229	+	0.620471i
$122$	−1.75710	−	6.55758i	−0.159080	−	0.593695i
$123$	−3.07978	−	11.4939i	−0.277694	−	1.03637i
$124$	5.16471	+	8.94554i	0.463805	+	0.803333i
$125$	0.732658	+	11.1563i	0.0655309	+	0.997851i
$126$	−2.48155	−	0.917556i	−0.221074	−	0.0817424i
$127$	12.5444	+	12.5444i	1.11313	+	1.11313i	0.992724	+	0.120409i	$0.0384206\pi$
$127$	12.5444	+	12.5444i	1.11313	+	1.11313i	0.120409	+	0.992724i	$0.461579\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	2.44896	−	4.24172i	0.215619	−	0.373462i
$130$	−8.58020	+	0.187587i	−0.752533	+	0.0164525i
$131$	0.830756	−	0.479637i	0.0725835	−	0.0419061i	−0.463269	−	0.886218i	$-0.653324\pi$
$131$	0.830756	−	0.479637i	0.0725835	−	0.0419061i	0.535853	+	0.844312i	$0.319990\pi$
$132$	−1.24879	+	1.24879i	−0.108693	+	0.108693i
$133$	−4.67353	−	0.432886i	−0.405246	−	0.0375359i
$134$		−	7.63862i		−	0.659877i
$135$	2.14671	−	0.625808i	0.184759	−	0.0538610i
$136$	−1.92342	−	1.11049i	−0.164932	−	0.0952233i
$137$	−10.7669	+	2.88499i	−0.919880	+	0.246481i	−0.687534	−	0.726152i	$-0.741307\pi$
$137$	−10.7669	+	2.88499i	−0.919880	+	0.246481i	−0.232346	+	0.972633i	$0.574640\pi$
$138$	1.04741	−	3.90900i	0.0891616	−	0.332756i
$139$	−13.5695			−1.15095			−0.575477	−	0.817818i	$-0.695184\pi$
$139$	−13.5695			−1.15095			−0.575477	+	0.817818i	$0.695184\pi$
$140$	5.90138	+	0.416751i	0.498758	+	0.0352219i
$141$	6.14785			0.517742
$142$	2.77435	−	10.3540i	0.232819	−	0.868891i
$143$	6.54733	−	1.75435i	0.547516	−	0.146706i
$144$	0.866025	+	0.500000i	0.0721688	+	0.0416667i
$145$	4.13644	−	7.54050i	0.343513	−	0.626205i
$146$			10.6328i			0.879979i
$147$	−3.95640	−	5.77468i	−0.326318	−	0.476288i
$148$	2.35366	−	2.35366i	0.193470	−	0.193470i
$149$	8.74565	−	5.04930i	0.716471	−	0.413655i	−0.0969812	−	0.995286i	$-0.530919\pi$
$149$	8.74565	−	5.04930i	0.716471	−	0.413655i	0.813453	+	0.581631i	$0.197585\pi$
$150$	−4.21673	+	2.68686i	−0.344294	+	0.219381i
$151$	7.15497	−	12.3928i	0.582263	−	1.00851i	−0.412948	−	0.910755i	$-0.635501\pi$
$151$	7.15497	−	12.3928i	0.582263	−	1.00851i	0.995211	−	0.0977541i	$-0.0311659\pi$
$152$	1.71354	+	0.459142i	0.138987	+	0.0372413i
$153$	−1.57046	−	1.57046i	−0.126964	−	0.126964i
$154$	−4.60563	+	0.787924i	−0.371133	+	0.0634927i
$155$	−11.9831	−	19.7456i	−0.962506	−	1.58601i
$156$	−1.91905	−	3.32389i	−0.153647	−	0.266124i
$157$	−2.48036	−	9.25683i	−0.197954	−	0.738776i	−0.991482	−	0.130242i	$-0.958425\pi$
$157$	−2.48036	−	9.25683i	−0.197954	−	0.738776i	0.793528	−	0.608534i	$-0.208242\pi$
$158$	−3.28465	−	12.2585i	−0.261313	−	0.975233i
$159$	0.205275	+	0.355547i	0.0162794	+	0.0281967i
$160$	−2.17201	−	0.531389i	−0.171712	−	0.0420100i
$161$	8.23705	−	6.84049i	0.649170	−	0.539106i
$162$	0.707107	+	0.707107i	0.0555556	+	0.0555556i
$163$	−11.4401	−	3.06537i	−0.896058	−	0.240098i	−0.218736	−	0.975784i	$-0.570193\pi$
$163$	−11.4401	−	3.06537i	−0.896058	−	0.240098i	−0.677323	+	0.735686i	$0.736860\pi$
$164$	−5.94967	+	10.3051i	−0.464591	+	0.804695i
$165$	2.73068	−	2.85275i	0.212583	−	0.222086i
$166$	2.37878	−	1.37339i	0.184629	−	0.106596i
$167$	6.95883	−	6.95883i	0.538490	−	0.538490i	−0.384595	−	0.923085i	$-0.625659\pi$
$167$	6.95883	−	6.95883i	0.538490	−	0.538490i	0.923085	+	0.384595i	$0.125659\pi$
$168$	1.10591	+	2.40353i	0.0853229	+	0.185436i
$169$			1.73100i			0.133154i
$170$	4.35414	+	2.38852i	0.333947	+	0.183191i
$171$	1.53632	+	0.886994i	0.117485	+	0.0678301i
$172$	−4.73102	+	1.26767i	−0.360737	+	0.0966592i
$173$	−2.24296	+	8.37084i	−0.170529	+	0.636423i	0.826741	+	0.562583i	$0.190192\pi$
$173$	−2.24296	+	8.37084i	−0.170529	+	0.636423i	−0.997270	+	0.0738403i	$0.976474\pi$
$174$	3.84628			0.291586
$175$	−13.2131	−	0.643231i	−0.998817	−	0.0486237i
$176$	1.76606			0.133122
$177$	2.68333	−	10.0143i	0.201691	−	0.752722i
$178$	1.07822	−	0.288908i	0.0808160	−	0.0216546i
$179$	11.5646	+	6.67682i	0.864378	+	0.499049i	0.865476	−	0.500951i	$-0.167016\pi$
$179$	11.5646	+	6.67682i	0.864378	+	0.499049i	−0.00109809	+	0.999999i	$0.500350\pi$
$180$	−1.96047	−	1.07544i	−0.146125	−	0.0801586i
$181$		−	8.73922i		−	0.649581i	−0.945786	−	0.324791i	$-0.894706\pi$
$181$		−	8.73922i		−	0.649581i	0.945786	−	0.324791i	$-0.105294\pi$
$182$	0.936566	−	10.1114i	0.0694229	−	0.749505i
$183$	−4.80048	+	4.80048i	−0.354862	+	0.354862i
$184$	−3.50471	+	2.02344i	−0.258371	+	0.149170i
$185$	−5.14665	+	5.37672i	−0.378389	+	0.395304i
$186$	5.16471	−	8.94554i	0.378695	−	0.655919i
$187$	−3.78871	−	1.01518i	−0.277058	−	0.0742374i
$188$	−4.34719	−	4.34719i	−0.317051	−	0.317051i
$189$	0.446149	+	2.60786i	0.0324525	+	0.189694i
$190$	−3.85312	−	0.942678i	−0.279535	−	0.0683891i
$191$	5.43796	+	9.41883i	0.393477	+	0.681523i	0.992906	−	0.118906i	$-0.0379386\pi$
$191$	5.43796	+	9.41883i	0.393477	+	0.681523i	−0.599428	+	0.800429i	$0.704605\pi$
$192$	−0.258819	−	0.965926i	−0.0186787	−	0.0697097i
$193$	2.89908	+	10.8195i	0.208680	+	0.778806i	0.988296	+	0.152548i	$0.0487478\pi$
$193$	2.89908	+	10.8195i	0.208680	+	0.778806i	−0.779616	+	0.626258i	$0.784586\pi$
$194$	−5.13869	−	8.90047i	−0.368936	−	0.639016i
$195$	4.45255	+	7.33688i	0.318854	+	0.525405i
$196$	−1.28572	+	6.88091i	−0.0918371	+	0.491494i
$197$	−10.3775	−	10.3775i	−0.739367	−	0.739367i	0.233088	−	0.972456i	$-0.425117\pi$
$197$	−10.3775	−	10.3775i	−0.739367	−	0.739367i	−0.972456	+	0.233088i	$0.925117\pi$
$198$	1.70588	+	0.457089i	0.121232	+	0.0324839i
$199$	−9.28152	+	16.0761i	−0.657949	+	1.13960i	0.323197	+	0.946332i	$0.395243\pi$
$199$	−9.28152	+	16.0761i	−0.657949	+	1.13960i	−0.981146	+	0.193270i	$0.938091\pi$
$200$	4.88157	+	1.08178i	0.345179	+	0.0764935i
$201$	−6.61524	+	3.81931i	−0.466603	+	0.269394i
$202$	−12.9730	+	12.9730i	−0.912780	+	0.912780i
$203$	8.30609	+	5.87928i	0.582973	+	0.412645i
$204$			2.22097i			0.155499i
$205$	12.7970	−	23.3283i	0.893783	−	1.62932i
$206$	7.89804	+	4.55993i	0.550282	+	0.317706i
$207$	−3.90900	+	1.04741i	−0.271694	+	0.0728002i
$208$	−0.993373	+	3.70732i	−0.0688780	+	0.257056i
$209$	3.13296			0.216712
$210$	−2.58977	−	5.31912i	−0.178711	−	0.367054i
$211$	−0.453133			−0.0311950			−0.0155975	−	0.999878i	$-0.504965\pi$
$211$	−0.453133			−0.0311950			−0.0155975	+	0.999878i	$0.504965\pi$
$212$	0.106258	−	0.396561i	0.00729784	−	0.0272359i
$213$	−10.3540	+	2.77435i	−0.709446	+	0.190096i
$214$	−12.7779	−	7.37735i	−0.873483	−	0.504305i
$215$	10.5144	−	3.06515i	0.717076	−	0.209042i
$216$		−	1.00000i		−	0.0680414i
$217$	24.8271	−	11.4234i	1.68537	−	0.775473i
$218$	−14.2474	+	14.2474i	−0.964955	+	0.964955i
$219$	9.20830	−	5.31641i	0.622239	−	0.359250i
$220$	−3.94808	+	0.0863160i	−0.266179	+	0.00581942i
$221$	4.26215	−	7.38226i	0.286703	−	0.496585i
$222$	−3.21516	−	0.861499i	−0.215787	−	0.0578201i
$223$	4.67260	+	4.67260i	0.312901	+	0.312901i	0.846032	−	0.533132i	$-0.178985\pi$
$223$	4.67260	+	4.67260i	0.312901	+	0.312901i	−0.533132	+	0.846032i	$0.678985\pi$
$224$	0.917556	−	2.48155i	0.0613068	−	0.165806i
$225$	4.43525	+	2.30836i	0.295683	+	0.153891i
$226$	−4.62927	−	8.01813i	−0.307934	−	0.533358i
$227$	−4.29835	−	16.0416i	−0.285291	−	1.06472i	−0.948626	−	0.316399i	$-0.897526\pi$
$227$	−4.29835	−	16.0416i	−0.285291	−	1.06472i	0.663335	−	0.748323i	$-0.269140\pi$
$228$	−0.459142	−	1.71354i	−0.0304074	−	0.113482i
$229$	−6.77075	−	11.7273i	−0.447423	−	0.774960i	0.550794	−	0.834641i	$-0.314325\pi$
$229$	−6.77075	−	11.7273i	−0.447423	−	0.774960i	−0.998217	+	0.0596810i	$0.980992\pi$
$230$	7.73600	−	4.69477i	0.510097	−	0.309564i
$231$	2.98518	+	3.59463i	0.196410	+	0.236510i
$232$	−2.71973	−	2.71973i	−0.178559	−	0.178559i
$233$	−11.1838	−	2.99668i	−0.732672	−	0.196319i	−0.126853	−	0.991922i	$-0.540488\pi$
$233$	−11.1838	−	2.99668i	−0.732672	−	0.196319i	−0.605819	+	0.795603i	$0.707154\pi$
$234$	−1.91905	+	3.32389i	−0.125452	+	0.217290i
$235$	9.93075	+	9.50581i	0.647811	+	0.620091i
$236$	−8.97859	+	5.18379i	−0.584456	+	0.337436i
$237$	−8.97383	+	8.97383i	−0.582913	+	0.582913i
$238$	−3.39489	+	4.79621i	−0.220058	+	0.310892i
$239$			17.0264i			1.10135i	0.834721	+	0.550673i	$0.185629\pi$
$239$			17.0264i			1.10135i	−0.834721	+	0.550673i	$0.814371\pi$
$240$	0.625808	+	2.14671i	0.0403958	+	0.138570i
$241$	16.3866	+	9.46081i	1.05555	+	0.609424i	0.924199	−	0.381911i	$-0.124734\pi$
$241$	16.3866	+	9.46081i	1.05555	+	0.609424i	0.131355	+	0.991335i	$0.458067\pi$
$242$	−7.61250	+	2.03976i	−0.489350	+	0.131121i
$243$	0.258819	−	0.965926i	0.0166032	−	0.0619642i
$244$	6.78891			0.434615
$245$	2.53797	−	15.4453i	0.162145	−	0.986767i
$246$	11.8993			0.758674
$247$	−1.76223	+	6.57674i	−0.112128	+	0.418468i
$248$	−9.97746	+	2.67345i	−0.633569	+	0.169764i
$249$	−2.37878	−	1.37339i	−0.150749	−	0.0870350i
$250$	−10.9658	−	2.17977i	−0.693538	−	0.137861i
$251$		−	18.1527i		−	1.14579i	−0.819629	−	0.572894i	$-0.805821\pi$
$251$		−	18.1527i		−	1.14579i	0.819629	−	0.572894i	$-0.194179\pi$
$252$	1.52856	−	2.15951i	0.0962904	−	0.136037i
$253$	−5.05372	+	5.05372i	−0.317725	+	0.317725i
$254$	−15.3637	+	8.87021i	−0.964002	+	0.556567i
$255$	−0.108550	−	4.96506i	−0.00679766	−	0.310924i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−23.2500	−	6.22983i	−1.45030	−	0.388606i	−0.554170	−	0.832403i	$-0.686964\pi$
$257$	−23.2500	−	6.22983i	−1.45030	−	0.388606i	−0.896127	+	0.443797i	$0.853631\pi$
$258$	3.46335	+	3.46335i	0.215619	+	0.215619i
$259$	−5.62632	−	6.77499i	−0.349603	−	0.420978i
$260$	2.03952	−	8.33639i	0.126486	−	0.517001i
$261$	−1.92314	−	3.33098i	−0.119039	−	0.206182i
$262$	0.248279	+	0.926588i	0.0153387	+	0.0572448i
$263$	3.63274	+	13.5576i	0.224004	+	0.835995i	0.982801	+	0.184668i	$0.0591209\pi$
$263$	3.63274	+	13.5576i	0.224004	+	0.835995i	−0.758797	+	0.651328i	$0.774212\pi$
$264$	−0.883028	−	1.52945i	−0.0543466	−	0.0941311i
$265$	−0.218162	+	0.891719i	−0.0134016	+	0.0547779i
$266$	1.62773	−	4.40224i	0.0998027	−	0.269919i
$267$	−0.789311	−	0.789311i	−0.0483051	−	0.0483051i
$268$	7.37834	+	1.97702i	0.450704	+	0.120766i
$269$	−13.2762	+	22.9951i	−0.809466	+	1.40204i	0.103768	+	0.994602i	$0.466910\pi$
$269$	−13.2762	+	22.9951i	−0.809466	+	1.40204i	−0.913234	+	0.407435i	$0.866423\pi$
$270$	0.0488750	+	2.23553i	0.00297444	+	0.136050i
$271$	10.3582	−	5.98031i	0.629216	−	0.363278i	−0.151232	−	0.988498i	$-0.548324\pi$
$271$	10.3582	−	5.98031i	0.629216	−	0.363278i	0.780448	+	0.625220i	$0.214991\pi$
$272$	1.57046	−	1.57046i	0.0952233	−	0.0952233i
$273$	−9.22499	+	4.24460i	−0.558322	+	0.256895i
$274$		−	11.1467i		−	0.673399i
$275$	8.82185	−	0.385925i	0.531977	−	0.0232721i
$276$	3.50471	+	2.02344i	0.210959	+	0.121797i
$277$	2.28118	−	0.611241i	0.137063	−	0.0367259i	−0.189635	−	0.981855i	$-0.560731\pi$
$277$	2.28118	−	0.611241i	0.137063	−	0.0367259i	0.326698	+	0.945129i	$0.394064\pi$
$278$	3.51206	−	13.1072i	0.210639	−	0.786116i
$279$	−10.3294			−0.618406
$280$	−1.92994	+	5.59243i	−0.115336	+	0.334212i
$281$	−11.0306			−0.658033			−0.329017	−	0.944324i	$-0.606717\pi$
$281$	−11.0306			−0.658033			−0.329017	+	0.944324i	$0.606717\pi$
$282$	−1.59118	+	5.93837i	−0.0947534	+	0.353625i
$283$	22.6131	−	6.05917i	1.34421	−	0.360180i	0.486217	−	0.873838i	$-0.338377\pi$
$283$	22.6131	−	6.05917i	1.34421	−	0.360180i	0.857995	+	0.513658i	$0.171710\pi$
$284$	9.28317	+	5.35964i	0.550855	+	0.318036i
$285$	1.11018	+	3.80824i	0.0657612	+	0.225581i
$286$			6.77830i			0.400809i
$287$	25.6968	+	18.1889i	1.51683	+	1.07366i
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$	10.4506	−	6.03364i	0.614740	−	0.354920i
$290$	6.21298	+	5.94712i	0.364839	+	0.349227i
$291$	−5.13869	+	8.90047i	−0.301235	+	0.521755i
$292$	−10.2705	−	2.75198i	−0.601037	−	0.161047i
$293$	−15.4837	−	15.4837i	−0.904565	−	0.904565i	0.0912620	−	0.995827i	$-0.470910\pi$
$293$	−15.4837	−	15.4837i	−0.904565	−	0.904565i	−0.995827	+	0.0912620i	$0.970910\pi$
$294$	6.60190	−	2.32699i	0.385031	−	0.135713i
$295$	19.8186	−	12.0274i	1.15388	−	0.700261i
$296$	1.66429	+	2.88263i	0.0967348	+	0.167550i
$297$	−0.457089	−	1.70588i	−0.0265230	−	0.0989852i
$298$	2.61371	+	9.75450i	0.151408	+	0.565063i
$299$	−7.76618	−	13.4514i	−0.449130	−	0.777916i
$300$	−1.50394	−	4.76846i	−0.0868298	−	0.275307i
$301$	2.18520	+	12.7731i	0.125953	+	0.736228i
$302$	10.1186	+	10.1186i	0.582263	+	0.582263i
$303$	17.7215	+	4.74846i	1.01807	+	0.272792i
$304$	−0.886994	+	1.53632i	−0.0508726	+	0.0881139i
$305$	−15.1768	+	0.331808i	−0.869023	+	0.0189992i
$306$	1.92342	−	1.11049i	0.109954	−	0.0634822i
$307$	2.12149	−	2.12149i	0.121080	−	0.121080i	−0.643971	−	0.765050i	$-0.722714\pi$
$307$	2.12149	−	2.12149i	0.121080	−	0.121080i	0.765050	+	0.643971i	$0.222714\pi$
$308$	0.430950	−	4.65263i	0.0245557	−	0.265108i
$309$		−	9.11987i		−	0.518811i
$310$	22.1743	−	6.46424i	1.25941	−	0.367144i
$311$	13.0082	+	7.51027i	0.737626	+	0.425868i	0.821205	−	0.570633i	$-0.193302\pi$
$311$	13.0082	+	7.51027i	0.737626	+	0.425868i	−0.0835796	+	0.996501i	$0.526635\pi$
$312$	3.70732	−	0.993373i	0.209886	−	0.0562387i
$313$	−3.44701	+	12.8644i	−0.194836	+	0.727139i	0.797473	+	0.603355i	$0.206170\pi$
$313$	−3.44701	+	12.8644i	−0.194836	+	0.727139i	−0.992309	+	0.123784i	$0.960497\pi$
$314$	9.58338			0.540821
$315$	−3.31161	+	4.90237i	−0.186588	+	0.276217i
$316$	12.6909			0.713920
$317$	3.59802	−	13.4280i	0.202085	−	0.754192i	−0.788233	−	0.615377i	$-0.789004\pi$
$317$	3.59802	−	13.4280i	0.202085	−	0.754192i	0.990318	−	0.138815i	$-0.0443294\pi$
$318$	−0.396561	+	0.106258i	−0.0222380	+	0.00595867i
$319$	−5.88269	−	3.39638i	−0.329368	−	0.190160i
$320$	1.07544	−	1.96047i	0.0601189	−	0.109593i
$321$			14.7547i			0.823527i
$322$	4.47550	+	9.72682i	0.249410	+	0.542055i
$323$	2.78598	−	2.78598i	0.155016	−	0.155016i
$324$	−0.866025	+	0.500000i	−0.0481125	+	0.0277778i
$325$	−4.15198	+	18.7360i	−0.230311	+	1.03928i
$326$	5.92183	−	10.2569i	0.327980	−	0.568078i
$327$	19.4623	+	5.21491i	1.07627	+	0.288385i
$328$	−8.41410	−	8.41410i	−0.464591	−	0.464591i
$329$	−12.5133	+	10.3918i	−0.689883	+	0.572916i
$330$	2.04879	+	3.37598i	0.112782	+	0.185842i
$331$	9.31631	+	16.1363i	0.512071	+	0.886932i	0.999902	+	0.0139944i	$0.00445470\pi$
$331$	9.31631	+	16.1363i	0.512071	+	0.886932i	−0.487832	+	0.872938i	$0.662212\pi$
$332$	0.710918	+	2.65318i	0.0390167	+	0.145612i
$333$	0.861499	+	3.21516i	0.0472099	+	0.176190i
$334$	4.92063	+	8.52279i	0.269245	+	0.466346i
$335$	−16.5912	−	4.05908i	−0.906472	−	0.221771i
$336$	−2.60786	+	0.446149i	−0.142271	+	0.0243394i
$337$	9.63568	+	9.63568i	0.524889	+	0.524889i	0.919044	−	0.394155i	$-0.128963\pi$
$337$	9.63568	+	9.63568i	0.524889	+	0.524889i	−0.394155	+	0.919044i	$0.628963\pi$
$338$	−1.67202	−	0.448015i	−0.0909456	−	0.0243688i
$339$	−4.62927	+	8.01813i	−0.251427	+	0.435485i
$340$	−3.43407	+	3.58758i	−0.186238	+	0.194564i
$341$	−15.7983	+	9.12117i	−0.855528	+	0.493939i
$342$	−1.25440	+	1.25440i	−0.0678301	+	0.0678301i
$343$	17.8138	+	5.06626i	0.961857	+	0.273552i
$344$		−	4.89791i		−	0.264078i
$345$	−7.93379	−	4.35219i	−0.427141	−	0.234314i
$346$	−7.50509	−	4.33306i	−0.403476	−	0.232947i
$347$	−33.6890	+	9.02693i	−1.80852	+	0.484591i	−0.995255	−	0.0973042i	$-0.968978\pi$
$347$	−33.6890	+	9.02693i	−1.80852	+	0.484591i	−0.813264	+	0.581895i	$0.802311\pi$
$348$	−0.995491	+	3.71522i	−0.0533639	+	0.199157i
$349$	−1.49727			−0.0801469			−0.0400735	−	0.999197i	$-0.512759\pi$
$349$	−1.49727			−0.0801469			−0.0400735	+	0.999197i	$0.512759\pi$
$350$	4.04112	−	12.5964i	0.216007	−	0.673306i
$351$	3.83810			0.204863
$352$	−0.457089	+	1.70588i	−0.0243629	+	0.0909237i
$353$	−5.76343	+	1.54431i	−0.306756	+	0.0821951i	−0.408913	−	0.912573i	$-0.634092\pi$
$353$	−5.76343	+	1.54431i	−0.306756	+	0.0821951i	0.102157	+	0.994768i	$0.467426\pi$
$354$	8.97859	+	5.18379i	0.477207	+	0.275515i
$355$	−21.0148	−	11.5279i	−1.11535	−	0.611840i
$356$			1.11625i			0.0591614i
$357$	5.85109	+	0.541957i	0.309673	+	0.0286834i
$358$	−9.44244	+	9.44244i	−0.499049	+	0.499049i
$359$	14.9989	−	8.65964i	0.791613	−	0.457038i	−0.0489170	−	0.998803i	$-0.515577\pi$
$359$	14.9989	−	8.65964i	0.791613	−	0.457038i	0.840530	+	0.541765i	$0.182244\pi$
$360$	1.54620	−	1.61532i	0.0814920	−	0.0851349i
$361$	7.92648	−	13.7291i	0.417183	−	0.722583i
$362$	8.44144	+	2.26188i	0.443672	+	0.118882i
$363$	5.57274	+	5.57274i	0.292493	+	0.292493i
$364$	9.52443	+	3.52167i	0.499216	+	0.184586i
$365$	23.0946	+	5.65017i	1.20883	+	0.295743i
$366$	−3.39445	−	5.87936i	−0.177431	−	0.307319i
$367$	1.41960	+	5.29802i	0.0741025	+	0.276554i	0.993028	−	0.117876i	$-0.0376086\pi$
$367$	1.41960	+	5.29802i	0.0741025	+	0.276554i	−0.918926	+	0.394430i	$0.870942\pi$
$368$	−1.04741	−	3.90900i	−0.0546001	−	0.203770i
$369$	−5.94967	−	10.3051i	−0.309727	−	0.536464i
$370$	−3.86146	−	6.36288i	−0.200748	−	0.330790i
$371$	−1.01880	−	0.376703i	−0.0528935	−	0.0195574i
$372$	7.30401	+	7.30401i	0.378695	+	0.378695i
$373$	−29.7901	−	7.98224i	−1.54247	−	0.413305i	−0.615410	−	0.788207i	$-0.711009\pi$
$373$	−29.7901	−	7.98224i	−1.54247	−	0.413305i	−0.927064	+	0.374903i	$0.877676\pi$
$374$	1.96118	−	3.39686i	0.101410	−	0.175648i
$375$	3.59516	+	10.5865i	0.185653	+	0.546687i
$376$	5.32419	−	3.07393i	0.274574	−	0.158526i
$377$	10.4386	−	10.4386i	0.537615	−	0.537615i
$378$	−2.63447	−	0.244018i	−0.135503	−	0.0125509i
$379$			12.9203i			0.663670i	0.943337	+	0.331835i	$0.107668\pi$
$379$			12.9203i			0.663670i	−0.943337	+	0.331835i	$0.892332\pi$
$380$	1.90782	−	3.47785i	0.0978690	−	0.178410i
$381$	15.3637	+	8.87021i	0.787104	+	0.454435i
$382$	−10.5053	+	2.81490i	−0.537500	+	0.144023i
$383$	−0.308002	+	1.14948i	−0.0157382	+	0.0587356i	−0.973348	−	0.229332i	$-0.926346\pi$
$383$	−0.308002	+	1.14948i	−0.0157382	+	0.0587356i	0.957610	+	0.288067i	$0.0930127\pi$
$384$	1.00000			0.0510310
$385$	−0.736006	+	10.4222i	−0.0375103	+	0.531163i
$386$	−11.2012			−0.570126
$387$	1.26767	−	4.73102i	0.0644394	−	0.240491i
$388$	9.92718	−	2.65998i	0.503976	−	0.135040i
$389$	−8.25213	−	4.76437i	−0.418400	−	0.241563i	0.275993	−	0.961160i	$-0.410993\pi$
$389$	−8.25213	−	4.76437i	−0.418400	−	0.241563i	−0.694392	+	0.719597i	$0.744327\pi$
$390$	−8.23928	+	2.40191i	−0.417212	+	0.121626i
$391$			8.98802i			0.454544i
$392$	−6.31368	−	3.02282i	−0.318889	−	0.152675i
$393$	0.678310	−	0.678310i	0.0342162	−	0.0342162i
$394$	12.7098	−	7.33801i	0.640311	−	0.369684i
$395$	−28.3710	+	0.620268i	−1.42750	+	0.0312091i
$396$	−0.883028	+	1.52945i	−0.0443738	+	0.0768578i
$397$	−27.5610	−	7.38494i	−1.38324	−	0.370639i	−0.510946	−	0.859613i	$-0.670705\pi$
$397$	−27.5610	−	7.38494i	−1.38324	−	0.370639i	−0.872299	+	0.488974i	$0.837371\pi$
$398$	−13.1260	−	13.1260i	−0.657949	−	0.657949i
$399$	−4.62632	+	0.791463i	−0.231606	+	0.0396227i
$400$	−2.30836	+	4.43525i	−0.115418	+	0.221763i
$401$	−19.6150	−	33.9741i	−0.979526	−	1.69659i	−0.664111	−	0.747634i	$-0.731190\pi$
$401$	−19.6150	−	33.9741i	−0.979526	−	1.69659i	−0.315415	−	0.948954i	$-0.602144\pi$
$402$	−1.97702	−	7.37834i	−0.0986049	−	0.367998i
$403$	−10.2610	−	38.2945i	−0.511135	−	1.90758i
$404$	−9.17333	−	15.8887i	−0.456390	−	0.790491i
$405$	1.91159	−	1.16009i	0.0949877	−	0.0576455i
$406$	−7.82873	+	6.50140i	−0.388533	+	0.322659i
$407$	4.15670	+	4.15670i	0.206040	+	0.206040i
$408$	−2.14529	−	0.574830i	−0.106208	−	0.0284583i
$409$	4.32912	−	7.49826i	0.214061	−	0.370765i	−0.738920	−	0.673793i	$-0.764664\pi$
$409$	4.32912	−	7.49826i	0.214061	−	0.370765i	0.952982	+	0.303028i	$0.0979974\pi$
$410$	19.2212	+	18.3988i	0.949270	+	0.908651i
$411$	−9.65336	+	5.57337i	−0.476165	+	0.274914i
$412$	−6.44872	+	6.44872i	−0.317706	+	0.317706i
$413$	11.4656	+	24.9188i	0.564187	+	1.22617i
$414$		−	4.04689i		−	0.198894i
$415$	−1.71896	−	5.89654i	−0.0843802	−	0.289450i
$416$	−3.32389	−	1.91905i	−0.162967	−	0.0940891i
$417$	−13.1072	+	3.51206i	−0.641861	+	0.171986i
$418$	−0.810871	+	3.02621i	−0.0396610	+	0.148017i
$419$	4.29623			0.209884			0.104942	−	0.994478i	$-0.466534\pi$
$419$	4.29623			0.209884			0.104942	+	0.994478i	$0.466534\pi$
$420$	5.80816	−	1.12484i	0.283409	−	0.0548866i
$421$	−18.8346			−0.917945			−0.458972	−	0.888451i	$-0.651782\pi$
$421$	−18.8346			−0.917945			−0.458972	+	0.888451i	$0.651782\pi$
$422$	0.117279	−	0.437693i	0.00570907	−	0.0213066i
$423$	5.93837	−	1.59118i	0.288733	−	0.0773659i
$424$	0.355547	+	0.205275i	0.0172669	+	0.00996904i
$425$	7.50163	−	8.18800i	0.363883	−	0.397176i
$426$		−	10.7193i		−	0.519351i
$427$	1.65662	−	17.8852i	0.0801693	−	0.865525i
$428$	10.4332	−	10.4332i	0.504305	−	0.504305i
$429$	5.87018	−	3.38915i	0.283415	−	0.163630i
$430$	0.239385	+	10.9494i	0.0115442	+	0.528029i
$431$	−3.46231	+	5.99690i	−0.166774	+	0.288860i	−0.937284	−	0.348567i	$-0.886668\pi$
$431$	−3.46231	+	5.99690i	−0.166774	+	0.288860i	0.770510	+	0.637428i	$0.220002\pi$
$432$	0.965926	+	0.258819i	0.0464731	+	0.0124524i
$433$	11.5154	+	11.5154i	0.553393	+	0.553393i	0.927419	−	0.374025i	$-0.122023\pi$
$433$	11.5154	+	11.5154i	0.553393	+	0.553393i	−0.374025	+	0.927419i	$0.622023\pi$
$434$	4.60846	+	26.9377i	0.221213	+	1.29305i
$435$	2.04387	−	8.35416i	0.0979961	−	0.400551i
$436$	−10.0744	−	17.4494i	−0.482477	−	0.835675i
$437$	−1.85810	−	6.93451i	−0.0888848	−	0.331723i
$438$	2.75198	+	10.2705i	0.131495	+	0.490745i
$439$	9.11194	+	15.7823i	0.434889	+	0.753250i	0.997287	−	0.0736169i	$-0.0234542\pi$
$439$	9.11194	+	15.7823i	0.434889	+	0.753250i	−0.562397	+	0.826867i	$0.690121\pi$
$440$	0.938463	−	3.83589i	0.0447395	−	0.182869i
$441$	−5.31618	−	4.55392i	−0.253152	−	0.216853i
$442$	6.02759	+	6.02759i	0.286703	+	0.286703i
$443$	31.7136	+	8.49765i	1.50676	+	0.403735i	0.915358	−	0.402641i	$-0.131908\pi$
$443$	31.7136	+	8.49765i	1.50676	+	0.403735i	0.591403	+	0.806376i	$0.298574\pi$
$444$	1.66429	−	2.88263i	0.0789837	−	0.136804i
$445$	−0.0545569	−	2.49543i	−0.00258625	−	0.118295i
$446$	−5.72275	+	3.30403i	−0.270980	+	0.156450i
$447$	7.14079	−	7.14079i	0.337748	−	0.337748i
$448$	2.15951	+	1.52856i	0.102027	+	0.0722178i
$449$			8.14032i			0.384165i	0.981379	+	0.192083i	$0.0615242\pi$
$449$			8.14032i			0.384165i	−0.981379	+	0.192083i	$0.938476\pi$
$450$	−3.37764	+	3.68668i	−0.159223	+	0.173792i
$451$	−18.1994	−	10.5075i	−0.856978	−	0.494777i
$452$	8.94306	−	2.39629i	0.420646	−	0.112712i
$453$	3.70368	−	13.8223i	0.174014	−	0.649430i
$454$	16.6075			0.779430
$455$	−21.4643	−	7.40730i	−1.00626	−	0.347260i
$456$	1.77399			0.0830746
$457$	1.18177	−	4.41041i	0.0552806	−	0.206310i	−0.932762	−	0.360494i	$-0.882608\pi$
$457$	1.18177	−	4.41041i	0.0552806	−	0.206310i	0.988042	+	0.154184i	$0.0492748\pi$
$458$	13.0801	−	3.50480i	0.611192	−	0.163768i
$459$	−1.92342	−	1.11049i	−0.0897774	−	0.0518330i
$460$	2.53258	+	8.68750i	0.118082	+	0.405057i
$461$			7.54894i			0.351589i	0.984427	+	0.175795i	$0.0562495\pi$
$461$			7.54894i			0.351589i	−0.984427	+	0.175795i	$0.943751\pi$
$462$	−4.24477	+	1.95310i	−0.197485	+	0.0908665i
$463$	−8.87647	+	8.87647i	−0.412525	+	0.412525i	−0.882617	−	0.470092i	$-0.844221\pi$
$463$	−8.87647	+	8.87647i	−0.412525	+	0.412525i	0.470092	+	0.882617i	$0.344221\pi$
$464$	3.33098	−	1.92314i	0.154637	−	0.0892796i
$465$	−16.6853	−	15.9714i	−0.773764	−	0.740654i
$466$	5.78914	−	10.0271i	0.268177	−	0.464495i
$467$	11.1162	+	2.97858i	0.514397	+	0.137832i	0.506674	−	0.862138i	$-0.330875\pi$
$467$	11.1162	+	2.97858i	0.514397	+	0.137832i	0.00772331	+	0.999970i	$0.497542\pi$
$468$	−2.71395	−	2.71395i	−0.125452	−	0.125452i
$469$	7.00886	−	18.9556i	0.323639	−	0.875290i
$470$	−11.7522	+	7.13208i	−0.542088	+	0.328979i
$471$	−4.79169	−	8.29945i	−0.220789	−	0.382418i
$472$	−2.68333	−	10.0143i	−0.123510	−	0.460946i
$473$	−2.23878	−	8.35525i	−0.102939	−	0.384175i
$474$	−6.34546	−	10.9907i	−0.291457	−	0.504817i
$475$	−4.09501	+	7.86808i	−0.187892	+	0.361012i
$476$	−3.75412	−	4.52057i	−0.172070	−	0.207200i
$477$	0.290303	+	0.290303i	0.0132921	+	0.0132921i
$478$	−16.4462	−	4.40676i	−0.752233	−	0.201560i
$479$	6.17379	−	10.6933i	0.282088	−	0.488590i	−0.689811	−	0.723989i	$-0.742306\pi$
$479$	6.17379	−	10.6933i	0.282088	−	0.488590i	0.971899	+	0.235399i	$0.0756398\pi$
$480$	−2.23553	+	0.0488750i	−0.102038	+	0.00223083i
$481$	−11.0638	+	6.38770i	−0.504467	+	0.291254i
$482$	−13.3796	+	13.3796i	−0.609424	+	0.609424i
$483$	6.18593	−	8.73931i	0.281469	−	0.397652i
$484$		−	7.88104i		−	0.358229i
$485$	−22.0625	+	6.43167i	−1.00181	+	0.292047i
$486$	0.866025	+	0.500000i	0.0392837	+	0.0226805i
$487$	15.0556	−	4.03414i	0.682235	−	0.182804i	0.0989752	−	0.995090i	$-0.468444\pi$
$487$	15.0556	−	4.03414i	0.682235	−	0.182804i	0.583260	+	0.812286i	$0.301777\pi$
$488$	−1.75710	+	6.55758i	−0.0795401	+	0.296848i
$489$	−11.8437			−0.535589
$490$	14.2622	+	6.44904i	0.644300	+	0.291338i
$491$	−2.67474			−0.120709			−0.0603547	−	0.998177i	$-0.519223\pi$
$491$	−2.67474			−0.120709			−0.0603547	+	0.998177i	$0.519223\pi$
$492$	−3.07978	+	11.4939i	−0.138847	+	0.518184i
$493$	−8.25140	+	2.21096i	−0.371624	+	0.0995764i
$494$	−5.89654	−	3.40437i	−0.265298	−	0.153170i
$495$	1.89929	−	3.46230i	0.0853666	−	0.155619i
$496$		−	10.3294i		−	0.463805i
$497$	16.3851	−	23.1484i	0.734972	−	1.03835i
$498$	1.94227	−	1.94227i	0.0870350	−	0.0870350i
$499$	−15.7413	+	9.08825i	−0.704678	+	0.406846i	−0.809087	−	0.587688i	$-0.800038\pi$
$499$	−15.7413	+	9.08825i	−0.704678	+	0.406846i	0.104410	+	0.994534i	$0.466705\pi$
$500$	4.94365	−	10.0280i	0.221087	−	0.448465i
$501$	4.92063	−	8.52279i	0.219838	−	0.380770i
$502$	17.5342	+	4.69827i	0.782588	+	0.209694i
$503$	−3.59630	−	3.59630i	−0.160351	−	0.160351i	0.622371	−	0.782722i	$-0.286169\pi$
$503$	−3.59630	−	3.59630i	−0.160351	−	0.160351i	−0.782722	+	0.622371i	$0.786169\pi$
$504$	1.69031	+	2.03540i	0.0752923	+	0.0906640i
$505$	21.2838	+	35.0713i	0.947119	+	1.56065i
$506$	−3.57352	−	6.18952i	−0.158862	−	0.275158i
$507$	0.448015	+	1.67202i	0.0198971	+	0.0742568i
$508$	−4.59156	−	17.1359i	−0.203718	−	0.760284i
$509$	2.40629	+	4.16782i	0.106657	+	0.184735i	0.914414	−	0.404780i	$-0.132652\pi$
$509$	2.40629	+	4.16782i	0.106657	+	0.184735i	−0.807757	+	0.589516i	$0.799319\pi$
$510$	4.82397	+	1.18020i	0.213609	+	0.0522601i
$511$	−9.75621	+	26.3859i	−0.431589	+	1.16724i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	1.71354	+	0.459142i	0.0756547	+	0.0202716i
$514$	12.0351	−	20.8454i	0.530846	−	0.919452i
$515$	14.1011	−	14.7315i	0.621371	−	0.649148i
$516$	−4.24172	+	2.44896i	−0.186731	+	0.107809i
$517$	7.67738	−	7.67738i	0.337651	−	0.337651i
$518$	8.00034	−	3.68111i	0.351515	−	0.161739i
$519$			8.66613i			0.380401i
$520$	7.52446	+	4.12764i	0.329970	+	0.181009i
$521$	4.61481	+	2.66436i	0.202178	+	0.116728i	0.597671	−	0.801741i	$-0.296093\pi$
$521$	4.61481	+	2.66436i	0.202178	+	0.116728i	−0.395493	+	0.918469i	$0.629426\pi$
$522$	3.71522	−	0.995491i	0.162611	−	0.0435714i
$523$	1.58561	−	5.91757i	0.0693338	−	0.258757i	−0.922555	−	0.385866i	$-0.873903\pi$
$523$	1.58561	−	5.91757i	0.0693338	−	0.258757i	0.991889	+	0.127108i	$0.0405695\pi$
$524$	−0.959275			−0.0419061
$525$	−12.9294	+	2.79849i	−0.564284	+	0.122136i
$526$	−14.0358			−0.611991
$527$	−5.93766	+	22.1596i	−0.258648	+	0.965289i
$528$	1.70588	−	0.457089i	0.0742389	−	0.0198923i
$529$	−5.73541	−	3.31134i	−0.249366	−	0.143971i
$530$	−0.804870	−	0.441522i	−0.0349613	−	0.0191785i
$531$		−	10.3676i		−	0.449915i
$532$	3.83095	+	2.71165i	0.166093	+	0.117565i
$533$	32.2942	−	32.2942i	1.39881	−	1.39881i
$534$	0.966705	−	0.558127i	0.0418334	−	0.0241525i
$535$	−22.8137	+	23.8336i	−0.986324	+	1.03042i
$536$	−3.81931	+	6.61524i	−0.164969	+	0.285735i
$537$	12.8986	+	3.45617i	0.556617	+	0.149145i
$538$	−18.7754	−	18.7754i	−0.809466	−	0.809466i
$539$	−12.1521	−	2.27065i	−0.523427	−	0.0978040i
$540$	−2.17201	−	0.531389i	−0.0934684	−	0.0228673i
$541$	6.81239	+	11.7994i	0.292887	+	0.507296i	0.974491	−	0.224426i	$-0.0720506\pi$
$541$	6.81239	+	11.7994i	0.292887	+	0.507296i	−0.681604	+	0.731721i	$0.738717\pi$
$542$	3.09564	+	11.5531i	0.132969	+	0.496247i
$543$	−2.26188	−	8.44144i	−0.0970664	−	0.362257i
$544$	1.11049	+	1.92342i	0.0476117	+	0.0824658i
$545$	23.3746	+	38.5164i	1.00126	+	1.64986i
$546$	−1.71236	−	10.0092i	−0.0732823	−	0.428356i
$547$	−14.8290	−	14.8290i	−0.634042	−	0.634042i	0.315037	−	0.949079i	$-0.397983\pi$
$547$	−14.8290	−	14.8290i	−0.634042	−	0.634042i	−0.949079	+	0.315037i	$0.897983\pi$
$548$	10.7669	+	2.88499i	0.459940	+	0.123241i
$549$	−3.39445	+	5.87936i	−0.144872	+	0.250925i
$550$	−1.91049	+	8.62113i	−0.0814635	+	0.367606i
$551$	5.90911	−	3.41163i	0.251737	−	0.145340i
$552$	−2.86158	+	2.86158i	−0.121797	+	0.121797i
$553$	3.09681	−	33.4339i	0.131690	−	1.42175i
$554$			2.36165i			0.100337i
$555$	−3.57969	+	6.52557i	−0.151949	+	0.276995i
$556$	11.7516	+	6.78477i	0.498378	+	0.287738i
$557$	−0.0387479	+	0.0103825i	−0.00164180	+	0.000439920i	−0.259640	−	0.965706i	$-0.583604\pi$
$557$	−0.0387479	+	0.0103825i	−0.00164180	+	0.000439920i	0.257998	+	0.966145i	$0.416937\pi$
$558$	2.67345	−	9.97746i	0.113176	−	0.422379i
$559$	18.7987			0.795099
$560$	−4.90237	−	3.31161i	−0.207163	−	0.139941i
$561$	−3.92236			−0.165602
$562$	2.85494	−	10.6548i	0.120428	−	0.449445i
$563$	13.4327	−	3.59929i	0.566122	−	0.151692i	0.0356047	−	0.999366i	$-0.488664\pi$
$563$	13.4327	−	3.59929i	0.566122	−	0.151692i	0.530518	+	0.847674i	$0.321998\pi$
$564$	−5.32419	−	3.07393i	−0.224189	−	0.129436i
$565$	−19.8754	+	5.79407i	−0.836164	+	0.243758i
$566$			23.4108i			0.984031i
$567$	1.10591	+	2.40353i	0.0464439	+	0.100939i
$568$	−7.57968	+	7.57968i	−0.318036	+	0.318036i
$569$	17.1817	−	9.91984i	0.720293	−	0.415861i	−0.0945677	−	0.995518i	$-0.530147\pi$
$569$	17.1817	−	9.91984i	0.720293	−	0.415861i	0.814860	+	0.579657i	$0.196814\pi$
$570$	−3.96581	+	0.0867037i	−0.166110	+	0.00363162i
$571$	2.94454	−	5.10010i	0.123225	−	0.213432i	−0.797813	−	0.602906i	$-0.794010\pi$
$571$	2.94454	−	5.10010i	0.123225	−	0.213432i	0.921038	+	0.389473i	$0.127343\pi$
$572$	−6.54733	−	1.75435i	−0.273758	−	0.0733532i
$573$	7.69044	+	7.69044i	0.321273	+	0.321273i
$574$	−24.2199	+	20.1135i	−1.01092	+	0.839523i
$575$	−6.08626	−	19.2974i	−0.253815	−	0.804758i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	3.85984	+	14.4051i	0.160687	+	0.599692i	0.998551	+	0.0538132i	$0.0171375\pi$
$577$	3.85984	+	14.4051i	0.160687	+	0.599692i	−0.837864	+	0.545879i	$0.816196\pi$
$578$	3.12324	+	11.6561i	0.129910	+	0.484830i
$579$	5.60060	+	9.70052i	0.232753	+	0.403140i
$580$	−7.35252	+	4.46205i	−0.305297	+	0.185276i
$581$	7.16322	−	1.22547i	0.297180	−	0.0508411i
$582$	−7.26720	−	7.26720i	−0.301235	−	0.301235i
$583$	0.700349	+	0.187658i	0.0290055	+	0.00777200i
$584$	5.31641	−	9.20830i	0.219995	−	0.381042i
$585$	6.19976	+	5.93447i	0.256329	+	0.245360i
$586$	18.9635	−	10.9486i	0.783376	−	0.452282i
$587$	−4.86057	+	4.86057i	−0.200617	+	0.200617i	−0.800264	−	0.599647i	$-0.795308\pi$
$587$	−4.86057	+	4.86057i	−0.200617	+	0.200617i	0.599647	+	0.800264i	$0.295308\pi$
$588$	0.539001	+	6.97922i	0.0222280	+	0.287818i
$589$		−	18.3243i		−	0.755039i
$590$	6.48812	+	22.2562i	0.267112	+	0.916273i
$591$	−12.7098	−	7.33801i	−0.522812	−	0.301846i
$592$	−3.21516	+	0.861499i	−0.132142	+	0.0354074i
$593$	−5.48532	+	20.4715i	−0.225255	+	0.840664i	0.757047	+	0.653361i	$0.226641\pi$
$593$	−5.48532	+	20.4715i	−0.225255	+	0.840664i	−0.982302	+	0.187304i	$0.940025\pi$
$594$	1.76606			0.0724622
$595$	8.61341	+	9.92240i	0.353116	+	0.406779i
$596$	−10.0986			−0.413655
$597$	−4.80447	+	17.9305i	−0.196634	+	0.733847i
$598$	15.0031	−	4.02007i	0.613523	−	0.164393i
$599$	10.0409	+	5.79712i	0.410260	+	0.236864i	0.690902	−	0.722949i	$-0.257214\pi$
$599$	10.0409	+	5.79712i	0.410260	+	0.236864i	−0.280641	+	0.959813i	$0.590547\pi$
$600$	4.99522	−	0.218523i	0.203929	−	0.00892118i
$601$		−	15.3561i		−	0.626387i	−0.949689	−	0.313193i	$-0.898601\pi$
$601$		−	15.3561i		−	0.626387i	0.949689	−	0.313193i	$-0.101399\pi$
$602$	−12.9034	−	1.19518i	−0.525904	−	0.0487119i
$603$	−5.40132	+	5.40132i	−0.219959	+	0.219959i
$604$	−12.3928	+	7.15497i	−0.504254	+	0.291131i
$605$	0.385186	+	17.6183i	0.0156600	+	0.716287i
$606$	−9.17333	+	15.8887i	−0.372641	+	0.645433i
$607$	21.7853	+	5.83734i	0.884237	+	0.236931i	0.672234	−	0.740339i	$-0.265335\pi$
$607$	21.7853	+	5.83734i	0.884237	+	0.236931i	0.212003	+	0.977269i	$0.432001\pi$
$608$	−1.25440	−	1.25440i	−0.0508726	−	0.0508726i
$609$	9.54474	+	3.52918i	0.386772	+	0.143009i
$610$	3.60755	−	14.7456i	0.146065	−	0.597031i
$611$	11.7980	+	20.4348i	0.477297	+	0.826703i
$612$	0.574830	+	2.14529i	0.0232361	+	0.0867183i
$613$	−1.23846	−	4.62200i	−0.0500209	−	0.186681i	0.936395	−	0.350948i	$-0.114141\pi$
$613$	−1.23846	−	4.62200i	−0.0500209	−	0.186681i	−0.986416	+	0.164267i	$0.947474\pi$
$614$	1.50012	+	2.59828i	0.0605399	+	0.104858i
$615$	6.32318	−	25.8455i	0.254975	−	1.04219i
$616$	4.38256	+	1.62046i	0.176578	+	0.0652900i
$617$	17.3498	+	17.3498i	0.698475	+	0.698475i	0.964082	−	0.265606i	$-0.0855722\pi$
$617$	17.3498	+	17.3498i	0.698475	+	0.698475i	−0.265606	+	0.964082i	$0.585572\pi$
$618$	8.80911	+	2.36040i	0.354355	+	0.0949490i
$619$	10.4801	−	18.1521i	0.421232	−	0.729596i	−0.574828	−	0.818274i	$-0.694931\pi$
$619$	10.4801	−	18.1521i	0.421232	−	0.729596i	0.996060	+	0.0886786i	$0.0282644\pi$
$620$	0.504850	+	23.0918i	0.0202753	+	0.927388i
$621$	−3.50471	+	2.02344i	−0.140639	+	0.0811980i
$622$	−10.6211	+	10.6211i	−0.425868	+	0.425868i
$623$	2.94074	+	0.272387i	0.117818	+	0.0109129i
$624$			3.83810i			0.153647i
$625$	−10.5616	+	22.6595i	−0.422464	+	0.906380i
$626$	−11.5339	−	6.65911i	−0.460988	−	0.266152i
$627$	3.02621	−	0.810871i	0.120855	−	0.0323831i
$628$	−2.48036	+	9.25683i	−0.0989772	+	0.369388i
$629$	7.39267			0.294765
$630$	−3.87822	−	4.46760i	−0.154512	−	0.177993i
$631$	−48.7823			−1.94199			−0.970996	−	0.239095i	$-0.923149\pi$
$631$	−48.7823			−1.94199			−0.970996	+	0.239095i	$0.923149\pi$
$632$	−3.28465	+	12.2585i	−0.130656	+	0.487616i
$633$	−0.437693	+	0.117279i	−0.0173967	+	0.00466144i
$634$	12.0392	+	6.95084i	0.478138	+	0.276053i
$635$	11.1021	+	38.0836i	0.440574	+	1.51130i
$636$		−	0.410550i		−	0.0162794i
$637$	11.6019	−	24.2325i	0.459683	−	0.960128i
$638$	4.80320	−	4.80320i	0.190160	−	0.190160i
$639$	−9.28317	+	5.35964i	−0.367237	+	0.212024i
$640$	1.61532	+	1.54620i	0.0638512	+	0.0611190i
$641$	−6.03196	+	10.4477i	−0.238248	+	0.412658i	−0.960212	−	0.279273i	$-0.909906\pi$
$641$	−6.03196	+	10.4477i	−0.238248	+	0.412658i	0.721964	+	0.691931i	$0.243240\pi$
$642$	−14.2519	−	3.81880i	−0.562480	−	0.150716i
$643$	15.5935	+	15.5935i	0.614947	+	0.614947i	0.944231	−	0.329284i	$-0.106807\pi$
$643$	15.5935	+	15.5935i	0.614947	+	0.614947i	−0.329284	+	0.944231i	$0.606807\pi$
$644$	−10.5537	+	1.80551i	−0.415875	+	0.0711472i
$645$	9.36281	−	5.68204i	0.368660	−	0.223730i
$646$	1.96999	+	3.41212i	0.0775082	+	0.134248i
$647$	−1.69672	−	6.33226i	−0.0667051	−	0.248947i	0.924520	−	0.381135i	$-0.124467\pi$
$647$	−1.69672	−	6.33226i	−0.0667051	−	0.248947i	−0.991225	+	0.132188i	$0.957800\pi$
$648$	−0.258819	−	0.965926i	−0.0101674	−	0.0379452i
$649$	−9.15487	−	15.8567i	−0.359360	−	0.622430i
$650$	−17.0229	−	8.85973i	−0.667694	−	0.347507i
$651$	21.0245	−	17.4599i	0.824016	−	0.684308i
$652$	8.37474	+	8.37474i	0.327980	+	0.327980i
$653$	22.3037	+	5.97625i	0.872811	+	0.233869i	0.667303	−	0.744787i	$-0.267449\pi$
$653$	22.3037	+	5.97625i	0.872811	+	0.233869i	0.205508	+	0.978655i	$0.434115\pi$
$654$	−10.0744	+	17.4494i	−0.393941	+	0.682326i
$655$	2.14449	−	0.0468845i	0.0837922	−	0.00183193i
$656$	10.3051	−	5.94967i	0.402348	−	0.232296i
$657$	7.51854	−	7.51854i	0.293326	−	0.293326i
$658$	−6.79898	−	14.7765i	−0.265052	−	0.576050i
$659$			8.89429i			0.346472i	0.984880	+	0.173236i	$0.0554224\pi$
$659$			8.89429i			0.346472i	−0.984880	+	0.173236i	$0.944578\pi$
$660$	−3.79121	+	1.10521i	−0.147573	+	0.0430204i
$661$	7.24046	+	4.18028i	0.281621	+	0.162594i	0.634157	−	0.773204i	$-0.281347\pi$
$661$	7.24046	+	4.18028i	0.281621	+	0.162594i	−0.352536	+	0.935798i	$0.614681\pi$
$662$	−17.9977	+	4.82248i	−0.699501	+	0.187431i
$663$	2.20625	−	8.23385i	0.0856837	−	0.319776i
$664$	−2.74678			−0.106596
$665$	−8.69675	−	5.87476i	−0.337246	−	0.227813i
$666$	−3.32858			−0.128980
$667$	−4.02864	+	15.0351i	−0.155990	+	0.582161i
$668$	−9.50594	+	2.54711i	−0.367796	+	0.0985506i
$669$	5.72275	+	3.30403i	0.221254	+	0.127741i
$670$	8.21488	−	14.9753i	0.317369	−	0.578545i
$671$			11.9896i			0.462853i
$672$	0.244018	−	2.63447i	0.00941321	−	0.101627i
$673$	−11.1305	+	11.1305i	−0.429048	+	0.429048i	−0.888304	−	0.459256i	$-0.848116\pi$
$673$	−11.1305	+	11.1305i	−0.429048	+	0.429048i	0.459256	+	0.888304i	$0.348116\pi$
$674$	−11.8013	+	6.81346i	−0.454567	+	0.262444i
$675$	4.88157	+	1.08178i	0.187892	+	0.0416378i
$676$	0.865499	−	1.49909i	0.0332884	−	0.0576572i
$677$	41.9335	+	11.2360i	1.61163	+	0.431836i	0.948529	−	0.316690i	$-0.102571\pi$
$677$	41.9335	+	11.2360i	1.61163	+	0.431836i	0.663106	+	0.748526i	$0.269238\pi$
$678$	−6.54677	−	6.54677i	−0.251427	−	0.251427i
$679$	−4.58524	−	26.8020i	−0.175965	−	1.02857i
$680$	−2.57653	−	4.24559i	−0.0988056	−	0.162811i
$681$	−8.30377	−	14.3825i	−0.318201	−	0.551140i
$682$	−4.72147	−	17.6208i	−0.180794	−	0.674734i
$683$	−4.62860	−	17.2742i	−0.177108	−	0.660977i	−0.996183	−	0.0872904i	$-0.972179\pi$
$683$	−4.62860	−	17.2742i	−0.177108	−	0.660977i	0.819075	−	0.573687i	$-0.194487\pi$
$684$	−0.886994	−	1.53632i	−0.0339151	−	0.0587426i
$685$	−24.2108	−	5.92326i	−0.925048	−	0.226316i
$686$	−9.50420	+	15.8956i	−0.362872	+	0.606897i
$687$	−9.57528	−	9.57528i	−0.365320	−	0.365320i
$688$	4.73102	+	1.26767i	0.180368	+	0.0483296i
$689$	−0.787866	+	1.36462i	−0.0300153	+	0.0519880i
$690$	6.25731	−	6.53703i	0.238212	−	0.248860i
$691$	30.5564	−	17.6417i	1.16242	−	0.671123i	0.210537	−	0.977586i	$-0.432479\pi$
$691$	30.5564	−	17.6417i	1.16242	−	0.671123i	0.951883	+	0.306463i	$0.0991456\pi$
$692$	6.12788	−	6.12788i	0.232947	−	0.232947i
$693$	3.81382	+	2.69953i	0.144875	+	0.102547i
$694$		−	34.8774i		−	1.32393i
$695$	−26.6026	−	14.5932i	−1.00910	−	0.553553i
$696$	−3.33098	−	1.92314i	−0.126260	−	0.0728964i
$697$	−25.5276	+	6.84009i	−0.966926	+	0.259087i
$698$	0.387522	−	1.44625i	0.0146679	−	0.0547414i
$699$	−11.5783			−0.437930
$700$	11.1213	+	7.16361i	0.420345	+	0.270759i
$701$	−14.9862			−0.566020			−0.283010	−	0.959117i	$-0.591333\pi$
$701$	−14.9862			−0.566020			−0.283010	+	0.959117i	$0.591333\pi$
$702$	−0.993373	+	3.70732i	−0.0374924	+	0.139924i
$703$	−5.70366	+	1.52829i	−0.215117	+	0.0576405i
$704$	−1.52945	−	0.883028i	−0.0576433	−	0.0332804i
$705$	12.0527	+	6.61164i	0.453929	+	0.249009i
$706$		−	5.96674i		−	0.224561i
$707$	−44.0968	+	20.2898i	−1.65843	+	0.763075i
$708$	−7.33099	+	7.33099i	−0.275515	+	0.275515i
$709$	7.19605	−	4.15464i	0.270253	−	0.156031i	−0.358750	−	0.933434i	$-0.616797\pi$
$709$	7.19605	−	4.15464i	0.270253	−	0.156031i	0.629003	+	0.777403i	$0.283463\pi$
$710$	16.5742	−	17.3151i	0.622017	−	0.649823i
$711$	−6.34546	+	10.9907i	−0.237973	+	0.412182i
$712$	−1.07822	−	0.288908i	−0.0404080	−	0.0108273i
$713$	29.5585	+	29.5585i	1.10697	+	1.10697i
$714$	−2.03786	+	5.51145i	−0.0762652	+	0.206261i
$715$	14.7225	+	3.60191i	0.550591	+	0.134704i
$716$	−6.67682	−	11.5646i	−0.249524	−	0.432189i
$717$	4.40676	+	16.4462i	0.164573	+	0.614196i
$718$	4.48256	+	16.7291i	0.167288	+	0.624326i
$719$	7.07678	+	12.2574i	0.263920	+	0.457122i	0.967280	−	0.253711i	$-0.0816513\pi$
$719$	7.07678	+	12.2574i	0.263920	+	0.457122i	−0.703360	+	0.710833i	$0.748318\pi$
$720$	1.16009	+	1.91159i	0.0432341	+	0.0712408i
$721$	15.4154	+	18.5626i	0.574099	+	0.691307i
$722$	11.2097	+	11.2097i	0.417183	+	0.417183i
$723$	18.2769	+	4.89728i	0.679725	+	0.182132i
$724$	−4.36961	+	7.56839i	−0.162395	+	0.281277i
$725$	16.2187	−	10.3344i	0.602348	−	0.383810i
$726$	−6.82518	+	3.94052i	−0.253306	+	0.146246i
$727$	19.9622	−	19.9622i	0.740357	−	0.740357i	−0.232290	−	0.972647i	$-0.574622\pi$
$727$	19.9622	−	19.9622i	0.740357	−	0.740357i	0.972647	+	0.232290i	$0.0746217\pi$
$728$	−5.86678	+	8.28842i	−0.217437	+	0.307189i
$729$		−	1.00000i		−	0.0370370i
$730$	−11.4350	+	20.8453i	−0.423227	+	0.771519i
$731$	−9.42073	−	5.43906i	−0.348438	−	0.201171i
$732$	6.55758	−	1.75710i	0.242375	−	0.0649442i
$733$	−12.0119	+	44.8290i	−0.443670	+	1.65580i	0.275755	+	0.961228i	$0.411072\pi$
$733$	−12.0119	+	44.8290i	−0.443670	+	1.65580i	−0.719425	+	0.694570i	$0.755595\pi$
$734$	−5.48491			−0.202452
$735$	−1.54606	−	15.5759i	−0.0570274	−	0.574527i
$736$	4.04689			0.149170
$737$	−3.49153	+	13.0306i	−0.128612	+	0.479987i
$738$	11.4939	−	3.07978i	0.423095	−	0.113368i
$739$	15.1424	+	8.74246i	0.557022	+	0.321597i	0.751949	−	0.659221i	$-0.229114\pi$
$739$	15.1424	+	8.74246i	0.557022	+	0.321597i	−0.194927	+	0.980818i	$0.562447\pi$
$740$	7.14549	−	2.08305i	0.262673	−	0.0765745i
$741$			6.80874i			0.250125i
$742$	0.627552	−	0.886588i	0.0230382	−	0.0325477i
$743$	−12.2427	+	12.2427i	−0.449143	+	0.449143i	−0.895069	−	0.445927i	$-0.852874\pi$
$743$	−12.2427	+	12.2427i	−0.449143	+	0.449143i	0.445927	+	0.895069i	$0.352874\pi$
$744$	−8.94554	+	5.16471i	−0.327960	+	0.189348i
$745$	22.5758	−	0.493569i	0.827112	−	0.0180830i
$746$	15.4205	−	26.7091i	0.564585	−	0.977889i
$747$	−2.65318	−	0.710918i	−0.0970749	−	0.0260111i
$748$	2.77353	+	2.77353i	0.101410	+	0.101410i
$749$	−24.9400	−	30.0317i	−0.911287	−	1.09734i
$750$	−11.1563	+	0.732658i	−0.407371	+	0.0267529i
$751$	12.4732	+	21.6042i	0.455154	+	0.788350i	0.998697	−	0.0510312i	$-0.0162508\pi$
$751$	12.4732	+	21.6042i	0.455154	+	0.788350i	−0.543543	+	0.839381i	$0.682917\pi$
$752$	1.59118	+	5.93837i	0.0580244	+	0.216550i
$753$	−4.69827	−	17.5342i	−0.171214	−	0.638981i
$754$	7.38120	+	12.7846i	0.268808	+	0.465588i
$755$	27.3547	−	16.6009i	0.995541	−	0.604167i
$756$	0.917556	−	2.48155i	0.0333712	−	0.0902531i
$757$	−32.4637	−	32.4637i	−1.17991	−	1.17991i	−0.979765	−	0.200149i	$-0.935857\pi$
$757$	−32.4637	−	32.4637i	−1.17991	−	1.17991i	−0.200149	−	0.979765i	$-0.564143\pi$
$758$	−12.4800	−	3.34401i	−0.453295	−	0.121460i
$759$	−3.57352	+	6.18952i	−0.129711	+	0.224665i
$760$	2.86556	+	2.74294i	0.103945	+	0.0994970i
$761$	28.5750	−	16.4978i	1.03584	−	0.598045i	0.117191	−	0.993109i	$-0.462611\pi$
$761$	28.5750	−	16.4978i	1.03584	−	0.598045i	0.918653	+	0.395065i	$0.129278\pi$
$762$	−12.5444	+	12.5444i	−0.454435	+	0.454435i
$763$	−48.4284	+	22.2828i	−1.75322	+	0.806693i
$764$		−	10.8759i		−	0.393477i
$765$	−1.38990	−	4.76778i	−0.0502520	−	0.172379i
$766$	−1.03059	−	0.595014i	−0.0372369	−	0.0214987i
$767$	38.4359	−	10.2989i	1.38784	−	0.371871i
$768$	−0.258819	+	0.965926i	−0.00933933	+	0.0348548i
$769$	10.0980			0.364144			0.182072	−	0.983285i	$-0.441720\pi$
$769$	10.0980			0.364144			0.182072	+	0.983285i	$0.441720\pi$
$770$	−9.87656	−	3.40839i	−0.355926	−	0.122830i
$771$	−24.0702			−0.866867
$772$	2.89908	−	10.8195i	0.104340	−	0.389403i
$773$	−11.4236	+	3.06094i	−0.410878	+	0.110094i	−0.458336	−	0.888779i	$-0.651554\pi$
$773$	−11.4236	+	3.06094i	−0.410878	+	0.110094i	0.0474585	+	0.998873i	$0.484888\pi$
$774$	4.24172	+	2.44896i	0.152465	+	0.0880259i
$775$	−2.25722	−	51.5978i	−0.0810817	−	1.85345i
$776$			10.2774i			0.368936i
$777$	−7.18811	−	5.08794i	−0.257872	−	0.182529i
$778$	6.73784	−	6.73784i	0.241563	−	0.241563i
$779$	18.2812	−	10.5546i	0.654991	−	0.378159i
$780$	−0.187587	−	8.58020i	−0.00671669	−	0.307220i
$781$	−9.46543	+	16.3946i	−0.338700	+	0.586645i
$782$	−8.68176	−	2.32627i	−0.310459	−	0.0831873i
$783$	−2.71973	−	2.71973i	−0.0971953	−	0.0971953i
$784$	4.55392	−	5.31618i	0.162640	−	0.189864i
$785$	5.09250	−	20.8152i	0.181759	−	0.742926i
$786$	0.479637	+	0.830756i	0.0171081	+	0.0296321i
$787$	−2.27001	−	8.47179i	−0.0809171	−	0.301987i	0.913593	−	0.406631i	$-0.133296\pi$
$787$	−2.27001	−	8.47179i	−0.0809171	−	0.301987i	−0.994510	+	0.104644i	$0.966630\pi$
$788$	3.79843	+	14.1760i	0.135314	+	0.504997i
$789$	7.01791	+	12.1554i	0.249844	+	0.432743i
$790$	6.74381	−	27.5648i	0.239934	−	0.980711i
$791$	−4.13068	−	24.1450i	−0.146870	−	0.858497i
$792$	−1.24879	−	1.24879i	−0.0443738	−	0.0443738i
$793$	−25.1686	−	6.74391i	−0.893764	−	0.239483i
$794$	14.2666	−	24.7105i	0.506303	−	0.876942i
$795$	0.0200656	+	0.917799i	0.000711655	+	0.0325510i
$796$	16.0761	−	9.28152i	0.569801	−	0.328975i
$797$	−26.4972	+	26.4972i	−0.938580	+	0.938580i	−0.998220	−	0.0596400i	$-0.981005\pi$
$797$	−26.4972	+	26.4972i	−0.938580	+	0.938580i	0.0596400	+	0.998220i	$0.481005\pi$
$798$	0.432886	−	4.67353i	0.0153240	−	0.165441i
$799$		−	13.6542i		−	0.483051i
$800$	−3.68668	−	3.37764i	−0.130344	−	0.119417i
$801$	−0.966705	−	0.558127i	−0.0341568	−	0.0197205i
$802$	37.8932	−	10.1535i	1.33806	−	0.358531i
$803$	4.86015	−	18.1383i	0.171511	−	0.640088i
$804$	7.63862			0.269394
$805$	23.5050	−	4.55210i	0.828442	−	0.160441i
$806$	39.6453			1.39645
$807$	−6.87229	+	25.6477i	−0.241916	+	0.902842i
$808$	17.7215	−	4.74846i	0.623441	−	0.167050i
$809$	−34.0232	−	19.6433i	−1.19619	−	0.690622i	−0.236489	−	0.971634i	$-0.575997\pi$
$809$	−34.0232	−	19.6433i	−1.19619	−	0.690622i	−0.959704	+	0.281012i	$0.909330\pi$
$810$	0.625808	+	2.14671i	0.0219887	+	0.0754277i
$811$		−	9.61165i		−	0.337511i	−0.985658	−	0.168755i	$-0.946025\pi$
$811$		−	9.61165i		−	0.337511i	0.985658	−	0.168755i	$-0.0539748\pi$
$812$	−4.25364	−	9.24465i	−0.149274	−	0.324424i
$813$	8.45744	−	8.45744i	0.296615	−	0.296615i
$814$	−5.09089	+	2.93923i	−0.178436	+	0.103020i
$815$	−19.1313	−	18.3127i	−0.670141	−	0.641466i
$816$	1.11049	−	1.92342i	0.0388748	−	0.0673331i
$817$	8.39277	+	2.24884i	0.293626	+	0.0786769i
$818$	6.12230	+	6.12230i	0.214061	+	0.214061i
$819$	−7.81207	+	6.48757i	−0.272976	+	0.226694i
$820$	−22.7467	+	13.8043i	−0.794348	+	0.482069i
$821$	−25.9357	−	44.9219i	−0.905162	−	1.56779i	−0.820700	−	0.571359i	$-0.806416\pi$
$821$	−25.9357	−	44.9219i	−0.905162	−	1.56779i	−0.0844618	−	0.996427i	$-0.526917\pi$
$822$	−2.88499	−	10.7669i	−0.100626	−	0.375540i
$823$	2.69263	+	10.0490i	0.0938592	+	0.350287i	0.996844	−	0.0793852i	$-0.0252957\pi$
$823$	2.69263	+	10.0490i	0.0938592	+	0.350287i	−0.902985	+	0.429672i	$0.858629\pi$
$824$	−4.55993	−	7.89804i	−0.158853	−	0.275141i
$825$	8.42136	−	2.65604i	0.293194	−	0.0924713i
$826$	−27.0372	+	4.62548i	−0.940746	+	0.160941i
$827$	7.55951	+	7.55951i	0.262870	+	0.262870i	0.826219	−	0.563349i	$-0.190487\pi$
$827$	7.55951	+	7.55951i	0.262870	+	0.262870i	−0.563349	+	0.826219i	$0.690487\pi$
$828$	3.90900	+	1.04741i	0.135847	+	0.0364001i
$829$	16.1525	−	27.9770i	0.561001	−	0.971682i	−0.436409	−	0.899748i	$-0.643750\pi$
$829$	16.1525	−	27.9770i	0.561001	−	0.971682i	0.997409	−	0.0719331i	$-0.0229168\pi$
$830$	6.14051	−	0.134249i	0.213140	−	0.00465984i
$831$	2.04525	−	1.18083i	0.0709490	−	0.0409624i
$832$	2.71395	−	2.71395i	0.0940891	−	0.0940891i
$833$	−12.8254	+	8.78704i	−0.444374	+	0.304453i
$834$		−	13.5695i		−	0.469875i
$835$	21.1264	−	6.15875i	0.731107	−	0.213132i
$836$	−2.71323	−	1.56648i	−0.0938389	−	0.0541779i
$837$	−9.97746	+	2.67345i	−0.344871	+	0.0924080i
$838$	−1.11195	+	4.14984i	−0.0384115	+	0.143354i
$839$	−24.7218			−0.853490			−0.426745	−	0.904372i	$-0.640340\pi$
$839$	−24.7218			−0.853490			−0.426745	+	0.904372i	$0.640340\pi$
$840$	−0.416751	+	5.90138i	−0.0143793	+	0.203617i
$841$	14.2061			0.489866
$842$	4.87477	−	18.1929i	0.167996	−	0.626968i
$843$	−10.6548	+	2.85494i	−0.366970	+	0.0983294i
$844$	0.392425	+	0.226566i	0.0135078	+	0.00779874i
$845$	−1.86158	+	3.39356i	−0.0640404	+	0.116742i
$846$			6.14785i			0.211367i
$847$	−20.7624	−	1.92312i	−0.713405	−	0.0660791i
$848$	−0.290303	+	0.290303i	−0.00996904	+	0.00996904i
$849$	20.2744	−	11.7054i	0.695815	−	0.401729i
$850$	5.96743	+	9.36523i	0.204681	+	0.321225i
$851$	6.73519	−	11.6657i	0.230879	−	0.399895i
$852$	10.3540	+	2.77435i	0.354723	+	0.0950478i
$853$	−28.0435	−	28.0435i	−0.960191	−	0.960191i	0.0390463	−	0.999237i	$-0.487568\pi$
$853$	−28.0435	−	28.0435i	−0.960191	−	0.960191i	−0.999237	+	0.0390463i	$0.987568\pi$
$854$	16.8470	+	6.22920i	0.576493	+	0.213159i
$855$	2.05799	+	3.39114i	0.0703819	+	0.115975i
$856$	7.37735	+	12.7779i	0.252153	+	0.436741i
$857$	−12.3144	−	45.9579i	−0.420652	−	1.56989i	−0.773239	−	0.634115i	$-0.781365\pi$
$857$	−12.3144	−	45.9579i	−0.420652	−	1.56989i	0.352587	−	0.935779i	$-0.385302\pi$
$858$	1.75435	+	6.54733i	0.0598926	+	0.223522i
$859$	26.8560	+	46.5160i	0.916315	+	1.58710i	0.804964	+	0.593324i	$0.202185\pi$
$859$	26.8560	+	46.5160i	0.916315	+	1.58710i	0.111351	+	0.993781i	$0.464482\pi$
$860$	−10.6383	−	2.60270i	−0.362763	−	0.0887512i
$861$	29.5288	+	10.9183i	1.00634	+	0.372095i
$862$	−4.89645	−	4.89645i	−0.166774	−	0.166774i
$863$	−38.6139	−	10.3466i	−1.31443	−	0.352201i	−0.467544	−	0.883970i	$-0.654861\pi$
$863$	−38.6139	−	10.3466i	−1.31443	−	0.352201i	−0.846890	+	0.531768i	$0.821528\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−13.3996	+	13.9986i	−0.455599	+	0.475966i
$866$	−14.1034	+	8.14260i	−0.479253	+	0.276697i
$867$	8.53286	−	8.53286i	0.289791	−	0.289791i
$868$	−27.2126	−	2.52057i	−0.923656	−	0.0855536i
$869$			22.4129i			0.760305i
$870$	7.54050	+	4.13644i	0.255647	+	0.140239i
$871$	−25.3900	−	14.6589i	−0.860306	−	0.496698i
$872$	19.4623	−	5.21491i	0.659076	−	0.176599i
$873$	−2.65998	+	9.92718i	−0.0900267	+	0.335984i
$874$	7.17914			0.242838
$875$	−25.2121	−	15.4709i	−0.852325	−	0.523013i
$876$	−10.6328			−0.359250
$877$	−1.96884	+	7.34780i	−0.0664829	+	0.248118i	−0.991167	−	0.132617i	$-0.957662\pi$
$877$	−1.96884	+	7.34780i	−0.0664829	+	0.248118i	0.924685	+	0.380734i	$0.124329\pi$
$878$	−17.6029	+	4.71669i	−0.594070	+	0.159180i
$879$	−18.9635	−	10.9486i	−0.639624	−	0.369287i
$880$	3.46230	+	1.89929i	0.116714	+	0.0640250i
$881$			37.1659i			1.25215i	0.779763	+	0.626075i	$0.215340\pi$
$881$			37.1659i			1.25215i	−0.779763	+	0.626075i	$0.784660\pi$
$882$	5.77468	−	3.95640i	0.194444	−	0.133219i
$883$	25.7803	−	25.7803i	0.867577	−	0.867577i	−0.124627	−	0.992204i	$-0.539773\pi$
$883$	25.7803	−	25.7803i	0.867577	−	0.867577i	0.992204	+	0.124627i	$0.0397734\pi$
$884$	−7.38226	+	4.26215i	−0.248292	+	0.143352i
$885$	16.0304	−	16.7470i	0.538855	−	0.562943i
$886$	−16.4162	+	28.4337i	−0.551513	+	0.955248i
$887$	−14.4006	−	3.85864i	−0.483526	−	0.129560i	0.00881809	−	0.999961i	$-0.497193\pi$
$887$	−14.4006	−	3.85864i	−0.483526	−	0.129560i	−0.492344	+	0.870401i	$0.663860\pi$
$888$	2.35366	+	2.35366i	0.0789837	+	0.0789837i
$889$	−46.2646	+	7.91487i	−1.55167	+	0.265456i
$890$	2.42452	+	0.593166i	0.0812700	+	0.0198830i
$891$	−0.883028	−	1.52945i	−0.0295826	−	0.0512385i
$892$	−1.71029	−	6.38289i	−0.0572648	−	0.213715i
$893$	2.82274	+	10.5346i	0.0944593	+	0.352527i
$894$	5.04930	+	8.74565i	0.168874	+	0.292498i
$895$	15.4915	+	25.5267i	0.517823	+	0.853263i
$896$	−2.03540	+	1.69031i	−0.0679980	+	0.0564692i
$897$	−10.9830	−	10.9830i	−0.366713	−	0.366713i
$898$	−7.86295	−	2.10687i	−0.262390	−	0.0703072i
$899$	−19.8649	+	34.4071i	−0.662533	+	1.14754i
$900$	−2.68686	−	4.21673i	−0.0895619	−	0.140558i
$901$	0.789659	−	0.455910i	0.0263074	−	0.0151886i
$902$	14.8598	−	14.8598i	0.494777	−	0.494777i
$903$	5.41666	+	11.7723i	0.180255	+	0.391757i
$904$			9.25854i			0.307934i
$905$	9.39851	−	17.1330i	0.312417	−	0.569519i
$906$	12.3928	+	7.15497i	0.411722	+	0.237708i
$907$	−20.7799	+	5.56795i	−0.689984	+	0.184881i	−0.586740	−	0.809775i	$-0.699589\pi$
$907$	−20.7799	+	5.56795i	−0.689984	+	0.184881i	−0.103244	+	0.994656i	$0.532922\pi$
$908$	−4.29835	+	16.0416i	−0.142646	+	0.532361i
$909$	18.3467			0.608520
$910$	12.7103	−	18.8158i	0.421342	−	0.623737i
$911$	23.6120			0.782301			0.391151	−	0.920327i	$-0.372077\pi$
$911$	23.6120			0.782301			0.391151	+	0.920327i	$0.372077\pi$
$912$	−0.459142	+	1.71354i	−0.0152037	+	0.0567410i
$913$	−4.68567	+	1.25552i	−0.155073	+	0.0415517i
$914$	3.95426	+	2.28300i	0.130795	+	0.0755148i
$915$	−14.5738	+	4.24855i	−0.481795	+	0.140453i
$916$			13.5415i			0.447423i
$917$	−0.234081	+	2.52719i	−0.00773002	+	0.0834550i
$918$	1.57046	−	1.57046i	0.0518330	−	0.0518330i
$919$	−38.2901	+	22.1068i	−1.26307	+	0.729236i	−0.973668	−	0.227971i	$-0.926791\pi$
$919$	−38.2901	+	22.1068i	−1.26307	+	0.729236i	−0.289406	+	0.957207i	$0.593458\pi$
$920$	−9.04696	+	0.197792i	−0.298269	+	0.00652100i
$921$	1.50012	−	2.59828i	0.0494306	−	0.0856163i
$922$	−7.29172	−	1.95381i	−0.240140	−	0.0643453i
$923$	−29.0915	−	29.0915i	−0.957560	−	0.957560i
$924$	−0.787924	−	4.60563i	−0.0259208	−	0.151514i
$925$	−15.8722	+	5.00597i	−0.521874	+	0.164595i
$926$	−6.27661	−	10.8714i	−0.206262	−	0.357257i
$927$	−2.36040	−	8.80911i	−0.0775255	−	0.289329i
$928$	0.995491	+	3.71522i	0.0326786	+	0.121958i
$929$	−0.388224	−	0.672424i	−0.0127372	−	0.0220615i	0.859587	−	0.510990i	$-0.170721\pi$
$929$	−0.388224	−	0.672424i	−0.0127372	−	0.0220615i	−0.872324	+	0.488929i	$0.837388\pi$
$930$	19.7456	−	11.9831i	0.647485	−	0.392941i
$931$	8.07860	−	9.43085i	0.264766	−	0.309084i
$932$	8.18707	+	8.18707i	0.268177	+	0.268177i
$933$	14.5087	+	3.88760i	0.474995	+	0.127274i
$934$	−5.75418	+	9.96652i	−0.188282	+	0.326115i
$935$	−6.33587	−	6.06476i	−0.207205	−	0.198339i
$936$	3.32389	−	1.91905i	0.108645	−	0.0627261i
$937$	0.494892	−	0.494892i	0.0161674	−	0.0161674i	−0.698977	−	0.715144i	$-0.746361\pi$
$937$	0.494892	−	0.494892i	0.0161674	−	0.0161674i	0.715144	+	0.698977i	$0.246361\pi$
$938$	16.4957	+	11.6761i	0.538604	+	0.381239i
$939$			13.3182i			0.434624i
$940$	−3.84738	−	13.1977i	−0.125488	−	0.430460i
$941$	15.9777	+	9.22471i	0.520857	+	0.300717i	0.737285	−	0.675582i	$-0.236107\pi$
$941$	15.9777	+	9.22471i	0.520857	+	0.300717i	−0.216428	+	0.976299i	$0.569441\pi$
$942$	9.25683	−	2.48036i	0.301604	−	0.0808145i
$943$	−12.4635	+	46.5145i	−0.405868	+	1.51472i
$944$	10.3676			0.337436
$945$	−1.92994	+	5.59243i	−0.0627810	+	0.181922i
$946$	8.64999			0.281235
$947$	−2.67536	+	9.98459i	−0.0869376	+	0.324456i	−0.995674	−	0.0929149i	$-0.970382\pi$
$947$	−2.67536	+	9.98459i	−0.0869376	+	0.324456i	0.908736	+	0.417370i	$0.137048\pi$
$948$	12.2585	−	3.28465i	0.398137	−	0.106680i
$949$	35.3424	+	20.4049i	1.14726	+	0.662372i
$950$	−6.54012	−	5.99189i	−0.212189	−	0.194403i
$951$		−	13.9017i		−	0.450793i
$952$	5.33817	−	2.45620i	0.173011	−	0.0796058i
$953$	11.1833	−	11.1833i	0.362263	−	0.362263i	−0.502383	−	0.864645i	$-0.667543\pi$
$953$	11.1833	−	11.1833i	0.362263	−	0.362263i	0.864645	+	0.502383i	$0.167543\pi$
$954$	−0.355547	+	0.205275i	−0.0115113	+	0.00664603i
$955$	0.531561	+	24.3135i	0.0172009	+	0.786767i
$956$	8.51320	−	14.7453i	0.275336	−	0.476897i
$957$	−6.56129	−	1.75809i	−0.212096	−	0.0568311i
$958$	8.73106	+	8.73106i	0.282088	+	0.282088i
$959$	10.2278	−	27.6612i	0.330271	−	0.893227i
$960$	0.531389	−	2.17201i	0.0171505	−	0.0701013i
$961$	37.8485	+	65.5555i	1.22092	+	2.11469i
$962$	−3.30652	−	12.3401i	−0.106606	−	0.397861i
$963$	3.81880	+	14.2519i	0.123059	+	0.459263i
$964$	−9.46081	−	16.3866i	−0.304712	−	0.527777i
$965$	−5.95219	+	24.3291i	−0.191608	+	0.783181i
$966$	6.84049	+	8.23705i	0.220089	+	0.265023i
$967$	−3.47333	−	3.47333i	−0.111695	−	0.111695i	0.649051	−	0.760745i	$-0.275166\pi$
$967$	−3.47333	−	3.47333i	−0.111695	−	0.111695i	−0.760745	+	0.649051i	$0.775166\pi$
$968$	7.61250	+	2.03976i	0.244675	+	0.0655605i
$969$	1.96999	−	3.41212i	0.0632851	−	0.109613i
$970$	−0.502306	−	22.9754i	−0.0161281	−	0.737696i
$971$	31.5326	−	18.2054i	1.01193	−	0.584238i	0.100174	−	0.994970i	$-0.468060\pi$
$971$	31.5326	−	18.2054i	1.01193	−	0.584238i	0.911756	+	0.410732i	$0.134727\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	20.7419	−	29.3036i	0.664955	−	0.939430i
$974$			15.5867i			0.499431i
$975$	0.838714	+	19.1722i	0.0268603	+	0.614000i
$976$	−5.87936	−	3.39445i	−0.188194	−	0.108654i
$977$	23.2951	−	6.24191i	0.745278	−	0.199697i	0.133855	−	0.991001i	$-0.457264\pi$
$977$	23.2951	−	6.24191i	0.745278	−	0.199697i	0.611422	+	0.791304i	$0.290598\pi$
$978$	3.06537	−	11.4401i	0.0980196	−	0.365814i
$979$	−1.97137			−0.0630052
$980$	−9.92062	+	12.1071i	−0.316902	+	0.386746i
$981$	20.1488			0.643303
$982$	0.692274	−	2.58360i	0.0220913	−	0.0824460i
$983$	−24.7118	+	6.62151i	−0.788184	+	0.211193i	−0.630390	−	0.776279i	$-0.717105\pi$
$983$	−24.7118	+	6.62151i	−0.788184	+	0.211193i	−0.157794	+	0.987472i	$0.550438\pi$
$984$	−10.3051	−	5.94967i	−0.328516	−	0.189669i
$985$	−9.18438	−	31.5052i	−0.292639	−	1.00384i
$986$		−	8.54248i		−	0.272048i
$987$	−9.39738	+	13.2764i	−0.299122	+	0.422591i
$988$	4.81451	−	4.81451i	0.153170	−	0.153170i
$989$	−17.1658	+	9.91066i	−0.545839	+	0.315141i
$990$	2.85275	+	2.73068i	0.0906663	+	0.0867867i
$991$	−13.1174	+	22.7201i	−0.416689	+	0.721726i	−0.995604	−	0.0936614i	$-0.970143\pi$
$991$	−13.1174	+	22.7201i	−0.416689	+	0.721726i	0.578915	+	0.815388i	$0.303476\pi$
$992$	9.97746	+	2.67345i	0.316785	+	0.0848822i
$993$	13.1752	+	13.1752i	0.418104	+	0.418104i
$994$	18.1189	+	21.8180i	0.574696	+	0.692026i
$995$	−35.4849	+	21.5349i	−1.12495	+	0.682701i
$996$	1.37339	+	2.37878i	0.0435175	+	0.0753745i
$997$	9.65822	+	36.0450i	0.305879	+	1.14156i	0.932186	+	0.361980i	$0.117899\pi$
$997$	9.65822	+	36.0450i	0.305879	+	1.14156i	−0.626307	+	0.779577i	$0.715434\pi$
$998$	−4.70442	−	17.5571i	−0.148916	−	0.555762i
$999$	1.66429	+	2.88263i	0.0526558	+	0.0912025i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.2.u.b.157.2	yes	16
3.2	odd	2		630.2.bv.b.577.3		16
5.2	odd	4		1050.2.bc.h.493.1		16
5.3	odd	4		210.2.u.a.73.3	✓	16
5.4	even	2		1050.2.bc.g.157.4		16
7.3	odd	6		1470.2.m.d.97.3		16
7.4	even	3		1470.2.m.e.97.2		16
7.5	odd	6		210.2.u.a.187.3	yes	16
15.8	even	4		630.2.bv.a.73.2		16
21.5	even	6		630.2.bv.a.397.2		16
35.3	even	12		1470.2.m.e.1273.2		16
35.12	even	12		1050.2.bc.g.943.4		16
35.18	odd	12		1470.2.m.d.1273.3		16
35.19	odd	6		1050.2.bc.h.607.1		16
35.33	even	12	inner	210.2.u.b.103.2	yes	16
105.68	odd	12		630.2.bv.b.523.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.2.u.a.73.3	✓	16	5.3	odd	4
210.2.u.a.187.3	yes	16	7.5	odd	6
210.2.u.b.103.2	yes	16	35.33	even	12	inner
210.2.u.b.157.2	yes	16	1.1	even	1	trivial
630.2.bv.a.73.2		16	15.8	even	4
630.2.bv.a.397.2		16	21.5	even	6
630.2.bv.b.523.3		16	105.68	odd	12
630.2.bv.b.577.3		16	3.2	odd	2
1050.2.bc.g.157.4		16	5.4	even	2
1050.2.bc.g.943.4		16	35.12	even	12
1050.2.bc.h.493.1		16	5.2	odd	4
1050.2.bc.h.607.1		16	35.19	odd	6
1470.2.m.d.97.3		16	7.3	odd	6
1470.2.m.d.1273.3		16	35.18	odd	12
1470.2.m.e.97.2		16	7.4	even	3
1470.2.m.e.1273.2		16	35.3	even	12

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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	210.u (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.96047 + 1.07544i) q^{5} +1.00000i q^{6} +(-1.52856 + 2.15951i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(0.965926 - 0.258819i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(1.96047 + 1.07544i) q^{5} +1.00000i q^{6} +(-1.52856 + 2.15951i) q^{7} +(0.707107 - 0.707107i) q^{8} +(0.866025 - 0.500000i) q^{9} +(-1.54620 + 1.61532i) q^{10} +(0.883028 - 1.52945i) q^{11} +(-0.965926 - 0.258819i) q^{12} +(2.71395 + 2.71395i) q^{13} +(-1.69031 - 2.03540i) q^{14} +(2.17201 + 0.531389i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.574830 - 2.14529i) q^{17} +(0.258819 + 0.965926i) q^{18} +(0.886994 + 1.53632i) q^{19} +(-1.16009 - 1.91159i) q^{20} +(-0.917556 + 2.48155i) q^{21} +(1.24879 + 1.24879i) q^{22} +(-3.90900 - 1.04741i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.68686 + 4.21673i) q^{25} +(-3.32389 + 1.91905i) q^{26} +(0.707107 - 0.707107i) q^{27} +(2.40353 - 1.10591i) q^{28} -3.84628i q^{29} +(-1.07544 + 1.96047i) q^{30} +(-8.94554 - 5.16471i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(0.457089 - 1.70588i) q^{33} +2.22097 q^{34} +(-5.31912 + 2.58977i) q^{35} -1.00000 q^{36} +(-0.861499 + 3.21516i) q^{37} +(-1.71354 + 0.459142i) q^{38} +(3.32389 + 1.91905i) q^{39} +(2.14671 - 0.625808i) q^{40} -11.8993i q^{41} +(-2.15951 - 1.52856i) q^{42} +(3.46335 - 3.46335i) q^{43} +(-1.52945 + 0.883028i) q^{44} +(2.23553 - 0.0488750i) q^{45} +(2.02344 - 3.50471i) q^{46} +(5.93837 + 1.59118i) q^{47} +(0.707107 + 0.707107i) q^{48} +(-2.32699 - 6.60190i) q^{49} +(-4.76846 + 1.50394i) q^{50} +(-1.11049 - 1.92342i) q^{51} +(-0.993373 - 3.70732i) q^{52} +(0.106258 + 0.396561i) q^{53} +(0.500000 + 0.866025i) q^{54} +(3.37598 - 2.04879i) q^{55} +(0.446149 + 2.60786i) q^{56} +(1.25440 + 1.25440i) q^{57} +(3.71522 + 0.995491i) q^{58} +(5.18379 - 8.97859i) q^{59} +(-1.61532 - 1.54620i) q^{60} +(-5.87936 + 3.39445i) q^{61} +(7.30401 - 7.30401i) q^{62} +(-0.244018 + 2.63447i) q^{63} -1.00000i q^{64} +(2.40191 + 8.23928i) q^{65} +(1.52945 + 0.883028i) q^{66} +(-7.37834 + 1.97702i) q^{67} +(-0.574830 + 2.14529i) q^{68} -4.04689 q^{69} +(-1.12484 - 5.80816i) q^{70} -10.7193 q^{71} +(0.258819 - 0.965926i) q^{72} +(10.2705 - 2.75198i) q^{73} +(-2.88263 - 1.66429i) q^{74} +(3.68668 + 3.37764i) q^{75} -1.77399i q^{76} +(1.95310 + 4.24477i) q^{77} +(-2.71395 + 2.71395i) q^{78} +(-10.9907 + 6.34546i) q^{79} +(0.0488750 + 2.23553i) q^{80} +(0.500000 - 0.866025i) q^{81} +(11.4939 + 3.07978i) q^{82} +(-1.94227 - 1.94227i) q^{83} +(2.03540 - 1.69031i) q^{84} +(1.18020 - 4.82397i) q^{85} +(2.44896 + 4.24172i) q^{86} +(-0.995491 - 3.71522i) q^{87} +(-0.457089 - 1.70588i) q^{88} +(-0.558127 - 0.966705i) q^{89} +(-0.531389 + 2.17201i) q^{90} +(-10.0092 + 1.71236i) q^{91} +(2.86158 + 2.86158i) q^{92} +(-9.97746 - 2.67345i) q^{93} +(-3.07393 + 5.32419i) q^{94} +(0.0867037 + 3.96581i) q^{95} +(-0.866025 + 0.500000i) q^{96} +(-7.26720 + 7.26720i) q^{97} +(6.97922 - 0.539001i) q^{98} -1.76606i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{5} - 4 q^{7}+O(q^{10}) \) 16 * q + 12 * q^5 - 4 * q^7	\( 16 q + 12 q^{5} - 4 q^{7} + 4 q^{10} + 4 q^{11} + 16 q^{13} - 16 q^{14} + 4 q^{15} + 8 q^{16} + 12 q^{17} + 8 q^{19} + 8 q^{20} + 8 q^{21} + 4 q^{22} - 40 q^{23} + 8 q^{24} + 16 q^{25} - 12 q^{26} - 4 q^{28} - 4 q^{30} - 24 q^{31} + 4 q^{33} - 16 q^{34} - 44 q^{35} - 16 q^{36} - 8 q^{37} - 20 q^{38} + 12 q^{39} + 8 q^{42} - 24 q^{43} - 4 q^{45} - 4 q^{46} - 52 q^{49} + 8 q^{51} + 8 q^{52} - 28 q^{53} + 8 q^{54} + 56 q^{55} + 8 q^{56} - 8 q^{57} - 12 q^{58} - 8 q^{59} + 24 q^{61} - 8 q^{62} - 4 q^{63} + 16 q^{65} - 84 q^{67} + 12 q^{68} + 8 q^{69} + 4 q^{70} - 32 q^{71} + 16 q^{73} + 24 q^{74} - 24 q^{75} + 44 q^{77} - 16 q^{78} - 12 q^{79} + 12 q^{80} + 8 q^{81} + 36 q^{82} + 16 q^{83} - 4 q^{84} + 8 q^{85} - 8 q^{86} + 48 q^{87} - 4 q^{88} + 16 q^{89} + 8 q^{91} + 8 q^{92} - 32 q^{93} - 8 q^{94} + 72 q^{95} - 44 q^{97} + 24 q^{98}+O(q^{100}) \) 16 * q + 12 * q^5 - 4 * q^7 + 4 * q^10 + 4 * q^11 + 16 * q^13 - 16 * q^14 + 4 * q^15 + 8 * q^16 + 12 * q^17 + 8 * q^19 + 8 * q^20 + 8 * q^21 + 4 * q^22 - 40 * q^23 + 8 * q^24 + 16 * q^25 - 12 * q^26 - 4 * q^28 - 4 * q^30 - 24 * q^31 + 4 * q^33 - 16 * q^34 - 44 * q^35 - 16 * q^36 - 8 * q^37 - 20 * q^38 + 12 * q^39 + 8 * q^42 - 24 * q^43 - 4 * q^45 - 4 * q^46 - 52 * q^49 + 8 * q^51 + 8 * q^52 - 28 * q^53 + 8 * q^54 + 56 * q^55 + 8 * q^56 - 8 * q^57 - 12 * q^58 - 8 * q^59 + 24 * q^61 - 8 * q^62 - 4 * q^63 + 16 * q^65 - 84 * q^67 + 12 * q^68 + 8 * q^69 + 4 * q^70 - 32 * q^71 + 16 * q^73 + 24 * q^74 - 24 * q^75 + 44 * q^77 - 16 * q^78 - 12 * q^79 + 12 * q^80 + 8 * q^81 + 36 * q^82 + 16 * q^83 - 4 * q^84 + 8 * q^85 - 8 * q^86 + 48 * q^87 - 4 * q^88 + 16 * q^89 + 8 * q^91 + 8 * q^92 - 32 * q^93 - 8 * q^94 + 72 * q^95 - 44 * q^97 + 24 * q^98

Introduction

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