LMFDB - Embedded newform 825.2.cu.a.53.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(53,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 7, 12]))

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

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

chi := DirichletCharacter("825.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.cu (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$928$
Relative dimension:	$116$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			53.12
Character	$\chi$	$=$	825.53
Dual form			825.2.cu.a.467.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.368019 - 2.32358i) q^{2} +(1.39525 - 1.02629i) q^{3} +(-3.36148 + 1.09221i) q^{4} +(0.0386766 + 2.23573i) q^{5} +(-2.89815 - 2.86429i) q^{6} +(-4.37796 + 0.693400i) q^{7} +(1.63886 + 3.21645i) q^{8} +(0.893463 - 2.86387i) q^{9} +O(q^{10})$	\(q+(-0.368019 - 2.32358i) q^{2} +(1.39525 - 1.02629i) q^{3} +(-3.36148 + 1.09221i) q^{4} +(0.0386766 + 2.23573i) q^{5} +(-2.89815 - 2.86429i) q^{6} +(-4.37796 + 0.693400i) q^{7} +(1.63886 + 3.21645i) q^{8} +(0.893463 - 2.86387i) q^{9} +(5.18068 - 0.912661i) q^{10} +(-2.31891 + 2.37122i) q^{11} +(-3.56919 + 4.97376i) q^{12} +(1.93391 + 1.93391i) q^{13} +(3.22234 + 9.91736i) q^{14} +(2.34847 + 3.07972i) q^{15} +(1.15166 - 0.836731i) q^{16} +(0.807188 + 5.09639i) q^{17} +(-6.98324 - 1.02208i) q^{18} +(1.09889 + 0.357052i) q^{19} +(-2.57190 - 7.47313i) q^{20} +(-5.39673 + 5.46052i) q^{21} +(6.36312 + 4.51551i) q^{22} +(-2.01896 - 3.96243i) q^{23} +(5.58764 + 2.80582i) q^{24} +(-4.99701 + 0.172941i) q^{25} +(3.78189 - 5.20532i) q^{26} +(-1.69254 - 4.91277i) q^{27} +(13.9591 - 7.11250i) q^{28} +(1.67339 + 5.15018i) q^{29} +(6.29170 - 6.59026i) q^{30} +(0.399958 + 1.23094i) q^{31} +(2.73713 + 2.73713i) q^{32} +(-0.801906 + 5.68832i) q^{33} +(11.5448 - 3.75114i) q^{34} +(-1.71958 - 9.76113i) q^{35} +(0.124586 + 10.6027i) q^{36} +(-1.96852 - 3.86344i) q^{37} +(0.425225 - 2.68477i) q^{38} +(4.68305 + 0.713545i) q^{39} +(-7.12774 + 3.78846i) q^{40} +(-5.83786 + 8.03513i) q^{41} +(14.6741 + 10.5302i) q^{42} +(2.36682 + 2.36682i) q^{43} +(5.20508 - 10.5035i) q^{44} +(6.43740 + 1.88678i) q^{45} +(-8.46401 + 6.14946i) q^{46} +(1.54134 + 1.54134i) q^{47} +(0.748132 - 2.34939i) q^{48} +(12.0283 - 3.90824i) q^{49} +(2.24084 + 11.5473i) q^{50} +(6.35660 + 6.28234i) q^{51} +(-8.61305 - 4.38857i) q^{52} +(-0.281963 + 1.78024i) q^{53} +(-10.7923 + 5.74076i) q^{54} +(-5.39110 - 5.09274i) q^{55} +(-9.40516 - 12.9451i) q^{56} +(1.89967 - 0.629603i) q^{57} +(11.3510 - 5.78363i) q^{58} +(-2.78053 + 8.55759i) q^{59} +(-11.2580 - 7.78739i) q^{60} -15.1527 q^{61} +(2.71301 - 1.38235i) q^{62} +(-1.92574 + 13.1574i) q^{63} +(7.02610 - 9.67059i) q^{64} +(-4.24892 + 4.39851i) q^{65} +(13.5124 - 0.230116i) q^{66} +(1.09499 - 6.91350i) q^{67} +(-8.27968 - 16.2498i) q^{68} +(-6.88355 - 3.45656i) q^{69} +(-22.0479 + 7.58787i) q^{70} +(1.91719 + 0.622933i) q^{71} +(10.6757 - 1.81970i) q^{72} +(3.24616 + 0.514142i) q^{73} +(-8.25257 + 5.99584i) q^{74} +(-6.79460 + 5.36967i) q^{75} -4.08388 q^{76} +(8.50787 - 11.9890i) q^{77} +(-0.0654713 - 11.1440i) q^{78} +(-6.30860 - 8.68304i) q^{79} +(1.91525 + 2.54245i) q^{80} +(-7.40345 - 5.11752i) q^{81} +(20.8187 + 10.6077i) q^{82} +(11.7809 - 1.86592i) q^{83} +(12.1770 - 24.2498i) q^{84} +(-11.3629 + 2.00177i) q^{85} +(4.62847 - 6.37054i) q^{86} +(7.62038 + 5.46842i) q^{87} +(-11.4273 - 3.57254i) q^{88} +(-1.38721 + 4.26940i) q^{89} +(2.01501 - 15.6522i) q^{90} +(-9.80756 - 7.12561i) q^{91} +(11.1145 + 11.1145i) q^{92} +(1.82135 + 1.30701i) q^{93} +(3.01419 - 4.14868i) q^{94} +(-0.755771 + 2.47064i) q^{95} +(6.62808 + 1.00991i) q^{96} +(-1.26023 + 7.95677i) q^{97} +(-13.5078 - 26.5105i) q^{98} +(4.71899 + 8.75963i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 928 q - 8 q^{3} - 20 q^{4} - 2 q^{6}+O(q^{10}) $ 928 * q - 8 * q^3 - 20 * q^4 - 2 * q^6	$ 928 q - 8 q^{3} - 20 q^{4} - 2 q^{6} - 60 q^{10} + 2 q^{12} - 4 q^{13} - 14 q^{15} + 204 q^{16} - 38 q^{18} - 40 q^{19} - 12 q^{21} - 60 q^{22} - 40 q^{24} - 48 q^{25} - 14 q^{27} + 8 q^{28} - 26 q^{30} - 4 q^{31} - 12 q^{33} - 40 q^{34} + 6 q^{36} + 16 q^{37} - 28 q^{40} - 6 q^{42} - 40 q^{43} - 78 q^{45} - 4 q^{46} - 6 q^{48} + 20 q^{49} - 12 q^{51} - 108 q^{52} + 40 q^{54} + 68 q^{55} + 30 q^{57} - 28 q^{58} - 80 q^{60} - 24 q^{61} + 56 q^{63} - 220 q^{64} + 30 q^{66} - 92 q^{67} + 90 q^{69} - 80 q^{70} - 138 q^{72} - 80 q^{73} - 46 q^{75} + 32 q^{76} - 160 q^{79} + 8 q^{81} + 52 q^{82} - 70 q^{84} + 28 q^{85} - 66 q^{87} + 124 q^{88} + 206 q^{90} - 4 q^{91} - 68 q^{93} - 20 q^{94} + 4 q^{96} - 56 q^{97} - 170 q^{99}+O(q^{100}) $ 928 * q - 8 * q^3 - 20 * q^4 - 2 * q^6 - 60 * q^10 + 2 * q^12 - 4 * q^13 - 14 * q^15 + 204 * q^16 - 38 * q^18 - 40 * q^19 - 12 * q^21 - 60 * q^22 - 40 * q^24 - 48 * q^25 - 14 * q^27 + 8 * q^28 - 26 * q^30 - 4 * q^31 - 12 * q^33 - 40 * q^34 + 6 * q^36 + 16 * q^37 - 28 * q^40 - 6 * q^42 - 40 * q^43 - 78 * q^45 - 4 * q^46 - 6 * q^48 + 20 * q^49 - 12 * q^51 - 108 * q^52 + 40 * q^54 + 68 * q^55 + 30 * q^57 - 28 * q^58 - 80 * q^60 - 24 * q^61 + 56 * q^63 - 220 * q^64 + 30 * q^66 - 92 * q^67 + 90 * q^69 - 80 * q^70 - 138 * q^72 - 80 * q^73 - 46 * q^75 + 32 * q^76 - 160 * q^79 + 8 * q^81 + 52 * q^82 - 70 * q^84 + 28 * q^85 - 66 * q^87 + 124 * q^88 + 206 * q^90 - 4 * q^91 - 68 * q^93 - 20 * q^94 + 4 * q^96 - 56 * q^97 - 170 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$-1$	$e\left(\frac{7}{20}\right)$

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 $

$2$	−0.368019	−	2.32358i	−0.260229	−	1.64302i	−0.678429	−	0.734666i	$-0.737339\pi$
$2$	−0.368019	−	2.32358i	−0.260229	−	1.64302i	0.418201	−	0.908355i	$-0.362661\pi$
$3$	1.39525	−	1.02629i	0.805550	−	0.592528i
$3$	1.39525	−	1.02629i	0.805550	−	0.592528i
$4$	−3.36148	+	1.09221i	−1.68074	+	0.546105i
$5$	0.0386766	+	2.23573i	0.0172967	+	0.999850i
$5$	0.0386766	+	2.23573i	0.0172967	+	0.999850i
$6$	−2.89815	−	2.86429i	−1.18316	−	1.16934i
$7$	−4.37796	+	0.693400i	−1.65471	+	0.262081i	−0.912797	−	0.408413i	$-0.866082\pi$
$7$	−4.37796	+	0.693400i	−1.65471	+	0.262081i	−0.741915	+	0.670494i	$0.766082\pi$
$8$	1.63886	+	3.21645i	0.579426	+	1.13719i
$9$	0.893463	−	2.86387i	0.297821	−	0.954622i
$10$	5.18068	−	0.912661i	1.63827	−	0.288609i
$11$	−2.31891	+	2.37122i	−0.699176	+	0.714949i
$11$	−2.31891	+	2.37122i	−0.699176	+	0.714949i
$12$	−3.56919	+	4.97376i	−1.03034	+	1.43580i
$13$	1.93391	+	1.93391i	0.536371	+	0.536371i	0.922461	−	0.386090i	$-0.126175\pi$
$13$	1.93391	+	1.93391i	0.536371	+	0.536371i	−0.386090	+	0.922461i	$0.626175\pi$
$14$	3.22234	+	9.91736i	0.861208	+	2.65052i
$15$	2.34847	+	3.07972i	0.606373	+	0.795181i
$16$	1.15166	−	0.836731i	0.287915	−	0.209183i
$17$	0.807188	+	5.09639i	0.195772	+	1.23606i	0.868321	+	0.496003i	$0.165199\pi$
$17$	0.807188	+	5.09639i	0.195772	+	1.23606i	−0.672549	+	0.740053i	$0.734801\pi$
$18$	−6.98324	−	1.02208i	−1.64596	−	0.240906i
$19$	1.09889	+	0.357052i	0.252103	+	0.0819132i	0.432342	−	0.901710i	$-0.357687\pi$
$19$	1.09889	+	0.357052i	0.252103	+	0.0819132i	−0.180239	+	0.983623i	$0.557687\pi$
$20$	−2.57190	−	7.47313i	−0.575095	−	1.67104i
$21$	−5.39673	+	5.46052i	−1.17766	+	1.19158i
$22$	6.36312	+	4.51551i	1.35662	+	0.962710i
$23$	−2.01896	−	3.96243i	−0.420982	−	0.826224i	−0.999941	−	0.0108669i	$-0.996541\pi$
$23$	−2.01896	−	3.96243i	−0.420982	−	0.826224i	0.578959	−	0.815357i	$-0.303459\pi$
$24$	5.58764	+	2.80582i	1.14057	+	0.572735i
$25$	−4.99701	+	0.172941i	−0.999402	+	0.0345882i
$26$	3.78189	−	5.20532i	0.741689	−	1.02085i
$27$	−1.69254	−	4.91277i	−0.325730	−	0.945463i
$28$	13.9591	−	7.11250i	2.63802	−	1.34414i
$29$	1.67339	+	5.15018i	0.310742	+	0.956364i	0.977472	+	0.211065i	$0.0676932\pi$
$29$	1.67339	+	5.15018i	0.310742	+	0.956364i	−0.666730	+	0.745299i	$0.732307\pi$
$30$	6.29170	−	6.59026i	1.14870	−	1.20321i
$31$	0.399958	+	1.23094i	0.0718346	+	0.221084i	0.980528	−	0.196381i	$-0.0629188\pi$
$31$	0.399958	+	1.23094i	0.0718346	+	0.221084i	−0.908693	+	0.417465i	$0.862919\pi$
$32$	2.73713	+	2.73713i	0.483861	+	0.483861i
$33$	−0.801906	+	5.68832i	−0.139594	+	0.990209i
$34$	11.5448	−	3.75114i	1.97992	−	0.643314i
$35$	−1.71958	−	9.76113i	−0.290663	−	1.64993i
$36$	0.124586	+	10.6027i	0.0207643	+	1.76711i
$37$	−1.96852	−	3.86344i	−0.323623	−	0.635146i	0.670679	−	0.741748i	$-0.266003\pi$
$37$	−1.96852	−	3.86344i	−0.323623	−	0.635146i	−0.994302	+	0.106602i	$0.966003\pi$
$38$	0.425225	−	2.68477i	0.0689806	−	0.435527i
$39$	4.68305	+	0.713545i	0.749888	+	0.114259i
$40$	−7.12774	+	3.78846i	−1.12699	+	0.599009i
$41$	−5.83786	+	8.03513i	−0.911721	+	1.25488i	0.0548549	+	0.998494i	$0.482530\pi$
$41$	−5.83786	+	8.03513i	−0.911721	+	1.25488i	−0.966576	+	0.256382i	$0.917470\pi$
$42$	14.6741	+	10.5302i	2.26426	+	1.62484i
$43$	2.36682	+	2.36682i	0.360937	+	0.360937i	0.864158	−	0.503221i	$-0.167852\pi$
$43$	2.36682	+	2.36682i	0.360937	+	0.360937i	−0.503221	+	0.864158i	$0.667852\pi$
$44$	5.20508	−	10.5035i	0.784696	−	1.58347i
$45$	6.43740	+	1.88678i	0.959630	+	0.281265i
$46$	−8.46401	+	6.14946i	−1.24795	+	0.906689i
$47$	1.54134	+	1.54134i	0.224828	+	0.224828i	0.810528	−	0.585700i	$-0.199180\pi$
$47$	1.54134	+	1.54134i	0.224828	+	0.224828i	−0.585700	+	0.810528i	$0.699180\pi$
$48$	0.748132	−	2.34939i	0.107984	−	0.339105i
$49$	12.0283	−	3.90824i	1.71833	−	0.558319i
$50$	2.24084	+	11.5473i	0.316902	+	1.63304i
$51$	6.35660	+	6.28234i	0.890101	+	0.879704i
$52$	−8.61305	−	4.38857i	−1.19441	−	0.608585i
$53$	−0.281963	+	1.78024i	−0.0387306	+	0.244535i	−0.999457	−	0.0329636i	$-0.989505\pi$
$53$	−0.281963	+	1.78024i	−0.0387306	+	0.244535i	0.960726	+	0.277499i	$0.0895055\pi$
$54$	−10.7923	+	5.74076i	−1.46865	+	0.781218i
$55$	−5.39110	−	5.09274i	−0.726936	−	0.686705i
$56$	−9.40516	−	12.9451i	−1.25682	−	1.72986i
$57$	1.89967	−	0.629603i	0.251617	−	0.0833929i
$58$	11.3510	−	5.78363i	1.49046	−	0.759428i
$59$	−2.78053	+	8.55759i	−0.361994	+	1.11410i	0.589848	+	0.807514i	$0.299188\pi$
$59$	−2.78053	+	8.55759i	−0.361994	+	1.11410i	−0.951842	+	0.306589i	$0.900812\pi$
$60$	−11.2580	−	7.78739i	−1.45341	−	1.00535i
$61$	−15.1527			−1.94011			−0.970053	−	0.242892i	$-0.921904\pi$
$61$	−15.1527			−1.94011			−0.970053	+	0.242892i	$0.921904\pi$
$62$	2.71301	−	1.38235i	0.344552	−	0.175558i
$63$	−1.92574	+	13.1574i	−0.242620	+	1.65768i
$64$	7.02610	−	9.67059i	0.878262	−	1.20882i
$65$	−4.24892	+	4.39851i	−0.527013	+	0.545568i
$66$	13.5124	−	0.230116i	1.66326	−	0.0283254i
$67$	1.09499	−	6.91350i	0.133774	−	0.844618i	−0.825964	−	0.563723i	$-0.809369\pi$
$67$	1.09499	−	6.91350i	0.133774	−	0.844618i	0.959738	−	0.280896i	$-0.0906314\pi$
$68$	−8.27968	−	16.2498i	−1.00406	−	1.97058i
$69$	−6.88355	−	3.45656i	−0.828683	−	0.416121i
$70$	−22.0479	+	7.58787i	−2.63523	+	0.906924i
$71$	1.91719	+	0.622933i	0.227529	+	0.0739286i	0.420563	−	0.907264i	$-0.361833\pi$
$71$	1.91719	+	0.622933i	0.227529	+	0.0739286i	−0.193034	+	0.981192i	$0.561833\pi$
$72$	10.6757	−	1.81970i	1.25815	−	0.214454i
$73$	3.24616	+	0.514142i	0.379935	+	0.0601757i	0.343481	−	0.939160i	$-0.388394\pi$
$73$	3.24616	+	0.514142i	0.379935	+	0.0601757i	0.0364536	+	0.999335i	$0.488394\pi$
$74$	−8.25257	+	5.99584i	−0.959342	+	0.697003i
$75$	−6.79460	+	5.36967i	−0.784573	+	0.620036i
$76$	−4.08388			−0.468453
$77$	8.50787	−	11.9890i	0.969561	−	1.36628i
$78$	−0.0654713	−	11.1440i	−0.00741317	−	1.26181i
$79$	−6.30860	−	8.68304i	−0.709773	−	0.976919i	−0.999802	−	0.0199007i	$-0.993665\pi$
$79$	−6.30860	−	8.68304i	−0.709773	−	0.976919i	0.290029	−	0.957018i	$-0.406335\pi$
$80$	1.91525	+	2.54245i	0.214132	+	0.284254i
$81$	−7.40345	−	5.11752i	−0.822605	−	0.568613i
$82$	20.8187	+	10.6077i	2.29904	+	1.17142i
$83$	11.7809	−	1.86592i	1.29313	−	0.204811i	0.528306	−	0.849054i	$-0.322828\pi$
$83$	11.7809	−	1.86592i	1.29313	−	0.204811i	0.764821	+	0.644243i	$0.222828\pi$
$84$	12.1770	−	24.2498i	1.32862	−	2.64587i
$85$	−11.3629	+	2.00177i	−1.23248	+	0.217122i
$86$	4.62847	−	6.37054i	0.499101	−	0.686953i
$87$	7.62038	+	5.46842i	0.816990	+	0.586276i
$88$	−11.4273	−	3.57254i	−1.21815	−	0.380834i
$89$	−1.38721	+	4.26940i	−0.147044	+	0.452555i	−0.997268	−	0.0738658i	$-0.976466\pi$
$89$	−1.38721	+	4.26940i	−0.147044	+	0.452555i	0.850224	+	0.526421i	$0.176466\pi$
$90$	2.01501	−	15.6522i	0.212400	−	1.64989i
$91$	−9.80756	−	7.12561i	−1.02811	−	0.746967i
$92$	11.1145	+	11.1145i	1.15877	+	1.15877i
$93$	1.82135	+	1.30701i	0.188865	+	0.135530i
$94$	3.01419	−	4.14868i	0.310890	−	0.427904i
$95$	−0.755771	+	2.47064i	−0.0775404	+	0.253482i
$96$	6.62808	+	1.00991i	0.676476	+	0.103073i
$97$	−1.26023	+	7.95677i	−0.127957	+	0.807887i	0.837330	+	0.546697i	$0.184115\pi$
$97$	−1.26023	+	7.95677i	−0.127957	+	0.807887i	−0.965287	+	0.261190i	$0.915885\pi$
$98$	−13.5078	−	26.5105i	−1.36449	−	2.67796i
$99$	4.71899	+	8.75963i	0.474277	+	0.880376i
$100$	16.6085	−	6.03912i	1.66085	−	0.603912i
$101$	−16.1177	−	5.23696i	−1.60377	−	0.521097i	−0.635735	−	0.771907i	$-0.719303\pi$
$101$	−16.1177	−	5.23696i	−1.60377	−	0.521097i	−0.968036	+	0.250811i	$0.919303\pi$
$102$	12.2582	−	17.0821i	1.21374	−	1.69138i
$103$	5.01634	−	9.84511i	0.494274	−	0.970068i	−0.500282	−	0.865863i	$-0.666770\pi$
$103$	5.01634	−	9.84511i	0.494274	−	0.970068i	0.994556	−	0.104205i	$-0.0332298\pi$
$104$	−3.05092	+	9.38975i	−0.299167	+	0.920741i
$105$	−12.4170	−	11.8545i	−1.21177	−	1.15688i
$106$	4.24031			0.411855
$107$	−6.83574	−	1.08268i	−0.660836	−	0.104666i	−0.182997	−	0.983113i	$-0.558580\pi$
$107$	−6.83574	−	1.08268i	−0.660836	−	0.104666i	−0.477839	+	0.878447i	$0.658580\pi$
$108$	11.0552	+	14.6656i	1.06379	+	1.41119i
$109$	−18.2692	+	5.93602i	−1.74987	+	0.568568i	−0.996073	−	0.0885369i	$-0.971781\pi$
$109$	−18.2692	+	5.93602i	−1.74987	+	0.568568i	−0.753799	+	0.657105i	$0.771781\pi$
$110$	−9.84938	+	14.4009i	−0.939101	+	1.37307i
$111$	−6.71159	−	3.37021i	−0.637036	−	0.319886i
$112$	−4.46174	+	4.46174i	−0.421594	+	0.421594i
$113$	−14.0255	+	2.22143i	−1.31941	+	0.208974i	−0.776128	−	0.630575i	$-0.782819\pi$
$113$	−14.0255	+	2.22143i	−1.31941	+	0.208974i	−0.543283	+	0.839550i	$0.682819\pi$
$114$	−2.16205	−	4.18233i	−0.202494	−	0.391711i
$115$	8.78085	−	4.66711i	0.818818	−	0.435210i
$116$	−11.2502	−	15.4845i	−1.04455	−	1.43770i
$117$	7.26635	−	3.81058i	0.671774	−	0.352289i
$118$	20.9076	+	3.31143i	1.92470	+	0.304842i
$119$	−7.06767	−	21.7521i	−0.647892	−	1.99401i
$120$	−6.05695	+	12.6010i	−0.552921	+	1.15031i
$121$	−0.245356	−	10.9973i	−0.0223051	−	0.999751i
$122$	5.57649	+	35.2086i	0.504872	+	3.18763i
$123$	0.101064	+	17.2024i	0.00911263	+	1.55109i
$124$	−2.68890	−	3.70095i	−0.241470	−	0.332356i
$125$	−0.579917	−	11.1653i	−0.0518694	−	0.998654i
$126$	31.2810	−	0.367565i	2.78673	−	0.0327453i
$127$	−6.26006	+	6.26006i	−0.555491	+	0.555491i	−0.928020	−	0.372529i	$-0.878491\pi$
$127$	−6.26006	+	6.26006i	−0.555491	+	0.555491i	0.372529	+	0.928020i	$0.378491\pi$
$128$	−18.1582	−	9.25205i	−1.60497	−	0.817773i
$129$	5.73136	+	0.873274i	0.504618	+	0.0768875i
$130$	11.7840	+	8.25397i	1.03352	+	0.723921i
$131$	12.2954	+	16.9231i	1.07425	+	1.47858i	0.865696	+	0.500571i	$0.166877\pi$
$131$	12.2954	+	16.9231i	1.07425	+	1.47858i	0.208557	+	0.978010i	$0.433123\pi$
$132$	−3.51725	−	19.9970i	−0.306138	−	1.74052i
$133$	−5.05848	−	0.801185i	−0.438626	−	0.0694715i
$134$	−16.4671			−1.42254
$135$	10.9182	−	3.97409i	0.939687	−	0.342035i
$136$	−15.0694	+	10.9486i	−1.29219	+	0.938832i
$137$	10.9089	+	1.72780i	0.932011	+	0.147616i	0.603933	−	0.797035i	$-0.293599\pi$
$137$	10.9089	+	1.72780i	0.932011	+	0.147616i	0.328078	+	0.944651i	$0.393599\pi$
$138$	−5.49831	+	17.2666i	−0.468048	+	1.46983i
$139$	5.54409	+	7.63079i	0.470244	+	0.647235i	0.976594	−	0.215093i	$-0.0690055\pi$
$139$	5.54409	+	7.63079i	0.470244	+	0.647235i	−0.506350	+	0.862328i	$0.669005\pi$
$140$	16.4416	+	30.9337i	1.38956	+	2.61437i
$141$	3.73243	+	0.568701i	0.314327	+	0.0478933i
$142$	0.741873	−	4.68400i	0.0622566	−	0.393073i
$143$	−9.07029	+	0.101169i	−0.758496	+	0.00846020i
$144$	−1.36732	−	4.04579i	−0.113943	−	0.337149i
$145$	−11.4497	+	3.94046i	−0.950846	+	0.327237i
$146$		−	7.73194i		−	0.639900i
$147$	12.7716	−	17.7975i	1.05338	−	1.46791i
$148$	10.8368	+	10.8368i	0.890783	+	0.890783i
$149$	2.21707	+	6.82345i	0.181630	+	0.558998i	0.999874	−	0.0158720i	$-0.00505243\pi$
$149$	2.21707	+	6.82345i	0.181630	+	0.558998i	−0.818244	+	0.574870i	$0.805052\pi$
$150$	14.9774	+	13.8117i	1.22290	+	1.12772i
$151$	5.09117	−	3.69895i	0.414314	−	0.301017i	−0.361032	−	0.932553i	$-0.617576\pi$
$151$	5.09117	−	3.69895i	0.414314	−	0.301017i	0.775346	+	0.631537i	$0.217576\pi$
$152$	0.652495	+	4.11969i	0.0529243	+	0.334151i
$153$	15.3166	+	2.24176i	1.23827	+	0.181235i
$154$	−30.9885	−	15.3565i	−2.49713	−	1.23746i
$155$	−2.73659	+	0.941808i	−0.219808	+	0.0756478i
$156$	−16.5213	+	2.71631i	−1.32276	+	0.217479i
$157$	0.766320	−	4.83835i	0.0611590	−	0.386143i	−0.938054	−	0.346488i	$-0.887374\pi$
$157$	0.766320	−	4.83835i	0.0611590	−	0.386143i	0.999213	−	0.0396548i	$-0.0126258\pi$
$158$	−17.8541	+	17.8541i	−1.42039	+	1.42039i
$159$	1.43363	+	2.77327i	0.113695	+	0.219934i
$160$	−6.01364	+	6.22536i	−0.475420	+	0.492158i
$161$	11.5865	+	15.9474i	0.913141	+	1.25683i
$162$	−9.16636	+	19.0859i	−0.720177	+	1.49953i
$163$	0.250413	+	0.250413i	0.0196138	+	0.0196138i	0.716846	−	0.697232i	$-0.245585\pi$
$163$	0.250413	+	0.250413i	0.0196138	+	0.0196138i	−0.697232	+	0.716846i	$0.745585\pi$
$164$	10.8478	−	33.3861i	0.847071	−	2.60702i
$165$	−12.7486	−	1.57284i	−0.992475	−	0.122446i
$166$	−8.67122	−	26.6873i	−0.673017	−	2.07133i
$167$	5.61211	−	11.0144i	0.434278	−	0.852319i	−0.565344	−	0.824855i	$-0.691257\pi$
$167$	5.61211	−	11.0144i	0.434278	−	0.852319i	0.999623	−	0.0274644i	$-0.00874329\pi$
$168$	−26.4080	−	8.40928i	−2.03742	−	0.648790i
$169$		−	5.51996i		−	0.424613i
$170$	8.83305	+	25.6660i	0.677464	+	1.96849i
$171$	2.00437	−	2.82807i	0.153278	−	0.216268i
$172$	−10.5411	−	5.37096i	−0.803751	−	0.409532i
$173$	14.8030	+	7.54248i	1.12545	+	0.573444i	0.914715	−	0.404099i	$-0.132415\pi$
$173$	14.8030	+	7.54248i	1.12545	+	0.573444i	0.210733	+	0.977544i	$0.432415\pi$
$174$	9.90187	−	19.7191i	0.750659	−	1.49490i
$175$	21.7568	−	4.22206i	1.64466	−	0.319157i
$176$	−0.686522	+	4.67114i	−0.0517485	+	0.352101i
$177$	4.90302	+	14.7936i	0.368533	+	1.11196i
$178$	10.4308	+	1.65208i	0.781822	+	0.123828i
$179$	10.5658			0.789725			0.394863	−	0.918740i	$-0.370792\pi$
$179$	10.5658			0.789725			0.394863	+	0.918740i	$0.370792\pi$
$180$	−23.6999	+	0.688616i	−1.76649	+	0.0513264i
$181$	4.38334	+	3.18468i	0.325811	+	0.236716i	0.738651	−	0.674088i	$-0.235463\pi$
$181$	4.38334	+	3.18468i	0.325811	+	0.236716i	−0.412840	+	0.910804i	$0.635463\pi$
$182$	−12.9476	+	25.4110i	−0.959738	+	1.88359i
$183$	−21.1419	+	15.5511i	−1.56285	+	1.14957i
$184$	9.43616	−	12.9878i	0.695643	−	0.957470i
$185$	8.56149	−	4.55052i	0.629453	−	0.334561i
$186$	2.36665	−	4.71305i	0.173531	−	0.345578i
$187$	−13.9564	−	9.90402i	−1.02060	−	0.724254i
$188$	−6.86467	−	3.49772i	−0.500657	−	0.255098i
$189$	10.8164	+	20.3343i	0.786778	+	1.47910i
$190$	6.01887	+	0.846853i	0.436655	+	0.0614371i
$191$	−17.6444	−	5.73302i	−1.27671	−	0.414827i	−0.409287	−	0.912406i	$-0.634223\pi$
$191$	−17.6444	−	5.73302i	−1.27671	−	0.414827i	−0.867419	+	0.497579i	$0.834223\pi$
$192$	−0.121634	−	20.7037i	−0.00877821	−	1.49416i
$193$	7.71477	−	15.1411i	0.555321	−	1.08988i	−0.427275	−	0.904122i	$-0.640526\pi$
$193$	7.71477	−	15.1411i	0.555321	−	1.08988i	0.982596	−	0.185757i	$-0.0594737\pi$
$194$	18.9520			1.36067
$195$	−1.41417	+	10.4977i	−0.101271	+	0.751752i
$196$	−36.1643	+	26.2749i	−2.58316	+	1.87678i
$197$	1.34913	+	8.51809i	0.0961217	+	0.606889i	0.987981	+	0.154576i	$0.0494010\pi$
$197$	1.34913	+	8.51809i	0.0961217	+	0.606889i	−0.891859	+	0.452313i	$0.850599\pi$
$198$	18.6170	−	14.1887i	1.32305	−	1.00835i
$199$			0.595406i			0.0422072i	0.999777	+	0.0211036i	$0.00671798\pi$
$199$			0.595406i			0.0422072i	−0.999777	+	0.0211036i	$0.993282\pi$
$200$	−8.74567	−	15.7892i	−0.618412	−	1.11647i
$201$	−5.56746	−	10.7699i	−0.392698	−	0.759647i
$202$	−6.23688	+	39.3781i	−0.438825	+	2.77063i
$203$	−10.8972	−	21.3869i	−0.764832	−	1.50107i
$204$	−28.2292	−	14.1752i	−1.97644	−	0.992464i
$205$	−18.1902	−	12.7411i	−1.27046	−	0.889879i
$206$	−24.7220	−	8.03268i	−1.72247	−	0.559663i
$207$	−13.1517	+	2.24174i	−0.914108	+	0.155812i
$208$	3.84538	+	0.609048i	0.266629	+	0.0422299i
$209$	−3.39487	+	1.77774i	−0.234828	+	0.122969i
$210$	−22.9751	+	33.2145i	−1.58543	+	2.29202i
$211$	−2.89602	−	2.10408i	−0.199370	−	0.144851i	0.483621	−	0.875277i	$-0.339321\pi$
$211$	−2.89602	−	2.10408i	−0.199370	−	0.144851i	−0.682991	+	0.730427i	$0.739321\pi$
$212$	−0.996589	−	6.29222i	−0.0684460	−	0.432151i
$213$	3.31428	−	1.09844i	0.227091	−	0.0752640i
$214$			16.2818i			1.11300i
$215$	−5.20005	+	5.38313i	−0.354640	+	0.367126i
$216$	13.0278	−	13.4953i	0.886431	−	0.918242i
$217$	−2.60454	−	5.11169i	−0.176807	−	0.347004i
$218$	20.5162	+	40.2654i	1.38954	+	2.72712i
$219$	5.05688	−	2.61414i	0.341712	−	0.176647i
$220$	23.6844	+	11.2309i	1.59680	+	0.757190i
$221$	−8.29493	+	11.4170i	−0.557978	+	0.767990i
$222$	−5.36096	+	16.8352i	−0.359804	+	1.12991i
$223$	2.08982	−	4.10150i	0.139945	−	0.274657i	−0.810388	−	0.585894i	$-0.800743\pi$
$223$	2.08982	−	4.10150i	0.139945	−	0.274657i	0.950332	+	0.311237i	$0.100743\pi$
$224$	−13.8810	−	10.0851i	−0.927462	−	0.673841i
$225$	−3.96936	+	14.4653i	−0.264624	+	0.964352i
$226$	10.3233	+	31.7719i	0.686698	+	2.11344i
$227$	4.26372	+	0.675307i	0.282993	+	0.0448217i	0.296317	−	0.955090i	$-0.404241\pi$
$227$	4.26372	+	0.675307i	0.282993	+	0.0448217i	−0.0133243	+	0.999911i	$0.504241\pi$
$228$	−5.69804	+	4.19124i	−0.377362	+	0.277571i
$229$	16.9796	+	23.3704i	1.12204	+	1.54436i	0.802363	+	0.596836i	$0.203576\pi$
$229$	16.9796	+	23.3704i	1.12204	+	1.54436i	0.319681	+	0.947525i	$0.396424\pi$
$230$	−14.0759	−	18.6854i	−0.928139	−	1.23208i
$231$	−0.433572	−	25.4592i	−0.0285269	−	1.67510i
$232$	−13.8228	+	13.8228i	−0.907513	+	0.907513i
$233$	16.9217	+	8.62203i	1.10858	+	0.564848i	0.909738	−	0.415184i	$-0.136283\pi$
$233$	16.9217	+	8.62203i	1.10858	+	0.564848i	0.198840	+	0.980032i	$0.436283\pi$
$234$	−11.5284	−	15.4816i	−0.753632	−	1.01206i
$235$	−3.38642	+	3.50565i	−0.220906	+	0.228683i
$236$		−	31.8031i		−	2.07021i
$237$	−17.7134	−	5.64060i	−1.15061	−	0.366396i
$238$	−47.9416	+	24.4275i	−3.10759	+	1.58340i
$239$	−1.69190	−	5.20713i	−0.109440	−	0.336821i	0.881307	−	0.472544i	$-0.156664\pi$
$239$	−1.69190	−	5.20713i	−0.109440	−	0.336821i	−0.990747	+	0.135723i	$0.956664\pi$
$240$	5.28154	+	1.58176i	0.340922	+	0.102102i
$241$	6.92916	+	21.3258i	0.446347	+	1.37371i	0.881000	+	0.473116i	$0.156871\pi$
$241$	6.92916	+	21.3258i	0.446347	+	1.37371i	−0.434653	+	0.900598i	$0.643129\pi$
$242$	−25.4627	+	4.61731i	−1.63681	+	0.296812i
$243$	−15.5817	+	0.457840i	−0.999569	+	0.0293705i
$244$	50.9356	−	16.5500i	3.26081	−	1.05950i
$245$	9.20299	+	26.7409i	0.587957	+	1.70842i
$246$	39.9339	−	6.56563i	2.54609	−	0.418609i
$247$	1.43465	+	2.81567i	0.0912849	+	0.179157i
$248$	−3.30379	+	3.30379i	−0.209791	+	0.209791i
$249$	14.5224	−	14.6941i	0.920321	−	0.931199i
$250$	−25.7300	+	5.45653i	−1.62731	+	0.345101i
$251$	−1.15246	−	0.374455i	−0.0727423	−	0.0236354i	0.272420	−	0.962179i	$-0.412176\pi$
$251$	−1.15246	−	0.374455i	−0.0727423	−	0.0236354i	−0.345162	+	0.938543i	$0.612176\pi$
$252$	−7.89733	−	46.3317i	−0.497485	−	2.91862i
$253$	14.0776	+	4.40111i	0.885049	+	0.276695i
$254$	16.8496	+	12.2419i	1.05724	+	0.768128i
$255$	−13.7998	+	14.4546i	−0.864176	+	0.905184i
$256$	−7.42766	+	22.8600i	−0.464229	+	1.42875i
$257$	1.12193	+	7.08361i	0.0699843	+	0.441864i	0.997654	+	0.0684612i	$0.0218089\pi$
$257$	1.12193	+	7.08361i	0.0699843	+	0.441864i	−0.927669	+	0.373402i	$0.878191\pi$
$258$	−0.0801272	−	13.6387i	−0.00498850	−	0.849106i
$259$	11.2970	+	15.5490i	0.701963	+	0.966169i
$260$	9.47854	−	19.4262i	0.587834	−	1.20476i
$261$	16.2445	−	0.190880i	1.00551	−	0.0118152i
$262$	34.7973	−	34.7973i	2.14979	−	2.14979i
$263$	−16.0754	−	8.19084i	−0.991253	−	0.505069i	−0.118355	−	0.992971i	$-0.537762\pi$
$263$	−16.0754	−	8.19084i	−0.991253	−	0.505069i	−0.872898	+	0.487903i	$0.837762\pi$
$264$	−19.6104	+	6.74309i	−1.20694	+	0.415008i
$265$	−3.99106	−	0.561540i	−0.245169	−	0.0344951i
$266$			12.0486i			0.738750i
$267$	2.44612	+	7.38057i	0.149700	+	0.451683i
$268$	3.87021	+	24.4356i	0.236411	+	1.49264i
$269$	12.5364	+	9.10823i	0.764358	+	0.555339i	0.900244	−	0.435386i	$-0.143388\pi$
$269$	12.5364	+	9.10823i	0.764358	+	0.555339i	−0.135886	+	0.990724i	$0.543388\pi$
$270$	−13.2522	−	23.9067i	−0.806504	−	1.45492i
$271$	0.295041	+	0.908043i	0.0179225	+	0.0551597i	0.959618	−	0.281307i	$-0.0907680\pi$
$271$	0.295041	+	0.908043i	0.0179225	+	0.0551597i	−0.941695	+	0.336467i	$0.890768\pi$
$272$	5.19391	+	5.19391i	0.314927	+	0.314927i
$273$	−20.9970	+	0.123357i	−1.27079	+	0.00746592i
$274$		−	25.9836i		−	1.56973i
$275$	11.1775	−	12.2500i	0.674029	−	0.738705i
$276$	26.9142	+	4.10086i	1.62005	+	0.246843i
$277$	−7.25379	+	1.14889i	−0.435838	+	0.0690300i	−0.370498	−	0.928833i	$-0.620813\pi$
$277$	−7.25379	+	1.14889i	−0.435838	+	0.0690300i	−0.0653397	+	0.997863i	$0.520813\pi$
$278$	15.6904	−	15.6904i	0.941050	−	0.941050i
$279$	3.88261	−	0.0456222i	0.232445	−	0.00273133i
$280$	28.5780	−	21.5281i	1.70786	−	1.28655i
$281$	11.3029	−	15.5571i	0.674272	−	0.928056i	−0.325575	−	0.945516i	$-0.605558\pi$
$281$	11.3029	−	15.5571i	0.674272	−	0.928056i	0.999848	+	0.0174601i	$0.00555799\pi$
$282$	−0.0521811	−	8.88189i	−0.00310734	−	0.528909i
$283$	4.58501	−	2.33618i	0.272551	−	0.138871i	−0.312374	−	0.949959i	$-0.601124\pi$
$283$	4.58501	−	2.33618i	0.272551	−	0.138871i	0.584924	+	0.811088i	$0.301124\pi$
$284$	−7.12497			−0.422789
$285$	1.48110	+	4.22281i	0.0877326	+	0.250137i
$286$	3.57312	+	21.0383i	0.211283	+	1.24402i
$287$	19.9863	−	39.2254i	1.17976	−	2.31540i
$288$	10.2843	−	5.39325i	0.606009	−	0.317800i
$289$	−9.15364	+	2.97420i	−0.538449	+	0.174953i
$290$	13.3697	+	25.1542i	0.785095	+	1.47710i
$291$	6.40760	+	12.3951i	0.375620	+	0.726612i
$292$	−11.4735	+	1.81722i	−0.671434	+	0.106345i
$293$	13.0868	−	2.07274i	0.764536	−	0.121091i	0.238025	−	0.971259i	$-0.423500\pi$
$293$	13.0868	−	2.07274i	0.764536	−	0.121091i	0.526511	+	0.850168i	$0.323500\pi$
$294$	−46.0541	−	23.1259i	−2.68593	−	1.34873i
$295$	−19.2400	−	5.88555i	−1.12020	−	0.342670i
$296$	9.20043	−	12.6633i	0.534764	−	0.736040i
$297$	15.5741	+	7.37885i	0.903701	+	0.428164i
$298$	15.0389	−	7.66271i	0.871180	−	0.443889i
$299$	3.75850	−	11.5675i	0.217360	−	0.668965i
$300$	16.9751	−	25.4712i	0.980059	−	1.47058i
$301$	−12.0030	−	8.72070i	−0.691842	−	0.502653i
$302$	−10.4685	−	10.4685i	−0.602393	−	0.602393i
$303$	−27.8629	+	9.23453i	−1.60068	+	0.530510i
$304$	1.56431	−	0.508274i	0.0897192	−	0.0291515i
$305$	−0.586055	−	33.8774i	−0.0335574	−	1.93982i
$306$	−0.427883	−	36.4143i	−0.0244604	−	2.08167i
$307$	−17.0308	+	17.0308i	−0.972002	+	0.972002i	−0.999619	−	0.0276167i	$-0.991208\pi$
$307$	−17.0308	+	17.0308i	−0.972002	+	0.972002i	0.0276167	+	0.999619i	$0.491208\pi$
$308$	−15.5045	+	49.5932i	−0.883449	+	2.82584i
$309$	−3.10487	−	18.8846i	−0.176630	−	1.07431i
$310$	3.19549	+	6.01209i	0.181491	+	0.341464i
$311$	13.6792	−	4.44463i	0.775675	−	0.252032i	0.105682	−	0.994400i	$-0.466297\pi$
$311$	13.6792	−	4.44463i	0.775675	−	0.252032i	0.669992	+	0.742368i	$0.266297\pi$
$312$	5.37980	+	16.2322i	0.304571	+	0.918968i
$313$	−10.7103	−	1.69635i	−0.605383	−	0.0958832i	−0.153784	−	0.988104i	$-0.549146\pi$
$313$	−10.7103	−	1.69635i	−0.605383	−	0.0958832i	−0.451598	+	0.892221i	$0.649146\pi$
$314$	−11.5243			−0.650356
$315$	−29.4909	−	3.79656i	−1.66163	−	0.213912i
$316$	30.6899	+	22.2975i	1.72644	+	1.25434i
$317$	−11.1936	+	21.9687i	−0.628696	+	1.23388i	0.328517	+	0.944498i	$0.393451\pi$
$317$	−11.1936	+	21.9687i	−0.628696	+	1.23388i	−0.957212	+	0.289387i	$0.906549\pi$
$318$	5.91630	−	4.35178i	0.331770	−	0.244036i
$319$	−16.0926	−	7.97479i	−0.901015	−	0.446503i
$320$	21.8926	+	15.3345i	1.22383	+	0.857222i
$321$	−10.6487	+	5.50484i	−0.594354	+	0.307250i
$322$	32.7910	−	32.7910i	1.82737	−	1.82737i
$323$	−0.932660	+	5.88858i	−0.0518946	+	0.327650i
$324$	30.4759	+	9.11630i	1.69311	+	0.506461i
$325$	−9.99823	−	9.32932i	−0.554602	−	0.517498i
$326$	0.489698	−	0.674011i	0.0271219	−	0.0373300i
$327$	−19.3981	+	27.0317i	−1.07272	+	1.49486i
$328$	−35.4120	−	5.60872i	−1.95530	−	0.309690i
$329$	−7.81670	−	5.67917i	−0.430949	−	0.313103i
$330$	1.03709	+	30.2012i	0.0570900	+	1.66252i
$331$	18.6165	−	13.5257i	1.02326	−	0.743438i	0.0563074	−	0.998413i	$-0.482067\pi$
$331$	18.6165	−	13.5257i	1.02326	−	0.743438i	0.966948	+	0.254975i	$0.0820673\pi$
$332$	−37.5634	+	19.1395i	−2.06156	+	1.05042i
$333$	−12.8232	+	2.18574i	−0.702706	+	0.119778i
$334$	−27.6582	−	8.98670i	−1.51339	−	0.491730i
$335$	15.4991	+	2.18072i	0.846806	+	0.119145i
$336$	−1.64622	+	10.8043i	−0.0898088	+	0.589422i
$337$	−9.61885	−	18.8781i	−0.523972	−	1.02835i	−0.989664	−	0.143407i	$-0.954194\pi$
$337$	−9.61885	−	18.8781i	−0.523972	−	1.02835i	0.465691	−	0.884947i	$-0.345806\pi$
$338$	−12.8261	+	2.03145i	−0.697647	+	0.110496i
$339$	−17.2893	+	17.4937i	−0.939028	+	0.950127i
$340$	36.0099	−	19.1396i	1.95291	−	1.03799i
$341$	−3.84630	−	1.90605i	−0.208289	−	0.103219i
$342$	−7.30888	−	3.61653i	−0.395219	−	0.195559i
$343$	−22.3036	+	11.3642i	−1.20428	+	0.613611i
$344$	−3.73387	+	11.4917i	−0.201317	+	0.619589i
$345$	7.46171	−	15.5235i	0.401725	−	0.835756i
$346$	12.0778	−	37.1717i	0.649307	−	1.99836i
$347$	22.8192	−	11.6270i	1.22500	−	0.624168i	0.282786	−	0.959183i	$-0.408741\pi$
$347$	22.8192	−	11.6270i	1.22500	−	0.624168i	0.942213	+	0.335015i	$0.108741\pi$
$348$	−31.5884	−	10.0589i	−1.69332	−	0.539214i
$349$	6.19866	+	8.53172i	0.331807	+	0.456693i	0.942026	−	0.335540i	$-0.108919\pi$
$349$	6.19866	+	8.53172i	0.331807	+	0.456693i	−0.610219	+	0.792232i	$0.708919\pi$
$350$	−17.8172	−	48.9998i	−0.952369	−	2.61915i
$351$	6.22763	−	12.7741i	0.332406	−	0.681831i
$352$	−12.8375	+	0.143188i	−0.684241	+	0.00763196i
$353$	26.8236	−	4.24844i	1.42768	−	0.226122i	0.605723	−	0.795675i	$-0.292884\pi$
$353$	26.8236	−	4.24844i	1.42768	−	0.226122i	0.821954	+	0.569554i	$0.192884\pi$
$354$	32.5698	−	16.8369i	1.73107	−	0.894871i
$355$	−1.31856	+	4.31042i	−0.0699820	+	0.228773i
$356$		−	15.8666i		−	0.840929i
$357$	−32.1851	−	23.0962i	−1.70342	−	1.22238i
$358$	−3.88842	−	24.5505i	−0.205509	−	1.29753i
$359$	4.01597	−	12.3599i	0.211955	−	0.652330i	−0.787401	−	0.616441i	$-0.788574\pi$
$359$	4.01597	−	12.3599i	0.211955	−	0.652330i	0.999356	−	0.0358889i	$-0.0114262\pi$
$360$	4.48127	+	23.7977i	0.236184	+	1.25425i
$361$	−14.2912	−	10.3832i	−0.752171	−	0.546484i
$362$	5.78671	−	11.3571i	0.304143	−	0.596914i
$363$	−11.6287	−	15.0922i	−0.610348	−	0.792133i
$364$	40.7506	+	13.2407i	2.13591	+	0.694000i
$365$	−1.02393	+	7.27744i	−0.0535951	+	0.380919i
$366$	43.9148	+	43.4018i	2.29546	+	2.26865i
$367$	−11.8794	+	11.8794i	−0.620098	+	0.620098i	−0.945556	−	0.325458i	$-0.894481\pi$
$367$	−11.8794	+	11.8794i	−0.620098	+	0.620098i	0.325458	+	0.945556i	$0.394481\pi$
$368$	−5.64065	−	2.87405i	−0.294039	−	0.149820i
$369$	17.7956	+	23.8979i	0.926402	+	1.24408i
$370$	−13.7243	−	18.2186i	−0.713492	−	0.947142i
$371$		−	7.98934i		−	0.414786i
$372$	−7.54995	−	2.40418i	−0.391446	−	0.124651i
$373$	−6.01196	+	3.06325i	−0.311288	+	0.158609i	−0.602654	−	0.798003i	$-0.705890\pi$
$373$	−6.01196	+	3.06325i	−0.311288	+	0.158609i	0.291366	+	0.956612i	$0.405890\pi$
$374$	−17.8766	+	36.0738i	−0.924375	+	1.86533i
$375$	−12.2679	−	14.9832i	−0.633514	−	0.773731i
$376$	−2.43160	+	7.48371i	−0.125400	+	0.385943i
$377$	−6.72380	+	13.1962i	−0.346293	+	0.679639i
$378$	43.2677	−	32.6162i	2.22545	−	1.67760i
$379$	7.33420	+	2.38303i	0.376733	+	0.122408i	0.491262	−	0.871012i	$-0.336536\pi$
$379$	7.33420	+	2.38303i	0.376733	+	0.122408i	−0.114529	+	0.993420i	$0.536536\pi$
$380$	−0.157950	−	9.13046i	−0.00810269	−	0.468383i
$381$	−2.30974	+	15.1590i	−0.118332	+	0.776620i
$382$	−6.82766	+	43.1081i	−0.349333	+	2.20560i
$383$	1.50264	+	0.765636i	0.0767815	+	0.0391222i	0.491960	−	0.870618i	$-0.336281\pi$
$383$	1.50264	+	0.765636i	0.0767815	+	0.0391222i	−0.415178	+	0.909740i	$0.636281\pi$
$384$	−34.8305	+	5.72657i	−1.77744	+	0.292233i
$385$	27.1333	+	18.5576i	1.38284	+	0.945784i
$386$	−38.0207	−	12.3537i	−1.93520	−	0.628786i
$387$	8.89293	−	4.66359i	0.452053	−	0.237064i
$388$	−4.45424	−	28.1230i	−0.226130	−	1.42773i
$389$	−0.734494	+	0.533641i	−0.0372403	+	0.0270567i	−0.606250	−	0.795274i	$-0.707327\pi$
$389$	−0.734494	+	0.533641i	−0.0372403	+	0.0270567i	0.569009	+	0.822331i	$0.307327\pi$
$390$	24.9126	−	0.577390i	1.26150	−	0.0292373i
$391$	18.5644	−	13.4878i	0.938842	−	0.682108i
$392$	32.2834	+	32.2834i	1.63056	+	1.63056i
$393$	34.5232	+	10.9935i	1.74146	+	0.554546i
$394$	19.2960	−	6.26964i	0.972117	−	0.315860i
$395$	19.1690	−	14.4402i	0.964496	−	0.726564i
$396$	−25.4302	−	24.2912i	−1.27791	−	1.22068i
$397$	29.4458	−	4.66376i	1.47784	−	0.234067i	0.635119	−	0.772414i	$-0.280951\pi$
$397$	29.4458	−	4.66376i	1.47784	−	0.234067i	0.842724	+	0.538347i	$0.180951\pi$
$398$	1.38347	−	0.219121i	0.0693473	−	0.0109835i
$399$	−7.88011	+	4.07361i	−0.394499	+	0.203935i
$400$	−5.61016	+	4.38032i	−0.280508	+	0.219016i
$401$	12.7778	−	4.15174i	0.638090	−	0.207328i	0.0279348	−	0.999610i	$-0.491107\pi$
$401$	12.7778	−	4.15174i	0.638090	−	0.207328i	0.610156	+	0.792282i	$0.291107\pi$
$402$	−22.9757	+	16.9000i	−1.14592	+	0.842893i
$403$	−1.60705	+	3.15402i	−0.0800531	+	0.157113i
$404$	59.8992			2.98010
$405$	11.1551	−	16.7501i	0.554300	−	0.832317i
$406$	−45.6839	+	33.1913i	−2.26725	+	1.64726i
$407$	13.7259	+	4.29116i	0.680367	+	0.212705i
$408$	−9.78925	+	30.7416i	−0.484640	+	1.52193i
$409$			21.4376i			1.06002i	0.847991	+	0.530011i	$0.177812\pi$
$409$			21.4376i			1.06002i	−0.847991	+	0.530011i	$0.822188\pi$
$410$	−22.9107	+	46.9554i	−1.13148	+	2.31896i
$411$	16.9939	−	8.78497i	0.838248	−	0.433330i
$412$	−6.10937	+	38.5730i	−0.300987	+	1.90036i
$413$	6.23921	−	39.3928i	0.307011	−	1.93839i
$414$	10.0490	+	29.7341i	0.493879	+	1.46135i
$415$	4.62734	+	26.2669i	0.227147	+	1.28939i
$416$			10.5868i			0.519058i
$417$	15.5668	+	4.95705i	0.762310	+	0.242748i
$418$	5.38011	+	7.23402i	0.263150	+	0.353828i
$419$	−22.7760	+	16.5478i	−1.11268	+	0.808411i	−0.983084	−	0.183156i	$-0.941369\pi$
$419$	−22.7760	+	16.5478i	−1.11268	+	0.808411i	−0.129598	+	0.991567i	$0.541369\pi$
$420$	54.6870	+	26.2865i	2.66845	+	1.28265i
$421$	4.33047			0.211054			0.105527	−	0.994416i	$-0.466347\pi$
$421$	4.33047			0.211054			0.105527	+	0.994416i	$0.466347\pi$
$422$	−3.82321	+	7.50347i	−0.186111	+	0.365263i
$423$	5.79133	−	3.03707i	0.281584	−	0.147667i
$424$	−6.18816	+	2.01066i	−0.300524	+	0.0976461i
$425$	−4.91490	−	25.3271i	−0.238408	−	1.22854i
$426$	−3.77204	−	7.29674i	−0.182756	−	0.353528i
$427$	66.3380	−	10.5069i	3.21032	−	0.508465i
$428$	24.1607	−	3.82668i	1.16785	−	0.184970i
$429$	−12.5515	+	9.44989i	−0.605993	+	0.456245i
$430$	14.4218	+	10.1016i	0.695483	+	0.487144i
$431$	−26.3998	+	8.57782i	−1.27163	+	0.413179i	−0.865626	−	0.500691i	$-0.833079\pi$
$431$	−26.3998	+	8.57782i	−1.27163	+	0.413179i	−0.406008	+	0.913870i	$0.633079\pi$
$432$	−6.05991	−	4.24164i	−0.291557	−	0.204076i
$433$	6.92777	+	6.92777i	0.332927	+	0.332927i	0.853697	−	0.520770i	$-0.174355\pi$
$433$	6.92777	+	6.92777i	0.332927	+	0.332927i	−0.520770	+	0.853697i	$0.674355\pi$
$434$	−10.9189	+	7.93305i	−0.524124	+	0.380799i
$435$	−11.9312	+	17.2486i	−0.572057	+	0.827009i
$436$	54.9282	−	39.9076i	2.63058	−	1.91123i
$437$	−0.803825	−	5.07515i	−0.0384522	−	0.242777i
$438$	−7.93520	−	10.7880i	−0.379159	−	0.515471i
$439$	−5.03607	−	1.63632i	−0.240359	−	0.0780973i	0.186361	−	0.982481i	$-0.440331\pi$
$439$	−5.03607	−	1.63632i	−0.240359	−	0.0780973i	−0.426719	+	0.904384i	$0.640331\pi$
$440$	7.54528	−	25.6865i	0.359707	−	1.22456i
$441$	−0.445803	−	37.9393i	−0.0212287	−	1.80663i
$442$	29.5810	+	15.0723i	1.40703	+	0.716915i
$443$	−1.47581	+	9.31789i	−0.0701178	+	0.442707i	0.927506	+	0.373809i	$0.121948\pi$
$443$	−1.47581	+	9.31789i	−0.0701178	+	0.442707i	−0.997624	+	0.0688980i	$0.978052\pi$
$444$	26.2419	+	3.99841i	1.24538	+	0.189756i
$445$	−9.59889	−	2.93631i	−0.455031	−	0.139194i
$446$	−10.2993	−	3.34643i	−0.487684	−	0.158458i
$447$	10.0962	+	7.24508i	0.477534	+	0.342680i
$448$	−24.0544	+	47.2093i	−1.13646	+	2.23043i
$449$	−0.118228	+	0.363869i	−0.00557953	+	0.0171720i	−0.953808	−	0.300418i	$-0.902874\pi$
$449$	−0.118228	+	0.363869i	−0.00557953	+	0.0171720i	0.948228	+	0.317590i	$0.102874\pi$
$450$	35.0720	+	3.89964i	1.65331	+	0.183831i
$451$	−5.51559	−	32.4755i	−0.259719	−	1.52921i
$452$	44.7203	−	22.7861i	2.10346	−	1.07177i
$453$	3.30728	−	10.3860i	0.155390	−	0.487976i
$454$		−	10.1556i		−	0.476627i
$455$	15.5516	−	22.2027i	0.729072	−	1.04088i
$456$	5.13839	+	5.07836i	0.240627	+	0.237816i
$457$	−12.1073	−	6.16897i	−0.566355	−	0.288572i	0.147275	−	0.989096i	$-0.452950\pi$
$457$	−12.1073	−	6.16897i	−0.566355	−	0.288572i	−0.713629	+	0.700524i	$0.752950\pi$
$458$	48.0543	−	48.0543i	2.24543	−	2.24543i
$459$	23.6712	−	12.5914i	1.10488	−	0.587716i
$460$	−24.4192	+	25.2789i	−1.13855	+	1.17864i
$461$	−3.54536	−	1.15196i	−0.165124	−	0.0536519i	0.225289	−	0.974292i	$-0.427668\pi$
$461$	−3.54536	−	1.15196i	−0.165124	−	0.0536519i	−0.390412	+	0.920640i	$0.627668\pi$
$462$	−58.9971	+	10.3769i	−2.74479	+	0.482779i
$463$	−6.25625	+	12.2786i	−0.290753	+	0.570634i	−0.989466	−	0.144768i	$-0.953756\pi$
$463$	−6.25625	+	12.2786i	−0.290753	+	0.570634i	0.698713	+	0.715402i	$0.253756\pi$
$464$	6.23650	+	4.53108i	0.289522	+	0.210350i
$465$	−2.85167	+	4.12260i	−0.132243	+	0.191181i
$466$	13.8065	−	42.4920i	0.639573	−	1.96840i
$467$	−5.99301	−	37.8384i	−0.277323	−	1.75095i	−0.595905	−	0.803055i	$-0.703206\pi$
$467$	−5.99301	−	37.8384i	−0.277323	−	1.75095i	0.318581	−	0.947896i	$-0.396794\pi$
$468$	−20.2637	+	20.7456i	−0.936690	+	0.958965i
$469$			31.0263i			1.43266i
$470$	9.39192	+	6.57848i	0.433217	+	0.303442i
$471$	−3.89634	−	7.53720i	−0.179534	−	0.347296i
$472$	−32.0820	+	5.08129i	−1.47669	+	0.233885i
$473$	−11.1007	+	0.123816i	−0.510410	+	0.00569308i
$474$	−6.58752	+	43.2344i	−0.302575	+	1.98582i
$475$	−5.55292	−	1.59415i	−0.254785	−	0.0731444i
$476$	47.5157	+	65.3997i	2.17788	+	2.99759i
$477$	4.84645	+	2.39809i	0.221904	+	0.109801i
$478$	−11.4765	+	5.84759i	−0.524925	+	0.267463i
$479$	−7.50659	+	23.1029i	−0.342985	+	1.05560i	0.619669	+	0.784863i	$0.287267\pi$
$479$	−7.50659	+	23.1029i	−0.342985	+	1.05560i	−0.962654	+	0.270736i	$0.912733\pi$
$480$	−2.00153	+	14.8577i	−0.0913568	+	0.678157i
$481$	3.66461	−	11.2785i	0.167092	−	0.514256i
$482$	47.0021	−	23.9488i	2.14089	−	1.09084i
$483$	32.5327	+	10.3596i	1.48029	+	0.471378i
$484$	12.8361	+	36.6991i	0.583459	+	1.66814i
$485$	−17.8380	−	2.50979i	−0.809980	−	0.113964i
$486$	6.79820	+	36.0369i	0.308373	+	1.63467i
$487$	−14.0364	+	2.22315i	−0.636051	+	0.100741i	−0.466129	−	0.884717i	$-0.654352\pi$
$487$	−14.0364	+	2.22315i	−0.636051	+	0.100741i	−0.169922	+	0.985457i	$0.554352\pi$
$488$	−24.8332	−	48.7380i	−1.12415	−	2.20626i
$489$	0.606385	+	0.0923935i	0.0274217	+	0.00417818i
$490$	58.7479	−	31.2251i	2.65396	−	1.41060i
$491$	−5.66698	−	1.84131i	−0.255747	−	0.0830973i	0.178338	−	0.983969i	$-0.442928\pi$
$491$	−5.66698	−	1.84131i	−0.255747	−	0.0830973i	−0.434085	+	0.900872i	$0.642928\pi$
$492$	−19.1283	−	57.7150i	−0.862372	−	2.60199i
$493$	−24.8966	+	12.6854i	−1.12128	+	0.571323i
$494$	6.01445	−	4.36976i	0.270603	−	0.196605i
$495$	−19.4017	+	10.8892i	−0.872041	+	0.489433i
$496$	1.49059	+	1.08297i	0.0669293	+	0.0486270i
$497$	−8.82532	−	1.39779i	−0.395870	−	0.0626996i
$498$	−39.4874	−	28.3363i	−1.76947	−	1.26978i
$499$	−0.465411	+	0.640583i	−0.0208347	+	0.0286765i	−0.819307	−	0.573355i	$-0.805642\pi$
$499$	−0.465411	+	0.640583i	−0.0208347	+	0.0286765i	0.798473	+	0.602031i	$0.205642\pi$
$500$	14.1442	+	36.8985i	0.632549	+	1.65015i
$501$	−3.47363	−	21.1275i	−0.155190	−	0.943908i
$502$	−0.445952	+	2.81563i	−0.0199038	+	0.125668i
$503$	28.8151	−	28.8151i	1.28480	−	1.28480i	0.346899	−	0.937902i	$-0.387235\pi$
$503$	28.8151	−	28.8151i	1.28480	−	1.28480i	0.937902	−	0.346899i	$-0.112765\pi$
$504$	−45.4762	+	15.3691i	−2.02567	+	0.684596i
$505$	11.0851	−	36.2374i	0.493279	−	1.61254i
$506$	5.04552	−	34.3300i	0.224301	−	1.52616i
$507$	−5.66508	−	7.70175i	−0.251595	−	0.342047i
$508$	14.2058	−	27.8804i	0.630279	−	1.23699i
$509$	−5.22309	−	3.79480i	−0.231510	−	0.168202i	0.465983	−	0.884794i	$-0.345701\pi$
$509$	−5.22309	−	3.79480i	−0.231510	−	0.168202i	−0.697492	+	0.716592i	$0.745701\pi$
$510$	38.6651	+	26.7454i	1.71212	+	1.18430i
$511$	−14.5681			−0.644453
$512$	15.5936	+	2.46978i	0.689146	+	0.109150i
$513$	−0.105811	−	6.00293i	−0.00467169	−	0.265036i
$514$	16.0465	−	5.21381i	0.707779	−	0.229971i
$515$	22.2051	+	10.8344i	0.978472	+	0.477421i
$516$	−20.2197	+	3.32436i	−0.890121	+	0.146347i
$517$	−7.22909	+	0.0806327i	−0.317935	+	0.00354622i
$518$	31.9719	−	31.9719i	1.40476	−	1.40476i
$519$	28.3946	−	4.66843i	1.24639	−	0.204921i
$520$	−21.1110	−	6.45787i	−0.925778	−	0.283196i
$521$	−25.5961	+	8.31667i	−1.12139	+	0.364360i	−0.810296	−	0.586021i	$-0.800694\pi$
$521$	−25.5961	+	8.31667i	−1.12139	+	0.364360i	−0.311089	+	0.950381i	$0.600694\pi$
$522$	−6.42182	−	37.6752i	−0.281076	−	1.64900i
$523$	27.1164	+	27.1164i	1.18572	+	1.18572i	0.978240	+	0.207478i	$0.0665256\pi$
$523$	27.1164	+	27.1164i	1.18572	+	1.18572i	0.207478	+	0.978240i	$0.433474\pi$
$524$	−59.8143	−	43.4576i	−2.61300	−	1.89846i
$525$	26.0232	−	28.2196i	1.13574	−	1.23160i
$526$	−13.1160	+	40.3669i	−0.571885	+	1.76008i
$527$	−5.95052	+	3.03194i	−0.259209	+	0.132074i
$528$	3.83607	+	7.22200i	0.166943	+	0.314297i
$529$	1.89441	−	2.60743i	0.0823657	−	0.113367i
$530$	0.164001	+	9.48020i	0.00712373	+	0.411794i
$531$	22.0235	+	15.6090i	0.955738	+	0.677371i
$532$	17.8790	−	2.83176i	0.775155	−	0.122772i
$533$	−26.8291	+	4.24932i	−1.16210	+	0.184058i
$534$	16.2491	−	8.39995i	0.703169	−	0.363502i
$535$	2.15619	−	15.3248i	0.0932202	−	0.662548i
$536$	24.0315	−	7.80830i	1.03800	−	0.337267i
$537$	14.7420	−	10.8436i	0.636163	−	0.467934i
$538$	16.5501	−	32.4814i	0.713524	−	1.40037i
$539$	−18.6252	+	37.5846i	−0.802246	+	1.61888i
$540$	−32.3607	+	25.2838i	−1.39258	+	1.08804i
$541$	5.40613			0.232428			0.116214	−	0.993224i	$-0.462924\pi$
$541$	5.40613			0.232428			0.116214	+	0.993224i	$0.462924\pi$
$542$	2.00133	−	1.01973i	0.0859646	−	0.0438011i
$543$	9.38427	−	0.0551326i	0.402718	−	0.00236597i
$544$	−11.7401	+	16.1589i	−0.503353	+	0.692806i
$545$	−13.9780	−	40.6155i	−0.598750	−	1.73978i
$546$	8.01392	+	48.7428i	0.342964	+	2.08600i
$547$	10.6459	−	10.6459i	0.455184	−	0.455184i	−0.441887	−	0.897071i	$-0.645691\pi$
$547$	10.6459	−	10.6459i	0.455184	−	0.455184i	0.897071	+	0.441887i	$0.145691\pi$
$548$	−38.5572	+	6.10686i	−1.64708	+	0.260872i
$549$	−13.5384	+	43.3953i	−0.577805	+	1.85207i
$550$	−32.5775	−	21.4636i	−1.38911	−	0.915211i
$551$			6.25698i			0.266556i
$552$	−0.163357	−	27.8054i	−0.00695294	−	1.18348i
$553$	33.6396	+	33.6396i	1.43050	+	1.43050i
$554$	5.33907	+	16.4320i	0.226835	+	0.698127i
$555$	7.27531	−	15.1357i	0.308820	−	0.642474i
$556$	−26.9708	−	19.5954i	−1.14382	−	0.831031i
$557$	6.03235	+	38.0867i	0.255599	+	1.61379i	0.697405	+	0.716677i	$0.254338\pi$
$557$	6.03235	+	38.0867i	0.255599	+	1.61379i	−0.441807	+	0.897110i	$0.645662\pi$
$558$	−1.53488	−	9.00476i	−0.0649767	−	0.381202i
$559$			9.15446i			0.387192i
$560$	−10.1478	−	9.80269i	−0.428824	−	0.414239i
$561$	−29.6371	+	0.504722i	−1.25128	+	0.0213094i
$562$	−40.3078	−	20.5378i	−1.70028	−	0.866336i
$563$	−26.7084	+	26.7084i	−1.12562	+	1.12562i	−0.134744	+	0.990880i	$0.543021\pi$
$563$	−26.7084	+	26.7084i	−1.12562	+	1.12562i	−0.990880	+	0.134744i	$0.956979\pi$
$564$	−13.1676	+	2.16492i	−0.554457	+	0.0911596i
$565$	−5.50898	−	31.2714i	−0.231764	−	1.31560i
$566$	−7.11567	−	9.79389i	−0.299094	−	0.411668i
$567$	35.9605	+	17.2707i	1.51020	+	0.725302i
$568$	1.13838	+	7.18745i	0.0477654	+	0.301579i
$569$	1.27338	−	3.91906i	0.0533828	−	0.164295i	−0.920811	−	0.390010i	$-0.872472\pi$
$569$	1.27338	−	3.91906i	0.0533828	−	0.164295i	0.974194	+	0.225714i	$0.0724716\pi$
$570$	9.26696	−	4.99552i	0.388150	−	0.209239i
$571$	−8.33717	−	6.05731i	−0.348900	−	0.253490i	0.399508	−	0.916730i	$-0.369181\pi$
$571$	−8.33717	−	6.05731i	−0.348900	−	0.253490i	−0.748407	+	0.663239i	$0.769181\pi$
$572$	30.3791	−	10.2467i	1.27021	−	0.428438i
$573$	−30.5022	+	10.1093i	−1.27425	+	0.422320i
$574$	−98.4988	−	32.0042i	−4.11126	−	1.33583i
$575$	10.7740	+	19.4511i	0.449308	+	0.811168i
$576$	−21.4177	−	28.7621i	−0.892405	−	1.19842i
$577$	21.5849	−	21.5849i	0.898592	−	0.898592i	−0.0967199	−	0.995312i	$-0.530835\pi$
$577$	21.5849	−	21.5849i	0.898592	−	0.898592i	0.995312	+	0.0967199i	$0.0308351\pi$
$578$	10.2795	+	20.1747i	0.427571	+	0.839155i
$579$	−4.77507	−	29.0432i	−0.198445	−	1.20700i
$580$	34.1841	−	25.7513i	1.41942	−	1.06926i
$581$	−50.2826	+	16.3378i	−2.08607	+	0.677807i
$582$	26.4428	−	19.4502i	1.09609	−	0.806237i
$583$	−3.56750	−	4.79681i	−0.147751	−	0.198664i
$584$	3.66631	+	11.2837i	0.151713	+	0.466924i
$585$	8.80049	+	16.0982i	0.363855	+	0.665580i
$586$	−9.63235	−	29.6453i	−0.397909	−	1.22464i
$587$	−5.57544	+	2.84083i	−0.230123	+	0.117254i	−0.565251	−	0.824919i	$-0.691221\pi$
$587$	−5.57544	+	2.84083i	−0.230123	+	0.117254i	0.335128	+	0.942173i	$0.391221\pi$
$588$	−23.4927	+	73.7752i	−0.968824	+	3.04244i
$589$			1.49548i			0.0616202i
$590$	−6.59484	+	46.8718i	−0.271505	+	1.92968i
$591$	10.6244	+	10.5003i	0.437029	+	0.431924i
$592$	−5.49973	−	2.80225i	−0.226038	−	0.115172i
$593$	−4.19387	+	4.19387i	−0.172221	+	0.172221i	−0.787955	−	0.615733i	$-0.788860\pi$
$593$	−4.19387	+	4.19387i	−0.172221	+	0.172221i	0.615733	+	0.787955i	$0.288860\pi$
$594$	11.4138	−	38.9032i	0.468314	−	1.59622i
$595$	48.3584	−	16.6427i	1.98250	−	0.682285i
$596$	−14.9053	−	20.5154i	−0.610544	−	0.840342i
$597$	0.611058	+	0.830742i	0.0250089	+	0.0340000i
$598$	−28.2612	−	4.47613i	−1.15569	−	0.183043i
$599$	4.85870	+	14.9536i	0.198521	+	0.610986i	0.999917	+	0.0128517i	$0.00409093\pi$
$599$	4.85870	+	14.9536i	0.198521	+	0.610986i	−0.801396	+	0.598134i	$0.795909\pi$
$600$	−28.4067	−	13.0544i	−1.15970	−	0.532942i
$601$	1.64300	+	1.19371i	0.0670194	+	0.0486924i	0.620791	−	0.783976i	$-0.286812\pi$
$601$	1.64300	+	1.19371i	0.0670194	+	0.0486924i	−0.553771	+	0.832669i	$0.686812\pi$
$602$	−15.8459	+	31.0993i	−0.645831	+	1.26751i
$603$	−18.8210	−	9.31287i	−0.766450	−	0.379249i
$604$	−13.0738	+	17.9946i	−0.531967	+	0.732190i
$605$	24.5775	−	0.973886i	0.999216	−	0.0395941i
$606$	31.7113	+	61.3432i	1.28818	+	2.49190i
$607$	−19.1698	−	37.6229i	−0.778080	−	1.52707i	−0.848288	−	0.529535i	$-0.822367\pi$
$607$	−19.1698	−	37.6229i	−0.778080	−	1.52707i	0.0702087	−	0.997532i	$-0.477633\pi$
$608$	2.03052	+	3.98511i	0.0823483	+	0.161618i
$609$	−37.1535	−	18.6565i	−1.50554	−	0.756001i
$610$	−78.5013	+	13.8293i	−3.17843	+	0.559932i
$611$			5.96165i			0.241182i
$612$	−53.9348	+	9.19329i	−2.18018	+	0.371617i
$613$	−0.547754	−	3.45838i	−0.0221236	−	0.139683i	0.974154	−	0.225884i	$-0.0725271\pi$
$613$	−0.547754	−	3.45838i	−0.0221236	−	0.139683i	−0.996278	+	0.0862016i	$0.972527\pi$
$614$	45.8402	+	33.3049i	1.84996	+	1.34408i
$615$	−38.4560	+	0.891281i	−1.55070	+	0.0359399i
$616$	52.5053	+	7.71676i	2.11550	+	0.310917i
$617$	−3.73151	−	0.591014i	−0.150225	−	0.0237933i	0.0808689	−	0.996725i	$-0.474230\pi$
$617$	−3.73151	−	0.591014i	−0.150225	−	0.0237933i	−0.231094	+	0.972931i	$0.574230\pi$
$618$	−42.7373	+	14.1643i	−1.71915	+	0.569773i
$619$	−30.1566	−	9.79848i	−1.21210	−	0.393834i	−0.367899	−	0.929866i	$-0.619923\pi$
$619$	−30.1566	−	9.79848i	−1.21210	−	0.393834i	−0.844198	+	0.536032i	$0.819923\pi$
$620$	8.17035	−	6.15481i	0.328129	−	0.247183i
$621$	−16.0493	+	16.6253i	−0.644037	+	0.667149i
$622$	−15.3617	−	30.1490i	−0.615947	−	1.20886i
$623$	3.11275	−	19.6531i	0.124710	−	0.787386i
$624$	5.99034	−	3.09669i	0.239805	−	0.123967i
$625$	24.9402	−	1.72838i	0.997607	−	0.0691350i
$626$			25.5106i			1.01961i
$627$	−2.91223	+	5.96452i	−0.116303	+	0.238200i
$628$	2.70853	+	17.1010i	0.108082	+	0.682405i
$629$	18.1006	−	13.1509i	0.721719	−	0.524360i
$630$	2.03162	+	69.9218i	0.0809417	+	2.78575i
$631$	14.9534			0.595284			0.297642	−	0.954678i	$-0.403800\pi$
$631$	14.9534			0.595284			0.297642	+	0.954678i	$0.403800\pi$
$632$	17.5896	−	34.5216i	0.699678	−	1.37320i
$633$	−6.20007	+	0.0364254i	−0.246431	+	0.00144778i
$634$	55.1655	+	17.9244i	2.19090	+	0.711867i
$635$	−14.2380	−	13.7537i	−0.565016	−	0.545800i
$636$	−7.84812	−	7.75645i	−0.311198	−	0.307563i
$637$	30.8199	+	15.7035i	1.22113	+	0.622196i
$638$	−12.6077	+	40.3274i	−0.499143	+	1.59658i
$639$	3.49694	−	4.93401i	0.138337	−	0.195186i
$640$	19.9828	−	40.9547i	0.789890	−	1.61888i
$641$	−8.84201	+	12.1700i	−0.349238	+	0.480685i	−0.947111	−	0.320906i	$-0.896013\pi$
$641$	−8.84201	+	12.1700i	−0.349238	+	0.480685i	0.597873	+	0.801591i	$0.296013\pi$
$642$	16.7099	+	22.7173i	0.659486	+	0.896580i
$643$	−11.1001	+	21.7851i	−0.437744	+	0.859121i	0.561750	+	0.827307i	$0.310128\pi$
$643$	−11.1001	+	21.7851i	−0.437744	+	0.859121i	−0.999494	+	0.0318135i	$0.989872\pi$
$644$	−56.3656	−	40.9520i	−2.22112	−	1.61373i
$645$	−1.73074	+	12.8476i	−0.0681478	+	0.505873i
$646$	14.0258			0.551839
$647$	9.04422	+	1.43246i	0.355565	+	0.0563160i	0.331662	−	0.943398i	$-0.392391\pi$
$647$	9.04422	+	1.43246i	0.355565	+	0.0563160i	0.0239031	+	0.999714i	$0.492391\pi$
$648$	4.32700	−	32.1997i	0.169981	−	1.26493i
$649$	−13.8441	−	26.4375i	−0.543430	−	1.03776i
$650$	−17.9979	+	26.6651i	−0.705936	+	1.04589i
$651$	−8.88006	−	4.45910i	−0.348037	−	0.174766i
$652$	−1.11526	−	0.568254i	−0.0436770	−	0.0222545i
$653$	−5.33993	−	2.72083i	−0.208968	−	0.106474i	0.346374	−	0.938096i	$-0.387413\pi$
$653$	−5.33993	−	2.72083i	−0.208968	−	0.106474i	−0.555342	+	0.831622i	$0.687413\pi$
$654$	69.9493	+	35.1248i	2.73523	+	1.37349i
$655$	−37.3601	+	28.1437i	−1.45978	+	1.09967i
$656$			14.1385i			0.552015i
$657$	4.37276	−	8.83721i	0.170598	−	0.344772i
$658$	−10.3193	+	20.2528i	−0.402289	+	0.789536i
$659$	−3.18918	−	9.81530i	−0.124233	−	0.382350i	0.869528	−	0.493884i	$-0.164423\pi$
$659$	−3.18918	−	9.81530i	−0.124233	−	0.382350i	−0.993761	+	0.111535i	$0.964423\pi$
$660$	44.5720	−	8.63705i	1.73496	−	0.336197i
$661$	−13.7868	+	42.4315i	−0.536245	+	1.65039i	0.204699	+	0.978825i	$0.434379\pi$
$661$	−13.7868	+	42.4315i	−0.536245	+	1.65039i	−0.740944	+	0.671567i	$0.765621\pi$
$662$	−38.2792	−	38.2792i	−1.48776	−	1.48776i
$663$	0.143600	+	24.4426i	0.00557698	+	0.949272i
$664$	25.3090	+	34.8348i	0.982179	+	1.35185i
$665$	1.59559	−	11.3404i	0.0618743	−	0.439762i
$666$	9.79792	+	28.9913i	0.379661	+	1.12339i
$667$	17.0287	−	17.0287i	0.659354	−	0.659354i
$668$	−6.83497	+	43.1543i	−0.264453	+	1.66969i
$669$	−1.29350	−	7.86739i	−0.0500095	−	0.304171i
$670$	−0.636890	−	36.8160i	−0.0246052	−	1.42232i
$671$	35.1377	−	35.9304i	1.35648	−	1.38708i
$672$	−29.7177	+	0.174592i	−1.14639	+	0.00673502i
$673$	−3.71830	−	23.4764i	−0.143330	−	0.904950i	−0.949614	−	0.313421i	$-0.898525\pi$
$673$	−3.71830	−	23.4764i	−0.143330	−	0.904950i	0.806284	−	0.591528i	$-0.201475\pi$
$674$	−40.3248	+	29.2977i	−1.55325	+	1.12850i
$675$	9.30728	+	24.2564i	0.358237	+	0.933631i
$676$	6.02896	+	18.5552i	0.231883	+	0.713663i
$677$	−28.8326	−	28.8326i	−1.10813	−	1.10813i	−0.993397	−	0.114728i	$-0.963400\pi$
$677$	−28.8326	−	28.8326i	−1.10813	−	1.10813i	−0.114728	−	0.993397i	$-0.536600\pi$
$678$	47.0108	+	33.7352i	1.80544	+	1.29559i
$679$		−	35.7082i		−	1.37036i
$680$	−25.0609	−	33.2677i	−0.961042	−	1.27576i
$681$	6.64203	−	3.43358i	0.254523	−	0.131575i
$682$	−3.01336	+	9.63866i	−0.115388	+	0.369083i
$683$	−4.41902	+	27.9006i	−0.169089	+	1.06759i	0.746475	+	0.665414i	$0.231745\pi$
$683$	−4.41902	+	27.9006i	−0.169089	+	1.06759i	−0.915564	+	0.402173i	$0.868255\pi$
$684$	−3.64880	+	11.6957i	−0.139515	+	0.447195i
$685$	−3.44098	+	24.4562i	−0.131473	+	0.934425i
$686$	34.6139	+	47.6419i	1.32156	+	1.81898i
$687$	47.6757	+	15.1817i	1.81894	+	0.579217i
$688$	4.70618	+	0.745385i	0.179421	+	0.0284175i
$689$	−3.98813	+	2.89754i	−0.151936	+	0.110388i
$690$	−38.8161	−	11.6250i	−1.47770	−	0.442554i
$691$	−6.43701			−0.244876			−0.122438	−	0.992476i	$-0.539071\pi$
$691$	−6.43701			−0.244876			−0.122438	+	0.992476i	$0.539071\pi$
$692$	−57.9978	−	9.18595i	−2.20475	−	0.349198i
$693$	−26.7335	−	35.0771i	−1.01552	−	1.33247i
$694$	−35.4141	−	48.7433i	−1.34430	−	1.85027i
$695$	−16.8460	+	12.6903i	−0.639005	+	0.481369i
$696$	−5.10014	+	33.4726i	−0.193320	+	1.26877i
$697$	−45.6624	−	23.2661i	−1.72959	−	0.881268i
$698$	17.5429	−	17.5429i	0.664009	−	0.664009i
$699$	32.4587	−	5.33662i	1.22770	−	0.201850i
$700$	−68.5236	+	37.9553i	−2.58995	+	1.43458i
$701$	−17.8313	−	24.5427i	−0.673479	−	0.926965i	0.326354	−	0.945248i	$-0.394180\pi$
$701$	−17.8313	−	24.5427i	−0.673479	−	0.926965i	−0.999833	+	0.0182832i	$0.994180\pi$
$702$	−31.9735	−	9.76930i	−1.20676	−	0.368718i
$703$	−0.783745	−	4.94837i	−0.0295595	−	0.186631i
$704$	6.63824	+	39.0856i	0.250188	+	1.47309i
$705$	−1.12711	+	8.36671i	−0.0424493	+	0.315108i
$706$	−19.7432	−	60.7634i	−0.743046	−	2.28686i
$707$	74.1939	+	11.7512i	2.79035	+	0.441948i
$708$	−32.6392	−	44.3734i	−1.22665	−	1.66765i
$709$	−19.9524	−	27.4621i	−0.749329	−	1.03136i	−0.998027	−	0.0627815i	$-0.980003\pi$
$709$	−19.9524	−	27.4621i	−0.749329	−	1.03136i	0.248699	−	0.968581i	$-0.419997\pi$
$710$	10.5009	+	1.47747i	0.394091	+	0.0554484i
$711$	−30.5036	+	10.3090i	−1.14397	+	0.386618i
$712$	−16.0058	+	2.53506i	−0.599841	+	0.0950055i
$713$	4.07003	−	4.07003i	0.152424	−	0.152424i
$714$	−41.8211	+	83.2845i	−1.56511	+	3.11684i
$715$	−0.576995	−	20.2748i	−0.0215784	−	0.758236i
$716$	−35.5167	+	11.5401i	−1.32732	+	0.431273i
$717$	−7.70465	−	5.52889i	−0.287735	−	0.206480i
$718$	−30.1972	−	4.78276i	−1.12695	−	0.178491i
$719$	11.4357			0.426480			0.213240	−	0.977000i	$-0.431598\pi$
$719$	11.4357			0.426480			0.213240	+	0.977000i	$0.431598\pi$
$720$	8.99243	−	3.21344i	0.335128	−	0.119758i
$721$	−15.1347	+	46.5798i	−0.563646	+	1.73472i
$722$	−18.8668	+	37.0281i	−0.702148	+	1.37804i
$723$	31.5543	+	22.6435i	1.17352	+	0.842122i
$724$	−18.2128	−	5.91771i	−0.676875	−	0.219930i
$725$	−9.25264	−	25.4461i	−0.343635	−	0.945044i
$726$	−30.7883	+	32.5744i	−1.14266	+	1.20895i
$727$	22.4818	+	44.1231i	0.833806	+	1.63644i	0.769624	+	0.638498i	$0.220444\pi$
$727$	22.4818	+	44.1231i	0.833806	+	1.63644i	0.0641818	+	0.997938i	$0.479556\pi$
$728$	6.84592	−	43.2235i	0.253727	−	1.60197i
$729$	−21.2706	+	16.6302i	−0.787800	+	0.615932i
$730$	17.2866	−	0.299045i	0.639804	−	0.0110682i
$731$	−10.1518	+	13.9727i	−0.375477	+	0.516800i
$732$	54.0830	−	75.3660i	1.99896	−	2.78561i
$733$	3.84626	+	3.84626i	0.142065	+	0.142065i	0.774562	−	0.632498i	$-0.217970\pi$
$733$	3.84626	+	3.84626i	0.142065	+	0.142065i	−0.632498	+	0.774562i	$0.717970\pi$
$734$	31.9745	+	23.2309i	1.18020	+	0.857467i
$735$	40.2844	+	27.8655i	1.48591	+	1.02783i
$736$	5.31954	−	16.3719i	0.196081	−	0.603474i
$737$	13.8542	+	18.6282i	0.510328	+	0.686179i
$738$	48.9797	−	50.1444i	1.80297	−	1.84584i
$739$	10.0847	−	13.8804i	0.370973	−	0.510600i	−0.582192	−	0.813051i	$-0.697805\pi$
$739$	10.0847	−	13.8804i	0.370973	−	0.510600i	0.953165	+	0.302451i	$0.0978048\pi$
$740$	−23.8092	+	24.6474i	−0.875242	+	0.906057i
$741$	4.89139	+	2.45620i	0.179690	+	0.0902308i
$742$	−18.5639	+	2.94023i	−0.681502	+	0.107939i
$743$	−27.3188	−	13.9196i	−1.00223	−	0.510662i	−0.125731	−	0.992064i	$-0.540128\pi$
$743$	−27.3188	−	13.9196i	−1.00223	−	0.510662i	−0.876500	+	0.481402i	$0.840128\pi$
$744$	−1.21898	+	8.00028i	−0.0446901	+	0.293304i
$745$	−15.1697	+	5.22069i	−0.555773	+	0.191271i
$746$	9.33023	+	12.8420i	0.341604	+	0.470177i
$747$	5.18210	−	35.4062i	0.189603	−	1.29544i
$748$	57.7316	+	18.0488i	2.11088	+	0.659929i
$749$	30.6773			1.12092
$750$	−30.3000	+	34.0197i	−1.10640	+	1.24222i
$751$	23.4704	−	17.0522i	0.856446	−	0.622244i	−0.0704700	−	0.997514i	$-0.522450\pi$
$751$	23.4704	−	17.0522i	0.856446	−	0.622244i	0.926916	+	0.375270i	$0.122450\pi$
$752$	3.06480	+	0.485416i	0.111762	+	0.0177013i
$753$	−1.99227	+	0.660292i	−0.0726022	+	0.0240624i
$754$	33.1369	+	10.7668i	1.20678	+	0.392105i
$755$	8.46678	+	11.2394i	0.308138	+	0.409045i
$756$	−58.5684	−	56.5395i	−2.13011	−	2.05632i
$757$	6.84536	+	13.4348i	0.248799	+	0.488295i	0.981304	−	0.192467i	$-0.0616487\pi$
$757$	6.84536	+	13.4348i	0.248799	+	0.488295i	−0.732505	+	0.680762i	$0.761649\pi$
$758$	2.83803	−	17.9186i	0.103082	−	0.650833i
$759$	24.1586	−	8.30698i	0.876900	−	0.301524i
$760$	−9.18529	+	1.61814i	−0.333186	+	0.0586961i
$761$	22.8429	−	31.4405i	0.828053	−	1.13972i	−0.160229	−	0.987080i	$-0.551223\pi$
$761$	22.8429	−	31.4405i	0.828053	−	1.13972i	0.988282	−	0.152638i	$-0.0487768\pi$
$762$	36.0732	−	0.211930i	1.30679	−	0.00767742i
$763$	75.8657	−	38.6555i	2.74652	−	1.39942i
$764$	65.5731			2.37235
$765$	−4.41958	+	34.3304i	−0.159790	+	1.24122i
$766$	1.22601	−	3.77329i	0.0442977	−	0.136334i
$767$	−21.9269	+	11.1723i	−0.791736	+	0.403410i
$768$	13.0975	+	39.5184i	0.472615	+	1.42600i
$769$	30.8785	+	42.5006i	1.11351	+	1.53261i	0.816145	+	0.577847i	$0.196107\pi$
$769$	30.8785	+	42.5006i	1.11351	+	1.53261i	0.297363	+	0.954765i	$0.403893\pi$
$770$	33.1346	−	69.8760i	1.19409	−	2.51816i
$771$	8.83521	+	8.73201i	0.318192	+	0.314476i
$772$	−9.39577	+	59.3226i	−0.338161	+	2.13507i
$773$	−9.52402	−	4.85273i	−0.342555	−	0.174541i	0.274246	−	0.961660i	$-0.411572\pi$
$773$	−9.52402	−	4.85273i	−0.342555	−	0.174541i	−0.616801	+	0.787119i	$0.711572\pi$
$774$	−14.1090	−	18.9472i	−0.507138	−	0.681042i
$775$	−2.21147	−	6.08187i	−0.0794385	−	0.218467i
$776$	−27.6579	+	8.98660i	−0.992861	+	0.322600i
$777$	31.7200	+	10.1008i	1.13795	+	0.362364i
$778$	1.51027	+	1.51027i	0.0541457	+	0.0541457i
$779$	−9.28413	+	6.74532i	−0.332639	+	0.241676i
$780$	−6.71193	−	36.8322i	−0.240326	−	1.31880i
$781$	−5.92290	+	3.10156i	−0.211938	+	0.110982i
$782$	−38.1721	−	38.1721i	−1.36503	−	1.36503i
$783$	22.4693	−	16.9379i	0.802989	−	0.605311i
$784$	10.5824	−	14.5654i	0.377943	−	0.520194i
$785$	10.8469	+	1.52616i	0.387143	+	0.0544709i
$786$	12.8390	−	84.2632i	0.457952	−	3.00557i
$787$	0.211695	−	1.33659i	0.00754610	−	0.0476442i	−0.983628	−	0.180211i	$-0.942322\pi$
$787$	0.211695	−	1.33659i	0.00754610	−	0.0476442i	0.991174	+	0.132567i	$0.0423219\pi$
$788$	−13.8386	−	27.1598i	−0.492981	−	0.967529i
$789$	−30.8354	+	5.06973i	−1.09777	+	0.180487i
$790$	−40.6075	−	39.2264i	−1.44475	−	1.39561i
$791$	59.8628	−	19.4506i	2.12848	−	0.691584i
$792$	−20.4411	+	29.5342i	−0.726344	+	1.04945i
$793$	−29.3040	−	29.3040i	−1.04062	−	1.04062i
$794$	−21.6732	−	66.7034i	−0.769155	−	2.36721i
$795$	−6.14484	+	3.31248i	−0.217935	+	0.117482i
$796$	−0.650309	−	2.00144i	−0.0230496	−	0.0709393i
$797$	−48.4512	+	24.6871i	−1.71623	+	0.874462i	−0.735900	+	0.677090i	$0.763241\pi$
$797$	−48.4512	+	24.6871i	−1.71623	+	0.874462i	−0.980329	+	0.197372i	$0.936759\pi$
$798$	12.3654	+	16.8109i	0.437730	+	0.595100i
$799$	−6.61113	+	9.09944i	−0.233885	+	0.321915i
$800$	−14.1508	−	13.2041i	−0.500308	−	0.466836i
$801$	10.9876	+	7.78733i	0.388226	+	0.275152i
$802$	−14.3494	−	28.1622i	−0.506694	−	0.994443i
$803$	−8.74669	+	6.50512i	−0.308664	+	0.229561i
$804$	30.4779	+	30.1218i	1.07487	+	1.06232i
$805$	−35.2060	+	26.5210i	−1.24085	+	0.934744i
$806$	7.92005	+	2.57338i	0.278972	+	0.0906435i
$807$	26.8391	−	0.157680i	0.944782	−	0.00555060i
$808$	−9.57029	−	60.4245i	−0.336682	−	2.12572i
$809$	−35.5317	+	25.8153i	−1.24923	+	0.907618i	−0.998177	−	0.0603553i	$-0.980777\pi$
$809$	−35.5317	+	25.8153i	−1.24923	+	0.907618i	−0.251052	+	0.967974i	$0.580777\pi$
$810$	−43.0254	−	19.7554i	−1.51176	−	0.694133i
$811$	9.53336	+	29.3407i	0.334761	+	1.03029i	0.966839	+	0.255385i	$0.0822022\pi$
$811$	9.53336	+	29.3407i	0.334761	+	1.03029i	−0.632078	+	0.774905i	$0.717798\pi$
$812$	59.9897	+	59.9897i	2.10523	+	2.10523i
$813$	1.34357	+	0.964153i	0.0471211	+	0.0338143i
$814$	4.91947	−	33.4724i	0.172427	−	1.17321i
$815$	−0.550171	+	0.569541i	−0.0192717	+	0.0199502i
$816$	12.5773	+	1.91637i	0.440293	+	0.0670864i
$817$	1.75580	+	3.44596i	0.0614278	+	0.120559i
$818$	49.8121	−	7.88946i	1.74164	−	0.275848i
$819$	−29.1695	+	21.7211i	−1.01926	+	0.758995i
$820$	75.0620	+	22.9615i	2.62128	+	0.801851i
$821$	−21.4772	+	6.97836i	−0.749559	+	0.243546i	−0.658791	−	0.752326i	$-0.728932\pi$
$821$	−21.4772	+	6.97836i	−0.749559	+	0.243546i	−0.0907675	+	0.995872i	$0.528932\pi$
$822$	−26.6667	−	36.2537i	−0.930107	−	1.26449i
$823$	−1.64832	−	10.4071i	−0.0574569	−	0.362768i	−0.999619	−	0.0276103i	$-0.991210\pi$
$823$	−1.64832	−	10.4071i	−0.0574569	−	0.362768i	0.942162	−	0.335158i	$-0.108790\pi$
$824$	39.8874			1.38954
$825$	3.02339	−	28.5632i	0.105261	−	0.994445i
$826$	−93.8285			−3.26471
$827$	6.99337	+	44.1544i	0.243183	+	1.53540i	0.743013	+	0.669276i	$0.233396\pi$
$827$	6.99337	+	44.1544i	0.243183	+	1.53540i	−0.499830	+	0.866124i	$0.666604\pi$
$828$	41.7608	−	21.9000i	1.45129	−	0.761078i
$829$	52.9000	−	17.1883i	1.83729	−	0.596973i	0.838664	−	0.544649i	$-0.183337\pi$
$829$	52.9000	−	17.1883i	1.83729	−	0.596973i	0.998630	−	0.0523235i	$-0.0166627\pi$
$830$	59.3303	−	20.4187i	2.05938	−	0.708744i
$831$	−8.94179	+	9.04747i	−0.310187	+	0.313853i
$832$	32.2899	−	5.11422i	1.11945	−	0.177304i
$833$	29.6270	+	58.1462i	1.02651	+	2.01465i
$834$	5.78922	−	37.9950i	0.200464	−	1.31566i
$835$	24.8423	+	12.1212i	0.859703	+	0.419471i
$836$	9.47013	−	9.68377i	0.327531	−	0.334920i
$837$	5.37040	−	4.04833i	0.185628	−	0.139931i
$838$	46.8321	+	46.8321i	1.61779	+	1.61779i
$839$	−14.4963	−	44.6150i	−0.500468	−	1.54028i	−0.808259	−	0.588828i	$-0.799590\pi$
$839$	−14.4963	−	44.6150i	−0.500468	−	1.54028i	0.307791	−	0.951454i	$-0.400410\pi$
$840$	17.7795	−	59.3665i	0.613452	−	2.04834i
$841$	−0.262594	+	0.190786i	−0.00905497	+	0.00657882i
$842$	−1.59369	−	10.0622i	−0.0549223	−	0.346766i
$843$	−0.195673	−	33.3060i	−0.00673934	−	1.14712i
$844$	12.0330	+	3.90976i	0.414193	+	0.134579i
$845$	12.3412	−	0.213493i	0.424549	−	0.00734439i
$846$	−9.18819	−	12.3389i	−0.315897	−	0.424221i
$847$	8.69966	+	47.9754i	0.298924	+	1.64845i
$848$	1.16486	+	2.28617i	0.0400014	+	0.0785073i
$849$	3.99966	−	7.96511i	0.137268	−	0.273362i
$850$	−57.0408	+	20.7410i	−1.95648	+	0.711411i
$851$	−11.3343	+	15.6003i	−0.388533	+	0.534770i
$852$	−9.94114	+	7.31228i	−0.340578	+	0.250515i
$853$	31.9514	−	16.2801i	1.09400	−	0.557419i	0.188629	−	0.982048i	$-0.439596\pi$
$853$	31.9514	−	16.2801i	1.09400	−	0.557419i	0.905367	+	0.424629i	$0.139596\pi$
$854$	−48.8273	−	150.275i	−1.67083	−	5.14230i
$855$	6.40032	+	4.37185i	0.218886	+	0.149514i
$856$	−7.72048	−	23.7612i	−0.263881	−	0.812141i
$857$	−3.28690	−	3.28690i	−0.112278	−	0.112278i	0.648736	−	0.761014i	$-0.275298\pi$
$857$	−3.28690	−	3.28690i	−0.112278	−	0.112278i	−0.761014	+	0.648736i	$0.775298\pi$
$858$	26.5768	+	25.6867i	0.907317	+	0.876931i
$859$	−19.6913	+	6.39809i	−0.671859	+	0.218300i	−0.625028	−	0.780603i	$-0.714912\pi$
$859$	−19.6913	+	6.39809i	−0.671859	+	0.218300i	−0.0468311	+	0.998903i	$0.514912\pi$
$860$	11.6003	−	23.7748i	0.395568	−	0.810715i
$861$	−12.3706	−	75.2412i	−0.421588	−	2.56421i
$862$	29.6469	+	58.1853i	1.00978	+	1.98180i
$863$	−6.38595	+	40.3193i	−0.217380	+	1.37248i	0.601662	+	0.798751i	$0.294505\pi$
$863$	−6.38595	+	40.3193i	−0.217380	+	1.37248i	−0.819042	+	0.573733i	$0.805495\pi$
$864$	8.81418	−	18.0796i	0.299865	−	0.615081i
$865$	−16.2905	+	33.3872i	−0.553892	+	1.13520i
$866$	13.5477	−	18.6468i	0.460369	−	0.633643i
$867$	−9.71926	+	13.5440i	−0.330083	+	0.459980i
$868$	14.3381	+	14.3381i	0.486668	+	0.486668i
$869$	35.2184	+	5.17608i	1.19470	+	0.175587i
$870$	44.4695	+	21.3753i	1.50766	+	0.724690i
$871$	15.4877	−	11.2525i	0.524781	−	0.381276i
$872$	−49.0337	−	49.0337i	−1.66049	−	1.66049i
$873$	21.6611	+	10.7182i	0.733119	+	0.362756i
$874$	−11.4967	+	3.73551i	−0.388882	+	0.126355i
$875$	10.2809	+	48.4790i	0.347557	+	1.63889i
$876$	−14.1434	+	14.3106i	−0.477861	+	0.483509i
$877$	−6.17611	−	3.14688i	−0.208552	−	0.106263i	0.346595	−	0.938015i	$-0.387338\pi$
$877$	−6.17611	−	3.14688i	−0.208552	−	0.106263i	−0.555147	+	0.831752i	$0.687338\pi$
$878$	−1.94875	+	12.3039i	−0.0657671	+	0.415237i
$879$	16.1321	−	16.3228i	0.544122	−	0.550554i
$880$	−10.4700	−	1.35422i	−0.352943	−	0.0456506i
$881$	28.0779	+	38.6459i	0.945968	+	1.30201i	0.953295	+	0.302040i	$0.0976677\pi$
$881$	28.0779	+	38.6459i	0.945968	+	1.30201i	−0.00732695	+	0.999973i	$0.502332\pi$
$882$	−87.9910	+	14.9983i	−2.96281	+	0.505018i
$883$	1.73453	−	0.883789i	0.0583717	−	0.0297419i	−0.424561	−	0.905399i	$-0.639572\pi$
$883$	1.73453	−	0.883789i	0.0583717	−	0.0297419i	0.482933	+	0.875657i	$0.339572\pi$
$884$	15.4135	−	47.4378i	0.518412	−	1.59551i
$885$	−32.8850	+	11.5340i	−1.10542	+	0.387711i
$886$	22.1940			0.745622
$887$	29.9711	−	15.2710i	1.00633	−	0.512751i	0.128494	−	0.991710i	$-0.458986\pi$
$887$	29.9711	−	15.2710i	1.00633	−	0.512751i	0.877837	+	0.478959i	$0.158986\pi$
$888$	−0.159276	−	27.1108i	−0.00534496	−	0.909780i
$889$	23.0656	−	31.7470i	0.773594	−	1.06476i
$890$	−3.29018	+	23.3844i	−0.110287	+	0.783847i
$891$	29.3026	−	5.68815i	0.981676	−	0.190560i
$892$	−2.54518	+	16.0696i	−0.0852189	+	0.538051i
$893$	1.14343	+	2.24411i	0.0382634	+	0.0750962i
$894$	13.1189	−	26.1257i	0.438763	−	0.873773i
$895$	0.408649	+	23.6223i	0.0136596	+	0.789607i
$896$	85.9111	+	27.9142i	2.87009	+	0.932548i
$897$	−6.62751	−	19.9969i	−0.221286	−	0.667676i
$898$	0.888989	+	0.140802i	0.0296659	+	0.00469862i
$899$	−5.67029	+	4.11971i	−0.189115	+	0.137400i
$900$	−2.45619	−	52.9601i	−0.0818731	−	1.76534i
$901$	−9.30041			−0.309841
$902$	−73.4297	+	24.7676i	−2.44494	+	0.824669i
$903$	−25.6972	+	0.150971i	−0.855149	+	0.00502400i
$904$	−30.1310	−	41.4718i	−1.00214	−	1.37933i
$905$	−6.95057	+	9.92315i	−0.231045	+	0.329857i
$906$	−25.3498	−	3.86249i	−0.842192	−	0.128323i
$907$	27.2927	+	13.9063i	0.906240	+	0.461752i	0.844021	−	0.536310i	$-0.180182\pi$
$907$	27.2927	+	13.9063i	0.906240	+	0.461752i	0.0622188	+	0.998063i	$0.480182\pi$
$908$	−15.0700	+	2.38685i	−0.500115	+	0.0792105i
$909$	−29.3985	+	41.4799i	−0.975087	+	1.37580i
$910$	−57.3131	−	27.9645i	−1.89991	−	0.927014i
$911$	−11.3308	+	15.5955i	−0.375406	+	0.516702i	−0.954360	−	0.298658i	$-0.903461\pi$
$911$	−11.3308	+	15.5955i	−0.375406	+	0.516702i	0.578954	+	0.815360i	$0.303461\pi$
$912$	1.66097	−	2.31460i	0.0550002	−	0.0766442i
$913$	−22.8944	+	32.2621i	−0.757694	+	1.06772i
$914$	−9.87839	+	30.4026i	−0.326748	+	1.00563i
$915$	−35.5857	−	46.6661i	−1.17643	−	1.54274i
$916$	−82.6020	−	60.0139i	−2.72925	−	1.98291i
$917$	−65.5631	−	65.5631i	−2.16509	−	2.16509i
$918$	−37.9686	−	50.3680i	−1.25315	−	1.66239i
$919$	−14.4780	+	19.9273i	−0.477586	+	0.657341i	−0.978039	−	0.208423i	$-0.933167\pi$
$919$	−14.4780	+	19.9273i	−0.477586	+	0.657341i	0.500452	+	0.865764i	$0.333167\pi$
$920$	29.4021	+	20.5944i	0.969360	+	0.678978i
$921$	−6.28378	+	41.2409i	−0.207058	+	1.35893i
$922$	−1.37190	+	8.66186i	−0.0451813	+	0.285263i
$923$	2.50298	+	4.91238i	0.0823867	+	0.161693i
$924$	29.2643	+	85.1072i	0.962725	+	2.79982i
$925$	10.5049	+	18.9652i	0.345398	+	0.623572i
$926$	30.8327	+	10.0182i	1.01323	+	0.329217i
$927$	−23.7132	−	23.1624i	−0.778843	−	0.760752i
$928$	−9.51642	+	18.6770i	−0.312392	+	0.613103i
$929$	−8.46606	+	26.0558i	−0.277762	+	0.854864i	0.710713	+	0.703482i	$0.248372\pi$
$929$	−8.46606	+	26.0558i	−0.277762	+	0.854864i	−0.988475	+	0.151382i	$0.951628\pi$
$930$	10.6287	+	5.10890i	0.348527	+	0.167528i
$931$	14.6133			0.478930
$932$	−66.2990	−	10.5007i	−2.17170	−	0.343963i
$933$	14.5244	−	20.2402i	0.475509	−	0.662633i
$934$	−85.7150	+	27.8505i	−2.80468	+	0.911296i
$935$	21.6030	−	31.5859i	0.706492	−	1.03297i
$936$	24.1651	+	17.1268i	0.789861	+	0.559807i
$937$	−43.1531	+	43.1531i	−1.40975	+	1.40975i	−0.648734	+	0.761015i	$0.724701\pi$
$937$	−43.1531	+	43.1531i	−1.40975	+	1.40975i	−0.761015	+	0.648734i	$0.775299\pi$
$938$	72.0921	−	11.4183i	2.35389	−	0.372820i
$939$	−16.6845	+	8.62504i	−0.544479	+	0.281467i
$940$	7.55447	−	15.4828i	0.246400	−	0.504995i
$941$	13.2685	+	18.2626i	0.432542	+	0.595343i	0.968534	−	0.248880i	$-0.0800624\pi$
$941$	13.2685	+	18.2626i	0.432542	+	0.595343i	−0.535992	+	0.844223i	$0.680062\pi$
$942$	−16.0794	+	11.8273i	−0.523894	+	0.385354i
$943$	43.6250	+	6.90952i	1.42063	+	0.225005i
$944$	3.95817	+	12.1820i	0.128828	+	0.396491i
$945$	−45.0437	+	24.9691i	−1.46527	+	0.812243i
$946$	4.37297	+	25.7478i	0.142177	+	0.837133i
$947$	−4.75233	−	30.0051i	−0.154430	−	0.975033i	−0.936200	−	0.351467i	$-0.885683\pi$
$947$	−4.75233	−	30.0051i	−0.154430	−	0.975033i	0.781770	−	0.623567i	$-0.214317\pi$
$948$	65.7040	−	0.386011i	2.13397	−	0.0125371i
$949$	5.28349	+	7.27210i	0.171509	+	0.236062i
$950$	−1.66055	+	13.4893i	−0.0538753	+	0.437652i
$951$	6.92830	+	42.1398i	0.224666	+	1.36648i
$952$	58.3815	−	58.3815i	1.89215	−	1.89215i
$953$	35.1476	+	17.9086i	1.13854	+	0.580116i	0.918518	−	0.395378i	$-0.129387\pi$
$953$	35.1476	+	17.9086i	1.13854	+	0.580116i	0.220024	+	0.975495i	$0.429387\pi$
$954$	3.78856	−	12.1437i	0.122659	−	0.393166i
$955$	12.1351	−	39.6700i	0.392682	−	1.28369i
$956$	11.3746	+	15.6558i	0.367880	+	0.506343i
$957$	−30.6377	+	5.38884i	−0.990378	+	0.174196i
$958$	56.4441	+	8.93986i	1.82363	+	0.288834i
$959$	−48.9568			−1.58090
$960$	46.2833	−	1.07269i	1.49379	−	0.0346210i
$961$	23.7243	−	17.2367i	0.765299	−	0.556022i
$962$	−27.5552	−	4.36431i	−0.888415	−	0.140711i
$963$	−9.20812	+	18.6093i	−0.296728	+	0.599677i
$964$	−46.5845	−	64.1180i	−1.50039	−	2.06510i
$965$	34.1498	+	16.6626i	1.09932	+	0.536387i
$966$	12.0987	−	79.4049i	0.389270	−	2.55481i
$967$	−3.14608	+	19.8636i	−0.101171	+	0.638770i	0.884038	+	0.467415i	$0.154814\pi$
$967$	−3.14608	+	19.8636i	−0.101171	+	0.638770i	−0.985209	+	0.171355i	$0.945186\pi$
$968$	34.9701	−	18.8122i	1.12398	−	0.604647i
$969$	4.74209	+	9.17325i	0.152338	+	0.294687i
$970$	0.732998	+	42.3716i	0.0235352	+	1.36047i
$971$			14.9465i			0.479655i	0.970815	+	0.239828i	$0.0770910\pi$
$971$			14.9465i			0.479655i	−0.970815	+	0.239828i	$0.922909\pi$
$972$	51.8776	−	18.5576i	1.66398	−	0.595234i
$973$	−29.5630	−	29.5630i	−0.947746	−	0.947746i
$974$	10.3313	+	31.7966i	0.331038	+	1.01883i
$975$	−23.5246	−	2.75570i	−0.753392	−	0.0882531i
$976$	−17.4508	+	12.6788i	−0.558587	+	0.405837i
$977$	−2.02915	−	12.8116i	−0.0649184	−	0.409879i	−0.998652	−	0.0519095i	$-0.983469\pi$
$977$	−2.02915	−	12.8116i	−0.0649184	−	0.409879i	0.933733	−	0.357969i	$-0.116531\pi$
$978$	−0.00847756	−	1.44299i	−0.000271082	−	0.0461417i
$979$	−6.90686	−	13.1897i	−0.220744	−	0.421545i
$980$	−60.1424	−	79.8375i	−1.92118	−	2.55032i
$981$	0.677108	+	57.6241i	0.0216184	+	1.83980i
$982$	−2.19288	+	13.8453i	−0.0699777	+	0.441822i
$983$	11.9787	−	11.9787i	0.382061	−	0.382061i	−0.489783	−	0.871844i	$-0.662924\pi$
$983$	11.9787	−	11.9787i	0.382061	−	0.382061i	0.871844	+	0.489783i	$0.162924\pi$
$984$	−55.1649	+	28.5174i	−1.75859	+	0.909102i
$985$	−18.9920	+	3.34575i	−0.605135	+	0.106604i
$986$	38.6380	+	53.1807i	1.23049	+	1.69362i
$987$	−16.7347	+	0.0983167i	−0.532673	+	0.00312945i
$988$	−7.89786	−	7.89786i	−0.251264	−	0.251264i
$989$	4.59985	−	14.1569i	0.146267	−	0.450163i
$990$	32.4421	+	41.0740i	1.03108	+	1.30542i
$991$	16.6060	+	51.1081i	0.527508	+	1.62350i	0.759302	+	0.650738i	$0.225541\pi$
$991$	16.6060	+	51.1081i	0.527508	+	1.62350i	−0.231794	+	0.972765i	$0.574459\pi$
$992$	−2.27452	+	4.46400i	−0.0722161	+	0.141732i
$993$	12.0935	−	37.9776i	0.383775	−	1.20518i
$994$			21.0208i			0.666739i
$995$	−1.33117	+	0.0230283i	−0.0422009	+	0.000730045i
$996$	−32.7678	+	65.2554i	−1.03829	+	2.06770i
$997$	−25.4093	−	12.9467i	−0.804719	−	0.410025i	0.00270481	−	0.999996i	$-0.499139\pi$
$997$	−25.4093	−	12.9467i	−0.804719	−	0.410025i	−0.807424	+	0.589971i	$0.799139\pi$
$998$	1.65973	+	0.845674i	0.0525378	+	0.0267693i
$999$	−15.6484	+	16.2099i	−0.495093	+	0.512860i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.cu.a.53.12	yes	928
3.2	odd	2	inner	825.2.cu.a.53.105	yes	928
11.5	even	5		825.2.ci.a.203.105	yes	928
25.17	odd	20		825.2.ci.a.317.12	yes	928
33.5	odd	10		825.2.ci.a.203.12	✓	928
75.17	even	20		825.2.ci.a.317.105	yes	928
275.192	odd	20	inner	825.2.cu.a.467.105	yes	928
825.467	even	20	inner	825.2.cu.a.467.12	yes	928

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
825.2.ci.a.203.12	✓	928	33.5	odd	10
825.2.ci.a.203.105	yes	928	11.5	even	5
825.2.ci.a.317.12	yes	928	25.17	odd	20
825.2.ci.a.317.105	yes	928	75.17	even	20
825.2.cu.a.53.12	yes	928	1.1	even	1	trivial
825.2.cu.a.53.105	yes	928	3.2	odd	2	inner
825.2.cu.a.467.12	yes	928	825.467	even	20	inner
825.2.cu.a.467.105	yes	928	275.192	odd	20	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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.cu (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.368019 - 2.32358i) q^{2} +(1.39525 - 1.02629i) q^{3} +(-3.36148 + 1.09221i) q^{4} +(0.0386766 + 2.23573i) q^{5} +(-2.89815 - 2.86429i) q^{6} +(-4.37796 + 0.693400i) q^{7} +(1.63886 + 3.21645i) q^{8} +(0.893463 - 2.86387i) q^{9} +O(q^{10})\)	\(q+(-0.368019 - 2.32358i) q^{2} +(1.39525 - 1.02629i) q^{3} +(-3.36148 + 1.09221i) q^{4} +(0.0386766 + 2.23573i) q^{5} +(-2.89815 - 2.86429i) q^{6} +(-4.37796 + 0.693400i) q^{7} +(1.63886 + 3.21645i) q^{8} +(0.893463 - 2.86387i) q^{9} +(5.18068 - 0.912661i) q^{10} +(-2.31891 + 2.37122i) q^{11} +(-3.56919 + 4.97376i) q^{12} +(1.93391 + 1.93391i) q^{13} +(3.22234 + 9.91736i) q^{14} +(2.34847 + 3.07972i) q^{15} +(1.15166 - 0.836731i) q^{16} +(0.807188 + 5.09639i) q^{17} +(-6.98324 - 1.02208i) q^{18} +(1.09889 + 0.357052i) q^{19} +(-2.57190 - 7.47313i) q^{20} +(-5.39673 + 5.46052i) q^{21} +(6.36312 + 4.51551i) q^{22} +(-2.01896 - 3.96243i) q^{23} +(5.58764 + 2.80582i) q^{24} +(-4.99701 + 0.172941i) q^{25} +(3.78189 - 5.20532i) q^{26} +(-1.69254 - 4.91277i) q^{27} +(13.9591 - 7.11250i) q^{28} +(1.67339 + 5.15018i) q^{29} +(6.29170 - 6.59026i) q^{30} +(0.399958 + 1.23094i) q^{31} +(2.73713 + 2.73713i) q^{32} +(-0.801906 + 5.68832i) q^{33} +(11.5448 - 3.75114i) q^{34} +(-1.71958 - 9.76113i) q^{35} +(0.124586 + 10.6027i) q^{36} +(-1.96852 - 3.86344i) q^{37} +(0.425225 - 2.68477i) q^{38} +(4.68305 + 0.713545i) q^{39} +(-7.12774 + 3.78846i) q^{40} +(-5.83786 + 8.03513i) q^{41} +(14.6741 + 10.5302i) q^{42} +(2.36682 + 2.36682i) q^{43} +(5.20508 - 10.5035i) q^{44} +(6.43740 + 1.88678i) q^{45} +(-8.46401 + 6.14946i) q^{46} +(1.54134 + 1.54134i) q^{47} +(0.748132 - 2.34939i) q^{48} +(12.0283 - 3.90824i) q^{49} +(2.24084 + 11.5473i) q^{50} +(6.35660 + 6.28234i) q^{51} +(-8.61305 - 4.38857i) q^{52} +(-0.281963 + 1.78024i) q^{53} +(-10.7923 + 5.74076i) q^{54} +(-5.39110 - 5.09274i) q^{55} +(-9.40516 - 12.9451i) q^{56} +(1.89967 - 0.629603i) q^{57} +(11.3510 - 5.78363i) q^{58} +(-2.78053 + 8.55759i) q^{59} +(-11.2580 - 7.78739i) q^{60} -15.1527 q^{61} +(2.71301 - 1.38235i) q^{62} +(-1.92574 + 13.1574i) q^{63} +(7.02610 - 9.67059i) q^{64} +(-4.24892 + 4.39851i) q^{65} +(13.5124 - 0.230116i) q^{66} +(1.09499 - 6.91350i) q^{67} +(-8.27968 - 16.2498i) q^{68} +(-6.88355 - 3.45656i) q^{69} +(-22.0479 + 7.58787i) q^{70} +(1.91719 + 0.622933i) q^{71} +(10.6757 - 1.81970i) q^{72} +(3.24616 + 0.514142i) q^{73} +(-8.25257 + 5.99584i) q^{74} +(-6.79460 + 5.36967i) q^{75} -4.08388 q^{76} +(8.50787 - 11.9890i) q^{77} +(-0.0654713 - 11.1440i) q^{78} +(-6.30860 - 8.68304i) q^{79} +(1.91525 + 2.54245i) q^{80} +(-7.40345 - 5.11752i) q^{81} +(20.8187 + 10.6077i) q^{82} +(11.7809 - 1.86592i) q^{83} +(12.1770 - 24.2498i) q^{84} +(-11.3629 + 2.00177i) q^{85} +(4.62847 - 6.37054i) q^{86} +(7.62038 + 5.46842i) q^{87} +(-11.4273 - 3.57254i) q^{88} +(-1.38721 + 4.26940i) q^{89} +(2.01501 - 15.6522i) q^{90} +(-9.80756 - 7.12561i) q^{91} +(11.1145 + 11.1145i) q^{92} +(1.82135 + 1.30701i) q^{93} +(3.01419 - 4.14868i) q^{94} +(-0.755771 + 2.47064i) q^{95} +(6.62808 + 1.00991i) q^{96} +(-1.26023 + 7.95677i) q^{97} +(-13.5078 - 26.5105i) q^{98} +(4.71899 + 8.75963i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 928 q - 8 q^{3} - 20 q^{4} - 2 q^{6}+O(q^{10}) \) 928 * q - 8 * q^3 - 20 * q^4 - 2 * q^6	\( 928 q - 8 q^{3} - 20 q^{4} - 2 q^{6} - 60 q^{10} + 2 q^{12} - 4 q^{13} - 14 q^{15} + 204 q^{16} - 38 q^{18} - 40 q^{19} - 12 q^{21} - 60 q^{22} - 40 q^{24} - 48 q^{25} - 14 q^{27} + 8 q^{28} - 26 q^{30} - 4 q^{31} - 12 q^{33} - 40 q^{34} + 6 q^{36} + 16 q^{37} - 28 q^{40} - 6 q^{42} - 40 q^{43} - 78 q^{45} - 4 q^{46} - 6 q^{48} + 20 q^{49} - 12 q^{51} - 108 q^{52} + 40 q^{54} + 68 q^{55} + 30 q^{57} - 28 q^{58} - 80 q^{60} - 24 q^{61} + 56 q^{63} - 220 q^{64} + 30 q^{66} - 92 q^{67} + 90 q^{69} - 80 q^{70} - 138 q^{72} - 80 q^{73} - 46 q^{75} + 32 q^{76} - 160 q^{79} + 8 q^{81} + 52 q^{82} - 70 q^{84} + 28 q^{85} - 66 q^{87} + 124 q^{88} + 206 q^{90} - 4 q^{91} - 68 q^{93} - 20 q^{94} + 4 q^{96} - 56 q^{97} - 170 q^{99}+O(q^{100}) \) 928 * q - 8 * q^3 - 20 * q^4 - 2 * q^6 - 60 * q^10 + 2 * q^12 - 4 * q^13 - 14 * q^15 + 204 * q^16 - 38 * q^18 - 40 * q^19 - 12 * q^21 - 60 * q^22 - 40 * q^24 - 48 * q^25 - 14 * q^27 + 8 * q^28 - 26 * q^30 - 4 * q^31 - 12 * q^33 - 40 * q^34 + 6 * q^36 + 16 * q^37 - 28 * q^40 - 6 * q^42 - 40 * q^43 - 78 * q^45 - 4 * q^46 - 6 * q^48 + 20 * q^49 - 12 * q^51 - 108 * q^52 + 40 * q^54 + 68 * q^55 + 30 * q^57 - 28 * q^58 - 80 * q^60 - 24 * q^61 + 56 * q^63 - 220 * q^64 + 30 * q^66 - 92 * q^67 + 90 * q^69 - 80 * q^70 - 138 * q^72 - 80 * q^73 - 46 * q^75 + 32 * q^76 - 160 * q^79 + 8 * q^81 + 52 * q^82 - 70 * q^84 + 28 * q^85 - 66 * q^87 + 124 * q^88 + 206 * q^90 - 4 * q^91 - 68 * q^93 - 20 * q^94 + 4 * q^96 - 56 * q^97 - 170 * q^99

Introduction

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