LMFDB - Embedded newform 70.2.k.a.17.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [70,2,Mod(3,70)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(70, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([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("70.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 70 = 2 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	70.k (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:	$0.558952814149$
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} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 $ x^16 + 10x^14 + 61x^12 + 266x^10 + 852x^8 + 1438x^6 + 1933x^4 + 3038*x^2 + 2401
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			17.1
Root			$-0.587308 + 2.01725i$ of defining polynomial
Character	$\chi$	$=$	70.17
Dual form			70.2.k.a.33.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 + 0.965926i) q^{2} +(-2.80762 + 0.752300i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.21323 + 0.318742i) q^{5} -2.90667i q^{6} +(0.559876 + 2.58583i) q^{7} +(0.707107 - 0.707107i) q^{8} +(4.71872 - 2.72435i) q^{9} +O(q^{10})$	\(q+(-0.258819 + 0.965926i) q^{2} +(-2.80762 + 0.752300i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.21323 + 0.318742i) q^{5} -2.90667i q^{6} +(0.559876 + 2.58583i) q^{7} +(0.707107 - 0.707107i) q^{8} +(4.71872 - 2.72435i) q^{9} +(0.264946 - 2.22032i) q^{10} +(-1.83557 + 3.17930i) q^{11} +(2.80762 + 0.752300i) q^{12} +(0.830578 + 0.830578i) q^{13} +(-2.64263 - 0.128464i) q^{14} +(5.97414 - 2.55992i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.204036 - 0.761471i) q^{17} +(1.41023 + 5.26305i) q^{18} +(1.09461 + 1.89593i) q^{19} +(2.07609 + 0.830578i) q^{20} +(-3.51725 - 6.83885i) q^{21} +(-2.59589 - 2.59589i) q^{22} +(-4.54529 - 1.21791i) q^{23} +(-1.45333 + 2.51725i) q^{24} +(4.79681 - 1.41090i) q^{25} +(-1.01725 + 0.587308i) q^{26} +(-5.03288 + 5.03288i) q^{27} +(0.808050 - 2.51934i) q^{28} +2.62236i q^{29} +(0.926476 + 6.43313i) q^{30} +(0.0359651 + 0.0207644i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(2.76180 - 10.3072i) q^{33} +0.788333 q^{34} +(-2.06335 - 5.54460i) q^{35} -5.44871 q^{36} +(0.0664979 - 0.248174i) q^{37} +(-2.11463 + 0.566614i) q^{38} +(-2.95680 - 1.70711i) q^{39} +(-1.33961 + 1.79038i) q^{40} +8.98026i q^{41} +(7.51616 - 1.62737i) q^{42} +(-0.474569 + 0.474569i) q^{43} +(3.17930 - 1.83557i) q^{44} +(-9.57526 + 7.53368i) q^{45} +(2.35282 - 4.07520i) q^{46} +(6.18205 + 1.65648i) q^{47} +(-2.05532 - 2.05532i) q^{48} +(-6.37308 + 2.89549i) q^{49} +(0.121320 + 4.99853i) q^{50} +(1.14571 + 1.98443i) q^{51} +(-0.304013 - 1.13459i) q^{52} +(2.04824 + 7.64413i) q^{53} +(-3.55879 - 6.16400i) q^{54} +(3.04917 - 7.62161i) q^{55} +(2.22435 + 1.43257i) q^{56} +(-4.49957 - 4.49957i) q^{57} +(-2.53301 - 0.678717i) q^{58} +(5.35616 - 9.27713i) q^{59} +(-6.45372 - 0.770110i) q^{60} +(1.72539 - 0.996157i) q^{61} +(-0.0293654 + 0.0293654i) q^{62} +(9.68662 + 10.6765i) q^{63} -1.00000i q^{64} +(-2.10300 - 1.57352i) q^{65} +(9.24117 + 5.33539i) q^{66} +(6.39671 - 1.71399i) q^{67} +(-0.204036 + 0.761471i) q^{68} +13.6777 q^{69} +(5.88971 - 0.557996i) q^{70} +8.11777 q^{71} +(1.41023 - 5.26305i) q^{72} +(9.52910 - 2.55331i) q^{73} +(0.222506 + 0.128464i) q^{74} +(-12.4062 + 7.56992i) q^{75} -2.18923i q^{76} +(-9.24884 - 2.96647i) q^{77} +(2.41421 - 2.41421i) q^{78} +(-11.6145 + 6.70563i) q^{79} +(-1.38266 - 1.75735i) q^{80} +(2.17114 - 3.76053i) q^{81} +(-8.67427 - 2.32426i) q^{82} +(-9.73033 - 9.73033i) q^{83} +(-0.373402 + 7.68124i) q^{84} +(0.694291 + 1.62028i) q^{85} +(-0.335571 - 0.581226i) q^{86} +(-1.97280 - 7.36260i) q^{87} +(0.950161 + 3.54605i) q^{88} +(0.715130 + 1.23864i) q^{89} +(-4.79872 - 11.1989i) q^{90} +(-1.68272 + 2.61276i) q^{91} +(3.32739 + 3.32739i) q^{92} +(-0.116597 - 0.0312422i) q^{93} +(-3.20007 + 5.54268i) q^{94} +(-3.02695 - 3.84723i) q^{95} +(2.51725 - 1.45333i) q^{96} +(-3.16693 + 3.16693i) q^{97} +(-1.14736 - 6.90533i) q^{98} +20.0030i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 12 q^{5} + 8 q^{7}+O(q^{10}) $ 16 * q - 12 * q^5 + 8 * q^7	$ 16 q - 12 q^{5} + 8 q^{7} - 12 q^{10} - 12 q^{11} + 16 q^{15} + 8 q^{16} - 36 q^{17} - 8 q^{18} - 28 q^{21} - 8 q^{22} - 4 q^{23} + 12 q^{25} + 12 q^{26} + 4 q^{28} + 20 q^{30} + 24 q^{31} + 48 q^{33} + 8 q^{35} - 8 q^{36} + 4 q^{37} + 24 q^{38} + 36 q^{42} - 8 q^{43} - 12 q^{45} - 8 q^{46} + 12 q^{47} - 32 q^{50} - 16 q^{51} - 28 q^{53} - 4 q^{56} + 8 q^{57} - 32 q^{58} + 8 q^{60} - 12 q^{61} - 36 q^{63} - 8 q^{65} + 32 q^{67} - 36 q^{68} - 12 q^{70} + 16 q^{71} - 8 q^{72} - 12 q^{73} - 48 q^{75} + 16 q^{77} + 16 q^{78} - 12 q^{80} - 48 q^{82} + 24 q^{85} + 12 q^{86} - 24 q^{87} - 4 q^{88} - 16 q^{91} + 8 q^{92} + 28 q^{93} + 20 q^{95} + 12 q^{96} + 40 q^{98}+O(q^{100}) $ 16 * q - 12 * q^5 + 8 * q^7 - 12 * q^10 - 12 * q^11 + 16 * q^15 + 8 * q^16 - 36 * q^17 - 8 * q^18 - 28 * q^21 - 8 * q^22 - 4 * q^23 + 12 * q^25 + 12 * q^26 + 4 * q^28 + 20 * q^30 + 24 * q^31 + 48 * q^33 + 8 * q^35 - 8 * q^36 + 4 * q^37 + 24 * q^38 + 36 * q^42 - 8 * q^43 - 12 * q^45 - 8 * q^46 + 12 * q^47 - 32 * q^50 - 16 * q^51 - 28 * q^53 - 4 * q^56 + 8 * q^57 - 32 * q^58 + 8 * q^60 - 12 * q^61 - 36 * q^63 - 8 * q^65 + 32 * q^67 - 36 * q^68 - 12 * q^70 + 16 * q^71 - 8 * q^72 - 12 * q^73 - 48 * q^75 + 16 * q^77 + 16 * q^78 - 12 * q^80 - 48 * q^82 + 24 * q^85 + 12 * q^86 - 24 * q^87 - 4 * q^88 - 16 * q^91 + 8 * q^92 + 28 * q^93 + 20 * q^95 + 12 * q^96 + 40 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

$n$	$31$	$57$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{4}\right)$

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
$3$	−2.80762	+	0.752300i	−1.62098	+	0.434341i	−0.951290	−	0.308298i	$-0.900241\pi$
$3$	−2.80762	+	0.752300i	−1.62098	+	0.434341i	−0.669692	+	0.742639i	$0.733574\pi$
$4$	−0.866025	−	0.500000i	−0.433013	−	0.250000i
$5$	−2.21323	+	0.318742i	−0.989788	+	0.142546i
$5$	−2.21323	+	0.318742i	−0.989788	+	0.142546i
$6$		−	2.90667i		−	1.18664i
$7$	0.559876	+	2.58583i	0.211613	+	0.977353i
$7$	0.559876	+	2.58583i	0.211613	+	0.977353i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	4.71872	−	2.72435i	1.57291	−	0.908118i
$10$	0.264946	−	2.22032i	0.0837833	−	0.702126i
$11$	−1.83557	+	3.17930i	−0.553445	+	0.958596i	0.444577	+	0.895741i	$0.353354\pi$
$11$	−1.83557	+	3.17930i	−0.553445	+	0.958596i	−0.998023	+	0.0628551i	$0.979979\pi$
$12$	2.80762	+	0.752300i	0.810491	+	0.217170i
$13$	0.830578	+	0.830578i	0.230361	+	0.230361i	0.812843	−	0.582482i	$-0.197918\pi$
$13$	0.830578	+	0.830578i	0.230361	+	0.230361i	−0.582482	+	0.812843i	$0.697918\pi$
$14$	−2.64263	−	0.128464i	−0.706273	−	0.0343335i
$15$	5.97414	−	2.55992i	1.54252	−	0.660970i
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.204036	−	0.761471i	−0.0494859	−	0.184684i	0.936759	−	0.349976i	$-0.113810\pi$
$17$	−0.204036	−	0.761471i	−0.0494859	−	0.184684i	−0.986245	+	0.165292i	$0.947143\pi$
$18$	1.41023	+	5.26305i	0.332394	+	1.24051i
$19$	1.09461	+	1.89593i	0.251122	+	0.434955i	0.963835	−	0.266500i	$-0.0858673\pi$
$19$	1.09461	+	1.89593i	0.251122	+	0.434955i	−0.712713	+	0.701455i	$0.752534\pi$
$20$	2.07609	+	0.830578i	0.464227	+	0.185723i
$21$	−3.51725	−	6.83885i	−0.767526	−	1.49236i
$22$	−2.59589	−	2.59589i	−0.553445	−	0.553445i
$23$	−4.54529	−	1.21791i	−0.947759	−	0.253951i	−0.248348	−	0.968671i	$-0.579888\pi$
$23$	−4.54529	−	1.21791i	−0.947759	−	0.253951i	−0.699411	+	0.714719i	$0.746554\pi$
$24$	−1.45333	+	2.51725i	−0.296660	+	0.513831i
$25$	4.79681	−	1.41090i	0.959361	−	0.282180i
$26$	−1.01725	+	0.587308i	−0.199498	+	0.115180i
$27$	−5.03288	+	5.03288i	−0.968579	+	0.968579i
$28$	0.808050	−	2.51934i	0.152707	−	0.476110i
$29$			2.62236i			0.486960i	0.969906	+	0.243480i	$0.0782891\pi$
$29$			2.62236i			0.486960i	−0.969906	+	0.243480i	$0.921711\pi$
$30$	0.926476	+	6.43313i	0.169151	+	1.17452i
$31$	0.0359651	+	0.0207644i	0.00645952	+	0.00372940i	0.503226	−	0.864155i	$-0.332146\pi$
$31$	0.0359651	+	0.0207644i	0.00645952	+	0.00372940i	−0.496767	+	0.867884i	$0.665480\pi$
$32$	−0.965926	+	0.258819i	−0.170753	+	0.0457532i
$33$	2.76180	−	10.3072i	0.480768	−	1.79425i
$34$	0.788333			0.135198
$35$	−2.06335	−	5.54460i	−0.348770	−	0.937208i
$36$	−5.44871			−0.908118
$37$	0.0664979	−	0.248174i	0.0109322	−	0.0407995i	−0.960244	−	0.279161i	$-0.909944\pi$
$37$	0.0664979	−	0.248174i	0.0109322	−	0.0407995i	0.971176	+	0.238362i	$0.0766103\pi$
$38$	−2.11463	+	0.566614i	−0.343038	+	0.0919169i
$39$	−2.95680	−	1.70711i	−0.473466	−	0.273356i
$40$	−1.33961	+	1.79038i	−0.211811	+	0.283083i
$41$			8.98026i			1.40248i	0.712925	+	0.701241i	$0.247370\pi$
$41$			8.98026i			1.40248i	−0.712925	+	0.701241i	$0.752630\pi$
$42$	7.51616	−	1.62737i	1.15977	−	0.251109i
$43$	−0.474569	+	0.474569i	−0.0723711	+	0.0723711i	−0.742366	−	0.669995i	$-0.766296\pi$
$43$	−0.474569	+	0.474569i	−0.0723711	+	0.0723711i	0.669995	+	0.742366i	$0.266296\pi$
$44$	3.17930	−	1.83557i	0.479298	−	0.276723i
$45$	−9.57526	+	7.53368i	−1.42740	+	1.12306i
$46$	2.35282	−	4.07520i	0.346904	−	0.600855i
$47$	6.18205	+	1.65648i	0.901745	+	0.241622i	0.679766	−	0.733429i	$-0.262081\pi$
$47$	6.18205	+	1.65648i	0.901745	+	0.241622i	0.221980	+	0.975051i	$0.428748\pi$
$48$	−2.05532	−	2.05532i	−0.296660	−	0.296660i
$49$	−6.37308	+	2.89549i	−0.910440	+	0.413642i
$50$	0.121320	+	4.99853i	0.0171573	+	0.706899i
$51$	1.14571	+	1.98443i	0.160432	+	0.277876i
$52$	−0.304013	−	1.13459i	−0.0421590	−	0.157339i
$53$	2.04824	+	7.64413i	0.281347	+	1.05000i	0.951468	+	0.307749i	$0.0995758\pi$
$53$	2.04824	+	7.64413i	0.281347	+	1.05000i	−0.670120	+	0.742252i	$0.733758\pi$
$54$	−3.55879	−	6.16400i	−0.484289	−	0.838814i
$55$	3.04917	−	7.62161i	0.411150	−	1.02770i
$56$	2.22435	+	1.43257i	0.297242	+	0.191435i
$57$	−4.49957	−	4.49957i	−0.595982	−	0.595982i
$58$	−2.53301	−	0.678717i	−0.332600	−	0.0891199i
$59$	5.35616	−	9.27713i	0.697312	−	1.20778i	−0.272083	−	0.962274i	$-0.587713\pi$
$59$	5.35616	−	9.27713i	0.697312	−	1.20778i	0.969395	−	0.245506i	$-0.0789541\pi$
$60$	−6.45372	−	0.770110i	−0.833171	−	0.0994207i
$61$	1.72539	−	0.996157i	0.220914	−	0.127545i	−0.385459	−	0.922725i	$-0.625957\pi$
$61$	1.72539	−	0.996157i	0.220914	−	0.127545i	0.606373	+	0.795180i	$0.292624\pi$
$62$	−0.0293654	+	0.0293654i	−0.00372940	+	0.00372940i
$63$	9.68662	+	10.6765i	1.22040	+	1.34512i
$64$		−	1.00000i		−	0.125000i
$65$	−2.10300	−	1.57352i	−0.260846	−	0.195172i
$66$	9.24117	+	5.33539i	1.13751	+	0.656741i
$67$	6.39671	−	1.71399i	0.781482	−	0.209398i	0.154044	−	0.988064i	$-0.450770\pi$
$67$	6.39671	−	1.71399i	0.781482	−	0.209398i	0.627438	+	0.778666i	$0.284103\pi$
$68$	−0.204036	+	0.761471i	−0.0247430	+	0.0923420i
$69$	13.6777			1.64660
$70$	5.88971	−	0.557996i	0.703955	−	0.0666933i
$71$	8.11777			0.963402			0.481701	−	0.876336i	$-0.340019\pi$
$71$	8.11777			0.963402			0.481701	+	0.876336i	$0.340019\pi$
$72$	1.41023	−	5.26305i	0.166197	−	0.620256i
$73$	9.52910	−	2.55331i	1.11530	−	0.298843i	0.346318	−	0.938117i	$-0.387432\pi$
$73$	9.52910	−	2.55331i	1.11530	−	0.298843i	0.768979	+	0.639274i	$0.220765\pi$
$74$	0.222506	+	0.128464i	0.0258658	+	0.0149336i
$75$	−12.4062	+	7.56992i	−1.43255	+	0.874099i
$76$		−	2.18923i		−	0.251122i
$77$	−9.24884	−	2.96647i	−1.05400	−	0.338060i
$78$	2.41421	−	2.41421i	0.273356	−	0.273356i
$79$	−11.6145	+	6.70563i	−1.30673	+	0.754443i	−0.981550	−	0.191208i	$-0.938760\pi$
$79$	−11.6145	+	6.70563i	−1.30673	+	0.754443i	−0.325184	+	0.945651i	$0.605426\pi$
$80$	−1.38266	−	1.75735i	−0.154586	−	0.196477i
$81$	2.17114	−	3.76053i	0.241238	−	0.417836i
$82$	−8.67427	−	2.32426i	−0.957912	−	0.256672i
$83$	−9.73033	−	9.73033i	−1.06804	−	1.06804i	−0.997509	−	0.0705331i	$-0.977530\pi$
$83$	−9.73033	−	9.73033i	−1.06804	−	1.06804i	−0.0705331	−	0.997509i	$-0.522470\pi$
$84$	−0.373402	+	7.68124i	−0.0407415	+	0.838092i
$85$	0.694291	+	1.62028i	0.0753065	+	0.175744i
$86$	−0.335571	−	0.581226i	−0.0361855	−	0.0626752i
$87$	−1.97280	−	7.36260i	−0.211507	−	0.789354i
$88$	0.950161	+	3.54605i	0.101288	+	0.378010i
$89$	0.715130	+	1.23864i	0.0758036	+	0.131296i	0.901435	−	0.432914i	$-0.142514\pi$
$89$	0.715130	+	1.23864i	0.0758036	+	0.131296i	−0.825632	+	0.564209i	$0.809181\pi$
$90$	−4.79872	−	11.1989i	−0.505829	−	1.18046i
$91$	−1.68272	+	2.61276i	−0.176397	+	0.273892i
$92$	3.32739	+	3.32739i	0.346904	+	0.346904i
$93$	−0.116597	−	0.0312422i	−0.0120906	−	0.00323967i
$94$	−3.20007	+	5.54268i	−0.330062	+	0.571684i
$95$	−3.02695	−	3.84723i	−0.310558	−	0.394717i
$96$	2.51725	−	1.45333i	0.256915	−	0.148330i
$97$	−3.16693	+	3.16693i	−0.321553	+	0.321553i	−0.849363	−	0.527810i	$-0.823013\pi$
$97$	−3.16693	+	3.16693i	−0.321553	+	0.321553i	0.527810	+	0.849363i	$0.323013\pi$
$98$	−1.14736	−	6.90533i	−0.115901	−	0.697544i
$99$			20.0030i			2.01037i
$100$	−4.85961	−	1.17653i	−0.485961	−	0.117653i
$101$	−0.0622734	−	0.0359536i	−0.00619644	−	0.00357751i	0.496899	−	0.867809i	$-0.334472\pi$
$101$	−0.0622734	−	0.0359536i	−0.00619644	−	0.00357751i	−0.503095	+	0.864231i	$0.667805\pi$
$102$	−2.21334	+	0.593063i	−0.219154	+	0.0587220i
$103$	−4.29116	+	16.0148i	−0.422820	+	1.57799i	0.345817	+	0.938302i	$0.387602\pi$
$103$	−4.29116	+	16.0148i	−0.422820	+	1.57799i	−0.768638	+	0.639685i	$0.779065\pi$
$104$	1.17462			0.115180
$105$	9.96432	+	14.0149i	0.972418	+	1.36771i
$106$	−7.91378			−0.768654
$107$	1.18265	−	4.41372i	0.114331	−	0.426690i	−0.884905	−	0.465772i	$-0.845777\pi$
$107$	1.18265	−	4.41372i	0.114331	−	0.426690i	0.999236	+	0.0390819i	$0.0124433\pi$
$108$	6.87505	−	1.84216i	0.661552	−	0.177262i
$109$	−15.6773	−	9.05131i	−1.50162	−	0.866958i	−0.999998	−	0.00186842i	$-0.999405\pi$
$109$	−15.6773	−	9.05131i	−1.50162	−	0.866958i	−0.501617	−	0.865090i	$-0.667261\pi$
$110$	6.57273	+	4.91789i	0.626685	+	0.468902i
$111$			0.746804i			0.0708835i
$112$	−1.95946	+	1.77778i	−0.185152	+	0.167985i
$113$	1.52064	−	1.52064i	0.143049	−	0.143049i	−0.631955	−	0.775005i	$-0.717747\pi$
$113$	1.52064	−	1.52064i	0.143049	−	0.143049i	0.775005	+	0.631955i	$0.217747\pi$
$114$	5.51082	−	3.18168i	0.516136	−	0.297991i
$115$	10.4480	+	1.24674i	0.974281	+	0.116259i
$116$	1.31118	−	2.27103i	0.121740	−	0.210860i
$117$	6.18205	+	1.65648i	0.571531	+	0.153141i
$118$	7.57475	+	7.57475i	0.697312	+	0.697312i
$119$	1.85480	−	0.953932i	0.170030	−	0.0874468i
$120$	2.41421	−	6.03449i	0.220387	−	0.550871i
$121$	−1.23864	−	2.14539i	−0.112604	−	0.195035i
$122$	0.515649	+	1.92443i	0.0466846	+	0.174229i
$123$	−6.75585	−	25.2132i	−0.609155	−	2.27340i
$124$	−0.0207644	−	0.0359651i	−0.00186470	−	0.00322976i
$125$	−10.1667	+	4.65160i	−0.909341	+	0.416051i
$126$	−12.8198	+	6.59327i	−1.14208	+	0.587376i
$127$	−13.2527	−	13.2527i	−1.17599	−	1.17599i	−0.980757	−	0.195234i	$-0.937453\pi$
$127$	−13.2527	−	13.2527i	−1.17599	−	1.17599i	−0.195234	−	0.980757i	$-0.562547\pi$
$128$	0.965926	+	0.258819i	0.0853766	+	0.0228766i
$129$	0.975392	−	1.68943i	0.0858785	−	0.148746i
$130$	2.06420	−	1.62409i	0.181043	−	0.142442i
$131$	12.2929	−	7.09731i	1.07404	−	0.620095i	0.144755	−	0.989468i	$-0.453761\pi$
$131$	12.2929	−	7.09731i	1.07404	−	0.620095i	0.929281	+	0.369372i	$0.120427\pi$
$132$	−7.54538	+	7.54538i	−0.656741	+	0.656741i
$133$	−4.28970	+	3.89197i	−0.371964	+	0.337477i
$134$			6.62236i			0.572085i
$135$	9.53476	−	12.7431i	0.820621	−	1.09675i
$136$	−0.682717	−	0.394167i	−0.0585425	−	0.0337995i
$137$	18.3201	−	4.90887i	1.56519	−	0.419393i	0.630891	−	0.775871i	$-0.282689\pi$
$137$	18.3201	−	4.90887i	1.56519	−	0.419393i	0.934303	+	0.356479i	$0.116023\pi$
$138$	−3.54005	+	13.2117i	−0.301349	+	1.12465i
$139$	8.23706			0.698658			0.349329	−	0.937000i	$-0.386409\pi$
$139$	8.23706			0.698658			0.349329	+	0.937000i	$0.386409\pi$
$140$	−0.985385	+	5.83344i	−0.0832803	+	0.493016i
$141$	−18.6030			−1.56666
$142$	−2.10103	+	7.84116i	−0.176315	+	0.658016i
$143$	−4.16524	+	1.11607i	−0.348315	+	0.0933308i
$144$	4.71872	+	2.72435i	0.393227	+	0.227029i
$145$	−0.835856	−	5.80390i	−0.0694141	−	0.481988i
$146$			9.86525i			0.816454i
$147$	15.7149	−	12.9239i	1.29614	−	1.06595i
$148$	−0.181676	+	0.181676i	−0.0149336	+	0.0149336i
$149$	4.19317	−	2.42093i	0.343518	−	0.198330i	−0.318309	−	0.947987i	$-0.603115\pi$
$149$	4.19317	−	2.42093i	0.343518	−	0.198330i	0.661826	+	0.749657i	$0.269782\pi$
$150$	−4.10102	−	13.9427i	−0.334847	−	1.13842i
$151$	−5.02292	+	8.69995i	−0.408759	+	0.707992i	−0.994751	−	0.102325i	$-0.967372\pi$
$151$	−5.02292	+	8.69995i	−0.408759	+	0.707992i	0.585992	+	0.810317i	$0.300705\pi$
$152$	2.11463	+	0.566614i	0.171519	+	0.0459584i
$153$	−3.03730	−	3.03730i	−0.245551	−	0.245551i
$154$	5.25916	−	8.16592i	0.423795	−	0.658028i
$155$	−0.0862176	−	0.0344930i	−0.00692516	−	0.00277054i
$156$	1.70711	+	2.95680i	0.136678	+	0.236733i
$157$	6.33762	+	23.6523i	0.505797	+	1.88766i	0.458320	+	0.888788i	$0.348452\pi$
$157$	6.33762	+	23.6523i	0.505797	+	1.88766i	0.0474774	+	0.998872i	$0.484882\pi$
$158$	−3.47109	−	12.9543i	−0.276145	−	1.03059i
$159$	−11.5014	−	19.9209i	−0.912117	−	1.57983i
$160$	2.05532	−	0.880708i	0.162488	−	0.0696261i
$161$	0.604505	−	12.4353i	0.0476417	−	0.980035i
$162$	3.07046	+	3.07046i	0.241238	+	0.241238i
$163$	21.2171	+	5.68510i	1.66185	+	0.445291i	0.962895	−	0.269875i	$-0.0869823\pi$
$163$	21.2171	+	5.68510i	1.66185	+	0.445291i	0.698954	+	0.715166i	$0.253649\pi$
$164$	4.49013	−	7.77713i	0.350620	−	0.607292i
$165$	−2.82718	+	23.6925i	−0.220096	+	1.84446i
$166$	11.9172	−	6.88038i	0.924952	−	0.534021i
$167$	−3.14616	+	3.14616i	−0.243457	+	0.243457i	−0.818279	−	0.574821i	$-0.805072\pi$
$167$	−3.14616	+	3.14616i	−0.243457	+	0.243457i	0.574821	+	0.818279i	$0.305072\pi$
$168$	−7.32287	−	2.34873i	−0.564972	−	0.181209i
$169$		−	11.6203i		−	0.893868i
$170$	−1.74477	+	0.251275i	−0.133817	+	0.0192719i
$171$	10.3303	+	5.96423i	0.789981	+	0.456096i
$172$	0.648273	−	0.173704i	0.0494304	−	0.0132448i
$173$	−1.35273	+	5.04844i	−0.102846	+	0.383826i	−0.998092	−	0.0617463i	$-0.980333\pi$
$173$	−1.35273	+	5.04844i	−0.102846	+	0.383826i	0.895246	+	0.445572i	$0.147000\pi$
$174$	7.62233			0.577847
$175$	6.33397	+	11.6138i	0.478803	+	0.877922i
$176$	−3.67114			−0.276723
$177$	−8.05888	+	30.0761i	−0.605742	+	2.26066i
$178$	−1.38152	+	0.370178i	−0.103550	+	0.0277460i
$179$	10.8847	+	6.28428i	0.813560	+	0.469709i	0.848191	−	0.529691i	$-0.177692\pi$
$179$	10.8847	+	6.28428i	0.813560	+	0.469709i	−0.0346308	+	0.999400i	$0.511026\pi$
$180$	12.0593	−	1.73673i	0.898844	−	0.129448i
$181$		−	11.6742i		−	0.867740i	−0.900976	−	0.433870i	$-0.857148\pi$
$181$		−	11.6742i		−	0.867740i	0.900976	−	0.433870i	$-0.142852\pi$
$182$	−2.08821	−	2.30161i	−0.154789	−	0.170607i
$183$	−4.09485	+	4.09485i	−0.302700	+	0.302700i
$184$	−4.07520	+	2.35282i	−0.300428	+	0.173452i
$185$	−0.0680721	+	0.570462i	−0.00500476	+	0.0419412i
$186$	0.0603553	−	0.104538i	0.00442546	−	0.00766513i
$187$	2.79547	+	0.749044i	0.204425	+	0.0547755i
$188$	−4.52558	−	4.52558i	−0.330062	−	0.330062i
$189$	−15.8320	−	10.1964i	−1.15161	−	0.741680i
$190$	4.49957	−	1.92807i	0.326433	−	0.139877i
$191$	−7.75170	−	13.4263i	−0.560894	−	0.971496i	−0.997419	−	0.0718040i	$-0.977124\pi$
$191$	−7.75170	−	13.4263i	−0.560894	−	0.971496i	0.436525	−	0.899692i	$-0.356209\pi$
$192$	0.752300	+	2.80762i	0.0542926	+	0.202623i
$193$	2.32883	+	8.69132i	0.167633	+	0.625615i	0.997690	+	0.0679359i	$0.0216413\pi$
$193$	2.32883	+	8.69132i	0.167633	+	0.625615i	−0.830057	+	0.557679i	$0.811692\pi$
$194$	−2.23936	−	3.87868i	−0.160776	−	0.278473i
$195$	7.08821	+	2.83577i	0.507597	+	0.203074i
$196$	6.96699	+	0.678966i	0.497642	+	0.0484976i
$197$	12.1951	+	12.1951i	0.868865	+	0.868865i	0.992347	−	0.123482i	$-0.0394061\pi$
$197$	12.1951	+	12.1951i	0.868865	+	0.868865i	−0.123482	+	0.992347i	$0.539406\pi$
$198$	−19.3214	−	5.17715i	−1.37311	−	0.367924i
$199$	4.36557	−	7.56140i	0.309467	−	0.536013i	−0.668779	−	0.743462i	$-0.733183\pi$
$199$	4.36557	−	7.56140i	0.309467	−	0.536013i	0.978246	+	0.207448i	$0.0665159\pi$
$200$	2.39420	−	4.38951i	0.169295	−	0.310385i
$201$	−16.6701	+	9.62450i	−1.17582	+	0.678860i
$202$	0.0508460	−	0.0508460i	0.00357751	−	0.00357751i
$203$	−6.78099	+	1.46820i	−0.475932	+	0.103047i
$204$		−	2.29142i		−	0.160432i
$205$	−2.86239	−	19.8754i	−0.199918	−	1.38816i
$206$	−14.3585	−	8.28988i	−1.00040	−	0.577583i
$207$	−24.7660	+	6.63602i	−1.72135	+	0.461235i
$208$	−0.304013	+	1.13459i	−0.0210795	+	0.0786697i
$209$	−8.03696			−0.555928
$210$	−16.1163	+	5.99747i	−1.11213	+	0.413865i
$211$	−11.1745			−0.769288			−0.384644	−	0.923065i	$-0.625676\pi$
$211$	−11.1745			−0.769288			−0.384644	+	0.923065i	$0.625676\pi$
$212$	2.04824	−	7.64413i	0.140674	−	0.525001i
$213$	−22.7916	+	6.10700i	−1.56166	+	0.418445i
$214$	3.95723	+	2.28471i	0.270511	+	0.156179i
$215$	0.899067	−	1.20160i	0.0613158	−	0.0819482i
$216$			7.11757i			0.484289i
$217$	−0.0335574	+	0.104625i	−0.00227803	+	0.00710242i
$218$	12.8005	−	12.8005i	0.866958	−	0.866958i
$219$	−24.8333	+	14.3375i	−1.67808	+	0.968838i
$220$	−6.45147	+	5.07592i	−0.434958	+	0.342219i
$221$	0.462994	−	0.801929i	0.0311443	−	0.0539436i
$222$	−0.721358	−	0.193287i	−0.0484143	−	0.0129726i
$223$	0.746804	+	0.746804i	0.0500097	+	0.0500097i	0.731669	−	0.681660i	$-0.238742\pi$
$223$	0.746804	+	0.746804i	0.0500097	+	0.0500097i	−0.681660	+	0.731669i	$0.738742\pi$
$224$	−1.21006	−	2.35282i	−0.0808507	−	0.157204i
$225$	18.7910	−	19.7258i	1.25273	−	1.31506i
$226$	1.07525	+	1.86239i	0.0715247	+	0.123884i
$227$	−0.807609	−	3.01404i	−0.0536029	−	0.200049i	0.933932	−	0.357452i	$-0.116354\pi$
$227$	−0.807609	−	3.01404i	−0.0536029	−	0.200049i	−0.987534	+	0.157403i	$0.949688\pi$
$228$	1.64696	+	6.14653i	0.109072	+	0.407064i
$229$	4.21091	+	7.29350i	0.278264	+	0.481968i	0.970954	−	0.239268i	$-0.0769075\pi$
$229$	4.21091	+	7.29350i	0.278264	+	0.481968i	−0.692689	+	0.721236i	$0.743574\pi$
$230$	−3.90840	+	9.76931i	−0.257712	+	0.644169i
$231$	28.1989	+	1.37081i	1.85535	+	0.0901928i
$232$	1.85429	+	1.85429i	0.121740	+	0.121740i
$233$	22.0201	+	5.90027i	1.44259	+	0.386540i	0.893439	−	0.449186i	$-0.148286\pi$
$233$	22.0201	+	5.90027i	1.44259	+	0.386540i	0.549148	+	0.835725i	$0.314952\pi$
$234$	−3.20007	+	5.54268i	−0.209195	+	0.362336i
$235$	−14.2103	−	1.69569i	−0.926979	−	0.110615i
$236$	−9.27713	+	5.35616i	−0.603890	+	0.348656i
$237$	27.5645	−	27.5645i	1.79051	−	1.79051i
$238$	0.441369	+	2.03850i	0.0286097	+	0.132136i
$239$			23.9971i			1.55224i	0.630585	+	0.776120i	$0.282815\pi$
$239$			23.9971i			1.55224i	−0.630585	+	0.776120i	$0.717185\pi$
$240$	5.20403	+	3.89379i	0.335919	+	0.251343i
$241$	−21.4666	−	12.3937i	−1.38278	−	0.798350i	−0.390295	−	0.920690i	$-0.627627\pi$
$241$	−21.4666	−	12.3937i	−1.38278	−	0.798350i	−0.992488	+	0.122340i	$0.960960\pi$
$242$	2.39287	−	0.641168i	0.153820	−	0.0412158i
$243$	2.25979	−	8.43364i	0.144965	−	0.541018i
$244$	−1.99231			−0.127545
$245$	13.1822	−	8.43977i	0.842179	−	0.539197i
$246$	26.1026			1.66424
$247$	−0.665553	+	2.48388i	−0.0423481	+	0.158045i
$248$	0.0401138	−	0.0107485i	0.00254723	−	0.000682528i
$249$	34.6392	+	19.9990i	2.19517	+	1.26738i
$250$	−1.86175	−	11.0242i	−0.117747	−	0.697234i
$251$			11.1158i			0.701623i	0.936446	+	0.350811i	$0.114094\pi$
$251$			11.1158i			0.701623i	−0.936446	+	0.350811i	$0.885906\pi$
$252$	−3.05060	−	14.0895i	−0.192170	−	0.887552i
$253$	12.2153	−	12.2153i	0.767970	−	0.767970i
$254$	16.2312	−	9.37110i	1.01844	−	0.587995i
$255$	−3.16825	−	4.02682i	−0.198403	−	0.252169i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−24.4314	−	6.54637i	−1.52399	−	0.408351i	−0.602935	−	0.797790i	$-0.706002\pi$
$257$	−24.4314	−	6.54637i	−1.52399	−	0.408351i	−0.921052	+	0.389439i	$0.872669\pi$
$258$	1.37941	+	1.37941i	0.0858785	+	0.0858785i
$259$	0.678966	+	0.0330060i	0.0421889	+	0.00205090i
$260$	1.03449	+	2.41421i	0.0641565	+	0.149723i
$261$	7.14424	+	12.3742i	0.442217	+	0.765943i
$262$	3.67384	+	13.7110i	0.226971	+	0.847066i
$263$	2.93659	+	10.9595i	0.181078	+	0.675792i	0.995436	+	0.0954297i	$0.0304225\pi$
$263$	2.93659	+	10.9595i	0.181078	+	0.675792i	−0.814358	+	0.580363i	$0.802911\pi$
$264$	−5.33539	−	9.24117i	−0.328371	−	0.568755i
$265$	−6.96973	−	16.2654i	−0.428147	−	0.999174i
$266$	−2.64910	−	5.15085i	−0.162427	−	0.315819i
$267$	−2.93964	−	2.93964i	−0.179903	−	0.179903i
$268$	−6.39671	−	1.71399i	−0.390741	−	0.104699i
$269$	−4.03346	+	6.98616i	−0.245924	+	0.425954i	−0.962391	−	0.271668i	$-0.912425\pi$
$269$	−4.03346	+	6.98616i	−0.245924	+	0.425954i	0.716467	+	0.697621i	$0.245758\pi$
$270$	9.84115	+	12.5080i	0.598913	+	0.761215i
$271$	7.27419	−	4.19976i	0.441876	−	0.255117i	−0.262517	−	0.964927i	$-0.584553\pi$
$271$	7.27419	−	4.19976i	0.441876	−	0.255117i	0.704393	+	0.709810i	$0.251219\pi$
$272$	0.557436	−	0.557436i	0.0337995	−	0.0337995i
$273$	2.75885	−	8.60155i	0.166974	−	0.520590i
$274$			18.9664i			1.14580i
$275$	−4.31920	+	17.8403i	−0.260458	+	1.07581i
$276$	−11.8452	−	6.83885i	−0.713000	−	0.411651i
$277$	−5.48646	+	1.47009i	−0.329650	+	0.0883293i	−0.419848	−	0.907594i	$-0.637917\pi$
$277$	−5.48646	+	1.47009i	−0.329650	+	0.0883293i	0.0901983	+	0.995924i	$0.471250\pi$
$278$	−2.13191	+	7.95639i	−0.127863	+	0.477193i
$279$	0.226279			0.0135470
$280$	−5.37963	−	2.46161i	−0.321495	−	0.147110i
$281$	7.27627			0.434066			0.217033	−	0.976164i	$-0.430362\pi$
$281$	7.27627			0.434066			0.217033	+	0.976164i	$0.430362\pi$
$282$	4.81482	−	17.9692i	0.286719	−	1.07005i
$283$	−7.44729	+	1.99550i	−0.442696	+	0.118620i	−0.473280	−	0.880912i	$-0.656930\pi$
$283$	−7.44729	+	1.99550i	−0.442696	+	0.118620i	0.0305840	+	0.999532i	$0.490263\pi$
$284$	−7.03019	−	4.05888i	−0.417165	−	0.240850i
$285$	11.3928	+	8.52440i	0.674851	+	0.504942i
$286$		−	4.31218i		−	0.254984i
$287$	−23.2215	+	5.02784i	−1.37072	+	0.296784i
$288$	−3.85282	+	3.85282i	−0.227029	+	0.227029i
$289$	14.1842	−	8.18927i	0.834366	−	0.481721i
$290$	5.82247	+	0.694784i	0.341907	+	0.0407991i
$291$	6.50906	−	11.2740i	0.381568	−	0.660895i
$292$	−9.52910	−	2.55331i	−0.557648	−	0.149421i
$293$	3.35198	+	3.35198i	0.195824	+	0.195824i	0.798207	−	0.602383i	$-0.205782\pi$
$293$	3.35198	+	3.35198i	0.195824	+	0.195824i	−0.602383	+	0.798207i	$0.705782\pi$
$294$	8.41624	+	18.5244i	0.490845	+	1.08037i
$295$	−8.89741	+	22.2397i	−0.518027	+	1.29485i
$296$	−0.128464	−	0.222506i	−0.00746682	−	0.0129329i
$297$	−6.76284	−	25.2393i	−0.392420	−	1.46453i
$298$	1.25316	+	4.67687i	0.0725938	+	0.270924i
$299$	−2.76365	−	4.78679i	−0.159826	−	0.276827i
$300$	14.5291	−	0.352638i	0.838835	−	0.0203595i
$301$	−1.49286	−	0.961456i	−0.0860468	−	0.0554174i
$302$	−7.10348	−	7.10348i	−0.408759	−	0.408759i
$303$	0.201888	+	0.0540958i	0.0115982	+	0.00310772i
$304$	−1.09461	+	1.89593i	−0.0627804	+	0.108739i
$305$	−3.50118	+	2.75468i	−0.200477	+	0.157733i
$306$	3.71992	−	2.14770i	0.212654	−	0.122776i
$307$	−1.06546	+	1.06546i	−0.0608089	+	0.0608089i	−0.736857	−	0.676048i	$-0.763691\pi$
$307$	−1.06546	+	1.06546i	−0.0608089	+	0.0608089i	0.676048	+	0.736857i	$0.263691\pi$
$308$	6.52650	+	7.19345i	0.371882	+	0.409885i
$309$		−	48.1918i		−	2.74154i
$310$	0.0556324	−	0.0743524i	0.00315971	−	0.00422293i
$311$	11.9584	+	6.90417i	0.678097	+	0.391500i	0.799138	−	0.601148i	$-0.205290\pi$
$311$	11.9584	+	6.90417i	0.678097	+	0.391500i	−0.121040	+	0.992648i	$0.538623\pi$
$312$	−3.29788	+	0.883663i	−0.186706	+	0.0500276i
$313$	6.04266	−	22.5515i	0.341551	−	1.27469i	−0.555038	−	0.831825i	$-0.687296\pi$
$313$	6.04266	−	22.5515i	0.341551	−	1.27469i	0.896590	−	0.442863i	$-0.146037\pi$
$314$	−24.4867			−1.38186
$315$	−24.8418	−	20.5421i	−1.39968	−	1.15742i
$316$	13.4113			0.754443
$317$	3.41352	−	12.7394i	0.191722	−	0.715518i	−0.801369	−	0.598171i	$-0.795894\pi$
$317$	3.41352	−	12.7394i	0.191722	−	0.715518i	0.993091	−	0.117347i	$-0.0374390\pi$
$318$	22.2189	−	5.95354i	1.24598	−	0.333858i
$319$	−8.33728	−	4.81353i	−0.466798	−	0.269506i
$320$	0.318742	+	2.21323i	0.0178182	+	0.123724i
$321$			13.2818i			0.741316i
$322$	11.8551	+	3.80239i	0.660658	+	0.211899i
$323$	1.22035	−	1.22035i	0.0679023	−	0.0679023i
$324$	−3.76053	+	2.17114i	−0.208918	+	0.120619i
$325$	5.15599	+	2.81226i	0.286003	+	0.155996i
$326$	−10.9828	+	19.0227i	−0.608279	+	1.05357i
$327$	50.8253	+	13.6186i	2.81065	+	0.753111i
$328$	6.35000	+	6.35000i	0.350620	+	0.350620i
$329$	−0.822187	+	16.9132i	−0.0453286	+	0.932454i
$330$	−22.1535	−	8.86292i	−1.21951	−	0.487888i
$331$	9.54799	+	16.5376i	0.524805	+	0.908989i	0.999583	+	0.0288830i	$0.00919501\pi$
$331$	9.54799	+	16.5376i	0.524805	+	0.908989i	−0.474778	+	0.880106i	$0.657472\pi$
$332$	3.56155	+	13.2919i	0.195465	+	0.729487i
$333$	−0.362328	−	1.35222i	−0.0198554	−	0.0741015i
$334$	−2.22467	−	3.85325i	−0.121729	−	0.210840i
$335$	−13.6111	+	5.83237i	−0.743653	+	0.318656i
$336$	4.16400	−	6.46545i	0.227165	−	0.352719i
$337$	0.488226	+	0.488226i	0.0265953	+	0.0265953i	0.720279	−	0.693684i	$-0.244014\pi$
$337$	0.488226	+	0.488226i	0.0265953	+	0.0265953i	−0.693684	+	0.720279i	$0.744014\pi$
$338$	11.2243	+	3.00755i	0.610523	+	0.163589i
$339$	−3.12540	+	5.41335i	−0.169748	+	0.294013i
$340$	0.208866	−	1.75035i	0.0113273	−	0.0949260i
$341$	−0.132033	+	0.0762292i	−0.00714998	+	0.00412804i
$342$	−8.43469	+	8.43469i	−0.456096	+	0.456096i
$343$	−11.0554	−	14.8586i	−0.596936	−	0.802289i
$344$			0.671142i			0.0361855i
$345$	−30.2720	+	4.35966i	−1.62979	+	0.234716i
$346$	−4.52631	−	2.61327i	−0.243336	−	0.140490i
$347$	−3.68015	+	0.986094i	−0.197561	+	0.0529363i	−0.356243	−	0.934393i	$-0.615942\pi$
$347$	−3.68015	+	0.986094i	−0.197561	+	0.0529363i	0.158682	+	0.987330i	$0.449276\pi$
$348$	−1.97280	+	7.36260i	−0.105753	+	0.394677i
$349$	−7.91303			−0.423575			−0.211787	−	0.977316i	$-0.567928\pi$
$349$	−7.91303			−0.423575			−0.211787	+	0.977316i	$0.567928\pi$
$350$	−12.8574	+	3.11227i	−0.687259	+	0.166358i
$351$	−8.36041			−0.446246
$352$	0.950161	−	3.54605i	0.0506438	−	0.189005i
$353$	−24.9004	+	6.67203i	−1.32531	+	0.355116i	−0.850965	−	0.525222i	$-0.823982\pi$
$353$	−24.9004	+	6.67203i	−1.32531	+	0.355116i	−0.474347	+	0.880338i	$0.657316\pi$
$354$	−26.9655	−	15.5686i	−1.43320	−	0.827459i
$355$	−17.9665	+	2.58747i	−0.953564	+	0.137329i
$356$		−	1.43026i		−	0.0758036i
$357$	−4.48995	+	4.07365i	−0.237633	+	0.215601i
$358$	−8.88731	+	8.88731i	−0.469709	+	0.469709i
$359$	8.99497	−	5.19325i	0.474737	−	0.274089i	−0.243484	−	0.969905i	$-0.578290\pi$
$359$	8.99497	−	5.19325i	0.474737	−	0.274089i	0.718220	+	0.695816i	$0.244957\pi$
$360$	−1.44361	+	12.0979i	−0.0760851	+	0.637613i
$361$	7.10364	−	12.3039i	0.373876	−	0.647572i
$362$	11.2765	+	3.02152i	0.592677	+	0.158807i
$363$	5.09161	+	5.09161i	0.267240	+	0.267240i
$364$	2.76365	−	1.42136i	0.144855	−	0.0744994i
$365$	−20.2763	+	8.68840i	−1.06131	+	0.454772i
$366$	−2.89549	−	5.01514i	−0.151350	−	0.262146i
$367$	−2.24811	−	8.39004i	−0.117350	−	0.437957i	0.882102	−	0.471059i	$-0.156128\pi$
$367$	−2.24811	−	8.39004i	−0.117350	−	0.437957i	−0.999452	+	0.0331020i	$0.989461\pi$
$368$	−1.21791	−	4.54529i	−0.0634878	−	0.236940i
$369$	24.4654	+	42.3753i	1.27362	+	2.20597i
$370$	−0.533405	−	0.213399i	−0.0277304	−	0.0110941i
$371$	−18.6197	+	9.57617i	−0.966686	+	0.497170i
$372$	0.0853553	+	0.0853553i	0.00442546	+	0.00442546i
$373$	−12.8560	−	3.44476i	−0.665660	−	0.178363i	−0.0898611	−	0.995954i	$-0.528642\pi$
$373$	−12.8560	−	3.44476i	−0.665660	−	0.178363i	−0.575799	+	0.817591i	$0.695309\pi$
$374$	−1.44704	+	2.50635i	−0.0748247	+	0.129600i
$375$	25.0450	−	20.7084i	1.29332	−	1.06938i
$376$	5.54268	−	3.20007i	0.285842	−	0.165031i
$377$	−2.17808	+	2.17808i	−0.112177	+	0.112177i
$378$	13.9466	−	12.6535i	0.717336	−	0.650826i
$379$		−	25.3453i		−	1.30190i	−0.759121	−	0.650949i	$-0.774371\pi$
$379$		−	25.3453i		−	1.30190i	0.759121	−	0.650949i	$-0.225629\pi$
$380$	0.697798	+	4.84527i	0.0357963	+	0.248557i
$381$	47.1788	+	27.2387i	2.41704	+	1.39548i
$382$	14.9751	−	4.01258i	0.766195	−	0.205301i
$383$	4.76251	−	17.7739i	0.243353	−	0.908205i	−0.730851	−	0.682537i	$-0.760877\pi$
$383$	4.76251	−	17.7739i	0.243353	−	0.908205i	0.974204	−	0.225668i	$-0.0724565\pi$
$384$	−2.90667			−0.148330
$385$	21.4154	+	3.61749i	1.09143	+	0.184364i
$386$	−8.99792			−0.457982
$387$	−0.946464	+	3.53225i	−0.0481114	+	0.179554i
$388$	4.32611	−	1.15918i	0.219625	−	0.0588483i
$389$	−19.3621	−	11.1787i	−0.981699	−	0.566784i	−0.0789164	−	0.996881i	$-0.525146\pi$
$389$	−19.3621	−	11.1787i	−0.981699	−	0.566784i	−0.902783	+	0.430097i	$0.858479\pi$
$390$	−4.57371	+	6.11273i	−0.231599	+	0.309530i
$391$			3.70961i			0.187603i
$392$	−2.45902	+	6.55387i	−0.124199	+	0.331020i
$393$	−29.1745	+	29.1745i	−1.47166	+	1.47166i
$394$	−14.9359	+	8.62324i	−0.752459	+	0.434432i
$395$	23.5682	−	18.5432i	1.18585	−	0.933008i
$396$	10.0015	−	17.3231i	0.502594	−	0.870518i
$397$	−15.2461	−	4.08518i	−0.765181	−	0.205029i	−0.144939	−	0.989441i	$-0.546299\pi$
$397$	−15.2461	−	4.08518i	−0.765181	−	0.205029i	−0.620241	+	0.784411i	$0.712965\pi$
$398$	6.17385	+	6.17385i	0.309467	+	0.309467i
$399$	9.11594	−	14.1543i	0.456368	−	0.708603i
$400$	3.62028	+	3.44871i	0.181014	+	0.172435i
$401$	−6.98528	−	12.0989i	−0.348828	−	0.604188i	0.637213	−	0.770687i	$-0.280087\pi$
$401$	−6.98528	−	12.0989i	−0.348828	−	0.604188i	−0.986042	+	0.166499i	$0.946754\pi$
$402$	−4.98201	−	18.5931i	−0.248480	−	0.927339i
$403$	0.0126253	+	0.0471183i	0.000628911	+	0.00234713i
$404$	0.0359536	+	0.0622734i	0.00178876	+	0.00309822i
$405$	−3.60661	+	9.01496i	−0.179214	+	0.447957i
$406$	0.336879	−	6.92993i	0.0167190	−	0.343927i
$407$	0.666957	+	0.666957i	0.0330598	+	0.0330598i
$408$	2.21334	+	0.593063i	0.109577	+	0.0293610i
$409$	−0.156681	+	0.271379i	−0.00774737	+	0.0134188i	−0.869873	−	0.493276i	$-0.835799\pi$
$409$	−0.156681	+	0.271379i	−0.00774737	+	0.0134188i	0.862126	+	0.506694i	$0.169133\pi$
$410$	19.9390	+	2.37928i	0.984718	+	0.117504i
$411$	−47.7431	+	27.5645i	−2.35499	+	1.35966i
$412$	11.7237	−	11.7237i	0.577583	−	0.577583i
$413$	26.9879	+	8.65608i	1.32799	+	0.425938i
$414$		−	25.6396i		−	1.26012i
$415$	24.6370	+	18.4340i	1.20938	+	0.904891i
$416$	−1.01725	−	0.587308i	−0.0498746	−	0.0287951i
$417$	−23.1266	+	6.19675i	−1.13251	+	0.303456i
$418$	2.08012	−	7.76311i	0.101742	−	0.379706i
$419$	31.6254			1.54500			0.772501	−	0.635014i	$-0.219006\pi$
$419$	31.6254			1.54500			0.772501	+	0.635014i	$0.219006\pi$
$420$	−1.62191	−	17.1194i	−0.0791410	−	0.835342i
$421$	24.2137			1.18011			0.590053	−	0.807365i	$-0.299107\pi$
$421$	24.2137			1.18011			0.590053	+	0.807365i	$0.299107\pi$
$422$	2.89219	−	10.7938i	0.140789	−	0.525433i
$423$	33.6842	−	9.02565i	1.63778	−	0.438842i
$424$	6.85354	+	3.95689i	0.332837	+	0.192164i
$425$	−2.05308	−	3.36476i	−0.0995890	−	0.163215i
$426$		−	23.5956i		−	1.14321i
$427$	3.54190	+	3.90386i	0.171405	+	0.188921i
$428$	−3.23107	+	3.23107i	−0.156179	+	0.156179i
$429$	10.8548	−	6.26703i	0.524075	−	0.302575i
$430$	0.927958	+	1.17943i	0.0447501	+	0.0568771i
$431$	−0.779037	+	1.34933i	−0.0375249	+	0.0649950i	−0.884178	−	0.467150i	$-0.845281\pi$
$431$	−0.779037	+	1.34933i	−0.0375249	+	0.0649950i	0.846653	+	0.532145i	$0.178614\pi$
$432$	−6.87505	−	1.84216i	−0.330776	−	0.0886311i
$433$	6.28166	+	6.28166i	0.301877	+	0.301877i	0.841748	−	0.539871i	$-0.181527\pi$
$433$	6.28166	+	6.28166i	0.301877	+	0.301877i	−0.539871	+	0.841748i	$0.681527\pi$
$434$	−0.0923749	−	0.0594930i	−0.00443414	−	0.00285575i
$435$	6.71305	+	15.6663i	0.321866	+	0.751144i
$436$	9.05131	+	15.6773i	0.433479	+	0.750808i
$437$	−2.66628	−	9.95068i	−0.127545	−	0.476006i
$438$	−7.42163	−	27.6979i	−0.354619	−	1.32346i
$439$	11.9571	+	20.7103i	0.570681	+	0.988449i	0.996496	+	0.0836389i	$0.0266542\pi$
$439$	11.9571	+	20.7103i	0.570681	+	0.988449i	−0.425815	+	0.904810i	$0.640012\pi$
$440$	−3.23320	−	7.54538i	−0.154137	−	0.359712i
$441$	−22.1844	+	31.0255i	−1.05640	+	1.47741i
$442$	0.654772	+	0.654772i	0.0311443	+	0.0311443i
$443$	−12.4238	−	3.32895i	−0.590272	−	0.158163i	−0.0486946	−	0.998814i	$-0.515506\pi$
$443$	−12.4238	−	3.32895i	−0.590272	−	0.158163i	−0.541578	+	0.840651i	$0.682173\pi$
$444$	0.373402	−	0.646751i	0.0177209	−	0.0306935i
$445$	−1.97756	−	2.51346i	−0.0937451	−	0.119149i
$446$	−0.914645	+	0.528070i	−0.0433097	+	0.0250049i
$447$	−9.95157	+	9.95157i	−0.470693	+	0.470693i
$448$	2.58583	−	0.559876i	0.122169	−	0.0264517i
$449$			17.8932i			0.844435i	0.906495	+	0.422217i	$0.138748\pi$
$449$			17.8932i			0.844435i	−0.906495	+	0.422217i	$0.861252\pi$
$450$	14.1902	+	23.2561i	0.668934	+	1.09630i
$451$	−28.5510	−	16.4839i	−1.34441	−	0.776197i
$452$	−2.07723	+	0.556592i	−0.0977046	+	0.0261799i
$453$	7.55749	−	28.2049i	0.355082	−	1.32518i
$454$	3.12036			0.146446
$455$	2.89145	−	6.31900i	0.135553	−	0.296239i
$456$	−6.36335			−0.297991
$457$	8.85449	−	33.0454i	0.414196	−	1.54580i	−0.372246	−	0.928134i	$-0.621412\pi$
$457$	8.85449	−	33.0454i	0.414196	−	1.54580i	0.786442	−	0.617665i	$-0.211921\pi$
$458$	−8.13485	+	2.17973i	−0.380116	+	0.101852i
$459$	4.85928	+	2.80551i	0.226812	+	0.130950i
$460$	−8.42486	−	6.30371i	−0.392811	−	0.293912i
$461$		−	23.3471i		−	1.08738i	−0.839286	−	0.543690i	$-0.817027\pi$
$461$		−	23.3471i		−	1.08738i	0.839286	−	0.543690i	$-0.182973\pi$
$462$	−8.62252	+	26.8833i	−0.401156	+	1.25072i
$463$	3.98510	−	3.98510i	0.185203	−	0.185203i	−0.608415	−	0.793619i	$-0.708195\pi$
$463$	3.98510	−	3.98510i	0.185203	−	0.185203i	0.793619	+	0.608415i	$0.208195\pi$
$464$	−2.27103	+	1.31118i	−0.105430	+	0.0608700i
$465$	0.268016	+	0.0319818i	0.0124289	+	0.00148312i
$466$	−11.3985	+	19.7427i	−0.528023	+	0.914563i
$467$	−4.71932	−	1.26454i	−0.218384	−	0.0585159i	0.147968	−	0.988992i	$-0.452727\pi$
$467$	−4.71932	−	1.26454i	−0.218384	−	0.0585159i	−0.366352	+	0.930476i	$0.619393\pi$
$468$	−4.52558	−	4.52558i	−0.209195	−	0.209195i
$469$	8.01347	+	15.5812i	0.370028	+	0.719473i
$470$	5.31581	−	13.2872i	0.245200	−	0.612895i
$471$	−35.5873	−	61.6390i	−1.63978	−	2.84017i
$472$	−2.77255	−	10.3473i	−0.127617	−	0.476273i
$473$	−0.637693	−	2.37990i	−0.0293212	−	0.109428i
$474$	19.4910	+	33.7595i	0.895253	+	1.55062i
$475$	7.92561	+	7.55000i	0.363652	+	0.346418i
$476$	−2.08327	−	0.101272i	−0.0954867	−	0.00464182i
$477$	30.4904	+	30.4904i	1.39606	+	1.39606i
$478$	−23.1794	−	6.21090i	−1.06020	−	0.284080i
$479$	−8.55572	+	14.8189i	−0.390921	+	0.677094i	−0.992571	−	0.121665i	$-0.961177\pi$
$479$	−8.55572	+	14.8189i	−0.390921	+	0.677094i	0.601651	+	0.798759i	$0.294510\pi$
$480$	−5.10802	+	4.01892i	−0.233148	+	0.183438i
$481$	0.261359	−	0.150896i	0.0119170	−	0.00688026i
$482$	17.5274	−	17.5274i	0.798350	−	0.798350i
$483$	7.65783	+	35.3683i	0.348443	+	1.60931i
$484$			2.47728i			0.112604i
$485$	5.99972	−	8.01859i	0.272433	−	0.364105i
$486$	7.56140	+	4.36557i	0.342992	+	0.198026i
$487$	−0.125860	+	0.0337240i	−0.00570325	+	0.00152818i	−0.261670	−	0.965158i	$-0.584273\pi$
$487$	−0.125860	+	0.0337240i	−0.00570325	+	0.00152818i	0.255966	+	0.966686i	$0.417606\pi$
$488$	0.515649	−	1.92443i	0.0233423	−	0.0871147i
$489$	−63.8465			−2.88724
$490$	4.74039	+	14.9174i	0.214149	+	0.673899i
$491$	26.9895			1.21802			0.609011	−	0.793162i	$-0.291567\pi$
$491$	26.9895			1.21802			0.609011	+	0.793162i	$0.291567\pi$
$492$	−6.75585	+	25.2132i	−0.304577	+	1.13670i
$493$	1.99685	−	0.535055i	0.0899337	−	0.0240977i
$494$	−2.22698	−	1.28575i	−0.100197	−	0.0578486i
$495$	−6.37579	−	44.2713i	−0.286570	−	1.98985i
$496$			0.0415289i			0.00186470i
$497$	4.54495	+	20.9912i	0.203869	+	0.941584i
$498$	−28.2828	+	28.2828i	−1.26738	+	1.26738i
$499$	−0.0833977	+	0.0481497i	−0.00373339	+	0.00215548i	−0.501866	−	0.864946i	$-0.667353\pi$
$499$	−0.0833977	+	0.0481497i	−0.00373339	+	0.00215548i	0.498132	+	0.867101i	$0.334019\pi$
$500$	11.1305	+	1.05497i	0.497769	+	0.0471797i
$501$	6.46638	−	11.2001i	0.288897	−	0.500384i
$502$	−10.7370	−	2.87698i	−0.479217	−	0.128406i
$503$	−13.6334	−	13.6334i	−0.607883	−	0.607883i	0.334509	−	0.942392i	$-0.391429\pi$
$503$	−13.6334	−	13.6334i	−0.607883	−	0.607883i	−0.942392	+	0.334509i	$0.891429\pi$
$504$	14.3989	+	0.699963i	0.641379	+	0.0311788i
$505$	0.149286	+	0.0597245i	0.00664312	+	0.00265771i
$506$	8.63753	+	14.9606i	0.383985	+	0.665081i
$507$	8.74194	+	32.6254i	0.388243	+	1.44894i
$508$	4.85084	+	18.1036i	0.215221	+	0.803217i
$509$	−6.16366	−	10.6758i	−0.273199	−	0.473195i	0.696480	−	0.717576i	$-0.254749\pi$
$509$	−6.16366	−	10.6758i	−0.273199	−	0.473195i	−0.969679	+	0.244381i	$0.921415\pi$
$510$	4.70961	−	2.01807i	0.208545	−	0.0893618i
$511$	11.9376	+	23.2111i	0.528087	+	1.02680i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	−15.0510	−	4.03291i	−0.664520	−	0.178057i
$514$	12.6466	−	21.9046i	0.557818	−	0.966169i
$515$	4.39274	−	36.8123i	0.193567	−	1.62214i
$516$	−1.68943	+	0.975392i	−0.0743730	+	0.0429393i
$517$	−16.6140	+	16.6140i	−0.730684	+	0.730684i
$518$	−0.207611	+	0.647288i	−0.00912189	+	0.0284402i
$519$		−	15.1918i		−	0.666845i
$520$	−2.59970	+	0.374399i	−0.114004	+	0.0164185i
$521$	14.1415	+	8.16461i	0.619551	+	0.357698i	0.776694	−	0.629878i	$-0.216895\pi$
$521$	14.1415	+	8.16461i	0.619551	+	0.357698i	−0.157143	+	0.987576i	$0.550228\pi$
$522$	−13.8016	+	3.69813i	−0.604080	+	0.161863i
$523$	−7.09270	+	26.4703i	−0.310142	+	1.15747i	0.618286	+	0.785953i	$0.287827\pi$
$523$	−7.09270	+	26.4703i	−0.310142	+	1.15747i	−0.928428	+	0.371512i	$0.878839\pi$
$524$	−14.1946			−0.620095
$525$	−26.5205	−	27.8422i	−1.15745	−	1.21513i
$526$	−11.3461			−0.494714
$527$	0.00847337	−	0.0316231i	0.000369106	−	0.00137752i
$528$	10.3072	−	2.76180i	0.448563	−	0.120192i
$529$	−0.742186	−	0.428501i	−0.0322689	−	0.0186305i
$530$	17.5151	−	2.52245i	0.760805	−	0.109568i
$531$		−	58.3682i		−	2.53297i
$532$	5.66098	−	1.22570i	0.245435	−	0.0531407i
$533$	−7.45881	+	7.45881i	−0.323077	+	0.323077i
$534$	3.60031	−	2.07864i	0.155801	−	0.0899517i
$535$	−1.21065	+	10.1456i	−0.0523409	+	0.438630i
$536$	3.31118	−	5.73513i	0.143021	−	0.247720i
$537$	−35.2878	−	9.45533i	−1.52278	−	0.408028i
$538$	−5.70417	−	5.70417i	−0.245924	−	0.245924i
$539$	2.49258	−	25.5768i	0.107363	−	1.10167i
$540$	−14.6289	+	6.26850i	−0.629528	+	0.269753i
$541$	20.5773	+	35.6410i	0.884689	+	1.53233i	0.846069	+	0.533073i	$0.178963\pi$
$541$	20.5773	+	35.6410i	0.884689	+	1.53233i	0.0386200	+	0.999254i	$0.487704\pi$
$542$	2.17395	+	8.11330i	0.0933793	+	0.348496i
$543$	8.78254	+	32.7769i	0.376895	+	1.40659i
$544$	0.394167	+	0.682717i	0.0168998	+	0.0292712i
$545$	37.5826	+	15.0356i	1.60986	+	0.644056i
$546$	7.59442	+	4.89109i	0.325011	+	0.209320i
$547$	8.06541	+	8.06541i	0.344852	+	0.344852i	0.858188	−	0.513336i	$-0.171590\pi$
$547$	8.06541	+	8.06541i	0.344852	+	0.344852i	−0.513336	+	0.858188i	$0.671590\pi$
$548$	−18.3201	−	4.90887i	−0.782597	−	0.209696i
$549$	5.42777	−	9.40117i	0.231651	−	0.401232i
$550$	−16.1145	−	8.78944i	−0.687126	−	0.374783i
$551$	−4.97180	+	2.87047i	−0.211806	+	0.122286i
$552$	9.67160	−	9.67160i	0.411651	−	0.411651i
$553$	−23.8423	−	26.2788i	−1.01388	−	1.11749i
$554$		−	5.68000i		−	0.241320i
$555$	−0.238038	−	1.65285i	−0.0101041	−	0.0701597i
$556$	−7.13350	−	4.11853i	−0.302528	−	0.174665i
$557$	24.7826	−	6.64049i	1.05007	−	0.281367i	0.307792	−	0.951454i	$-0.400410\pi$
$557$	24.7826	−	6.64049i	1.05007	−	0.281367i	0.742282	+	0.670087i	$0.233743\pi$
$558$	−0.0585652	+	0.218568i	−0.00247926	+	0.00925274i
$559$	−0.788333			−0.0333429
$560$	3.77009	−	4.55921i	0.159315	−	0.192662i
$561$	−8.41213			−0.355160
$562$	−1.88324	+	7.02834i	−0.0794396	+	0.296473i
$563$	−12.3749	+	3.31584i	−0.521539	+	0.139746i	−0.509978	−	0.860187i	$-0.670347\pi$
$563$	−12.3749	+	3.31584i	−0.521539	+	0.139746i	−0.0115606	+	0.999933i	$0.503680\pi$
$564$	16.1107	+	9.30152i	0.678383	+	0.391665i
$565$	−2.88083	+	3.85022i	−0.121198	+	0.161980i
$566$		−	7.71000i		−	0.324076i
$567$	10.9397	+	3.50878i	0.459423	+	0.147355i
$568$	5.74013	−	5.74013i	0.240850	−	0.240850i
$569$	−29.8291	+	17.2218i	−1.25050	+	0.721977i	−0.971209	−	0.238229i	$-0.923433\pi$
$569$	−29.8291	+	17.2218i	−1.25050	+	0.721977i	−0.279292	+	0.960206i	$0.590100\pi$
$570$	−11.1826	+	8.79832i	−0.468388	+	0.368521i
$571$	4.11985	−	7.13579i	0.172410	−	0.298623i	−0.766852	−	0.641824i	$-0.778178\pi$
$571$	4.11985	−	7.13579i	0.172410	−	0.298623i	0.939262	+	0.343201i	$0.111511\pi$
$572$	4.16524	+	1.11607i	0.174158	+	0.0466654i
$573$	31.8645	+	31.8645i	1.33116	+	1.33116i
$574$	1.15364	−	23.7315i	0.0481520	−	0.990534i
$575$	−23.5212	+	0.570889i	−0.980904	+	0.0238077i
$576$	−2.72435	−	4.71872i	−0.113515	−	0.196613i
$577$	−0.910086	−	3.39649i	−0.0378874	−	0.141398i	0.944391	−	0.328824i	$-0.106652\pi$
$577$	−0.910086	−	3.39649i	−0.0378874	−	0.141398i	−0.982279	+	0.187426i	$0.939985\pi$
$578$	4.23908	+	15.8204i	0.176322	+	0.658044i
$579$	−13.0770	−	22.6500i	−0.543460	−	0.941301i
$580$	−2.17808	+	5.44425i	−0.0904397	+	0.226060i
$581$	19.7132	−	30.6088i	0.817843	−	1.26987i
$582$	9.20520	+	9.20520i	0.381568	+	0.381568i
$583$	−28.0627	−	7.51937i	−1.16224	−	0.311421i
$584$	4.93262	−	8.54355i	0.204113	−	0.353535i
$585$	−14.2103	−	1.69569i	−0.587524	−	0.0701081i
$586$	−4.10531	+	2.37020i	−0.169589	+	0.0979122i
$587$	−5.37485	+	5.37485i	−0.221844	+	0.221844i	−0.809275	−	0.587431i	$-0.800139\pi$
$587$	−5.37485	+	5.37485i	−0.221844	+	0.221844i	0.587431	+	0.809275i	$0.300139\pi$
$588$	−20.0715	+	3.33499i	−0.827734	+	0.137533i
$589$			0.0909162i			0.00374613i
$590$	−19.1791	−	14.3503i	−0.789590	−	0.590792i
$591$	−43.4136	−	25.0649i	−1.78580	−	1.03103i
$592$	0.248174	−	0.0664979i	0.0101999	−	0.00273305i
$593$	0.190155	−	0.709668i	0.00780872	−	0.0291426i	−0.961912	−	0.273361i	$-0.911865\pi$
$593$	0.190155	−	0.709668i	0.00780872	−	0.0291426i	0.969720	+	0.244218i	$0.0785314\pi$
$594$	26.1296			1.07211
$595$	−3.80106	+	2.70248i	−0.155828	+	0.110791i
$596$	−4.84185			−0.198330
$597$	−6.56845	+	24.5138i	−0.268829	+	1.00328i
$598$	5.33897	−	1.43057i	0.218327	−	0.0585005i
$599$	7.23778	+	4.17873i	0.295727	+	0.170738i	0.640522	−	0.767940i	$-0.278718\pi$
$599$	7.23778	+	4.17873i	0.295727	+	0.170738i	−0.344794	+	0.938678i	$0.612051\pi$
$600$	−3.41977	+	14.1253i	−0.139612	+	0.576661i
$601$			39.9236i			1.62852i	0.580501	+	0.814259i	$0.302857\pi$
$601$			39.9236i			1.62852i	−0.580501	+	0.814259i	$0.697143\pi$
$602$	1.31508	−	1.19315i	0.0535985	−	0.0486290i
$603$	25.5147	−	25.5147i	1.03904	−	1.03904i
$604$	8.69995	−	5.02292i	0.353996	−	0.204380i
$605$	3.42523	+	4.35344i	0.139255	+	0.176993i
$606$	−0.104505	+	0.181008i	−0.00424523	+	0.00735295i
$607$	33.2758	+	8.91623i	1.35062	+	0.361899i	0.860365	−	0.509678i	$-0.170235\pi$
$607$	33.2758	+	8.91623i	1.35062	+	0.361899i	0.490259	+	0.871577i	$0.336902\pi$
$608$	−1.54802	−	1.54802i	−0.0627804	−	0.0627804i
$609$	17.9339	−	9.22349i	0.726720	−	0.373755i
$610$	−1.75465	−	4.09485i	−0.0710436	−	0.165796i
$611$	3.75885	+	6.51051i	0.152067	+	0.263387i
$612$	1.11173	+	4.14903i	0.0449390	+	0.167715i
$613$	−8.46832	−	31.6042i	−0.342032	−	1.27648i	−0.896041	−	0.443971i	$-0.853569\pi$
$613$	−8.46832	−	31.6042i	−0.342032	−	1.27648i	0.554009	−	0.832510i	$-0.313097\pi$
$614$	−0.753393	−	1.30491i	−0.0304044	−	0.0526620i
$615$	22.9888	+	53.6493i	0.926997	+	2.16335i
$616$	−8.63753	+	4.44231i	−0.348016	+	0.178986i
$617$	−15.5005	−	15.5005i	−0.624025	−	0.624025i	0.322533	−	0.946558i	$-0.395466\pi$
$617$	−15.5005	−	15.5005i	−0.624025	−	0.624025i	−0.946558	+	0.322533i	$0.895466\pi$
$618$	46.5497	+	12.4730i	1.87250	+	0.501736i
$619$	4.31138	−	7.46752i	0.173289	−	0.300145i	−0.766279	−	0.642508i	$-0.777894\pi$
$619$	4.31138	−	7.46752i	0.173289	−	0.300145i	0.939568	+	0.342363i	$0.111227\pi$
$620$	0.0574201	+	0.0729806i	0.00230605	+	0.00293097i
$621$	29.0055	−	16.7463i	1.16395	−	0.672008i
$622$	−9.76397	+	9.76397i	−0.391500	+	0.391500i
$623$	−2.80254	+	2.54269i	−0.112281	+	0.101871i
$624$		−	3.41421i		−	0.136678i
$625$	21.0187	−	13.5356i	0.840749	−	0.541425i
$626$	20.2191	+	11.6735i	0.808119	+	0.466568i
$627$	22.5648	−	6.04621i	0.901150	−	0.241462i
$628$	6.33762	−	23.6523i	0.252898	−	0.943830i
$629$	−0.202545			−0.00807600
$630$	26.2717	−	18.6787i	1.04669	−	0.744176i
$631$	−4.13675			−0.164682			−0.0823408	−	0.996604i	$-0.526240\pi$
$631$	−4.13675			−0.164682			−0.0823408	+	0.996604i	$0.526240\pi$
$632$	−3.47109	+	12.9543i	−0.138073	+	0.515294i
$633$	31.3739	−	8.40662i	1.24700	−	0.334133i
$634$	11.4219	+	6.59442i	0.453620	+	0.261898i
$635$	33.5556	+	25.1072i	1.33161	+	0.996349i
$636$			23.0027i			0.912117i
$637$	−7.69827	−	2.88840i	−0.305017	−	0.114443i
$638$	6.80736	−	6.80736i	0.269506	−	0.269506i
$639$	38.3055	−	22.1157i	1.51534	−	0.874882i
$640$	−2.22032	−	0.264946i	−0.0877657	−	0.0104729i
$641$	−5.42807	+	9.40169i	−0.214396	+	0.371345i	−0.953086	−	0.302701i	$-0.902112\pi$
$641$	−5.42807	+	9.40169i	−0.214396	+	0.371345i	0.738690	+	0.674046i	$0.235445\pi$
$642$	−12.8292	−	3.43757i	−0.506328	−	0.135670i
$643$	−8.06230	−	8.06230i	−0.317946	−	0.317946i	0.530032	−	0.847978i	$-0.322180\pi$
$643$	−8.06230	−	8.06230i	−0.317946	−	0.317946i	−0.847978	+	0.530032i	$0.822180\pi$
$644$	−6.74114	+	10.4670i	−0.265638	+	0.412457i
$645$	−1.62028	+	4.05000i	−0.0637984	+	0.159469i
$646$	0.862920	+	1.49462i	0.0339511	+	0.0588051i
$647$	−2.69865	−	10.0715i	−0.106095	−	0.395951i	0.892372	−	0.451300i	$-0.149040\pi$
$647$	−2.69865	−	10.0715i	−0.106095	−	0.395951i	−0.998467	+	0.0553490i	$0.982373\pi$
$648$	−1.12387	−	4.19432i	−0.0441496	−	0.164769i
$649$	19.6632	+	34.0577i	0.771848	+	1.33688i
$650$	−4.05090	+	4.25243i	−0.158889	+	0.166794i
$651$	0.0155070	−	0.318994i	0.000607766	−	0.0125023i
$652$	−15.5320	−	15.5320i	−0.608279	−	0.608279i
$653$	6.41946	+	1.72009i	0.251213	+	0.0673123i	0.382228	−	0.924068i	$-0.375157\pi$
$653$	6.41946	+	1.72009i	0.251213	+	0.0673123i	−0.131015	+	0.991380i	$0.541824\pi$
$654$	−26.3091	+	45.5687i	−1.02877	+	1.78188i
$655$	−24.9449	+	19.6263i	−0.974677	+	0.766862i
$656$	−7.77713	+	4.49013i	−0.303646	+	0.175310i
$657$	38.0090	−	38.0090i	1.48287	−	1.48287i
$658$	−16.1241	−	5.17163i	−0.628582	−	0.201611i
$659$		−	22.0345i		−	0.858343i	−0.903223	−	0.429172i	$-0.858806\pi$
$659$		−	22.0345i		−	0.858343i	0.903223	−	0.429172i	$-0.141194\pi$
$660$	14.2947	−	19.1047i	0.556419	−	0.743650i
$661$	−9.94278	−	5.74047i	−0.386729	−	0.223278i	0.294013	−	0.955802i	$-0.405009\pi$
$661$	−9.94278	−	5.74047i	−0.386729	−	0.223278i	−0.680742	+	0.732523i	$0.738343\pi$
$662$	−18.4453	+	4.94240i	−0.716897	+	0.192092i
$663$	−0.696621	+	2.59983i	−0.0270545	+	0.100969i
$664$	−13.7608			−0.534021
$665$	8.25358	−	9.98115i	0.320060	−	0.387053i
$666$	1.39993			0.0542460
$667$	3.19379	−	11.9194i	0.123664	−	0.461521i
$668$	4.29774	−	1.15158i	0.166285	−	0.0445558i
$669$	−2.65857	−	1.53492i	−0.102786	−	0.0593436i
$670$	−2.11082	−	14.6568i	−0.0815482	−	0.566243i
$671$			7.31407i			0.282356i
$672$	5.16742	+	5.69550i	0.199338	+	0.219708i
$673$	−15.2073	+	15.2073i	−0.586198	+	0.586198i	−0.936600	−	0.350402i	$-0.886045\pi$
$673$	−15.2073	+	15.2073i	−0.586198	+	0.586198i	0.350402	+	0.936600i	$0.386045\pi$
$674$	−0.597952	+	0.345228i	−0.0230322	+	0.0132977i
$675$	−17.0409	+	31.2427i	−0.655903	+	1.20253i
$676$	−5.81014	+	10.0635i	−0.223467	+	0.387056i
$677$	−5.54296	−	1.48523i	−0.213033	−	0.0570821i	0.150724	−	0.988576i	$-0.451840\pi$
$677$	−5.54296	−	1.48523i	−0.213033	−	0.0570821i	−0.363757	+	0.931494i	$0.618506\pi$
$678$	−4.41998	−	4.41998i	−0.169748	−	0.169748i
$679$	−9.96224	−	6.41606i	−0.382316	−	0.246226i
$680$	1.63665	+	0.654772i	0.0627626	+	0.0251094i
$681$	4.53492	+	7.85472i	0.173779	+	0.300993i
$682$	−0.0394591	−	0.147264i	−0.00151097	−	0.00563901i
$683$	5.02900	+	18.7685i	0.192430	+	0.718157i	0.992917	+	0.118808i	$0.0379072\pi$
$683$	5.02900	+	18.7685i	0.192430	+	0.718157i	−0.800488	+	0.599349i	$0.795426\pi$
$684$	−5.96423	−	10.3303i	−0.228048	−	0.394991i
$685$	−38.9821	+	16.7039i	−1.48943	+	0.638222i
$686$	17.2137	−	6.83301i	0.657220	−	0.260886i
$687$	−17.3095	−	17.3095i	−0.660400	−	0.660400i
$688$	−0.648273	−	0.173704i	−0.0247152	−	0.00662241i
$689$	−4.64782	+	8.05027i	−0.177068	+	0.306691i
$690$	3.62385	−	30.3688i	0.137958	−	1.15612i
$691$	19.0914	−	11.0224i	0.726270	−	0.419312i	−0.0907861	−	0.995870i	$-0.528938\pi$
$691$	19.0914	−	11.0224i	0.726270	−	0.419312i	0.817056	+	0.576558i	$0.195605\pi$
$692$	3.69572	−	3.69572i	0.140490	−	0.140490i
$693$	−51.7244	+	11.1992i	−1.96485	+	0.425422i
$694$		−	3.80998i		−	0.144625i
$695$	−18.2305	+	2.62550i	−0.691524	+	0.0995908i
$696$	−6.60113	−	3.81116i	−0.250215	−	0.144462i
$697$	6.83821	−	1.83229i	0.259016	−	0.0694031i
$698$	2.04804	−	7.64340i	0.0775196	−	0.289307i
$699$	−66.2630			−2.50630
$700$	0.321526	−	13.2248i	0.0121526	−	0.499852i
$701$	−18.0270			−0.680870			−0.340435	−	0.940268i	$-0.610574\pi$
$701$	−18.0270			−0.680870			−0.340435	+	0.940268i	$0.610574\pi$
$702$	2.16383	−	8.07553i	0.0816686	−	0.304791i
$703$	0.543308	−	0.145579i	0.0204913	−	0.00549062i
$704$	3.17930	+	1.83557i	0.119824	+	0.0691807i
$705$	41.1729	−	5.92957i	1.55066	−	0.223321i
$706$		−	25.7787i		−	0.970196i
$707$	0.0581046	−	0.181158i	0.00218525	−	0.00681316i
$708$	22.0173	−	22.0173i	0.827459	−	0.827459i
$709$	−37.0614	+	21.3974i	−1.39187	+	0.803597i	−0.993522	−	0.113637i	$-0.963750\pi$
$709$	−37.0614	+	21.3974i	−1.39187	+	0.803597i	−0.398349	+	0.917234i	$0.630417\pi$
$710$	2.15077	−	18.0240i	0.0807170	−	0.676429i
$711$	−36.5370	+	63.2840i	−1.37025	+	2.37334i
$712$	1.38152	+	0.370178i	0.0517748	+	0.0138730i
$713$	−0.138183	−	0.138183i	−0.00517498	−	0.00517498i
$714$	−2.77276	−	5.39130i	−0.103768	−	0.201764i
$715$	8.86292	−	3.79777i	0.331454	−	0.142029i
$716$	−6.28428	−	10.8847i	−0.234854	−	0.406780i
$717$	−18.0530	−	67.3747i	−0.674202	−	2.51615i
$718$	2.68822	+	10.0326i	0.100324	+	0.374413i
$719$	−2.72691	−	4.72315i	−0.101697	−	0.176144i	0.810687	−	0.585480i	$-0.199094\pi$
$719$	−2.72691	−	4.72315i	−0.101697	−	0.176144i	−0.912384	+	0.409336i	$0.865760\pi$
$720$	−11.3120	−	4.52558i	−0.421573	−	0.168658i
$721$	−43.8142	−	2.12990i	−1.63172	−	0.0793217i
$722$	10.0461	+	10.0461i	0.373876	+	0.373876i
$723$	69.5938	+	18.6476i	2.58822	+	0.693512i
$724$	−5.83712	+	10.1102i	−0.216935	+	0.375742i
$725$	3.69989	+	12.5790i	0.137411	+	0.467171i
$726$	−6.23593	+	3.60031i	−0.231437	+	0.133620i
$727$	16.6781	−	16.6781i	0.618555	−	0.618555i	−0.326606	−	0.945161i	$-0.605905\pi$
$727$	16.6781	−	16.6781i	0.618555	−	0.618555i	0.945161	+	0.326606i	$0.105905\pi$
$728$	0.657639	+	3.03736i	0.0243737	+	0.112572i
$729$			38.4054i			1.42242i
$730$	−3.14447	−	21.8341i	−0.116382	−	0.808116i
$731$	0.458200	+	0.264542i	0.0169471	+	0.00978443i
$732$	5.59367	−	1.49882i	0.206748	−	0.0553979i
$733$	−8.79960	+	32.8405i	−0.325021	+	1.21299i	0.589271	+	0.807936i	$0.299415\pi$
$733$	−8.79960	+	32.8405i	−0.325021	+	1.21299i	−0.914291	+	0.405057i	$0.867252\pi$
$734$	8.68601			0.320607
$735$	−30.6614	+	33.6127i	−1.13096	+	1.23982i
$736$	4.70563			0.173452
$737$	−6.29231	+	23.4832i	−0.231780	+	0.865016i
$738$	−47.2635	+	12.6642i	−1.73979	+	0.466177i
$739$	25.0733	+	14.4761i	0.922335	+	0.532510i	0.884379	−	0.466769i	$-0.154582\pi$
$739$	25.0733	+	14.4761i	0.922335	+	0.532510i	0.0379557	+	0.999279i	$0.487915\pi$
$740$	0.344183	−	0.459998i	0.0126524	−	0.0169099i
$741$		−	7.47449i		−	0.274582i
$742$	−4.43074	−	20.4637i	−0.162658	−	0.751247i
$743$	34.0351	−	34.0351i	1.24863	−	1.24863i	0.292300	−	0.956327i	$-0.405579\pi$
$743$	34.0351	−	34.0351i	1.24863	−	1.24863i	0.956327	−	0.292300i	$-0.0944206\pi$
$744$	−0.104538	+	0.0603553i	−0.00383257	+	0.00221273i
$745$	−8.50881	+	6.69461i	−0.311739	+	0.245272i
$746$	6.65477	−	11.5264i	0.243649	−	0.422012i
$747$	−72.4235	−	19.4058i	−2.64984	−	0.710022i
$748$	−2.04643	−	2.04643i	−0.0748247	−	0.0748247i
$749$	12.0753	+	0.587006i	0.441221	+	0.0214487i
$750$	13.5206	+	29.5513i	0.493704	+	1.07906i
$751$	9.30569	+	16.1179i	0.339569	+	0.588151i	0.984352	−	0.176215i	$-0.0563853\pi$
$751$	9.30569	+	16.1179i	0.339569	+	0.588151i	−0.644782	+	0.764366i	$0.723052\pi$
$752$	1.65648	+	6.18205i	0.0604055	+	0.225436i
$753$	−8.36242	−	31.2090i	−0.304743	−	1.13732i
$754$	−1.54013	−	2.66759i	−0.0560883	−	0.0971478i
$755$	8.34385	−	20.8560i	0.303664	−	0.759029i
$756$	8.61270	+	16.7463i	0.313241	+	0.609059i
$757$	29.7422	+	29.7422i	1.08100	+	1.08100i	0.996416	+	0.0845825i	$0.0269557\pi$
$757$	29.7422	+	29.7422i	1.08100	+	1.08100i	0.0845825	+	0.996416i	$0.473044\pi$
$758$	24.4816	+	6.55984i	0.889213	+	0.238264i
$759$	−25.1064	+	43.4856i	−0.911305	+	1.57843i
$760$	−4.86078	−	0.580027i	−0.176319	−	0.0210398i
$761$	17.6474	−	10.1887i	0.639718	−	0.369341i	−0.144788	−	0.989463i	$-0.546250\pi$
$761$	17.6474	−	10.1887i	0.639718	−	0.369341i	0.784506	+	0.620122i	$0.212917\pi$
$762$	−38.5213	+	38.5213i	−1.39548	+	1.39548i
$763$	14.6278	−	45.6066i	0.529563	−	1.65107i
$764$			15.5034i			0.560894i
$765$	7.69038	+	5.75415i	0.278046	+	0.208042i
$766$	15.9357	+	9.20046i	0.575779	+	0.332426i
$767$	12.1541	−	3.25668i	0.438859	−	0.117592i
$768$	0.752300	−	2.80762i	0.0271463	−	0.101311i
$769$	40.9728			1.47752			0.738759	−	0.673970i	$-0.235412\pi$
$769$	40.9728			1.47752			0.738759	+	0.673970i	$0.235412\pi$
$770$	−9.03694	+	19.7494i	−0.325669	+	0.711719i
$771$	73.5189			2.64772
$772$	2.32883	−	8.69132i	0.0838165	−	0.312808i
$773$	23.8577	−	6.39265i	0.858101	−	0.229928i	0.197166	−	0.980370i	$-0.436826\pi$
$773$	23.8577	−	6.39265i	0.858101	−	0.229928i	0.660936	+	0.750443i	$0.270160\pi$
$774$	−3.16693	−	1.82843i	−0.113833	−	0.0657215i
$775$	0.201814	+	0.0488599i	0.00724938	+	0.00175510i
$776$			4.47871i			0.160776i
$777$	−1.93111	+	0.418118i	−0.0692783	+	0.0149999i
$778$	15.8091	−	15.8091i	0.566784	−	0.566784i
$779$	−17.0259	+	9.82991i	−0.610017	+	0.352193i
$780$	−4.72068	−	5.99995i	−0.169027	−	0.214833i
$781$	−14.9007	+	25.8088i	−0.533190	+	0.923513i
$782$	−3.58321	−	0.960117i	−0.128135	−	0.0343337i
$783$	−13.1980	−	13.1980i	−0.471659	−	0.471659i
$784$	−5.69411	−	4.07150i	−0.203361	−	0.145411i
$785$	−21.5656	−	50.3280i	−0.769710	−	1.79628i
$786$	−20.6295	−	35.7314i	−0.735831	−	1.27450i
$787$	2.12442	+	7.92843i	0.0757273	+	0.282618i	0.993397	−	0.114725i	$-0.0365988\pi$
$787$	2.12442	+	7.92843i	0.0757273	+	0.282618i	−0.917670	+	0.397343i	$0.869932\pi$
$788$	−4.46372	−	16.6588i	−0.159013	−	0.593446i
$789$	−16.4897	−	28.5610i	−0.587048	−	1.01680i
$790$	11.8114	+	27.5645i	0.420231	+	0.980701i
$791$	4.78348	+	3.08075i	0.170081	+	0.109539i
$792$	14.1442	+	14.1442i	0.502594	+	0.502594i
$793$	2.26046	+	0.605689i	0.0802713	+	0.0215086i
$794$	7.89197	−	13.6693i	0.280076	−	0.485105i
$795$	31.8048	+	40.4237i	1.12800	+	1.43368i
$796$	−7.56140	+	4.36557i	−0.268007	+	0.154734i
$797$	11.7928	−	11.7928i	0.417722	−	0.417722i	−0.466696	−	0.884418i	$-0.654556\pi$
$797$	11.7928	−	11.7928i	0.417722	−	0.417722i	0.884418	+	0.466696i	$0.154556\pi$
$798$	11.3127	+	12.4687i	0.400464	+	0.441388i
$799$		−	5.04544i		−	0.178495i
$800$	−4.26819	+	2.60433i	−0.150903	+	0.0920770i
$801$	6.74899	+	3.89653i	0.238464	+	0.137677i
$802$	13.4945	−	3.61585i	0.476508	−	0.127680i
$803$	−9.37358	+	34.9827i	−0.330786	+	1.23451i
$804$	19.2490			0.678860
$805$	2.62573	+	27.7148i	0.0925447	+	0.976819i
$806$	−0.0487805			−0.00171822
$807$	6.06875	−	22.6489i	0.213630	−	0.797278i
$808$	−0.0694570	+	0.0186109i	−0.00244349	+	0.000654730i
$809$	−28.8498	−	16.6564i	−1.01430	−	0.585609i	−0.101855	−	0.994799i	$-0.532478\pi$
$809$	−28.8498	−	16.6564i	−1.01430	−	0.585609i	−0.912449	+	0.409191i	$0.865811\pi$
$810$	−7.77433	−	5.81696i	−0.273162	−	0.204387i
$811$		−	55.2368i		−	1.93963i	−0.243850	−	0.969813i	$-0.578410\pi$
$811$		−	55.2368i		−	1.93963i	0.243850	−	0.969813i	$-0.421590\pi$
$812$	6.60661	+	2.11900i	0.231847	+	0.0743623i
$813$	−17.2637	+	17.2637i	−0.605465	+	0.605465i
$814$	−0.816852	+	0.471610i	−0.0286307	+	0.0165299i
$815$	−48.7704	−	5.81968i	−1.70835	−	0.203855i
$816$	−1.14571	+	1.98443i	−0.0401079	+	0.0694689i
$817$	−1.41922	−	0.380278i	−0.0496521	−	0.0133042i
$818$	−0.221580	−	0.221580i	−0.00774737	−	0.00774737i
$819$	−0.822187	+	16.9132i	−0.0287295	+	0.590995i
$820$	−7.45881	+	18.6438i	−0.260473	+	0.651070i
$821$	−9.31457	−	16.1333i	−0.325081	−	0.563056i	0.656448	−	0.754371i	$-0.272058\pi$
$821$	−9.31457	−	16.1333i	−0.325081	−	0.563056i	−0.981529	+	0.191315i	$0.938725\pi$
$822$	−14.2684	−	53.2505i	−0.497669	−	1.85732i
$823$	−4.37130	−	16.3139i	−0.152374	−	0.568668i	−0.999316	−	0.0369821i	$-0.988226\pi$
$823$	−4.37130	−	16.3139i	−0.152374	−	0.568668i	0.846942	−	0.531685i	$-0.178441\pi$
$824$	8.28988	+	14.3585i	0.288792	+	0.500202i
$825$	−1.29458	−	53.3382i	−0.0450716	−	1.85700i
$826$	−15.3461	+	23.8280i	−0.533960	+	0.829081i
$827$	−5.62716	−	5.62716i	−0.195675	−	0.195675i	0.602468	−	0.798143i	$-0.294184\pi$
$827$	−5.62716	−	5.62716i	−0.195675	−	0.195675i	−0.798143	+	0.602468i	$0.794184\pi$
$828$	24.7660	+	6.63602i	0.860677	+	0.230618i
$829$	3.29757	−	5.71155i	0.114529	−	0.198370i	−0.803062	−	0.595895i	$-0.796797\pi$
$829$	3.29757	−	5.71155i	0.114529	−	0.198370i	0.917591	+	0.397525i	$0.130131\pi$
$830$	−24.1824	+	19.0264i	−0.839384	+	0.660416i
$831$	14.2980	−	8.25494i	0.495991	−	0.286361i
$832$	0.830578	−	0.830578i	0.0287951	−	0.0287951i
$833$	3.50517	+	4.26213i	0.121447	+	0.147674i
$834$		−	23.9424i		−	0.829057i
$835$	5.96038	−	7.96601i	0.206268	−	0.275675i
$836$	6.96021	+	4.01848i	0.240724	+	0.138982i
$837$	−0.285513	+	0.0765030i	−0.00986877	+	0.00264433i
$838$	−8.18525	+	30.5478i	−0.282755	+	1.05526i
$839$	46.0930			1.59131			0.795654	−	0.605752i	$-0.207128\pi$
$839$	46.0930			1.59131			0.795654	+	0.605752i	$0.207128\pi$
$840$	16.9559	+	2.86419i	0.585033	+	0.0988238i
$841$	22.1232			0.762870
$842$	−6.26698	+	23.3887i	−0.215974	+	0.806027i
$843$	−20.4290	+	5.47394i	−0.703613	+	0.188533i
$844$	9.67744	+	5.58727i	0.333111	+	0.192322i
$845$	3.70387	+	25.7184i	0.127417	+	0.884740i
$846$			34.8724i			1.19894i
$847$	4.85413	−	4.40407i	0.166790	−	0.151326i
$848$	−5.59589	+	5.59589i	−0.192164	+	0.192164i
$849$	19.4080	−	11.2052i	0.666080	−	0.384562i
$850$	3.78148	−	1.11226i	0.129704	−	0.0381502i
$851$	−0.604505	+	1.04703i	−0.0207222	+	0.0358918i
$852$	22.7916	+	6.10700i	0.780828	+	0.209222i
$853$	14.9594	+	14.9594i	0.512200	+	0.512200i	0.915200	−	0.403000i	$-0.132032\pi$
$853$	14.9594	+	14.9594i	0.512200	+	0.512200i	−0.403000	+	0.915200i	$0.632032\pi$
$854$	−4.68755	+	2.41082i	−0.160405	+	0.0824967i
$855$	−24.7645	−	9.90752i	−0.846929	−	0.338830i
$856$	−2.28471	−	3.95723i	−0.0780897	−	0.135255i
$857$	3.12136	+	11.6491i	0.106623	+	0.397924i	0.998524	−	0.0543068i	$-0.0172949\pi$
$857$	3.12136	+	11.6491i	0.106623	+	0.397924i	−0.891901	+	0.452231i	$0.850628\pi$
$858$	3.24405	+	12.1070i	0.110750	+	0.413325i
$859$	−2.90061	−	5.02401i	−0.0989677	−	0.171417i	0.812290	−	0.583254i	$-0.198221\pi$
$859$	−2.90061	−	5.02401i	−0.0989677	−	0.171417i	−0.911258	+	0.411837i	$0.864887\pi$
$860$	−1.37941	+	0.591080i	−0.0470376	+	0.0201557i
$861$	61.4147	−	31.5858i	2.09301	−	1.07644i
$862$	−1.10172	−	1.10172i	−0.0375249	−	0.0375249i
$863$	2.90586	+	0.778623i	0.0989167	+	0.0265046i	0.307938	−	0.951406i	$-0.400361\pi$
$863$	2.90586	+	0.778623i	0.0989167	+	0.0265046i	−0.209021	+	0.977911i	$0.567028\pi$
$864$	3.55879	−	6.16400i	0.121072	−	0.209703i
$865$	1.38475	−	11.6046i	0.0470829	−	0.394567i
$866$	−7.69343	+	4.44180i	−0.261433	+	0.150939i
$867$	−33.6632	+	33.6632i	−1.14326	+	1.14326i
$868$	0.0813742	−	0.0738294i	0.00276202	−	0.00250593i
$869$		−	49.2347i		−	1.67017i
$870$	−16.8700	+	2.42956i	−0.571946	+	0.0823696i
$871$	6.73657	+	3.88936i	0.228260	+	0.131786i
$872$	−17.4858	+	4.68530i	−0.592143	+	0.158664i
$873$	−6.31601	+	23.5717i	−0.213765	+	0.797780i
$874$	10.3017			0.348460
$875$	−17.7204	−	23.6852i	−0.599058	−	0.800706i
$876$	28.6750			0.968838
$877$	9.07228	−	33.8582i	0.306349	−	1.14331i	−0.625428	−	0.780282i	$-0.715076\pi$
$877$	9.07228	−	33.8582i	0.306349	−	1.14331i	0.931778	−	0.363030i	$-0.118258\pi$
$878$	−23.0994	+	6.18945i	−0.779565	+	0.208884i
$879$	−11.9328	−	6.88939i	−0.402483	−	0.232373i
$880$	8.12509	−	1.17015i	0.273897	−	0.0394456i
$881$			23.7116i			0.798864i	0.916763	+	0.399432i	$0.130793\pi$
$881$			23.7116i			0.798864i	−0.916763	+	0.399432i	$0.869207\pi$
$882$	−24.2266	−	29.4585i	−0.815753	−	0.991919i
$883$	−7.95370	+	7.95370i	−0.267663	+	0.267663i	−0.828158	−	0.560495i	$-0.810611\pi$
$883$	−7.95370	+	7.95370i	−0.267663	+	0.267663i	0.560495	+	0.828158i	$0.310611\pi$
$884$	−0.801929	+	0.462994i	−0.0269718	+	0.0155722i
$885$	8.24965	−	69.1342i	0.277309	−	2.32392i
$886$	6.43103	−	11.1389i	0.216055	−	0.374218i
$887$	−19.6954	−	5.27738i	−0.661308	−	0.177197i	−0.0874718	−	0.996167i	$-0.527879\pi$
$887$	−19.6954	−	5.27738i	−0.661308	−	0.177197i	−0.573836	+	0.818970i	$0.694545\pi$
$888$	0.528070	+	0.528070i	0.0177209	+	0.0177209i
$889$	26.8495	−	41.6893i	0.900503	−	1.39821i
$890$	2.93964	−	1.25964i	0.0985371	−	0.0422233i
$891$	7.97057	+	13.8054i	0.267024	+	0.462499i
$892$	−0.273349	−	1.02015i	−0.00915241	−	0.0341573i
$893$	3.62640	+	13.5339i	0.121353	+	0.452895i
$894$	−7.03682	−	12.1881i	−0.235347	−	0.407632i
$895$	−26.0934	−	10.4392i	−0.872207	−	0.348943i
$896$	−0.128464	+	2.64263i	−0.00429168	+	0.0882841i
$897$	11.3604	+	11.3604i	0.379313	+	0.379313i
$898$	−17.2836	−	4.63111i	−0.576760	−	0.154542i
$899$	−0.0544519	+	0.0943134i	−0.00181607	+	0.00314553i
$900$	−26.1364	+	7.68758i	−0.871213	+	0.256253i
$901$	5.40287	−	3.11935i	0.179996	−	0.103921i
$902$	23.3118	−	23.3118i	0.776197	−	0.776197i
$903$	4.91468	+	1.57633i	0.163550	+	0.0524570i
$904$		−	2.15051i		−	0.0715247i
$905$	3.72107	+	25.8378i	0.123693	+	0.858879i
$906$	25.2878	+	14.5999i	0.840132	+	0.485051i
$907$	6.29276	−	1.68614i	0.208948	−	0.0559874i	−0.152827	−	0.988253i	$-0.548838\pi$
$907$	6.29276	−	1.68614i	0.208948	−	0.0559874i	0.361775	+	0.932266i	$0.382171\pi$
$908$	−0.807609	+	3.01404i	−0.0268014	+	0.100024i
$909$	−0.391801			−0.0129952
$910$	5.35532	+	4.42840i	0.177527	+	0.146800i
$911$	−24.2528			−0.803531			−0.401765	−	0.915743i	$-0.631603\pi$
$911$	−24.2528			−0.803531			−0.401765	+	0.915743i	$0.631603\pi$
$912$	1.64696	−	6.14653i	0.0545362	−	0.203532i
$913$	48.7964	−	13.0749i	1.61492	−	0.432718i
$914$	29.6277	+	17.1056i	0.979997	+	0.565802i
$915$	7.75766	−	10.3681i	0.256460	−	0.342757i
$916$		−	8.42181i		−	0.278264i
$917$	25.2350	+	27.8138i	0.833333	+	0.918493i
$918$	−3.96759	+	3.96759i	−0.130950	+	0.130950i
$919$	−31.2542	+	18.0446i	−1.03098	+	0.595236i	−0.917265	−	0.398277i	$-0.869608\pi$
$919$	−31.2542	+	18.0446i	−1.03098	+	0.595236i	−0.113714	+	0.993513i	$0.536275\pi$
$920$	8.26943	−	6.50627i	0.272635	−	0.214505i
$921$	2.18986	−	3.79295i	0.0721583	−	0.124982i
$922$	22.5515	+	6.04266i	0.742695	+	0.199004i
$923$	6.74244	+	6.74244i	0.221930	+	0.221930i
$924$	−23.7356	−	15.2866i	−0.780844	−	0.502893i
$925$	−0.0311706	−	1.28426i	−0.00102488	−	0.0422263i
$926$	2.81789	+	4.88073i	0.0926017	+	0.160391i
$927$	23.3813	+	87.2600i	0.767941	+	2.86600i
$928$	−0.678717	−	2.53301i	−0.0222800	−	0.0831500i
$929$	−21.2041	−	36.7266i	−0.695685	−	1.20496i	−0.969949	−	0.243307i	$-0.921768\pi$
$929$	−21.2041	−	36.7266i	−0.695685	−	1.20496i	0.274264	−	0.961654i	$-0.411566\pi$
$930$	−0.100260	+	0.250606i	−0.00328764	+	0.00821769i
$931$	−12.4657	−	8.91344i	−0.408547	−	0.292126i
$932$	−16.1198	−	16.1198i	−0.528023	−	0.528023i
$933$	−38.7686	−	10.3880i	−1.26923	−	0.340089i
$934$	2.44290	−	4.23123i	0.0799342	−	0.138450i
$935$	−6.42578	−	0.766776i	−0.210145	−	0.0250762i
$936$	5.54268	−	3.20007i	0.181168	−	0.104597i
$937$	4.06709	−	4.06709i	0.132866	−	0.132866i	−0.637546	−	0.770412i	$-0.720050\pi$
$937$	4.06709	−	4.06709i	0.132866	−	0.132866i	0.770412	+	0.637546i	$0.220050\pi$
$938$	−17.1243	+	3.70770i	−0.559129	+	0.121061i
$939$			67.8621i			2.21460i
$940$	11.4587	+	8.57367i	0.373740	+	0.279642i
$941$	−17.4071	−	10.0500i	−0.567455	−	0.327621i	0.188677	−	0.982039i	$-0.439580\pi$
$941$	−17.4071	−	10.0500i	−0.567455	−	0.327621i	−0.756132	+	0.654419i	$0.772913\pi$
$942$	68.7494	−	18.4213i	2.23998	−	0.600200i
$943$	10.9371	−	40.8179i	0.356162	−	1.32921i
$944$	10.7123			0.348656
$945$	38.2899	+	17.5207i	1.24557	+	0.569949i
$946$	2.46386			0.0801069
$947$	−15.2583	+	56.9449i	−0.495830	+	1.85046i	0.0295030	+	0.999565i	$0.490608\pi$
$947$	−15.2583	+	56.9449i	−0.495830	+	1.85046i	−0.525333	+	0.850897i	$0.676059\pi$
$948$	−37.6538	+	10.0893i	−1.22294	+	0.327685i
$949$	10.0354	+	5.79393i	0.325762	+	0.188079i
$950$	−9.34404	+	5.70147i	−0.303161	+	0.184980i
$951$			38.3355i			1.24311i
$952$	0.637013	−	1.98608i	0.0206457	−	0.0643691i
$953$	−31.1044	+	31.1044i	−1.00757	+	1.00757i	−0.00759828	+	0.999971i	$0.502419\pi$
$953$	−31.1044	+	31.1044i	−1.00757	+	1.00757i	−0.999971	+	0.00759828i	$0.997581\pi$
$954$	−37.3429	+	21.5599i	−1.20902	+	0.698029i
$955$	21.4359	+	27.2448i	0.693648	+	0.881622i
$956$	11.9985	−	20.7821i	0.388060	−	0.672140i
$957$	27.0292	+	7.24244i	0.873729	+	0.234115i
$958$	−12.0996	−	12.0996i	−0.390921	−	0.390921i
$959$	22.9505	+	44.6245i	0.741111	+	1.44100i
$960$	−2.55992	−	5.97414i	−0.0826212	−	0.192814i
$961$	−15.4991	−	26.8453i	−0.499972	−	0.865977i
$962$	0.0781094	+	0.291508i	0.00251835	+	0.00939861i
$963$	−6.44392	−	24.0491i	−0.207653	−	0.774970i
$964$	12.3937	+	21.4666i	0.399175	+	0.691391i
$965$	−7.92454	−	18.4936i	−0.255100	−	0.595331i
$966$	−36.1451	−	1.75709i	−1.16295	−	0.0565336i
$967$	−21.5036	−	21.5036i	−0.691510	−	0.691510i	0.271054	−	0.962564i	$-0.412628\pi$
$967$	−21.5036	−	21.5036i	−0.691510	−	0.691510i	−0.962564	+	0.271054i	$0.912628\pi$
$968$	−2.39287	−	0.641168i	−0.0769098	−	0.0206079i
$969$	−2.50822	+	4.34437i	−0.0805756	+	0.139561i
$970$	6.19252	+	7.87065i	0.198830	+	0.252711i
$971$	−45.3034	+	26.1559i	−1.45385	+	0.839384i	−0.998697	−	0.0510273i	$-0.983750\pi$
$971$	−45.3034	+	26.1559i	−1.45385	+	0.839384i	−0.455158	+	0.890411i	$0.650417\pi$
$972$	−6.17385	+	6.17385i	−0.198026	+	0.198026i
$973$	4.61174	+	21.2997i	0.147845	+	0.682836i
$974$		−	0.130300i		−	0.00417507i
$975$	−16.5917	−	4.01692i	−0.531361	−	0.128644i
$976$	1.72539	+	0.996157i	0.0552285	+	0.0318862i
$977$	−54.6658	+	14.6477i	−1.74891	+	0.468620i	−0.984394	−	0.175979i	$-0.943691\pi$
$977$	−54.6658	+	14.6477i	−1.74891	+	0.468620i	−0.764520	+	0.644599i	$0.777024\pi$
$978$	16.5247	−	61.6710i	0.528401	−	1.97202i
$979$	−5.25068			−0.167813
$980$	−15.6360	+	0.717962i	−0.499474	+	0.0229345i
$981$	−98.6358			−3.14920
$982$	−6.98541	+	26.0699i	−0.222913	+	0.831924i
$983$	14.9514	−	4.00621i	0.476875	−	0.127778i	−0.0123723	−	0.999923i	$-0.503938\pi$
$983$	14.9514	−	4.00621i	0.476875	−	0.127778i	0.489247	+	0.872145i	$0.337272\pi$
$984$	−22.6055	−	13.0513i	−0.720638	−	0.416061i
$985$	−30.8777	−	23.1035i	−0.983845	−	0.736139i
$986$			2.06729i			0.0658361i
$987$	−10.4154	−	48.1044i	−0.331526	−	1.53118i
$988$	1.81832	−	1.81832i	0.0578486	−	0.0578486i
$989$	2.73504	−	1.57907i	0.0869691	−	0.0502116i
$990$	44.4129	+	5.29971i	1.41154	+	0.168436i
$991$	26.8648	−	46.5311i	0.853388	−	1.47811i	−0.0247453	−	0.999694i	$-0.507877\pi$
$991$	26.8648	−	46.5311i	0.853388	−	1.47811i	0.878133	−	0.478417i	$-0.158789\pi$
$992$	−0.0401138	−	0.0107485i	−0.00127362	−	0.000341264i
$993$	−39.2484	−	39.2484i	−1.24551	−	1.24551i
$994$	−21.4523	−	1.04284i	−0.680424	−	0.0330769i
$995$	−7.25190	+	18.1266i	−0.229901	+	0.574653i
$996$	−19.9990	−	34.6392i	−0.633692	−	1.09759i
$997$	9.97217	+	37.2167i	0.315822	+	1.17866i	0.923222	+	0.384267i	$0.125546\pi$
$997$	9.97217	+	37.2167i	0.315822	+	1.17866i	−0.607400	+	0.794396i	$0.707787\pi$
$998$	−0.0249241	−	0.0930180i	−0.000788959	−	0.00294443i
$999$	0.914352	+	1.58370i	0.0289288	+	0.0501062i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	70.2.k.a.17.1	yes	16
3.2	odd	2		630.2.bv.c.577.4		16
4.3	odd	2		560.2.ci.c.17.4		16
5.2	odd	4		350.2.o.c.143.2		16
5.3	odd	4	inner	70.2.k.a.3.3	✓	16
5.4	even	2		350.2.o.c.157.4		16
7.2	even	3		490.2.l.c.117.4		16
7.3	odd	6		490.2.g.c.97.1		16
7.4	even	3		490.2.g.c.97.4		16
7.5	odd	6	inner	70.2.k.a.47.3	yes	16
7.6	odd	2		490.2.l.c.227.2		16
15.8	even	4		630.2.bv.c.73.1		16
20.3	even	4		560.2.ci.c.353.4		16
21.5	even	6		630.2.bv.c.397.1		16
28.19	even	6		560.2.ci.c.257.4		16
35.3	even	12		490.2.g.c.293.4		16
35.12	even	12		350.2.o.c.243.4		16
35.13	even	4		490.2.l.c.423.4		16
35.18	odd	12		490.2.g.c.293.1		16
35.19	odd	6		350.2.o.c.257.2		16
35.23	odd	12		490.2.l.c.313.2		16
35.33	even	12	inner	70.2.k.a.33.1	yes	16
105.68	odd	12		630.2.bv.c.523.4		16
140.103	odd	12		560.2.ci.c.33.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.3	✓	16	5.3	odd	4	inner
70.2.k.a.17.1	yes	16	1.1	even	1	trivial
70.2.k.a.33.1	yes	16	35.33	even	12	inner
70.2.k.a.47.3	yes	16	7.5	odd	6	inner
350.2.o.c.143.2		16	5.2	odd	4
350.2.o.c.157.4		16	5.4	even	2
350.2.o.c.243.4		16	35.12	even	12
350.2.o.c.257.2		16	35.19	odd	6
490.2.g.c.97.1		16	7.3	odd	6
490.2.g.c.97.4		16	7.4	even	3
490.2.g.c.293.1		16	35.18	odd	12
490.2.g.c.293.4		16	35.3	even	12
490.2.l.c.117.4		16	7.2	even	3
490.2.l.c.227.2		16	7.6	odd	2
490.2.l.c.313.2		16	35.23	odd	12
490.2.l.c.423.4		16	35.13	even	4
560.2.ci.c.17.4		16	4.3	odd	2
560.2.ci.c.33.4		16	140.103	odd	12
560.2.ci.c.257.4		16	28.19	even	6
560.2.ci.c.353.4		16	20.3	even	4
630.2.bv.c.73.1		16	15.8	even	4
630.2.bv.c.397.1		16	21.5	even	6
630.2.bv.c.523.4		16	105.68	odd	12
630.2.bv.c.577.4		16	3.2	odd	2

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:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	70.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-2.80762 + 0.752300i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.21323 + 0.318742i) q^{5} -2.90667i q^{6} +(0.559876 + 2.58583i) q^{7} +(0.707107 - 0.707107i) q^{8} +(4.71872 - 2.72435i) q^{9} +O(q^{10})\)	\(q+(-0.258819 + 0.965926i) q^{2} +(-2.80762 + 0.752300i) q^{3} +(-0.866025 - 0.500000i) q^{4} +(-2.21323 + 0.318742i) q^{5} -2.90667i q^{6} +(0.559876 + 2.58583i) q^{7} +(0.707107 - 0.707107i) q^{8} +(4.71872 - 2.72435i) q^{9} +(0.264946 - 2.22032i) q^{10} +(-1.83557 + 3.17930i) q^{11} +(2.80762 + 0.752300i) q^{12} +(0.830578 + 0.830578i) q^{13} +(-2.64263 - 0.128464i) q^{14} +(5.97414 - 2.55992i) q^{15} +(0.500000 + 0.866025i) q^{16} +(-0.204036 - 0.761471i) q^{17} +(1.41023 + 5.26305i) q^{18} +(1.09461 + 1.89593i) q^{19} +(2.07609 + 0.830578i) q^{20} +(-3.51725 - 6.83885i) q^{21} +(-2.59589 - 2.59589i) q^{22} +(-4.54529 - 1.21791i) q^{23} +(-1.45333 + 2.51725i) q^{24} +(4.79681 - 1.41090i) q^{25} +(-1.01725 + 0.587308i) q^{26} +(-5.03288 + 5.03288i) q^{27} +(0.808050 - 2.51934i) q^{28} +2.62236i q^{29} +(0.926476 + 6.43313i) q^{30} +(0.0359651 + 0.0207644i) q^{31} +(-0.965926 + 0.258819i) q^{32} +(2.76180 - 10.3072i) q^{33} +0.788333 q^{34} +(-2.06335 - 5.54460i) q^{35} -5.44871 q^{36} +(0.0664979 - 0.248174i) q^{37} +(-2.11463 + 0.566614i) q^{38} +(-2.95680 - 1.70711i) q^{39} +(-1.33961 + 1.79038i) q^{40} +8.98026i q^{41} +(7.51616 - 1.62737i) q^{42} +(-0.474569 + 0.474569i) q^{43} +(3.17930 - 1.83557i) q^{44} +(-9.57526 + 7.53368i) q^{45} +(2.35282 - 4.07520i) q^{46} +(6.18205 + 1.65648i) q^{47} +(-2.05532 - 2.05532i) q^{48} +(-6.37308 + 2.89549i) q^{49} +(0.121320 + 4.99853i) q^{50} +(1.14571 + 1.98443i) q^{51} +(-0.304013 - 1.13459i) q^{52} +(2.04824 + 7.64413i) q^{53} +(-3.55879 - 6.16400i) q^{54} +(3.04917 - 7.62161i) q^{55} +(2.22435 + 1.43257i) q^{56} +(-4.49957 - 4.49957i) q^{57} +(-2.53301 - 0.678717i) q^{58} +(5.35616 - 9.27713i) q^{59} +(-6.45372 - 0.770110i) q^{60} +(1.72539 - 0.996157i) q^{61} +(-0.0293654 + 0.0293654i) q^{62} +(9.68662 + 10.6765i) q^{63} -1.00000i q^{64} +(-2.10300 - 1.57352i) q^{65} +(9.24117 + 5.33539i) q^{66} +(6.39671 - 1.71399i) q^{67} +(-0.204036 + 0.761471i) q^{68} +13.6777 q^{69} +(5.88971 - 0.557996i) q^{70} +8.11777 q^{71} +(1.41023 - 5.26305i) q^{72} +(9.52910 - 2.55331i) q^{73} +(0.222506 + 0.128464i) q^{74} +(-12.4062 + 7.56992i) q^{75} -2.18923i q^{76} +(-9.24884 - 2.96647i) q^{77} +(2.41421 - 2.41421i) q^{78} +(-11.6145 + 6.70563i) q^{79} +(-1.38266 - 1.75735i) q^{80} +(2.17114 - 3.76053i) q^{81} +(-8.67427 - 2.32426i) q^{82} +(-9.73033 - 9.73033i) q^{83} +(-0.373402 + 7.68124i) q^{84} +(0.694291 + 1.62028i) q^{85} +(-0.335571 - 0.581226i) q^{86} +(-1.97280 - 7.36260i) q^{87} +(0.950161 + 3.54605i) q^{88} +(0.715130 + 1.23864i) q^{89} +(-4.79872 - 11.1989i) q^{90} +(-1.68272 + 2.61276i) q^{91} +(3.32739 + 3.32739i) q^{92} +(-0.116597 - 0.0312422i) q^{93} +(-3.20007 + 5.54268i) q^{94} +(-3.02695 - 3.84723i) q^{95} +(2.51725 - 1.45333i) q^{96} +(-3.16693 + 3.16693i) q^{97} +(-1.14736 - 6.90533i) q^{98} +20.0030i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 12 q^{5} + 8 q^{7}+O(q^{10}) \) 16 * q - 12 * q^5 + 8 * q^7	\( 16 q - 12 q^{5} + 8 q^{7} - 12 q^{10} - 12 q^{11} + 16 q^{15} + 8 q^{16} - 36 q^{17} - 8 q^{18} - 28 q^{21} - 8 q^{22} - 4 q^{23} + 12 q^{25} + 12 q^{26} + 4 q^{28} + 20 q^{30} + 24 q^{31} + 48 q^{33} + 8 q^{35} - 8 q^{36} + 4 q^{37} + 24 q^{38} + 36 q^{42} - 8 q^{43} - 12 q^{45} - 8 q^{46} + 12 q^{47} - 32 q^{50} - 16 q^{51} - 28 q^{53} - 4 q^{56} + 8 q^{57} - 32 q^{58} + 8 q^{60} - 12 q^{61} - 36 q^{63} - 8 q^{65} + 32 q^{67} - 36 q^{68} - 12 q^{70} + 16 q^{71} - 8 q^{72} - 12 q^{73} - 48 q^{75} + 16 q^{77} + 16 q^{78} - 12 q^{80} - 48 q^{82} + 24 q^{85} + 12 q^{86} - 24 q^{87} - 4 q^{88} - 16 q^{91} + 8 q^{92} + 28 q^{93} + 20 q^{95} + 12 q^{96} + 40 q^{98}+O(q^{100}) \) 16 * q - 12 * q^5 + 8 * q^7 - 12 * q^10 - 12 * q^11 + 16 * q^15 + 8 * q^16 - 36 * q^17 - 8 * q^18 - 28 * q^21 - 8 * q^22 - 4 * q^23 + 12 * q^25 + 12 * q^26 + 4 * q^28 + 20 * q^30 + 24 * q^31 + 48 * q^33 + 8 * q^35 - 8 * q^36 + 4 * q^37 + 24 * q^38 + 36 * q^42 - 8 * q^43 - 12 * q^45 - 8 * q^46 + 12 * q^47 - 32 * q^50 - 16 * q^51 - 28 * q^53 - 4 * q^56 + 8 * q^57 - 32 * q^58 + 8 * q^60 - 12 * q^61 - 36 * q^63 - 8 * q^65 + 32 * q^67 - 36 * q^68 - 12 * q^70 + 16 * q^71 - 8 * q^72 - 12 * q^73 - 48 * q^75 + 16 * q^77 + 16 * q^78 - 12 * q^80 - 48 * q^82 + 24 * q^85 + 12 * q^86 - 24 * q^87 - 4 * q^88 - 16 * q^91 + 8 * q^92 + 28 * q^93 + 20 * q^95 + 12 * q^96 + 40 * q^98

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