LMFDB - Embedded newform 70.2.k.a.33.1

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			33.1
Root			$-0.587308 - 2.01725i$ of defining polynomial
Character	$\chi$	$=$	70.33
Dual form			70.2.k.a.17.1

$q$-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 $\left(\mathbb{Z}/70\mathbb{Z}\right)^\times$.

$n$	$31$	$57$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{4}\right)$

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	−0.669692	−	0.742639i	$-0.733574\pi$
$3$	−2.80762	−	0.752300i	−1.62098	−	0.434341i	−0.951290	+	0.308298i	$0.900241\pi$
$4$	−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	−0.998023	−	0.0628551i	$-0.979979\pi$
$11$	−1.83557	−	3.17930i	−0.553445	−	0.958596i	0.444577	−	0.895741i	$-0.353354\pi$
$12$	2.80762	−	0.752300i	0.810491	−	0.217170i
$13$	0.830578	−	0.830578i	0.230361	−	0.230361i	−0.582482	−	0.812843i	$-0.697918\pi$
$13$	0.830578	−	0.830578i	0.230361	−	0.230361i	0.812843	+	0.582482i	$0.197918\pi$
$14$	−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	−0.986245	−	0.165292i	$-0.947143\pi$
$17$	−0.204036	+	0.761471i	−0.0494859	+	0.184684i	0.936759	+	0.349976i	$0.113810\pi$
$18$	1.41023	−	5.26305i	0.332394	−	1.24051i
$19$	1.09461	−	1.89593i	0.251122	−	0.434955i	−0.712713	−	0.701455i	$-0.752534\pi$
$19$	1.09461	−	1.89593i	0.251122	−	0.434955i	0.963835	+	0.266500i	$0.0858673\pi$
$20$	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	−0.699411	−	0.714719i	$-0.746554\pi$
$23$	−4.54529	+	1.21791i	−0.947759	+	0.253951i	−0.248348	+	0.968671i	$0.579888\pi$
$24$	−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	$-0.921711\pi$
$29$		−	2.62236i		−	0.486960i	0.969906	−	0.243480i	$-0.0782891\pi$
$30$	0.926476	−	6.43313i	0.169151	−	1.17452i
$31$	0.0359651	−	0.0207644i	0.00645952	−	0.00372940i	−0.496767	−	0.867884i	$-0.665480\pi$
$31$	0.0359651	−	0.0207644i	0.00645952	−	0.00372940i	0.503226	+	0.864155i	$0.332146\pi$
$32$	−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	0.971176	−	0.238362i	$-0.0766103\pi$
$37$	0.0664979	+	0.248174i	0.0109322	+	0.0407995i	−0.960244	+	0.279161i	$0.909944\pi$
$38$	−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	$-0.752630\pi$
$41$		−	8.98026i		−	1.40248i	0.712925	−	0.701241i	$-0.247370\pi$
$42$	7.51616	+	1.62737i	1.15977	+	0.251109i
$43$	−0.474569	−	0.474569i	−0.0723711	−	0.0723711i	0.669995	−	0.742366i	$-0.266296\pi$
$43$	−0.474569	−	0.474569i	−0.0723711	−	0.0723711i	−0.742366	+	0.669995i	$0.766296\pi$
$44$	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	0.221980	−	0.975051i	$-0.428748\pi$
$47$	6.18205	−	1.65648i	0.901745	−	0.241622i	0.679766	+	0.733429i	$0.262081\pi$
$48$	−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	−0.670120	−	0.742252i	$-0.733758\pi$
$53$	2.04824	−	7.64413i	0.281347	−	1.05000i	0.951468	−	0.307749i	$-0.0995758\pi$
$54$	−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	0.969395	+	0.245506i	$0.0789541\pi$
$59$	5.35616	+	9.27713i	0.697312	+	1.20778i	−0.272083	+	0.962274i	$0.587713\pi$
$60$	−6.45372	+	0.770110i	−0.833171	+	0.0994207i
$61$	1.72539	+	0.996157i	0.220914	+	0.127545i	0.606373	−	0.795180i	$-0.292624\pi$
$61$	1.72539	+	0.996157i	0.220914	+	0.127545i	−0.385459	+	0.922725i	$0.625957\pi$
$62$	−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	0.627438	−	0.778666i	$-0.284103\pi$
$67$	6.39671	+	1.71399i	0.781482	+	0.209398i	0.154044	+	0.988064i	$0.450770\pi$
$68$	−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	0.768979	−	0.639274i	$-0.220765\pi$
$73$	9.52910	+	2.55331i	1.11530	+	0.298843i	0.346318	+	0.938117i	$0.387432\pi$
$74$	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	−0.325184	−	0.945651i	$-0.605426\pi$
$79$	−11.6145	−	6.70563i	−1.30673	−	0.754443i	−0.981550	+	0.191208i	$0.938760\pi$
$80$	−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	−0.0705331	+	0.997509i	$0.522470\pi$
$83$	−9.73033	+	9.73033i	−1.06804	+	1.06804i	−0.997509	+	0.0705331i	$0.977530\pi$
$84$	−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	−0.825632	−	0.564209i	$-0.809181\pi$
$89$	0.715130	−	1.23864i	0.0758036	−	0.131296i	0.901435	+	0.432914i	$0.142514\pi$
$90$	−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	0.527810	−	0.849363i	$-0.323013\pi$
$97$	−3.16693	−	3.16693i	−0.321553	−	0.321553i	−0.849363	+	0.527810i	$0.823013\pi$
$98$	−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	−0.503095	−	0.864231i	$-0.667805\pi$
$101$	−0.0622734	+	0.0359536i	−0.00619644	+	0.00357751i	0.496899	+	0.867809i	$0.334472\pi$
$102$	−2.21334	−	0.593063i	−0.219154	−	0.0587220i
$103$	−4.29116	−	16.0148i	−0.422820	−	1.57799i	−0.768638	−	0.639685i	$-0.779065\pi$
$103$	−4.29116	−	16.0148i	−0.422820	−	1.57799i	0.345817	−	0.938302i	$-0.387602\pi$
$104$	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	0.999236	−	0.0390819i	$-0.0124433\pi$
$107$	1.18265	+	4.41372i	0.114331	+	0.426690i	−0.884905	+	0.465772i	$0.845777\pi$
$108$	6.87505	+	1.84216i	0.661552	+	0.177262i
$109$	−15.6773	+	9.05131i	−1.50162	+	0.866958i	−0.501617	+	0.865090i	$0.667261\pi$
$109$	−15.6773	+	9.05131i	−1.50162	+	0.866958i	−0.999998	+	0.00186842i	$0.999405\pi$
$110$	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	0.775005	−	0.631955i	$-0.217747\pi$
$113$	1.52064	+	1.52064i	0.143049	+	0.143049i	−0.631955	+	0.775005i	$0.717747\pi$
$114$	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	−0.195234	+	0.980757i	$0.562547\pi$
$127$	−13.2527	+	13.2527i	−1.17599	+	1.17599i	−0.980757	+	0.195234i	$0.937453\pi$
$128$	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	0.929281	−	0.369372i	$-0.120427\pi$
$131$	12.2929	+	7.09731i	1.07404	+	0.620095i	0.144755	+	0.989468i	$0.453761\pi$
$132$	−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	0.934303	−	0.356479i	$-0.116023\pi$
$137$	18.3201	+	4.90887i	1.56519	+	0.419393i	0.630891	+	0.775871i	$0.282689\pi$
$138$	−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	0.661826	−	0.749657i	$-0.269782\pi$
$149$	4.19317	+	2.42093i	0.343518	+	0.198330i	−0.318309	+	0.947987i	$0.603115\pi$
$150$	−4.10102	+	13.9427i	−0.334847	+	1.13842i
$151$	−5.02292	−	8.69995i	−0.408759	−	0.707992i	0.585992	−	0.810317i	$-0.300705\pi$
$151$	−5.02292	−	8.69995i	−0.408759	−	0.707992i	−0.994751	+	0.102325i	$0.967372\pi$
$152$	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	0.0474774	−	0.998872i	$-0.484882\pi$
$157$	6.33762	−	23.6523i	0.505797	−	1.88766i	0.458320	−	0.888788i	$-0.348452\pi$
$158$	−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	0.698954	−	0.715166i	$-0.253649\pi$
$163$	21.2171	−	5.68510i	1.66185	−	0.445291i	0.962895	+	0.269875i	$0.0869823\pi$
$164$	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	0.574821	−	0.818279i	$-0.305072\pi$
$167$	−3.14616	−	3.14616i	−0.243457	−	0.243457i	−0.818279	+	0.574821i	$0.805072\pi$
$168$	−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	0.895246	−	0.445572i	$-0.147000\pi$
$173$	−1.35273	−	5.04844i	−0.102846	−	0.383826i	−0.998092	+	0.0617463i	$0.980333\pi$
$174$	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	−0.0346308	−	0.999400i	$-0.511026\pi$
$179$	10.8847	−	6.28428i	0.813560	−	0.469709i	0.848191	+	0.529691i	$0.177692\pi$
$180$	12.0593	+	1.73673i	0.898844	+	0.129448i
$181$			11.6742i			0.867740i	0.900976	+	0.433870i	$0.142852\pi$
$181$			11.6742i			0.867740i	−0.900976	+	0.433870i	$0.857148\pi$
$182$	−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	0.436525	+	0.899692i	$0.356209\pi$
$191$	−7.75170	+	13.4263i	−0.560894	+	0.971496i	−0.997419	+	0.0718040i	$0.977124\pi$
$192$	0.752300	−	2.80762i	0.0542926	−	0.202623i
$193$	2.32883	−	8.69132i	0.167633	−	0.625615i	−0.830057	−	0.557679i	$-0.811692\pi$
$193$	2.32883	−	8.69132i	0.167633	−	0.625615i	0.997690	−	0.0679359i	$-0.0216413\pi$
$194$	−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	−0.123482	−	0.992347i	$-0.539406\pi$
$197$	12.1951	−	12.1951i	0.868865	−	0.868865i	0.992347	+	0.123482i	$0.0394061\pi$
$198$	−19.3214	+	5.17715i	−1.37311	+	0.367924i
$199$	4.36557	+	7.56140i	0.309467	+	0.536013i	0.978246	−	0.207448i	$-0.0665159\pi$
$199$	4.36557	+	7.56140i	0.309467	+	0.536013i	−0.668779	+	0.743462i	$0.733183\pi$
$200$	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	−0.681660	−	0.731669i	$-0.738742\pi$
$223$	0.746804	−	0.746804i	0.0500097	−	0.0500097i	0.731669	+	0.681660i	$0.238742\pi$
$224$	−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	−0.987534	−	0.157403i	$-0.949688\pi$
$227$	−0.807609	+	3.01404i	−0.0536029	+	0.200049i	0.933932	+	0.357452i	$0.116354\pi$
$228$	1.64696	−	6.14653i	0.109072	−	0.407064i
$229$	4.21091	−	7.29350i	0.278264	−	0.481968i	−0.692689	−	0.721236i	$-0.743574\pi$
$229$	4.21091	−	7.29350i	0.278264	−	0.481968i	0.970954	+	0.239268i	$0.0769075\pi$
$230$	−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	0.549148	−	0.835725i	$-0.314952\pi$
$233$	22.0201	−	5.90027i	1.44259	−	0.386540i	0.893439	+	0.449186i	$0.148286\pi$
$234$	−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	$-0.717185\pi$
$239$		−	23.9971i		−	1.55224i	0.630585	−	0.776120i	$-0.282815\pi$
$240$	5.20403	−	3.89379i	0.335919	−	0.251343i
$241$	−21.4666	+	12.3937i	−1.38278	+	0.798350i	−0.992488	−	0.122340i	$-0.960960\pi$
$241$	−21.4666	+	12.3937i	−1.38278	+	0.798350i	−0.390295	+	0.920690i	$0.627627\pi$
$242$	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	$-0.885906\pi$
$251$		−	11.1158i		−	0.701623i	0.936446	−	0.350811i	$-0.114094\pi$
$252$	−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	−0.921052	−	0.389439i	$-0.872669\pi$
$257$	−24.4314	+	6.54637i	−1.52399	+	0.408351i	−0.602935	+	0.797790i	$0.706002\pi$
$258$	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	−0.814358	−	0.580363i	$-0.802911\pi$
$263$	2.93659	−	10.9595i	0.181078	−	0.675792i	0.995436	−	0.0954297i	$-0.0304225\pi$
$264$	−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	0.716467	−	0.697621i	$-0.245758\pi$
$269$	−4.03346	−	6.98616i	−0.245924	−	0.425954i	−0.962391	+	0.271668i	$0.912425\pi$
$270$	9.84115	−	12.5080i	0.598913	−	0.761215i
$271$	7.27419	+	4.19976i	0.441876	+	0.255117i	0.704393	−	0.709810i	$-0.251219\pi$
$271$	7.27419	+	4.19976i	0.441876	+	0.255117i	−0.262517	+	0.964927i	$0.584553\pi$
$272$	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	0.0901983	−	0.995924i	$-0.471250\pi$
$277$	−5.48646	−	1.47009i	−0.329650	−	0.0883293i	−0.419848	+	0.907594i	$0.637917\pi$
$278$	−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	0.0305840	−	0.999532i	$-0.490263\pi$
$283$	−7.44729	−	1.99550i	−0.442696	−	0.118620i	−0.473280	+	0.880912i	$0.656930\pi$
$284$	−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	−0.602383	−	0.798207i	$-0.705782\pi$
$293$	3.35198	−	3.35198i	0.195824	−	0.195824i	0.798207	+	0.602383i	$0.205782\pi$
$294$	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	0.676048	−	0.736857i	$-0.263691\pi$
$307$	−1.06546	−	1.06546i	−0.0608089	−	0.0608089i	−0.736857	+	0.676048i	$0.763691\pi$
$308$	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	−0.121040	−	0.992648i	$-0.538623\pi$
$311$	11.9584	−	6.90417i	0.678097	−	0.391500i	0.799138	+	0.601148i	$0.205290\pi$
$312$	−3.29788	−	0.883663i	−0.186706	−	0.0500276i
$313$	6.04266	+	22.5515i	0.341551	+	1.27469i	0.896590	+	0.442863i	$0.146037\pi$
$313$	6.04266	+	22.5515i	0.341551	+	1.27469i	−0.555038	+	0.831825i	$0.687296\pi$
$314$	−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	0.993091	+	0.117347i	$0.0374390\pi$
$317$	3.41352	+	12.7394i	0.191722	+	0.715518i	−0.801369	+	0.598171i	$0.795894\pi$
$318$	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	−0.474778	−	0.880106i	$-0.657472\pi$
$331$	9.54799	−	16.5376i	0.524805	−	0.908989i	0.999583	−	0.0288830i	$-0.00919501\pi$
$332$	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	−0.693684	−	0.720279i	$-0.744014\pi$
$337$	0.488226	−	0.488226i	0.0265953	−	0.0265953i	0.720279	+	0.693684i	$0.244014\pi$
$338$	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	0.158682	−	0.987330i	$-0.449276\pi$
$347$	−3.68015	−	0.986094i	−0.197561	−	0.0529363i	−0.356243	+	0.934393i	$0.615942\pi$
$348$	−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	−0.474347	−	0.880338i	$-0.657316\pi$
$353$	−24.9004	−	6.67203i	−1.32531	−	0.355116i	−0.850965	+	0.525222i	$0.823982\pi$
$354$	−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	0.718220	−	0.695816i	$-0.244957\pi$
$359$	8.99497	+	5.19325i	0.474737	+	0.274089i	−0.243484	+	0.969905i	$0.578290\pi$
$360$	−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	−0.999452	−	0.0331020i	$-0.989461\pi$
$367$	−2.24811	+	8.39004i	−0.117350	+	0.437957i	0.882102	+	0.471059i	$0.156128\pi$
$368$	−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	−0.575799	−	0.817591i	$-0.695309\pi$
$373$	−12.8560	+	3.44476i	−0.665660	+	0.178363i	−0.0898611	+	0.995954i	$0.528642\pi$
$374$	−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	$0.225629\pi$
$379$			25.3453i			1.30190i	−0.759121	+	0.650949i	$0.774371\pi$
$380$	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	0.974204	+	0.225668i	$0.0724565\pi$
$383$	4.76251	+	17.7739i	0.243353	+	0.908205i	−0.730851	+	0.682537i	$0.760877\pi$
$384$	−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	−0.902783	−	0.430097i	$-0.858479\pi$
$389$	−19.3621	+	11.1787i	−0.981699	+	0.566784i	−0.0789164	+	0.996881i	$0.525146\pi$
$390$	−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	−0.620241	−	0.784411i	$-0.712965\pi$
$397$	−15.2461	+	4.08518i	−0.765181	+	0.205029i	−0.144939	+	0.989441i	$0.546299\pi$
$398$	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	−0.986042	−	0.166499i	$-0.946754\pi$
$401$	−6.98528	+	12.0989i	−0.348828	+	0.604188i	0.637213	+	0.770687i	$0.280087\pi$
$402$	−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	0.862126	−	0.506694i	$-0.169133\pi$
$409$	−0.156681	−	0.271379i	−0.00774737	−	0.0134188i	−0.869873	+	0.493276i	$0.835799\pi$
$410$	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	0.846653	−	0.532145i	$-0.178614\pi$
$431$	−0.779037	−	1.34933i	−0.0375249	−	0.0649950i	−0.884178	+	0.467150i	$0.845281\pi$
$432$	−6.87505	+	1.84216i	−0.330776	+	0.0886311i
$433$	6.28166	−	6.28166i	0.301877	−	0.301877i	−0.539871	−	0.841748i	$-0.681527\pi$
$433$	6.28166	−	6.28166i	0.301877	−	0.301877i	0.841748	+	0.539871i	$0.181527\pi$
$434$	−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	−0.425815	−	0.904810i	$-0.640012\pi$
$439$	11.9571	−	20.7103i	0.570681	−	0.988449i	0.996496	−	0.0836389i	$-0.0266542\pi$
$440$	−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	−0.541578	−	0.840651i	$-0.682173\pi$
$443$	−12.4238	+	3.32895i	−0.590272	+	0.158163i	−0.0486946	+	0.998814i	$0.515506\pi$
$444$	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	$-0.861252\pi$
$449$		−	17.8932i		−	0.844435i	0.906495	−	0.422217i	$-0.138748\pi$
$450$	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	0.786442	+	0.617665i	$0.211921\pi$
$457$	8.85449	+	33.0454i	0.414196	+	1.54580i	−0.372246	+	0.928134i	$0.621412\pi$
$458$	−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	$0.182973\pi$
$461$			23.3471i			1.08738i	−0.839286	+	0.543690i	$0.817027\pi$
$462$	−8.62252	−	26.8833i	−0.401156	−	1.25072i
$463$	3.98510	+	3.98510i	0.185203	+	0.185203i	0.793619	−	0.608415i	$-0.208195\pi$
$463$	3.98510	+	3.98510i	0.185203	+	0.185203i	−0.608415	+	0.793619i	$0.708195\pi$
$464$	−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	−0.366352	−	0.930476i	$-0.619393\pi$
$467$	−4.71932	+	1.26454i	−0.218384	+	0.0585159i	0.147968	+	0.988992i	$0.452727\pi$
$468$	−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	0.601651	−	0.798759i	$-0.294510\pi$
$479$	−8.55572	−	14.8189i	−0.390921	−	0.677094i	−0.992571	+	0.121665i	$0.961177\pi$
$480$	−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	0.255966	−	0.966686i	$-0.417606\pi$
$487$	−0.125860	−	0.0337240i	−0.00570325	−	0.00152818i	−0.261670	+	0.965158i	$0.584273\pi$
$488$	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	0.498132	−	0.867101i	$-0.334019\pi$
$499$	−0.0833977	−	0.0481497i	−0.00373339	−	0.00215548i	−0.501866	+	0.864946i	$0.667353\pi$
$500$	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	−0.942392	−	0.334509i	$-0.891429\pi$
$503$	−13.6334	+	13.6334i	−0.607883	+	0.607883i	0.334509	+	0.942392i	$0.391429\pi$
$504$	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	−0.969679	−	0.244381i	$-0.921415\pi$
$509$	−6.16366	+	10.6758i	−0.273199	+	0.473195i	0.696480	+	0.717576i	$0.254749\pi$
$510$	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	−0.157143	−	0.987576i	$-0.550228\pi$
$521$	14.1415	−	8.16461i	0.619551	−	0.357698i	0.776694	+	0.629878i	$0.216895\pi$
$522$	−13.8016	−	3.69813i	−0.604080	−	0.161863i
$523$	−7.09270	−	26.4703i	−0.310142	−	1.15747i	−0.928428	−	0.371512i	$-0.878839\pi$
$523$	−7.09270	−	26.4703i	−0.310142	−	1.15747i	0.618286	−	0.785953i	$-0.287827\pi$
$524$	−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	0.0386200	−	0.999254i	$-0.487704\pi$
$541$	20.5773	−	35.6410i	0.884689	−	1.53233i	0.846069	−	0.533073i	$-0.178963\pi$
$542$	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	−0.513336	−	0.858188i	$-0.671590\pi$
$547$	8.06541	−	8.06541i	0.344852	−	0.344852i	0.858188	+	0.513336i	$0.171590\pi$
$548$	−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	0.742282	−	0.670087i	$-0.233743\pi$
$557$	24.7826	+	6.64049i	1.05007	+	0.281367i	0.307792	+	0.951454i	$0.400410\pi$
$558$	−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	−0.0115606	−	0.999933i	$-0.503680\pi$
$563$	−12.3749	−	3.31584i	−0.521539	−	0.139746i	−0.509978	+	0.860187i	$0.670347\pi$
$564$	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	−0.279292	−	0.960206i	$-0.590100\pi$
$569$	−29.8291	−	17.2218i	−1.25050	−	0.721977i	−0.971209	+	0.238229i	$0.923433\pi$
$570$	−11.1826	−	8.79832i	−0.468388	−	0.368521i
$571$	4.11985	+	7.13579i	0.172410	+	0.298623i	0.939262	−	0.343201i	$-0.111511\pi$
$571$	4.11985	+	7.13579i	0.172410	+	0.298623i	−0.766852	+	0.641824i	$0.778178\pi$
$572$	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	−0.982279	−	0.187426i	$-0.939985\pi$
$577$	−0.910086	+	3.39649i	−0.0378874	+	0.141398i	0.944391	+	0.328824i	$0.106652\pi$
$578$	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	0.587431	−	0.809275i	$-0.300139\pi$
$587$	−5.37485	−	5.37485i	−0.221844	−	0.221844i	−0.809275	+	0.587431i	$0.800139\pi$
$588$	−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	0.969720	−	0.244218i	$-0.0785314\pi$
$593$	0.190155	+	0.709668i	0.00780872	+	0.0291426i	−0.961912	+	0.273361i	$0.911865\pi$
$594$	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	−0.344794	−	0.938678i	$-0.612051\pi$
$599$	7.23778	−	4.17873i	0.295727	−	0.170738i	0.640522	+	0.767940i	$0.278718\pi$
$600$	−3.41977	−	14.1253i	−0.139612	−	0.576661i
$601$		−	39.9236i		−	1.62852i	−0.580501	−	0.814259i	$-0.697143\pi$
$601$		−	39.9236i		−	1.62852i	0.580501	−	0.814259i	$-0.302857\pi$
$602$	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	0.490259	−	0.871577i	$-0.336902\pi$
$607$	33.2758	−	8.91623i	1.35062	−	0.361899i	0.860365	+	0.509678i	$0.170235\pi$
$608$	−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	0.554009	+	0.832510i	$0.313097\pi$
$613$	−8.46832	+	31.6042i	−0.342032	+	1.27648i	−0.896041	+	0.443971i	$0.853569\pi$
$614$	−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	−0.946558	−	0.322533i	$-0.895466\pi$
$617$	−15.5005	+	15.5005i	−0.624025	+	0.624025i	0.322533	+	0.946558i	$0.395466\pi$
$618$	46.5497	−	12.4730i	1.87250	−	0.501736i
$619$	4.31138	+	7.46752i	0.173289	+	0.300145i	0.939568	−	0.342363i	$-0.111227\pi$
$619$	4.31138	+	7.46752i	0.173289	+	0.300145i	−0.766279	+	0.642508i	$0.777894\pi$
$620$	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	0.738690	−	0.674046i	$-0.235445\pi$
$641$	−5.42807	−	9.40169i	−0.214396	−	0.371345i	−0.953086	+	0.302701i	$0.902112\pi$
$642$	−12.8292	+	3.43757i	−0.506328	+	0.135670i
$643$	−8.06230	+	8.06230i	−0.317946	+	0.317946i	−0.847978	−	0.530032i	$-0.822180\pi$
$643$	−8.06230	+	8.06230i	−0.317946	+	0.317946i	0.530032	+	0.847978i	$0.322180\pi$
$644$	−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	−0.998467	−	0.0553490i	$-0.982373\pi$
$647$	−2.69865	+	10.0715i	−0.106095	+	0.395951i	0.892372	+	0.451300i	$0.149040\pi$
$648$	−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	−0.131015	−	0.991380i	$-0.541824\pi$
$653$	6.41946	−	1.72009i	0.251213	−	0.0673123i	0.382228	+	0.924068i	$0.375157\pi$
$654$	−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	$0.141194\pi$
$659$			22.0345i			0.858343i	−0.903223	+	0.429172i	$0.858806\pi$
$660$	14.2947	+	19.1047i	0.556419	+	0.743650i
$661$	−9.94278	+	5.74047i	−0.386729	+	0.223278i	−0.680742	−	0.732523i	$-0.738343\pi$
$661$	−9.94278	+	5.74047i	−0.386729	+	0.223278i	0.294013	+	0.955802i	$0.405009\pi$
$662$	−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	0.350402	−	0.936600i	$-0.386045\pi$
$673$	−15.2073	−	15.2073i	−0.586198	−	0.586198i	−0.936600	+	0.350402i	$0.886045\pi$
$674$	−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	−0.363757	−	0.931494i	$-0.618506\pi$
$677$	−5.54296	+	1.48523i	−0.213033	+	0.0570821i	0.150724	+	0.988576i	$0.451840\pi$
$678$	−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	−0.800488	−	0.599349i	$-0.795426\pi$
$683$	5.02900	−	18.7685i	0.192430	−	0.718157i	0.992917	−	0.118808i	$-0.0379072\pi$
$684$	−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	0.817056	−	0.576558i	$-0.195605\pi$
$691$	19.0914	+	11.0224i	0.726270	+	0.419312i	−0.0907861	+	0.995870i	$0.528938\pi$
$692$	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	−0.398349	−	0.917234i	$-0.630417\pi$
$709$	−37.0614	−	21.3974i	−1.39187	−	0.803597i	−0.993522	+	0.113637i	$0.963750\pi$
$710$	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	−0.912384	−	0.409336i	$-0.865760\pi$
$719$	−2.72691	+	4.72315i	−0.101697	+	0.176144i	0.810687	+	0.585480i	$0.199094\pi$
$720$	−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	0.945161	−	0.326606i	$-0.105905\pi$
$727$	16.6781	+	16.6781i	0.618555	+	0.618555i	−0.326606	+	0.945161i	$0.605905\pi$
$728$	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	−0.914291	−	0.405057i	$-0.867252\pi$
$733$	−8.79960	−	32.8405i	−0.325021	−	1.21299i	0.589271	−	0.807936i	$-0.299415\pi$
$734$	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	0.0379557	−	0.999279i	$-0.487915\pi$
$739$	25.0733	−	14.4761i	0.922335	−	0.532510i	0.884379	+	0.466769i	$0.154582\pi$
$740$	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	0.956327	+	0.292300i	$0.0944206\pi$
$743$	34.0351	+	34.0351i	1.24863	+	1.24863i	0.292300	+	0.956327i	$0.405579\pi$
$744$	−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	−0.644782	−	0.764366i	$-0.723052\pi$
$751$	9.30569	−	16.1179i	0.339569	−	0.588151i	0.984352	+	0.176215i	$0.0563853\pi$
$752$	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	0.0845825	−	0.996416i	$-0.473044\pi$
$757$	29.7422	−	29.7422i	1.08100	−	1.08100i	0.996416	−	0.0845825i	$-0.0269557\pi$
$758$	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	0.784506	−	0.620122i	$-0.212917\pi$
$761$	17.6474	+	10.1887i	0.639718	+	0.369341i	−0.144788	+	0.989463i	$0.546250\pi$
$762$	−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	0.660936	−	0.750443i	$-0.270160\pi$
$773$	23.8577	+	6.39265i	0.858101	+	0.229928i	0.197166	+	0.980370i	$0.436826\pi$
$774$	−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	−0.917670	−	0.397343i	$-0.869932\pi$
$787$	2.12442	−	7.92843i	0.0757273	−	0.282618i	0.993397	+	0.114725i	$0.0365988\pi$
$788$	−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	0.884418	−	0.466696i	$-0.154556\pi$
$797$	11.7928	+	11.7928i	0.417722	+	0.417722i	−0.466696	+	0.884418i	$0.654556\pi$
$798$	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	−0.912449	−	0.409191i	$-0.865811\pi$
$809$	−28.8498	+	16.6564i	−1.01430	+	0.585609i	−0.101855	+	0.994799i	$0.532478\pi$
$810$	−7.77433	+	5.81696i	−0.273162	+	0.204387i
$811$			55.2368i			1.93963i	0.243850	+	0.969813i	$0.421590\pi$
$811$			55.2368i			1.93963i	−0.243850	+	0.969813i	$0.578410\pi$
$812$	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	−0.981529	−	0.191315i	$-0.938725\pi$
$821$	−9.31457	+	16.1333i	−0.325081	+	0.563056i	0.656448	+	0.754371i	$0.272058\pi$
$822$	−14.2684	+	53.2505i	−0.497669	+	1.85732i
$823$	−4.37130	+	16.3139i	−0.152374	+	0.568668i	0.846942	+	0.531685i	$0.178441\pi$
$823$	−4.37130	+	16.3139i	−0.152374	+	0.568668i	−0.999316	+	0.0369821i	$0.988226\pi$
$824$	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	−0.798143	−	0.602468i	$-0.794184\pi$
$827$	−5.62716	+	5.62716i	−0.195675	+	0.195675i	0.602468	+	0.798143i	$0.294184\pi$
$828$	24.7660	−	6.63602i	0.860677	−	0.230618i
$829$	3.29757	+	5.71155i	0.114529	+	0.198370i	0.917591	−	0.397525i	$-0.130131\pi$
$829$	3.29757	+	5.71155i	0.114529	+	0.198370i	−0.803062	+	0.595895i	$0.796797\pi$
$830$	−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	−0.403000	−	0.915200i	$-0.632032\pi$
$853$	14.9594	−	14.9594i	0.512200	−	0.512200i	0.915200	+	0.403000i	$0.132032\pi$
$854$	−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	−0.891901	−	0.452231i	$-0.850628\pi$
$857$	3.12136	−	11.6491i	0.106623	−	0.397924i	0.998524	+	0.0543068i	$0.0172949\pi$
$858$	3.24405	−	12.1070i	0.110750	−	0.413325i
$859$	−2.90061	+	5.02401i	−0.0989677	+	0.171417i	−0.911258	−	0.411837i	$-0.864887\pi$
$859$	−2.90061	+	5.02401i	−0.0989677	+	0.171417i	0.812290	+	0.583254i	$0.198221\pi$
$860$	−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	−0.209021	−	0.977911i	$-0.567028\pi$
$863$	2.90586	−	0.778623i	0.0989167	−	0.0265046i	0.307938	+	0.951406i	$0.400361\pi$
$864$	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	0.931778	+	0.363030i	$0.118258\pi$
$877$	9.07228	+	33.8582i	0.306349	+	1.14331i	−0.625428	+	0.780282i	$0.715076\pi$
$878$	−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	$-0.869207\pi$
$881$		−	23.7116i		−	0.798864i	0.916763	−	0.399432i	$-0.130793\pi$
$882$	−24.2266	+	29.4585i	−0.815753	+	0.991919i
$883$	−7.95370	−	7.95370i	−0.267663	−	0.267663i	0.560495	−	0.828158i	$-0.310611\pi$
$883$	−7.95370	−	7.95370i	−0.267663	−	0.267663i	−0.828158	+	0.560495i	$0.810611\pi$
$884$	−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	−0.573836	−	0.818970i	$-0.694545\pi$
$887$	−19.6954	+	5.27738i	−0.661308	+	0.177197i	−0.0874718	+	0.996167i	$0.527879\pi$
$888$	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	0.361775	−	0.932266i	$-0.382171\pi$
$907$	6.29276	+	1.68614i	0.208948	+	0.0559874i	−0.152827	+	0.988253i	$0.548838\pi$
$908$	−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	−0.113714	−	0.993513i	$-0.536275\pi$
$919$	−31.2542	−	18.0446i	−1.03098	−	0.595236i	−0.917265	+	0.398277i	$0.869608\pi$
$920$	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	0.274264	+	0.961654i	$0.411566\pi$
$929$	−21.2041	+	36.7266i	−0.695685	+	1.20496i	−0.969949	+	0.243307i	$0.921768\pi$
$930$	−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	0.770412	−	0.637546i	$-0.220050\pi$
$937$	4.06709	+	4.06709i	0.132866	+	0.132866i	−0.637546	+	0.770412i	$0.720050\pi$
$938$	−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	−0.756132	−	0.654419i	$-0.772913\pi$
$941$	−17.4071	+	10.0500i	−0.567455	+	0.327621i	0.188677	+	0.982039i	$0.439580\pi$
$942$	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	−0.525333	−	0.850897i	$-0.676059\pi$
$947$	−15.2583	−	56.9449i	−0.495830	−	1.85046i	0.0295030	−	0.999565i	$-0.490608\pi$
$948$	−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	−0.999971	−	0.00759828i	$-0.997581\pi$
$953$	−31.1044	−	31.1044i	−1.00757	−	1.00757i	−0.00759828	−	0.999971i	$-0.502419\pi$
$954$	−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	−0.962564	−	0.271054i	$-0.912628\pi$
$967$	−21.5036	+	21.5036i	−0.691510	+	0.691510i	0.271054	+	0.962564i	$0.412628\pi$
$968$	−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	−0.455158	−	0.890411i	$-0.650417\pi$
$971$	−45.3034	−	26.1559i	−1.45385	−	0.839384i	−0.998697	+	0.0510273i	$0.983750\pi$
$972$	−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	−0.764520	−	0.644599i	$-0.777024\pi$
$977$	−54.6658	−	14.6477i	−1.74891	−	0.468620i	−0.984394	+	0.175979i	$0.943691\pi$
$978$	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	0.489247	−	0.872145i	$-0.337272\pi$
$983$	14.9514	+	4.00621i	0.476875	+	0.127778i	−0.0123723	+	0.999923i	$0.503938\pi$
$984$	−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	0.878133	+	0.478417i	$0.158789\pi$
$991$	26.8648	+	46.5311i	0.853388	+	1.47811i	−0.0247453	+	0.999694i	$0.507877\pi$
$992$	−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	−0.607400	−	0.794396i	$-0.707787\pi$
$997$	9.97217	−	37.2167i	0.315822	−	1.17866i	0.923222	−	0.384267i	$-0.125546\pi$
$998$	−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.33.1	yes	16
3.2	odd	2		630.2.bv.c.523.4		16
4.3	odd	2		560.2.ci.c.33.4		16
5.2	odd	4	inner	70.2.k.a.47.3	yes	16
5.3	odd	4		350.2.o.c.257.2		16
5.4	even	2		350.2.o.c.243.4		16
7.2	even	3		490.2.g.c.293.4		16
7.3	odd	6	inner	70.2.k.a.3.3	✓	16
7.4	even	3		490.2.l.c.423.4		16
7.5	odd	6		490.2.g.c.293.1		16
7.6	odd	2		490.2.l.c.313.2		16
15.2	even	4		630.2.bv.c.397.1		16
20.7	even	4		560.2.ci.c.257.4		16
21.17	even	6		630.2.bv.c.73.1		16
28.3	even	6		560.2.ci.c.353.4		16
35.2	odd	12		490.2.g.c.97.1		16
35.3	even	12		350.2.o.c.157.4		16
35.12	even	12		490.2.g.c.97.4		16
35.17	even	12	inner	70.2.k.a.17.1	yes	16
35.24	odd	6		350.2.o.c.143.2		16
35.27	even	4		490.2.l.c.117.4		16
35.32	odd	12		490.2.l.c.227.2		16
105.17	odd	12		630.2.bv.c.577.4		16
140.87	odd	12		560.2.ci.c.17.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.k.a.3.3	✓	16	7.3	odd	6	inner
70.2.k.a.17.1	yes	16	35.17	even	12	inner
70.2.k.a.33.1	yes	16	1.1	even	1	trivial
70.2.k.a.47.3	yes	16	5.2	odd	4	inner
350.2.o.c.143.2		16	35.24	odd	6
350.2.o.c.157.4		16	35.3	even	12
350.2.o.c.243.4		16	5.4	even	2
350.2.o.c.257.2		16	5.3	odd	4
490.2.g.c.97.1		16	35.2	odd	12
490.2.g.c.97.4		16	35.12	even	12
490.2.g.c.293.1		16	7.5	odd	6
490.2.g.c.293.4		16	7.2	even	3
490.2.l.c.117.4		16	35.27	even	4
490.2.l.c.227.2		16	35.32	odd	12
490.2.l.c.313.2		16	7.6	odd	2
490.2.l.c.423.4		16	7.4	even	3
560.2.ci.c.17.4		16	140.87	odd	12
560.2.ci.c.33.4		16	4.3	odd	2
560.2.ci.c.257.4		16	20.7	even	4
560.2.ci.c.353.4		16	28.3	even	6
630.2.bv.c.73.1		16	21.17	even	6
630.2.bv.c.397.1		16	15.2	even	4
630.2.bv.c.523.4		16	3.2	odd	2
630.2.bv.c.577.4		16	105.17	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 70 = 2 \cdot 5 \cdot 7 \)
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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