LMFDB - Embedded newform 76.2.k.a.3.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,2,Mod(3,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("76.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	76.k (of order $18$, degree $6$, 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:	$0.606863055362$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			3.3
Character	$\chi$	$=$	76.3
Dual form			76.2.k.a.51.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19877 - 0.750298i) q^{2} +(2.80443 - 1.02073i) q^{3} +(0.874105 + 1.79887i) q^{4} +(-0.165124 + 0.936467i) q^{5} +(-4.12772 - 0.880539i) q^{6} +(-2.67390 + 1.54378i) q^{7} +(0.301838 - 2.81228i) q^{8} +(4.52481 - 3.79677i) q^{9} +O(q^{10})$	\(q+(-1.19877 - 0.750298i) q^{2} +(2.80443 - 1.02073i) q^{3} +(0.874105 + 1.79887i) q^{4} +(-0.165124 + 0.936467i) q^{5} +(-4.12772 - 0.880539i) q^{6} +(-2.67390 + 1.54378i) q^{7} +(0.301838 - 2.81228i) q^{8} +(4.52481 - 3.79677i) q^{9} +(0.900576 - 0.998718i) q^{10} +(-3.39303 - 1.95897i) q^{11} +(4.28753 + 4.15259i) q^{12} +(-0.284588 + 0.781900i) q^{13} +(4.36368 + 0.155587i) q^{14} +(0.492800 + 2.79481i) q^{15} +(-2.47188 + 3.14481i) q^{16} +(-3.14351 - 2.63772i) q^{17} +(-8.27293 + 1.15650i) q^{18} +(-0.473541 + 4.33310i) q^{19} +(-1.82892 + 0.521533i) q^{20} +(-5.92298 + 7.05874i) q^{21} +(2.59766 + 4.89414i) q^{22} +(2.45271 - 0.432479i) q^{23} +(-2.02409 - 8.19493i) q^{24} +(3.84876 + 1.40083i) q^{25} +(0.927814 - 0.723793i) q^{26} +(4.33744 - 7.51266i) q^{27} +(-5.11432 - 3.46058i) q^{28} +(1.95130 + 2.32547i) q^{29} +(1.50618 - 3.72008i) q^{30} +(0.560318 + 0.970499i) q^{31} +(5.32276 - 1.91526i) q^{32} +(-11.5151 - 2.03042i) q^{33} +(1.78928 + 5.52059i) q^{34} +(-1.00417 - 2.75893i) q^{35} +(10.7851 + 4.82079i) q^{36} -11.0692i q^{37} +(3.81878 - 4.83910i) q^{38} +2.48327i q^{39} +(2.58376 + 0.747037i) q^{40} +(1.74742 + 4.80099i) q^{41} +(12.3965 - 4.01781i) q^{42} +(2.92630 + 0.515985i) q^{43} +(0.558065 - 7.81597i) q^{44} +(2.80839 + 4.86428i) q^{45} +(-3.26472 - 1.32182i) q^{46} +(-2.23924 - 2.66862i) q^{47} +(-3.72222 + 11.3425i) q^{48} +(1.26648 - 2.19361i) q^{49} +(-3.56274 - 4.56699i) q^{50} +(-11.5082 - 4.18863i) q^{51} +(-1.65530 + 0.171525i) q^{52} +(-4.27071 + 0.753042i) q^{53} +(-10.8363 + 5.75159i) q^{54} +(2.39478 - 2.85399i) q^{55} +(3.53444 + 7.98571i) q^{56} +(3.09491 + 12.6352i) q^{57} +(-0.594368 - 4.25176i) q^{58} +(-0.677042 - 0.568105i) q^{59} +(-4.59674 + 3.32944i) q^{60} +(-1.74615 - 9.90290i) q^{61} +(0.0564707 - 1.58381i) q^{62} +(-6.23753 + 17.1375i) q^{63} +(-7.81779 - 1.69770i) q^{64} +(-0.685231 - 0.395618i) q^{65} +(12.2805 + 11.0738i) q^{66} +(6.32640 - 5.30848i) q^{67} +(1.99716 - 7.96042i) q^{68} +(6.43701 - 3.71641i) q^{69} +(-0.866253 + 4.06076i) q^{70} +(-1.66114 + 9.42079i) q^{71} +(-9.31180 - 13.8710i) q^{72} +(2.43877 - 0.887641i) q^{73} +(-8.30520 + 13.2694i) q^{74} +12.2235 q^{75} +(-8.20862 + 2.93575i) q^{76} +12.0968 q^{77} +(1.86319 - 2.97687i) q^{78} +(-3.07726 + 1.12003i) q^{79} +(-2.53684 - 2.83412i) q^{80} +(1.41857 - 8.04512i) q^{81} +(1.50742 - 7.06637i) q^{82} +(10.7084 - 6.18250i) q^{83} +(-17.8751 - 4.48461i) q^{84} +(2.98921 - 2.50824i) q^{85} +(-3.12082 - 2.81414i) q^{86} +(7.84597 + 4.52987i) q^{87} +(-6.53330 + 8.95084i) q^{88} +(-0.254375 + 0.698890i) q^{89} +(0.283039 - 7.93829i) q^{90} +(-0.446118 - 2.53006i) q^{91} +(2.92190 + 4.03408i) q^{92} +(2.56199 + 2.14976i) q^{93} +(0.682075 + 4.87917i) q^{94} +(-3.97961 - 1.15896i) q^{95} +(12.9724 - 10.8043i) q^{96} +(-6.10468 + 7.27528i) q^{97} +(-3.16409 + 1.67940i) q^{98} +(-22.7906 + 4.01859i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	$ 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) $ 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	−1.19877	−	0.750298i	−0.847659	−	0.530541i
$2$	−1.19877	−	0.750298i	−0.847659	−	0.530541i
$3$	2.80443	−	1.02073i	1.61914	−	0.589319i	0.635921	−	0.771754i	$-0.280620\pi$
$3$	2.80443	−	1.02073i	1.61914	−	0.589319i	0.983218	+	0.182435i	$0.0583980\pi$
$4$	0.874105	+	1.79887i	0.437053	+	0.899436i
$5$	−0.165124	+	0.936467i	−0.0738459	+	0.418801i	0.925365	+	0.379078i	$0.123759\pi$
$5$	−0.165124	+	0.936467i	−0.0738459	+	0.418801i	−0.999211	+	0.0397232i	$0.987352\pi$
$6$	−4.12772	−	0.880539i	−1.68514	−	0.359478i
$7$	−2.67390	+	1.54378i	−1.01064	+	0.583492i	−0.911378	−	0.411569i	$-0.864981\pi$
$7$	−2.67390	+	1.54378i	−1.01064	+	0.583492i	−0.0992597	+	0.995062i	$0.531647\pi$
$8$	0.301838	−	2.81228i	0.106716	−	0.994290i
$9$	4.52481	−	3.79677i	1.50827	−	1.26559i
$10$	0.900576	−	0.998718i	0.284787	−	0.315822i
$11$	−3.39303	−	1.95897i	−1.02304	−	0.590651i	−0.108055	−	0.994145i	$-0.534462\pi$
$11$	−3.39303	−	1.95897i	−1.02304	−	0.590651i	−0.914982	+	0.403494i	$0.867795\pi$
$12$	4.28753	+	4.15259i	1.23770	+	1.19875i
$13$	−0.284588	+	0.781900i	−0.0789306	+	0.216860i	−0.972881	−	0.231306i	$-0.925700\pi$
$13$	−0.284588	+	0.781900i	−0.0789306	+	0.216860i	0.893951	+	0.448166i	$0.147922\pi$
$14$	4.36368	+	0.155587i	1.16624	+	0.0415823i
$15$	0.492800	+	2.79481i	0.127240	+	0.721616i
$16$	−2.47188	+	3.14481i	−0.617970	+	0.786202i
$17$	−3.14351	−	2.63772i	−0.762414	−	0.639741i	0.176340	−	0.984329i	$-0.443574\pi$
$17$	−3.14351	−	2.63772i	−0.762414	−	0.639741i	−0.938754	+	0.344588i	$0.888019\pi$
$18$	−8.27293	+	1.15650i	−1.94995	+	0.272589i
$19$	−0.473541	+	4.33310i	−0.108638	+	0.994081i
$19$	−0.473541	+	4.33310i	−0.108638	+	0.994081i
$20$	−1.82892	+	0.521533i	−0.408959	+	0.116618i
$21$	−5.92298	+	7.05874i	−1.29250	+	1.54034i
$22$	2.59766	+	4.89414i	0.553822	+	1.04343i
$23$	2.45271	−	0.432479i	0.511425	−	0.0901780i	0.0880203	−	0.996119i	$-0.471946\pi$
$23$	2.45271	−	0.432479i	0.511425	−	0.0901780i	0.423405	+	0.905941i	$0.360835\pi$
$24$	−2.02409	−	8.19493i	−0.413165	−	1.67278i
$25$	3.84876	+	1.40083i	0.769752	+	0.280167i
$26$	0.927814	−	0.723793i	0.181959	−	0.141947i
$27$	4.33744	−	7.51266i	0.834740	−	1.44581i
$28$	−5.11432	−	3.46058i	−0.966516	−	0.653987i
$29$	1.95130	+	2.32547i	0.362347	+	0.431829i	0.916160	−	0.400812i	$-0.131272\pi$
$29$	1.95130	+	2.32547i	0.362347	+	0.431829i	−0.553813	+	0.832641i	$0.686828\pi$
$30$	1.50618	−	3.72008i	0.274990	−	0.679191i
$31$	0.560318	+	0.970499i	0.100636	+	0.174307i	0.911947	−	0.410308i	$-0.134579\pi$
$31$	0.560318	+	0.970499i	0.100636	+	0.174307i	−0.811311	+	0.584615i	$0.801246\pi$
$32$	5.32276	−	1.91526i	0.940940	−	0.338573i
$33$	−11.5151	−	2.03042i	−2.00452	−	0.353451i
$34$	1.78928	+	5.52059i	0.306858	+	0.946774i
$35$	−1.00417	−	2.75893i	−0.169736	−	0.466345i
$36$	10.7851	+	4.82079i	1.79751	+	0.803464i
$37$		−	11.0692i		−	1.81976i	−0.414866	−	0.909882i	$-0.636172\pi$
$37$		−	11.0692i		−	1.81976i	0.414866	−	0.909882i	$-0.363828\pi$
$38$	3.81878	−	4.83910i	0.619489	−	0.785006i
$39$			2.48327i			0.397642i
$40$	2.58376	+	0.747037i	0.408529	+	0.118117i
$41$	1.74742	+	4.80099i	0.272901	+	0.749788i	0.998121	+	0.0612717i	$0.0195156\pi$
$41$	1.74742	+	4.80099i	0.272901	+	0.749788i	−0.725220	+	0.688517i	$0.758262\pi$
$42$	12.3965	−	4.01781i	1.91282	−	0.619961i
$43$	2.92630	+	0.515985i	0.446256	+	0.0786870i	0.392260	−	0.919854i	$-0.371693\pi$
$43$	2.92630	+	0.515985i	0.446256	+	0.0786870i	0.0539956	+	0.998541i	$0.482804\pi$
$44$	0.558065	−	7.81597i	0.0841315	−	1.17830i
$45$	2.80839	+	4.86428i	0.418651	+	0.725124i
$46$	−3.26472	−	1.32182i	−0.481357	−	0.194892i
$47$	−2.23924	−	2.66862i	−0.326627	−	0.389259i	0.577594	−	0.816324i	$-0.303992\pi$
$47$	−2.23924	−	2.66862i	−0.326627	−	0.389259i	−0.904221	+	0.427066i	$0.859547\pi$
$48$	−3.72222	+	11.3425i	−0.537256	+	1.63715i
$49$	1.26648	−	2.19361i	0.180926	−	0.313373i
$50$	−3.56274	−	4.56699i	−0.503847	−	0.645871i
$51$	−11.5082	−	4.18863i	−1.61147	−	0.586525i
$52$	−1.65530	+	0.171525i	−0.229548	+	0.0237862i
$53$	−4.27071	+	0.753042i	−0.586627	+	0.103438i	−0.459081	−	0.888394i	$-0.651821\pi$
$53$	−4.27071	+	0.753042i	−0.586627	+	0.103438i	−0.127546	+	0.991833i	$0.540710\pi$
$54$	−10.8363	+	5.75159i	−1.47464	+	0.782692i
$55$	2.39478	−	2.85399i	0.322912	−	0.384832i
$56$	3.53444	+	7.98571i	0.472309	+	1.06713i
$57$	3.09491	+	12.6352i	0.409931	+	1.67358i
$58$	−0.594368	−	4.25176i	−0.0780443	−	0.558284i
$59$	−0.677042	−	0.568105i	−0.0881433	−	0.0739610i	0.597651	−	0.801756i	$-0.296101\pi$
$59$	−0.677042	−	0.568105i	−0.0881433	−	0.0739610i	−0.685795	+	0.727795i	$0.740545\pi$
$60$	−4.59674	+	3.32944i	−0.593437	+	0.429829i
$61$	−1.74615	−	9.90290i	−0.223571	−	1.26794i	−0.865398	−	0.501086i	$-0.832934\pi$
$61$	−1.74615	−	9.90290i	−0.223571	−	1.26794i	0.641826	−	0.766850i	$-0.278177\pi$
$62$	0.0564707	−	1.58381i	0.00717178	−	0.201144i
$63$	−6.23753	+	17.1375i	−0.785855	+	2.15912i
$64$	−7.81779	−	1.69770i	−0.977223	−	0.212213i
$65$	−0.685231	−	0.395618i	−0.0849924	−	0.0490704i
$66$	12.2805	+	11.0738i	1.51163	+	1.36309i
$67$	6.32640	−	5.30848i	0.772893	−	0.648535i	−0.168555	−	0.985692i	$-0.553910\pi$
$67$	6.32640	−	5.30848i	0.772893	−	0.648535i	0.941448	+	0.337158i	$0.109466\pi$
$68$	1.99716	−	7.96042i	0.242191	−	0.965343i
$69$	6.43701	−	3.71641i	0.774925	−	0.447403i
$70$	−0.866253	+	4.06076i	−0.103537	+	0.485353i
$71$	−1.66114	+	9.42079i	−0.197141	+	1.11804i	0.712195	+	0.701981i	$0.247701\pi$
$71$	−1.66114	+	9.42079i	−0.197141	+	1.11804i	−0.909337	+	0.416061i	$0.863410\pi$
$72$	−9.31180	−	13.8710i	−1.09741	−	1.63472i
$73$	2.43877	−	0.887641i	0.285437	−	0.103891i	−0.195334	−	0.980737i	$-0.562579\pi$
$73$	2.43877	−	0.887641i	0.285437	−	0.103891i	0.480771	+	0.876846i	$0.340357\pi$
$74$	−8.30520	+	13.2694i	−0.965460	+	1.54254i
$75$	12.2235			1.41144
$76$	−8.20862	+	2.93575i	−0.941593	+	0.336753i
$77$	12.0968			1.37856
$78$	1.86319	−	2.97687i	0.210965	−	0.337065i
$79$	−3.07726	+	1.12003i	−0.346219	+	0.126013i	−0.509276	−	0.860603i	$-0.670087\pi$
$79$	−3.07726	+	1.12003i	−0.346219	+	0.126013i	0.163057	+	0.986617i	$0.447865\pi$
$80$	−2.53684	−	2.83412i	−0.283627	−	0.316864i
$81$	1.41857	−	8.04512i	0.157619	−	0.893903i
$82$	1.50742	−	7.06637i	0.166467	−	0.780350i
$83$	10.7084	−	6.18250i	1.17540	−	0.678618i	0.220455	−	0.975397i	$-0.429246\pi$
$83$	10.7084	−	6.18250i	1.17540	−	0.678618i	0.954946	+	0.296779i	$0.0959126\pi$
$84$	−17.8751	−	4.48461i	−1.95033	−	0.489311i
$85$	2.98921	−	2.50824i	0.324225	−	0.272057i
$86$	−3.12082	−	2.81414i	−0.336526	−	0.303457i
$87$	7.84597	+	4.52987i	0.841176	+	0.485653i
$88$	−6.53330	+	8.95084i	−0.696452	+	0.954163i
$89$	−0.254375	+	0.698890i	−0.0269637	+	0.0740822i	−0.952444	−	0.304713i	$-0.901439\pi$
$89$	−0.254375	+	0.698890i	−0.0269637	+	0.0740822i	0.925480	+	0.378795i	$0.123662\pi$
$90$	0.283039	−	7.93829i	0.0298350	−	0.836770i
$91$	−0.446118	−	2.53006i	−0.0467658	−	0.265222i
$92$	2.92190	+	4.03408i	0.304629	+	0.420582i
$93$	2.56199	+	2.14976i	0.265666	+	0.222920i
$94$	0.682075	+	4.87917i	0.0703506	+	0.503248i
$95$	−3.97961	−	1.15896i	−0.408300	−	0.118906i
$96$	12.9724	−	10.8043i	1.32399	−	1.10271i
$97$	−6.10468	+	7.27528i	−0.619837	+	0.738693i	−0.981042	−	0.193794i	$-0.937921\pi$
$97$	−6.10468	+	7.27528i	−0.619837	+	0.738693i	0.361206	+	0.932486i	$0.382365\pi$
$98$	−3.16409	+	1.67940i	−0.319621	+	0.169645i
$99$	−22.7906	+	4.01859i	−2.29054	+	0.403884i
$100$	0.844300	+	8.14790i	0.0844300	+	0.814790i
$101$	−9.25142	−	3.36724i	−0.920550	−	0.335053i	−0.162093	−	0.986776i	$-0.551824\pi$
$101$	−9.25142	−	3.36724i	−0.920550	−	0.335053i	−0.758457	+	0.651723i	$0.774047\pi$
$102$	10.6529	+	13.6558i	1.05480	+	1.35212i
$103$	−0.981169	+	1.69943i	−0.0966774	+	0.167450i	−0.910307	−	0.413933i	$-0.864155\pi$
$103$	−0.981169	+	1.69943i	−0.0966774	+	0.167450i	0.813630	+	0.581383i	$0.197488\pi$
$104$	2.11302	+	1.03635i	0.207198	+	0.101622i
$105$	−5.63225	−	6.71225i	−0.549651	−	0.655049i
$106$	5.68461	+	2.30158i	0.552138	+	0.223550i
$107$	−1.49933	−	2.59691i	−0.144945	−	0.251053i	0.784407	−	0.620246i	$-0.212967\pi$
$107$	−1.49933	−	2.59691i	−0.144945	−	0.251053i	−0.929353	+	0.369193i	$0.879634\pi$
$108$	17.3057	+	1.23564i	1.66524	+	0.118899i
$109$	9.12021	+	1.60814i	0.873558	+	0.154032i	0.592414	−	0.805634i	$-0.298175\pi$
$109$	9.12021	+	1.60814i	0.873558	+	0.154032i	0.281144	+	0.959666i	$0.409286\pi$
$110$	−5.01214	+	1.62448i	−0.477888	+	0.154888i
$111$	−11.2987	−	31.0428i	−1.07242	−	2.94645i
$112$	1.75468	−	12.2249i	0.165802	−	1.15515i
$113$			10.5830i			0.995568i	0.867301	+	0.497784i	$0.165853\pi$
$113$			10.5830i			0.995568i	−0.867301	+	0.497784i	$0.834147\pi$
$114$	5.77011	−	17.4689i	0.540420	−	1.63611i
$115$			2.36829i			0.220845i
$116$	−2.47758	+	5.54285i	−0.230038	+	0.514640i
$117$	1.68098	+	4.61847i	0.155407	+	0.426977i
$118$	0.385370	+	1.18901i	0.0354761	+	0.109457i
$119$	12.4775	+	2.20012i	1.14381	+	0.201684i
$120$	8.00851	−	0.542310i	0.731074	−	0.0495059i
$121$	2.17510	+	3.76738i	0.197736	+	0.342489i
$122$	−5.33689	+	13.1814i	−0.483180	+	1.19339i
$123$	9.80102	+	11.6804i	0.883728	+	1.05319i
$124$	−1.25603	+	1.85626i	−0.112794	+	0.166697i
$125$	−4.32464	+	7.49050i	−0.386808	+	0.669971i
$126$	20.3356	−	15.8639i	1.81164	−	1.41327i
$127$	−1.50832	−	0.548984i	−0.133842	−	0.0487144i	0.274231	−	0.961664i	$-0.411577\pi$
$127$	−1.50832	−	0.548984i	−0.133842	−	0.0487144i	−0.408073	+	0.912949i	$0.633799\pi$
$128$	8.09795	+	7.90083i	0.715765	+	0.698341i
$129$	8.73328	−	1.53991i	0.768922	−	0.135582i
$130$	0.524604	+	0.988383i	0.0460108	+	0.0866870i
$131$	−6.30386	+	7.51265i	−0.550771	+	0.656383i	−0.967566	−	0.252617i	$-0.918709\pi$
$131$	−6.30386	+	7.51265i	−0.550771	+	0.656383i	0.416795	+	0.909000i	$0.363153\pi$
$132$	−6.41293	−	22.4890i	−0.558174	−	1.95741i
$133$	−5.42313	−	12.3173i	−0.470245	−	1.06805i
$134$	−11.5669	+	1.61697i	−0.999224	+	0.139685i
$135$	6.31914	+	5.30239i	0.543865	+	0.456357i
$136$	−8.36683	+	8.04426i	−0.717449	+	0.689789i
$137$	−0.959987	−	5.44436i	−0.0820172	−	0.465143i	−0.997960	−	0.0638350i	$-0.979667\pi$
$137$	−0.959987	−	5.44436i	−0.0820172	−	0.465143i	0.915943	−	0.401308i	$-0.131444\pi$
$138$	−10.5049	−	0.374552i	−0.894238	−	0.0318840i
$139$	3.12444	−	8.58433i	0.265012	−	0.728113i	−0.733800	−	0.679366i	$-0.762255\pi$
$139$	3.12444	−	8.58433i	0.265012	−	0.728113i	0.998811	−	0.0487473i	$-0.0155229\pi$
$140$	4.08522	−	4.21797i	0.345264	−	0.356483i
$141$	−9.00374	−	5.19831i	−0.758252	−	0.437777i
$142$	9.05973	−	10.0470i	0.760276	−	0.843128i
$143$	2.49733	−	2.09551i	0.208837	−	0.175235i
$144$	0.755308	+	23.6148i	0.0629424	+	1.96790i
$145$	−2.49993	+	1.44334i	−0.207608	+	0.119863i
$146$	−3.58953	−	0.765729i	−0.297072	−	0.0633722i
$147$	1.31268	−	7.44458i	0.108268	−	0.614018i
$148$	19.9121	−	9.67564i	1.63676	−	0.795333i
$149$	−17.4242	+	6.34187i	−1.42744	+	0.519547i	−0.936197	−	0.351475i	$-0.885680\pi$
$149$	−17.4242	+	6.34187i	−1.42744	+	0.519547i	−0.491245	+	0.871021i	$0.663458\pi$
$150$	−14.6531	−	9.17123i	−1.19642	−	0.748828i
$151$	19.1746			1.56040			0.780202	−	0.625527i	$-0.215116\pi$
$151$	19.1746			1.56040			0.780202	+	0.625527i	$0.215116\pi$
$152$	12.0429	+	2.63962i	0.976811	+	0.214102i
$153$	−24.2386			−1.95958
$154$	−14.5013	−	9.07622i	−1.16855	−	0.731383i
$155$	−1.00136	+	0.364466i	−0.0804314	+	0.0292746i
$156$	−4.46709	+	2.17064i	−0.357653	+	0.173790i
$157$	−1.38284	+	7.84250i	−0.110363	+	0.625899i	0.878579	+	0.477597i	$0.158492\pi$
$157$	−1.38284	+	7.84250i	−0.110363	+	0.625899i	−0.988942	+	0.148303i	$0.952619\pi$
$158$	4.52929	+	0.966202i	0.360331	+	0.0768669i
$159$	−11.2083	+	6.47110i	−0.888874	+	0.513191i
$160$	0.914657	+	5.30085i	0.0723100	+	0.419069i
$161$	−5.89064	+	4.94283i	−0.464247	+	0.389550i
$162$	−7.73679	+	8.57991i	−0.607859	+	0.674101i
$163$	−14.7556	−	8.51913i	−1.15574	−	0.667269i	−0.205464	−	0.978665i	$-0.565870\pi$
$163$	−14.7556	−	8.51913i	−1.15574	−	0.667269i	−0.950281	+	0.311395i	$0.899204\pi$
$164$	−7.10894	+	7.33995i	−0.555115	+	0.573154i
$165$	3.80285	−	10.4482i	0.296051	−	0.813394i
$166$	−17.4757	−	0.623093i	−1.35637	−	0.0483614i
$167$	2.11555	+	11.9979i	0.163706	+	0.928422i	0.950389	+	0.311065i	$0.100686\pi$
$167$	2.11555	+	11.9979i	0.163706	+	0.928422i	−0.786683	+	0.617357i	$0.788203\pi$
$168$	18.0633	+	18.7877i	1.39362	+	1.44950i
$169$	9.42820	+	7.91120i	0.725246	+	0.608554i
$170$	−5.46531	+	0.764013i	−0.419170	+	0.0585971i
$171$	14.3091	+	21.4044i	1.09424	+	1.63684i
$172$	1.62970	+	5.71506i	0.124263	+	0.435769i
$173$	14.0933	−	16.7958i	1.07150	−	1.27696i	0.112465	−	0.993656i	$-0.464125\pi$
$173$	14.0933	−	16.7958i	1.07150	−	1.27696i	0.959030	−	0.283303i	$-0.0914303\pi$
$174$	−6.00676	−	11.3171i	−0.455372	−	0.857947i
$175$	−12.4538	+	2.19593i	−0.941415	+	0.165997i
$176$	14.5477	−	5.82809i	1.09658	−	0.439309i
$177$	−2.47860	−	0.902136i	−0.186303	−	0.0678087i
$178$	0.829313	−	0.646952i	0.0621597	−	0.0484911i
$179$	0.183973	−	0.318651i	0.0137508	−	0.0238171i	−0.859068	−	0.511861i	$-0.828956\pi$
$179$	0.183973	−	0.318651i	0.0137508	−	0.0238171i	0.872819	+	0.488044i	$0.162290\pi$
$180$	−6.29539	+	9.30383i	−0.469230	+	0.693467i
$181$	12.1366	+	14.4639i	0.902109	+	1.07509i	0.996828	+	0.0795875i	$0.0253603\pi$
$181$	12.1366	+	14.4639i	0.902109	+	1.07509i	−0.0947190	+	0.995504i	$0.530195\pi$
$182$	−1.36351	+	3.36768i	−0.101070	+	0.249629i
$183$	−15.0051	−	25.9896i	−1.10921	−	1.92121i
$184$	−0.475928	−	7.02823i	−0.0350859	−	0.518128i
$185$	10.3659	+	1.82780i	0.762119	+	0.134382i
$186$	−1.45828	−	4.49933i	−0.106926	−	0.329907i
$187$	5.49882	+	15.1079i	0.402114	+	1.10480i
$188$	2.84318	−	6.36077i	0.207360	−	0.463907i
$189$			26.7841i			1.94826i
$190$	3.90108	+	4.37522i	0.283014	+	0.317412i
$191$			14.9125i			1.07903i	0.841975	+	0.539516i	$0.181393\pi$
$191$			14.9125i			1.07903i	−0.841975	+	0.539516i	$0.818607\pi$
$192$	−23.6573	+	3.21875i	−1.70732	+	0.232293i
$193$	−2.55696	−	7.02519i	−0.184054	−	0.505684i	0.813011	−	0.582249i	$-0.197827\pi$
$193$	−2.55696	−	7.02519i	−0.184054	−	0.505684i	−0.997065	+	0.0765647i	$0.975605\pi$
$194$	12.7767	−	4.14106i	0.917317	−	0.297311i
$195$	−2.32550	−	0.410049i	−0.166533	−	0.0293642i
$196$	5.05307	+	0.360792i	0.360934	+	0.0257709i
$197$	−10.7161	−	18.5607i	−0.763487	−	1.32240i	−0.941043	−	0.338288i	$-0.890152\pi$
$197$	−10.7161	−	18.5607i	−0.763487	−	1.32240i	0.177556	−	0.984111i	$-0.443181\pi$
$198$	30.3358	+	12.2824i	2.15587	+	0.872869i
$199$	−16.4631	−	19.6199i	−1.16704	−	1.39082i	−0.904812	−	0.425812i	$-0.859988\pi$
$199$	−16.4631	−	19.6199i	−1.16704	−	1.39082i	−0.262224	−	0.965007i	$-0.584456\pi$
$200$	5.10123	−	10.4009i	0.360712	−	0.735458i
$201$	12.3234	−	21.3448i	0.869229	−	1.50555i
$202$	8.56390	+	10.9779i	0.602554	+	0.772400i
$203$	−8.80758	−	3.20570i	−0.618171	−	0.224996i
$204$	−2.52454	−	24.3630i	−0.176753	−	1.70575i
$205$	−4.78451	+	0.843638i	−0.334165	+	0.0589223i
$206$	2.45128	−	1.30106i	0.170789	−	0.0906494i
$207$	9.45603	−	11.2693i	0.657239	−	0.783267i
$208$	−1.75546	−	2.82774i	−0.121719	−	0.196068i
$209$	10.0951	−	13.7747i	0.698295	−	0.952815i
$210$	1.71559	+	12.2723i	0.118387	+	0.846871i
$211$	2.40668	+	2.01944i	0.165682	+	0.139024i	0.721859	−	0.692040i	$-0.243288\pi$
$211$	2.40668	+	2.01944i	0.165682	+	0.139024i	−0.556177	+	0.831064i	$0.687732\pi$
$212$	−5.08768	−	7.02423i	−0.349423	−	0.482426i
$213$	4.95753	+	28.1155i	0.339684	+	1.92645i
$214$	−0.151107	+	4.23804i	−0.0103295	+	0.289707i
$215$	−0.966406	+	2.65518i	−0.0659084	+	0.181082i
$216$	−19.8185	−	14.4657i	−1.34848	−	0.984264i
$217$	−2.99646	−	1.73001i	−0.203413	−	0.117441i
$218$	−9.72646	−	8.77067i	−0.658759	−	0.594025i
$219$	5.93333	−	4.97866i	0.400938	−	0.336427i
$220$	7.22725	+	1.81322i	0.487261	+	0.122247i
$221$	2.95704	−	1.70725i	0.198912	−	0.114842i
$222$	−9.74686	+	45.6906i	−0.654166	+	3.06655i
$223$	−0.648948	+	3.68036i	−0.0434567	+	0.246455i	−0.998796	−	0.0490557i	$-0.984379\pi$
$223$	−0.648948	+	3.68036i	−0.0434567	+	0.246455i	0.955339	+	0.295511i	$0.0954899\pi$
$224$	−11.2758	+	13.3383i	−0.753395	+	0.891206i
$225$	22.7336	−	8.27434i	1.51557	−	0.551623i
$226$	7.94043	−	12.6866i	0.528190	−	0.843903i
$227$	−14.1806			−0.941200			−0.470600	−	0.882347i	$-0.655963\pi$
$227$	−14.1806			−0.941200			−0.470600	+	0.882347i	$0.655963\pi$
$228$	−20.0239	+	16.6119i	−1.32612	+	1.10015i
$229$	−7.84295			−0.518276			−0.259138	−	0.965840i	$-0.583439\pi$
$229$	−7.84295			−0.518276			−0.259138	+	0.965840i	$0.583439\pi$
$230$	1.77693	−	2.83904i	0.117167	−	0.187201i
$231$	33.9247	−	12.3476i	2.23208	−	0.812411i
$232$	7.12884	−	4.78568i	0.468031	−	0.314195i
$233$	0.355231	−	2.01461i	0.0232719	−	0.131982i	−0.970958	−	0.239249i	$-0.923099\pi$
$233$	0.355231	−	2.01461i	0.0232719	−	0.131982i	0.994230	+	0.107267i	$0.0342100\pi$
$234$	1.45011	−	6.79772i	0.0947967	−	0.444381i
$235$	2.86883	−	1.65632i	0.187142	−	0.108047i
$236$	0.430143	−	1.71450i	0.0279999	−	0.111604i
$237$	−7.48672	+	6.28210i	−0.486315	+	0.408067i
$238$	−13.3069	−	11.9993i	−0.862558	−	0.777797i
$239$	19.1085	+	11.0323i	1.23603	+	0.713621i	0.968280	−	0.249867i	$-0.0803870\pi$
$239$	19.1085	+	11.0323i	1.23603	+	0.713621i	0.267749	+	0.963489i	$0.413720\pi$
$240$	−10.0073	−	5.35867i	−0.645966	−	0.345900i
$241$	−3.29430	+	9.05100i	−0.212204	+	0.583026i	−0.999434	−	0.0336331i	$-0.989292\pi$
$241$	−3.29430	+	9.05100i	−0.212204	+	0.583026i	0.787230	+	0.616659i	$0.211514\pi$
$242$	0.219214	−	6.14820i	0.0140916	−	0.395221i
$243$	0.285520	+	1.61927i	0.0183161	+	0.103876i
$244$	16.2877	−	11.7973i	1.04271	−	0.755243i
$245$	1.84512	+	1.54824i	0.117880	+	0.0989134i
$246$	−2.98540	−	21.3558i	−0.190342	−	1.36160i
$247$	−3.25329	−	1.60341i	−0.207002	−	0.102023i
$248$	2.89844	−	1.28283i	0.184051	−	0.0814601i
$249$	23.7203	−	28.2688i	1.50322	−	1.79146i
$250$	10.8044	−	5.73463i	0.683328	−	0.362690i
$251$	1.62834	−	0.287120i	0.102780	−	0.0181229i	−0.122022	−	0.992527i	$-0.538938\pi$
$251$	1.62834	−	0.287120i	0.102780	−	0.0181229i	0.224802	+	0.974405i	$0.427827\pi$
$252$	−36.2804	+	3.75944i	−2.28545	+	0.236822i
$253$	−9.16932	−	3.33736i	−0.576470	−	0.209818i
$254$	1.39623	+	1.78980i	0.0876072	+	0.112302i
$255$	5.82279	−	10.0854i	0.364638	−	0.631571i
$256$	−3.77962	−	15.5472i	−0.236226	−	0.971698i
$257$	13.2973	+	15.8471i	0.829460	+	0.988512i	0.999995	+	0.00316078i	$0.00100611\pi$
$257$	13.2973	+	15.8471i	0.829460	+	0.988512i	−0.170535	+	0.985352i	$0.554549\pi$
$258$	−11.6246	−	4.70656i	−0.723716	−	0.293018i
$259$	17.0884	+	29.5979i	1.06182	+	1.83912i
$260$	0.112703	−	1.57845i	0.00698952	−	0.0978916i
$261$	17.6585	+	3.11368i	1.09304	+	0.192732i
$262$	13.1936	−	4.27617i	0.815104	−	0.264183i
$263$	−5.04518	−	13.8615i	−0.311099	−	0.854738i	−0.992435	−	0.122767i	$-0.960823\pi$
$263$	−5.04518	−	13.8615i	−0.311099	−	0.854738i	0.681336	−	0.731970i	$-0.261399\pi$
$264$	−9.18580	+	31.7708i	−0.565347	+	1.95535i
$265$		−	4.12373i		−	0.253319i
$266$	−2.74056	+	18.8346i	−0.168034	+	1.15482i
$267$			2.21964i			0.135840i
$268$	15.0792	+	6.74022i	0.921110	+	0.411724i
$269$	−2.61291	−	7.17890i	−0.159312	−	0.437705i	0.834196	−	0.551468i	$-0.185932\pi$
$269$	−2.61291	−	7.17890i	−0.159312	−	0.437705i	−0.993508	+	0.113762i	$0.963710\pi$
$270$	−3.59683	−	11.0976i	−0.218896	−	0.675378i
$271$	1.47921	+	0.260825i	0.0898557	+	0.0158440i	0.218395	−	0.975860i	$-0.429918\pi$
$271$	1.47921	+	0.260825i	0.0898557	+	0.0158440i	−0.128540	+	0.991704i	$0.541029\pi$
$272$	16.0655	−	3.36561i	0.974114	−	0.204070i
$273$	−3.83361	−	6.64001i	−0.232021	−	0.401872i
$274$	−2.93409	+	7.24682i	−0.177255	+	0.437796i
$275$	−10.3148	−	12.2927i	−0.622004	−	0.741275i
$276$	12.3120	+	8.33082i	0.741093	+	0.501457i
$277$	−5.63204	+	9.75498i	−0.338397	+	0.586120i	−0.984131	−	0.177442i	$-0.943218\pi$
$277$	−5.63204	+	9.75498i	−0.338397	+	0.586120i	0.645735	+	0.763562i	$0.276551\pi$
$278$	−10.1863	+	7.94639i	−0.610934	+	0.476593i
$279$	6.22009	+	2.26393i	0.372387	+	0.135538i
$280$	−8.06198	+	1.99125i	−0.481795	+	0.119000i
$281$	−22.5573	+	3.97746i	−1.34566	+	0.237275i	−0.799630	−	0.600493i	$-0.794971\pi$
$281$	−22.5573	+	3.97746i	−1.34566	+	0.237275i	−0.546026	+	0.837769i	$0.683860\pi$
$282$	6.89314	+	12.9871i	0.410481	+	0.773370i
$283$	−11.9630	+	14.2570i	−0.711128	+	0.847490i	−0.993737	−	0.111746i	$-0.964356\pi$
$283$	−11.9630	+	14.2570i	−0.711128	+	0.847490i	0.282608	+	0.959235i	$0.408800\pi$
$284$	−18.3988	+	5.24659i	−1.09177	+	0.311328i
$285$	−12.3435	+	0.811895i	−0.731168	+	0.0480925i
$286$	−4.56599	+	0.638294i	−0.269992	+	0.0377431i
$287$	−12.0841	−	10.1397i	−0.713299	−	0.598529i
$288$	16.8127	−	28.8755i	0.990699	−	1.70150i
$289$	−0.0279168	−	0.158324i	−0.00164216	−	0.00931317i
$290$	4.07978	+	0.145464i	0.239573	+	0.00854196i
$291$	−9.69408	+	26.6343i	−0.568277	+	1.56133i
$292$	3.72850	+	3.61115i	0.218194	+	0.211327i
$293$	17.6564	+	10.1939i	1.03150	+	0.595536i	0.917414	−	0.397934i	$-0.130273\pi$
$293$	17.6564	+	10.1939i	1.03150	+	0.595536i	0.114086	+	0.993471i	$0.463606\pi$
$294$	−7.15926	+	7.93944i	−0.417536	+	0.463038i
$295$	0.643808	−	0.540219i	0.0374840	−	0.0314528i
$296$	−31.1296	−	3.34111i	−1.80937	−	0.194198i
$297$	−29.4341	+	16.9938i	−1.70794	+	0.986079i
$298$	25.6459	+	5.47086i	1.48563	+	0.316918i
$299$	−0.359857	+	2.04085i	−0.0208111	+	0.118025i
$300$	10.6846	+	21.9884i	0.616875	+	1.26950i
$301$	−8.62118	+	3.13785i	−0.496917	+	0.180863i
$302$	−22.9859	−	14.3866i	−1.32269	−	0.827859i
$303$	−29.3820			−1.68795
$304$	−12.4562	−	12.2001i	−0.714414	−	0.699724i
$305$	9.56207			0.547523
$306$	29.0566	+	18.1862i	1.66105	+	1.03964i
$307$	−27.2216	+	9.90786i	−1.55362	+	0.565472i	−0.969263	−	0.246025i	$-0.920875\pi$
$307$	−27.2216	+	9.90786i	−1.55362	+	0.565472i	−0.584357	+	0.811497i	$0.698653\pi$
$308$	10.5739	+	21.7606i	0.602503	+	1.23993i
$309$	−1.01696	+	5.76746i	−0.0578527	+	0.328099i
$310$	1.47386	+	0.314409i	0.0837098	+	0.0178572i
$311$	−8.00357	+	4.62086i	−0.453841	+	0.262025i	−0.709451	−	0.704755i	$-0.751057\pi$
$311$	−8.00357	+	4.62086i	−0.453841	+	0.262025i	0.255610	+	0.966780i	$0.417724\pi$
$312$	6.98364	+	0.749546i	0.395371	+	0.0424347i
$313$	−19.3111	+	16.2039i	−1.09153	+	0.915898i	−0.996826	−	0.0796075i	$-0.974633\pi$
$313$	−19.3111	+	16.2039i	−1.09153	+	0.915898i	−0.0946990	+	0.995506i	$0.530189\pi$
$314$	7.54193	−	8.36382i	0.425616	−	0.471997i
$315$	−15.0187	−	8.67106i	−0.846209	−	0.488559i
$316$	−4.70464	−	4.55657i	−0.264657	−	0.256327i
$317$	10.3833	−	28.5279i	0.583185	−	1.60229i	−0.199518	−	0.979894i	$-0.563938\pi$
$317$	10.3833	−	28.5279i	0.583185	−	1.60229i	0.782703	−	0.622395i	$-0.213840\pi$
$318$	18.2914	+	0.652179i	1.02573	+	0.0365724i
$319$	−2.06530	−	11.7129i	−0.115635	−	0.655798i
$320$	2.88075	−	7.04077i	0.161039	−	0.393591i
$321$	−6.85550	−	5.75245i	−0.382637	−	0.321071i
$322$	10.7701	−	1.50559i	0.600196	−	0.0839033i
$323$	12.9181	−	12.3721i	0.718782	−	0.688401i
$324$	15.7121	−	4.48045i	0.872896	−	0.248914i
$325$	−2.19062	+	2.61068i	−0.121514	+	0.144815i
$326$	11.2967	+	21.2836i	0.625664	+	1.17879i
$327$	27.2185	−	4.79935i	1.50519	−	0.265405i
$328$	14.0291	−	3.46510i	0.774630	−	0.191328i
$329$	10.1073	+	3.67874i	0.557231	+	0.202816i
$330$	−12.3980	+	9.67178i	−0.682490	+	0.532414i
$331$	10.1102	−	17.5114i	0.555707	−	0.962514i	−0.442141	−	0.896946i	$-0.645781\pi$
$331$	10.1102	−	17.5114i	0.555707	−	0.962514i	0.997848	−	0.0655678i	$-0.0208859\pi$
$332$	20.4818	+	13.8589i	1.12409	+	0.760606i
$333$	−42.0272	−	50.0861i	−2.30308	−	2.74470i
$334$	6.46591	−	15.9700i	0.353799	−	0.873838i
$335$	3.92658	+	6.80103i	0.214532	+	0.371580i
$336$	−7.55746	−	36.0750i	−0.412293	−	1.96805i
$337$	−12.9142	−	2.27711i	−0.703479	−	0.124042i	−0.189545	−	0.981872i	$-0.560701\pi$
$337$	−12.9142	−	2.27711i	−0.703479	−	0.124042i	−0.513934	+	0.857830i	$0.671812\pi$
$338$	−5.36650	−	16.5577i	−0.291899	−	0.900619i
$339$	10.8024	+	29.6794i	0.586707	+	1.61196i
$340$	7.12489	+	3.18474i	0.386402	+	0.172717i
$341$		−	4.39057i		−	0.237763i
$342$	−1.09365	−	36.3951i	−0.0591381	−	1.96802i
$343$		−	13.7922i		−	0.744708i
$344$	2.33436	−	8.07381i	0.125860	−	0.435311i
$345$	2.41739	+	6.64172i	0.130148	+	0.357578i
$346$	−29.4965	+	9.56009i	−1.58574	+	0.513954i
$347$	−4.62735	−	0.815927i	−0.248409	−	0.0438013i	0.0480569	−	0.998845i	$-0.484697\pi$
$347$	−4.62735	−	0.815927i	−0.248409	−	0.0438013i	−0.296466	+	0.955043i	$0.595808\pi$
$348$	−1.29046	+	18.0735i	−0.0691758	+	0.968840i
$349$	10.8285	+	18.7555i	0.579636	+	1.00396i	0.995521	+	0.0945424i	$0.0301388\pi$
$349$	10.8285	+	18.7555i	0.579636	+	1.00396i	−0.415884	+	0.909418i	$0.636528\pi$
$350$	16.5768	+	6.71161i	0.886068	+	0.358751i
$351$	4.63976	+	5.52945i	0.247652	+	0.295140i
$352$	−21.8122	−	3.92859i	−1.16259	−	0.209395i
$353$	−12.4664	+	21.5924i	−0.663519	+	1.14925i	0.316166	+	0.948704i	$0.397604\pi$
$353$	−12.4664	+	21.5924i	−0.663519	+	1.14925i	−0.979685	+	0.200544i	$0.935729\pi$
$354$	2.29440	+	2.94114i	0.121946	+	0.156320i
$355$	−8.54797	−	3.11121i	−0.453679	−	0.165126i
$356$	−1.47956	+	0.153315i	−0.0784167	+	0.00812568i
$357$	37.2379	−	6.56605i	1.97084	−	0.347512i
$358$	−0.459625	+	0.243955i	−0.0242919	+	0.0128934i
$359$	15.4763	−	18.4439i	0.816807	−	0.973433i	−0.183146	−	0.983086i	$-0.558628\pi$
$359$	15.4763	−	18.4439i	0.816807	−	0.973433i	0.999953	+	0.00965302i	$0.00307270\pi$
$360$	14.5274	−	6.42975i	0.765660	−	0.338878i
$361$	−18.5515	−	4.10380i	−0.976396	−	0.215990i
$362$	−3.69683	−	26.4450i	−0.194301	−	1.38992i
$363$	9.94539	+	8.34518i	0.521998	+	0.438008i
$364$	4.16130	−	3.01405i	0.218111	−	0.157979i
$365$	0.428546	+	2.43040i	0.0224311	+	0.127213i
$366$	−1.51227	+	42.4140i	−0.0790475	+	2.21701i
$367$	3.55314	−	9.76216i	0.185472	−	0.509581i	−0.811755	−	0.583998i	$-0.801487\pi$
$367$	3.55314	−	9.76216i	0.185472	−	0.509581i	0.997227	+	0.0744174i	$0.0237097\pi$
$368$	−4.70274	+	8.78233i	−0.245147	+	0.457811i
$369$	26.1350	+	15.0890i	1.36053	+	0.785504i
$370$	−11.0550	−	9.96866i	−0.574722	−	0.518246i
$371$	10.2569	−	8.60658i	0.532513	−	0.446831i
$372$	−1.62770	+	6.48781i	−0.0843924	+	0.336377i
$373$	7.05267	−	4.07186i	0.365173	−	0.210833i	−0.306174	−	0.951975i	$-0.599049\pi$
$373$	7.05267	−	4.07186i	0.365173	−	0.210833i	0.671348	+	0.741143i	$0.265716\pi$
$374$	4.74359	−	22.2367i	0.245285	−	1.14983i
$375$	−4.48239	+	25.4209i	−0.231470	+	1.31273i
$376$	−8.18080	+	5.49187i	−0.421892	+	0.283222i
$377$	−2.37360	+	0.863920i	−0.122247	+	0.0444941i
$378$	20.0961	−	32.1080i	1.03363	−	1.65146i
$379$	26.6265			1.36771			0.683856	−	0.729617i	$-0.260302\pi$
$379$	26.6265			1.36771			0.683856	+	0.729617i	$0.260302\pi$
$380$	−1.39379	−	8.17187i	−0.0714998	−	0.419208i
$381$	−4.79035			−0.245417
$382$	11.1888	−	17.8767i	0.572471	−	0.914652i
$383$	17.2405	−	6.27503i	0.880948	−	0.320639i	0.138356	−	0.990383i	$-0.455818\pi$
$383$	17.2405	−	6.27503i	0.880948	−	0.320639i	0.742592	+	0.669744i	$0.233596\pi$
$384$	30.7748	+	13.8915i	1.57047	+	0.708899i
$385$	−1.99748	+	11.3283i	−0.101801	+	0.577342i
$386$	−2.20578	+	10.3401i	−0.112271	+	0.526296i
$387$	15.2000	−	8.77574i	0.772661	−	0.446096i
$388$	−18.4234	−	4.62219i	−0.935308	−	0.234656i
$389$	13.8384	−	11.6118i	0.701634	−	0.588741i	−0.220604	−	0.975364i	$-0.570803\pi$
$389$	13.8384	−	11.6118i	0.701634	−	0.588741i	0.922238	+	0.386622i	$0.126358\pi$
$390$	2.48009	+	2.23638i	0.125584	+	0.113243i
$391$	−8.85088	−	5.11006i	−0.447608	−	0.258427i
$392$	−5.78677	−	4.22382i	−0.292276	−	0.213335i
$393$	−10.0104	+	27.5033i	−0.504956	+	1.38736i
$394$	−1.08000	+	30.2903i	−0.0544096	+	1.52600i
$395$	−0.540742	−	3.06670i	−0.0272077	−	0.154302i
$396$	−27.1503	−	37.4846i	−1.36435	−	1.88367i
$397$	0.378892	+	0.317928i	0.0190160	+	0.0159564i	0.652246	−	0.758007i	$-0.273827\pi$
$397$	0.378892	+	0.317928i	0.0190160	+	0.0159564i	−0.633230	+	0.773964i	$0.718271\pi$
$398$	5.01466	+	35.8720i	0.251362	+	1.79810i
$399$	−27.7814	−	29.0075i	−1.39081	−	1.45219i
$400$	−13.9190	+	8.64091i	−0.695951	+	0.432045i
$401$	−18.6318	+	22.2046i	−0.930430	+	1.10884i	0.0634064	+	0.997988i	$0.479804\pi$
$401$	−18.6318	+	22.2046i	−0.930430	+	1.10884i	−0.993837	+	0.110856i	$0.964641\pi$
$402$	−30.7880	+	16.3413i	−1.53556	+	0.815031i
$403$	−0.918292	+	0.161920i	−0.0457434	+	0.00806580i
$404$	−2.02948	−	19.5854i	−0.100970	−	0.974412i
$405$	7.29976	+	2.65689i	0.362728	+	0.132022i
$406$	8.15305	+	10.4512i	0.404629	+	0.518685i
$407$	−21.6842	+	37.5581i	−1.07485	+	1.86169i
$408$	−15.2532	+	31.0998i	−0.755145	+	1.53967i
$409$	4.45901	+	5.31404i	0.220484	+	0.262762i	0.864936	−	0.501882i	$-0.167359\pi$
$409$	4.45901	+	5.31404i	0.220484	+	0.262762i	−0.644452	+	0.764645i	$0.722914\pi$
$410$	6.36851	+	2.57848i	0.314519	+	0.127342i
$411$	−8.24944	−	14.2884i	−0.406915	−	0.704797i
$412$	−3.91471	−	0.279513i	−0.192864	−	0.0137706i
$413$	2.68737	+	0.473855i	0.132237	+	0.0233169i
$414$	−19.7909	+	6.41442i	−0.972671	+	0.315251i
$415$	4.02149	+	11.0490i	0.197407	+	0.542372i
$416$	−0.0172568	+	4.70692i	−0.000846084	+	0.230776i
$417$		−	27.2634i		−	1.33509i
$418$	−22.4369	+	8.93833i	−1.09742	+	0.437188i
$419$		−	25.1365i		−	1.22800i	−0.789307	−	0.613999i	$-0.789560\pi$
$419$		−	25.1365i		−	1.22800i	0.789307	−	0.613999i	$-0.210440\pi$
$420$	7.15130	−	15.9989i	0.348948	−	0.780667i
$421$	−8.13950	−	22.3631i	−0.396695	−	1.08991i	−0.963884	−	0.266323i	$-0.914191\pi$
$421$	−8.13950	−	22.3631i	−0.396695	−	1.08991i	0.567189	−	0.823588i	$-0.308031\pi$
$422$	−1.36987	−	4.22657i	−0.0666843	−	0.205746i
$423$	−20.2643	−	3.57314i	−0.985284	−	0.173732i
$424$	0.828697	+	12.2377i	0.0402451	+	0.594316i
$425$	−8.40361	−	14.5555i	−0.407635	−	0.706045i
$426$	15.1521	−	37.4237i	0.734122	−	1.81319i
$427$	19.9569	+	23.7837i	0.965780	+	1.15097i
$428$	3.36094	−	4.96707i	0.162457	−	0.240092i
$429$	4.86465	−	8.42581i	0.234867	−	0.406802i
$430$	3.15068	−	2.45786i	0.151939	−	0.118529i
$431$	3.86038	+	1.40506i	0.185948	+	0.0676795i	0.433316	−	0.901242i	$-0.357343\pi$
$431$	3.86038	+	1.40506i	0.185948	+	0.0676795i	−0.247368	+	0.968922i	$0.579566\pi$
$432$	12.9042	+	32.2108i	0.620856	+	1.54974i
$433$	11.0190	−	1.94295i	0.529540	−	0.0933721i	0.0975153	−	0.995234i	$-0.468911\pi$
$433$	11.0190	−	1.94295i	0.529540	−	0.0933721i	0.432024	+	0.901862i	$0.357799\pi$
$434$	2.29405	+	4.32213i	0.110118	+	0.207469i
$435$	−5.53764	+	6.59950i	−0.265509	+	0.316422i
$436$	5.07919	+	17.8118i	0.243249	+	0.853029i
$437$	0.712515	+	10.8326i	0.0340842	+	0.518195i
$438$	−10.8482	+	1.51650i	−0.518347	+	0.0724613i
$439$	18.6381	+	15.6392i	0.889549	+	0.746420i	0.968120	−	0.250488i	$-0.0805912\pi$
$439$	18.6381	+	15.6392i	0.889549	+	0.746420i	−0.0785707	+	0.996909i	$0.525036\pi$
$440$	−7.30337	−	7.59622i	−0.348174	−	0.362136i
$441$	−2.59804	−	14.7342i	−0.123716	−	0.701631i
$442$	−4.82576	−	0.172062i	−0.229538	−	0.00818416i
$443$	5.10633	−	14.0295i	0.242609	−	0.666563i	−0.757300	−	0.653068i	$-0.773482\pi$
$443$	5.10633	−	14.0295i	0.242609	−	0.666563i	0.999909	−	0.0134959i	$-0.00429601\pi$
$444$	45.9658	−	47.4595i	2.18144	−	2.25233i
$445$	−0.612484	−	0.353618i	−0.0290345	−	0.0167631i
$446$	3.53931	−	3.92501i	0.167591	−	0.185855i
$447$	−42.3915	+	35.5707i	−2.00505	+	1.68244i
$448$	23.5248	−	7.52942i	1.11144	−	0.355732i
$449$	29.1082	−	16.8057i	1.37370	−	0.793108i	0.382311	−	0.924034i	$-0.375128\pi$
$449$	29.1082	−	16.8057i	1.37370	−	0.793108i	0.991392	+	0.130926i	$0.0417950\pi$
$450$	−33.4606	−	7.13791i	−1.57735	−	0.336484i
$451$	3.47594	−	19.7130i	0.163676	−	0.928250i
$452$	−19.0375	+	9.25068i	−0.895450	+	0.435116i
$453$	53.7738	−	19.5721i	2.52651	−	0.919576i
$454$	16.9993	+	10.6397i	0.797817	+	0.499345i
$455$	2.44298			0.114529
$456$	36.4679	−	4.88994i	1.70777	−	0.228993i
$457$	42.0825			1.96853			0.984267	−	0.176687i	$-0.0565381\pi$
$457$	42.0825			1.96853			0.984267	+	0.176687i	$0.0565381\pi$
$458$	9.40190	+	5.88455i	0.439322	+	0.274967i
$459$	−33.4511	+	12.1752i	−1.56136	+	0.568289i
$460$	−4.26026	+	2.07014i	−0.198636	+	0.0965207i
$461$	1.07453	−	6.09398i	0.0500460	−	0.283825i	−0.949506	−	0.313748i	$-0.898415\pi$
$461$	1.07453	−	6.09398i	0.0500460	−	0.283825i	0.999552	+	0.0299234i	$0.00952635\pi$
$462$	−49.9323	−	10.6517i	−2.32306	−	0.495563i
$463$	10.3129	−	5.95417i	0.479282	−	0.276714i	−0.240835	−	0.970566i	$-0.577421\pi$
$463$	10.3129	−	5.95417i	0.479282	−	0.276714i	0.720117	+	0.693852i	$0.244088\pi$
$464$	−12.1365	+	0.388181i	−0.563424	+	0.0180208i
$465$	−2.43623	+	2.04424i	−0.112978	+	0.0947994i
$466$	−1.93740	+	2.14853i	−0.0897484	+	0.0995289i
$467$	−13.8551	−	7.99927i	−0.641139	−	0.370162i	0.143914	−	0.989590i	$-0.454031\pi$
$467$	−13.8551	−	7.99927i	−0.641139	−	0.370162i	−0.785053	+	0.619428i	$0.787364\pi$
$468$	−6.83867	+	7.06090i	−0.316118	+	0.326390i
$469$	−8.72105	+	23.9609i	−0.402701	+	1.10641i
$470$	−4.68181	−	0.166930i	−0.215956	−	0.00769989i
$471$	4.12698	+	23.4053i	0.190161	+	1.07846i
$472$	−1.80203	+	1.73255i	−0.0829450	+	0.0797472i
$473$	−8.91821	−	7.48327i	−0.410060	−	0.344081i
$474$	13.6883	−	1.91353i	0.628725	−	0.0878915i
$475$	−7.89250	+	16.0137i	−0.362133	+	0.734759i
$476$	6.94890	+	24.3685i	0.318502	+	1.11693i
$477$	−16.4651	+	19.6223i	−0.753883	+	0.898443i
$478$	−14.6292	−	27.5623i	−0.669126	−	1.26067i
$479$	12.1768	−	2.14710i	0.556372	−	0.0981034i	0.111610	−	0.993752i	$-0.464399\pi$
$479$	12.1768	−	2.14710i	0.556372	−	0.0981034i	0.444762	+	0.895649i	$0.353288\pi$
$480$	7.97583	+	13.9323i	0.364045	+	0.635917i
$481$	8.65500	+	3.15016i	0.394634	+	0.143635i
$482$	10.7401	−	8.37838i	0.489196	−	0.381625i
$483$	−11.4746	+	19.8746i	−0.522112	+	0.904325i
$484$	−4.87577	+	7.20581i	−0.221626	+	0.327537i
$485$	−5.80503	−	6.91816i	−0.263593	−	0.314138i
$486$	0.872660	−	2.15536i	0.0395846	−	0.0977690i
$487$	−5.21271	−	9.02868i	−0.236210	−	0.409128i	0.723413	−	0.690415i	$-0.242572\pi$
$487$	−5.21271	−	9.02868i	−0.236210	−	0.409128i	−0.959624	+	0.281287i	$0.909239\pi$
$488$	−28.3767	+	1.92158i	−1.28455	+	0.0869857i
$489$	−50.0767	−	8.82987i	−2.26455	−	0.399301i
$490$	−1.05024	−	3.24038i	−0.0474448	−	0.146385i
$491$	−5.18753	−	14.2526i	−0.234110	−	0.643212i	−1.00000		0.000240450i	$-0.999923\pi$
$491$	−5.18753	−	14.2526i	−0.234110	−	0.643212i	0.765890	−	0.642972i	$-0.222299\pi$
$492$	−12.4444	+	27.8407i	−0.561038	+	1.25516i
$493$		−	12.4571i		−	0.561041i
$494$	2.69691	+	4.36306i	0.121340	+	0.196303i
$495$		−	22.0062i		−	0.989105i
$496$	−4.43707	−	0.636866i	−0.199230	−	0.0285961i
$497$	−10.1019	−	27.7547i	−0.453131	−	1.24497i
$498$	−49.6453	+	16.0905i	−2.22466	+	0.721032i
$499$	−8.46511	−	1.49263i	−0.378950	−	0.0668192i	−0.0190713	−	0.999818i	$-0.506071\pi$
$499$	−8.46511	−	1.49263i	−0.378950	−	0.0668192i	−0.359879	+	0.932999i	$0.617182\pi$
$500$	−17.2546	−	1.23199i	−0.771651	−	0.0550964i
$501$	18.1795	+	31.4878i	0.812199	+	1.40677i
$502$	−2.16743	−	0.877549i	−0.0967373	−	0.0391669i
$503$	21.2815	+	25.3623i	0.948895	+	1.13085i	0.991283	+	0.131748i	$0.0420589\pi$
$503$	21.2815	+	25.3623i	0.948895	+	1.13085i	−0.0423882	+	0.999101i	$0.513497\pi$
$504$	46.3126	+	22.7144i	2.06293	+	1.01178i
$505$	4.68095	−	8.10764i	0.208299	−	0.360785i
$506$	8.48790	+	10.8805i	0.377333	+	0.483695i
$507$	34.5159	+	12.5628i	1.53291	+	0.557932i
$508$	−0.330879	−	3.19314i	−0.0146804	−	0.141673i
$509$	−30.6280	+	5.40055i	−1.35756	+	0.239375i	−0.804593	−	0.593826i	$-0.797617\pi$
$509$	−30.6280	+	5.40055i	−1.35756	+	0.239375i	−0.552970	+	0.833201i	$0.686506\pi$
$510$	−14.5472	+	7.72123i	−0.644162	+	0.341902i
$511$	−5.15071	+	6.13838i	−0.227854	+	0.271546i
$512$	−7.13412	+	21.4733i	−0.315286	+	0.948997i
$513$	30.4992	+	22.3521i	1.34657	+	0.986869i
$514$	−4.05036	−	28.9739i	−0.178654	−	1.27798i
$515$	−1.42945	−	1.19945i	−0.0629891	−	0.0528541i
$516$	10.4039	+	14.3640i	0.458007	+	0.632340i
$517$	2.37007	+	13.4413i	0.104235	+	0.591149i
$518$	1.72222	−	48.3025i	0.0756701	−	2.12229i
$519$	22.3798	−	61.4881i	0.982365	−	2.69903i
$520$	−1.31942	+	1.80765i	−0.0578602	+	0.0792705i
$521$	23.9923	+	13.8520i	1.05112	+	0.606866i	0.922964	−	0.384887i	$-0.125760\pi$
$521$	23.9923	+	13.8520i	1.05112	+	0.606866i	0.128160	+	0.991754i	$0.459093\pi$
$522$	−18.8324	−	16.9818i	−0.824271	−	0.743272i
$523$	0.617244	−	0.517929i	0.0269902	−	0.0226474i	−0.629193	−	0.777249i	$-0.716614\pi$
$523$	0.617244	−	0.517929i	0.0269902	−	0.0226474i	0.656183	+	0.754602i	$0.272170\pi$
$524$	−19.0245	−	4.77299i	−0.831091	−	0.208509i
$525$	−32.6842	+	18.8703i	−1.42646	+	0.823566i
$526$	−4.35225	+	20.4022i	−0.189767	+	0.889577i
$527$	0.798538	−	4.52874i	0.0347849	−	0.197275i
$528$	34.8492	−	31.1938i	1.51662	−	1.35754i
$529$	−15.7842	+	5.74498i	−0.686269	+	0.249782i
$530$	−3.09403	+	4.94341i	−0.134396	+	0.214728i
$531$	−5.22045			−0.226548
$532$	17.4169	−	20.5221i	0.755117	−	0.889748i
$533$	−4.25118			−0.184139
$534$	1.66539	−	2.66084i	0.0720685	−	0.115146i
$535$	2.67950	−	0.975258i	0.115845	−	0.0421641i
$536$	−13.0194	−	19.3939i	−0.562351	−	0.837689i
$537$	0.190684	−	1.08142i	0.00822861	−	0.0466668i
$538$	−2.25404	+	10.5663i	−0.0971785	+	0.455546i
$539$	−8.59443	+	4.96200i	−0.370188	+	0.213728i
$540$	−4.01473	+	16.0022i	−0.172766	+	0.688624i
$541$	21.0196	−	17.6376i	0.903705	−	0.758299i	−0.0672060	−	0.997739i	$-0.521408\pi$
$541$	21.0196	−	17.6376i	0.903705	−	0.758299i	0.970911	+	0.239441i	$0.0769640\pi$
$542$	−1.57754	−	1.42252i	−0.0677611	−	0.0611024i
$543$	48.8001	+	28.1747i	2.09421	+	1.20909i
$544$	−21.7841	−	8.01932i	−0.933985	−	0.343826i
$545$	−3.01194	+	8.27524i	−0.129017	+	0.354472i
$546$	−0.386364	+	10.8362i	−0.0165349	+	0.463747i
$547$	−6.63465	−	37.6270i	−0.283677	−	1.60881i	−0.709972	−	0.704229i	$-0.751293\pi$
$547$	−6.63465	−	37.6270i	−0.283677	−	1.60881i	0.426295	−	0.904584i	$-0.359818\pi$
$548$	8.95457	−	6.48583i	0.382520	−	0.277061i
$549$	−45.5000	−	38.1790i	−1.94189	−	1.62944i
$550$	3.14188	+	22.4752i	0.133970	+	0.958347i
$551$	−11.0005	+	7.35398i	−0.468638	+	0.313290i
$552$	−8.50863	−	19.2244i	−0.362151	−	0.818245i
$553$	6.49920	−	7.74545i	0.276374	−	0.329370i
$554$	14.0707	−	7.46828i	0.597806	−	0.317297i
$555$	30.9363	−	5.45490i	1.31317	−	0.231548i
$556$	18.1732	−	1.88314i	0.770715	−	0.0798629i
$557$	33.4845	+	12.1874i	1.41878	+	0.516395i	0.933695	−	0.358069i	$-0.116565\pi$
$557$	33.4845	+	12.1874i	1.41878	+	0.516395i	0.485089	+	0.874465i	$0.338787\pi$
$558$	−5.75785	−	7.38086i	−0.243749	−	0.312457i
$559$	−1.23624	+	2.14123i	−0.0522873	+	0.0905642i
$560$	11.1585	+	3.66183i	0.471532	+	0.154741i
$561$	30.8422	+	36.7562i	1.30216	+	1.55185i
$562$	30.0253	+	12.1566i	1.26654	+	0.512797i
$563$	2.01778	+	3.49489i	0.0850391	+	0.147292i	0.905408	−	0.424543i	$-0.139565\pi$
$563$	2.01778	+	3.49489i	0.0850391	+	0.147292i	−0.820369	+	0.571835i	$0.806232\pi$
$564$	1.48088	−	20.7405i	0.0623564	−	0.873331i
$565$	−9.91067	−	1.74752i	−0.416945	−	0.0735186i
$566$	25.0379	−	8.11502i	1.05242	−	0.341100i
$567$	8.62675	+	23.7018i	0.362289	+	0.995382i
$568$	25.9925	+	7.51514i	1.09062	+	0.315328i
$569$		−	22.5123i		−	0.943765i	−0.881661	−	0.471883i	$-0.843575\pi$
$569$		−	22.5123i		−	0.943765i	0.881661	−	0.471883i	$-0.156425\pi$
$570$	15.4062	+	8.28806i	0.645296	+	0.347149i
$571$		−	2.03284i		−	0.0850718i	−0.999095	−	0.0425359i	$-0.986456\pi$
$571$		−	2.03284i		−	0.0850718i	0.999095	−	0.0425359i	$-0.0135437\pi$
$572$	5.95248	+	2.66068i	0.248886	+	0.111249i
$573$	15.2217	+	41.8212i	0.635894	+	1.74710i
$574$	6.87820	+	21.2219i	0.287091	+	0.885784i
$575$	10.0457	+	1.77133i	0.418935	+	0.0738696i
$576$	−41.8198	+	22.0005i	−1.74249	+	0.916689i
$577$	−21.0040	−	36.3800i	−0.874409	−	1.51452i	−0.857391	−	0.514665i	$-0.827916\pi$
$577$	−21.0040	−	36.3800i	−0.874409	−	1.51452i	−0.0170172	−	0.999855i	$-0.505417\pi$
$578$	−0.0853243	+	0.210740i	−0.00354902	+	0.00876563i
$579$	−14.3416	−	17.0917i	−0.596018	−	0.710307i
$580$	−4.78159	−	3.23543i	−0.198545	−	0.134344i
$581$	−19.0888	+	33.0628i	−0.791936	+	1.37167i
$582$	31.6046	−	24.6549i	1.31005	−	1.02198i
$583$	15.9658	+	5.81109i	0.661237	+	0.240671i
$584$	−1.76018	−	7.12643i	−0.0728366	−	0.294894i
$585$	−4.60262	+	0.811565i	−0.190295	+	0.0335541i
$586$	−13.5175	−	25.4678i	−0.558404	−	1.05206i
$587$	−0.130312	+	0.155300i	−0.00537856	+	0.00640992i	−0.768727	−	0.639577i	$-0.779110\pi$
$587$	−0.130312	+	0.155300i	−0.00537856	+	0.00640992i	0.763348	+	0.645987i	$0.223554\pi$
$588$	14.5393	−	4.14600i	0.599589	−	0.170978i
$589$	−4.47060	+	1.96834i	−0.184208	+	0.0811041i
$590$	−1.17710	+	0.164551i	−0.0484606	+	0.00677447i
$591$	−48.9979	−	41.1142i	−2.01551	−	1.69121i
$592$	34.8105	+	27.3617i	1.43070	+	1.12456i
$593$	−3.92427	−	22.2556i	−0.161150	−	0.913930i	−0.952945	−	0.303143i	$-0.901964\pi$
$593$	−3.92427	−	22.2556i	−0.161150	−	0.913930i	0.791795	−	0.610787i	$-0.209147\pi$
$594$	48.0352	+	1.71269i	1.97091	+	0.0702725i
$595$	−4.12067	+	11.3215i	−0.168931	+	0.464134i
$596$	−26.6388	−	25.8004i	−1.09117	−	1.05682i
$597$	−66.1962	−	38.2184i	−2.70923	−	1.56417i
$598$	1.96263	−	2.17651i	0.0802580	−	0.0890042i
$599$	−24.7817	+	20.7943i	−1.01255	+	0.849632i	−0.988673	−	0.150083i	$-0.952046\pi$
$599$	−24.7817	+	20.7943i	−1.01255	+	0.849632i	−0.0238789	+	0.999715i	$0.507602\pi$
$600$	3.68950	−	34.3757i	0.150623	−	1.40338i
$601$	30.9510	−	17.8696i	1.26252	−	0.728915i	0.288957	−	0.957342i	$-0.406692\pi$
$601$	30.9510	−	17.8696i	1.26252	−	0.728915i	0.973561	+	0.228427i	$0.0733583\pi$
$602$	12.6891	+	2.70689i	0.517171	+	0.110325i
$603$	8.47071	−	48.0398i	0.344954	−	1.95633i
$604$	16.7606	+	34.4926i	0.681979	+	1.40348i
$605$	−3.88719	+	1.41482i	−0.158037	+	0.0575207i
$606$	35.2223	+	22.0453i	1.43081	+	0.895528i
$607$	−35.8454			−1.45492			−0.727460	−	0.686150i	$-0.759299\pi$
$607$	−35.8454			−1.45492			−0.727460	+	0.686150i	$0.759299\pi$
$608$	5.77845	+	23.9710i	0.234347	+	0.972153i
$609$	−27.9724			−1.13350
$610$	−11.4627	−	7.17440i	−0.464113	−	0.290483i
$611$	2.72386	−	0.991403i	0.110196	−	0.0401079i
$612$	−21.1871	−	43.6022i	−0.856438	−	1.76251i
$613$	−2.07723	+	11.7805i	−0.0838984	+	0.475812i	0.913690	+	0.406411i	$0.133220\pi$
$613$	−2.07723	+	11.7805i	−0.0838984	+	0.475812i	−0.997589	+	0.0694008i	$0.977891\pi$
$614$	40.0664	+	8.54708i	1.61695	+	0.344932i
$615$	−12.5567	+	7.24962i	−0.506335	+	0.292333i
$616$	3.65128	−	34.0196i	0.147114	−	1.37069i
$617$	−12.3624	+	10.3733i	−0.497691	+	0.417612i	−0.856773	−	0.515694i	$-0.827534\pi$
$617$	−12.3624	+	10.3733i	−0.497691	+	0.417612i	0.359082	+	0.933306i	$0.383090\pi$
$618$	5.54641	−	6.15084i	0.223109	−	0.247423i
$619$	−21.6900	−	12.5227i	−0.871796	−	0.503332i	−0.00385145	−	0.999993i	$-0.501226\pi$
$619$	−21.6900	−	12.5227i	−0.871796	−	0.503332i	−0.867945	+	0.496661i	$0.834559\pi$
$620$	−1.53092	−	1.48274i	−0.0614834	−	0.0595483i
$621$	7.38940	−	20.3022i	0.296526	−	0.814700i
$622$	13.0615	+	0.465706i	0.523718	+	0.0186731i
$623$	−0.398756	−	2.26146i	−0.0159758	−	0.0906034i
$624$	−7.80941	−	6.13835i	−0.312627	−	0.245731i
$625$	9.38717	+	7.87677i	0.375487	+	0.315071i
$626$	35.3073	−	4.93572i	1.41116	−	0.197271i
$627$	14.2509	−	48.9346i	0.569126	−	1.95426i
$628$	−15.3164	+	4.36761i	−0.611191	+	0.174287i
$629$	−29.1974	+	34.7962i	−1.16418	+	1.38741i
$630$	11.4981	+	21.6631i	0.458096	+	0.863080i
$631$	−33.3599	+	5.88225i	−1.32804	+	0.234169i	−0.792257	−	0.610188i	$-0.791094\pi$
$631$	−33.3599	+	5.88225i	−1.32804	+	0.234169i	−0.535781	+	0.844357i	$0.679983\pi$
$632$	2.22100	+	8.99218i	0.0883467	+	0.357690i
$633$	8.81066	+	3.20682i	0.350192	+	0.127460i
$634$	−33.8517	+	26.4079i	−1.34442	+	1.04879i
$635$	0.763166	−	1.32184i	0.0302853	−	0.0524557i
$636$	−21.4379	−	14.5058i	−0.850067	−	0.575193i
$637$	1.35476	+	1.61454i	0.0536775	+	0.0639704i
$638$	−6.31236	+	15.5907i	−0.249909	+	0.617242i
$639$	28.2522	+	48.9343i	1.11764	+	1.93581i
$640$	−8.73604	+	6.27885i	−0.345322	+	0.248193i
$641$	−7.27625	−	1.28300i	−0.287395	−	0.0506755i	0.0280923	−	0.999605i	$-0.491057\pi$
$641$	−7.27625	−	1.28300i	−0.287395	−	0.0506755i	−0.315487	+	0.948930i	$0.602168\pi$
$642$	3.90213	+	12.0395i	0.154005	+	0.475163i
$643$	15.7177	+	43.1840i	0.619845	+	1.70301i	0.707366	+	0.706847i	$0.249883\pi$
$643$	15.7177	+	43.1840i	0.619845	+	1.70301i	−0.0875217	+	0.996163i	$0.527895\pi$
$644$	−14.0406	−	6.27595i	−0.553276	−	0.247307i
$645$			8.43271i			0.332038i
$646$	−24.7686	+	5.13888i	−0.974507	+	0.202187i
$647$			41.8157i			1.64394i	0.569529	+	0.821971i	$0.307126\pi$
$647$			41.8157i			1.64394i	−0.569529	+	0.821971i	$0.692874\pi$
$648$	−22.1969	−	6.41774i	−0.871978	−	0.252113i
$649$	1.18432	+	3.25390i	0.0464887	+	0.127727i
$650$	4.58484	−	1.48599i	0.179832	−	0.0582853i
$651$	−10.1692	−	1.79311i	−0.398564	−	0.0702776i
$652$	2.42691	−	33.9900i	0.0950450	−	1.33115i
$653$	12.8848	+	22.3172i	0.504223	+	0.873339i	0.999988	+	0.00488267i	$0.00155421\pi$
$653$	12.8848	+	22.3172i	0.504223	+	0.873339i	−0.495766	+	0.868456i	$0.665112\pi$
$654$	−36.2297	−	14.6687i	−1.41669	−	0.573590i
$655$	−5.99443	−	7.14388i	−0.234222	−	0.279135i
$656$	−19.4176	−	6.37218i	−0.758129	−	0.248792i
$657$	7.66483	−	13.2759i	0.299034	−	0.517941i
$658$	−9.35614	−	11.9934i	−0.364740	−	0.467552i
$659$	20.9947	+	7.64146i	0.817839	+	0.297669i	0.716858	−	0.697219i	$-0.245580\pi$
$659$	20.9947	+	7.64146i	0.817839	+	0.297669i	0.100981	+	0.994888i	$0.467802\pi$
$660$	22.1191	−	2.29202i	0.860986	−	0.0892169i
$661$	29.7635	−	5.24811i	1.15767	−	0.204128i	0.438346	−	0.898807i	$-0.355565\pi$
$661$	29.7635	−	5.24811i	1.15767	−	0.204128i	0.719320	+	0.694679i	$0.244454\pi$
$662$	−25.2586	+	13.4065i	−0.981703	+	0.521058i
$663$	6.55017	−	7.80619i	0.254388	−	0.303167i
$664$	−14.1547	−	31.9811i	−0.549309	−	1.24111i
$665$	12.4302	−	3.04470i	0.482024	−	0.118068i
$666$	12.8015	+	91.5747i	0.496049	+	3.54845i
$667$	5.79169	+	4.85980i	0.224255	+	0.188172i
$668$	−19.7334	+	14.2930i	−0.763508	+	0.553012i
$669$	1.93673	+	10.9837i	0.0748782	+	0.424656i
$670$	0.395734	−	11.0990i	0.0152885	−	0.428791i
$671$	−13.4747	+	37.0215i	−0.520185	+	1.42920i
$672$	−18.0073	+	48.9160i	−0.694648	+	1.88698i
$673$	−13.8432	−	7.99236i	−0.533615	−	0.308083i	0.208872	−	0.977943i	$-0.433021\pi$
$673$	−13.8432	−	7.99236i	−0.533615	−	0.308083i	−0.742487	+	0.669860i	$0.766354\pi$
$674$	13.7726	+	12.4192i	0.530501	+	0.478370i
$675$	27.2177	−	22.8384i	1.04761	−	0.879050i
$676$	−5.99000	+	23.8753i	−0.230384	+	0.918283i
$677$	−15.2731	+	8.81795i	−0.586994	+	0.338901i	−0.763908	−	0.645325i	$-0.776722\pi$
$677$	−15.2731	+	8.81795i	−0.586994	+	0.338901i	0.176914	+	0.984226i	$0.443389\pi$
$678$	9.31877	−	43.6838i	0.357885	−	1.67767i
$679$	5.09190	−	28.8776i	0.195409	−	1.10822i
$680$	−6.15162	−	9.16356i	−0.235904	−	0.351407i
$681$	−39.7685	+	14.4746i	−1.52393	+	0.554667i
$682$	−3.29424	+	5.26329i	−0.126143	+	0.201542i
$683$	−28.6039			−1.09450			−0.547249	−	0.836970i	$-0.684325\pi$
$683$	−28.6039			−1.09450			−0.547249	+	0.836970i	$0.684325\pi$
$684$	−25.9961	+	44.4499i	−0.993986	+	1.69959i
$685$	5.25698			0.200859
$686$	−10.3483	+	16.5337i	−0.395098	+	0.631259i
$687$	−21.9950	+	8.00553i	−0.839162	+	0.305430i
$688$	−8.85613	+	7.92718i	−0.337637	+	0.302221i
$689$	0.626591	−	3.55358i	0.0238712	−	0.135380i
$690$	2.08537	−	9.77566i	0.0793889	−	0.372153i
$691$	4.66323	−	2.69231i	0.177397	−	0.102420i	−0.408672	−	0.912681i	$-0.634008\pi$
$691$	4.66323	−	2.69231i	0.177397	−	0.102420i	0.586069	+	0.810261i	$0.300675\pi$
$692$	42.5325	+	10.6708i	1.61684	+	0.405644i
$693$	54.7358	−	45.9288i	2.07924	−	1.74469i
$694$	4.93495	+	4.45000i	0.187328	+	0.168920i
$695$	7.52302	+	4.34342i	0.285365	+	0.164755i
$696$	15.1075	−	20.6977i	0.572647	−	0.784545i
$697$	7.17064	−	19.7012i	0.271607	−	0.746235i
$698$	1.09133	−	30.6082i	0.0413075	−	1.15854i
$699$	−1.06016	−	6.01244i	−0.0400988	−	0.227411i
$700$	−14.8361	−	20.4832i	−0.560752	−	0.774193i
$701$	4.35970	+	3.65823i	0.164664	+	0.138169i	0.721396	−	0.692523i	$-0.243501\pi$
$701$	4.35970	+	3.65823i	0.164664	+	0.138169i	−0.556732	+	0.830692i	$0.687945\pi$
$702$	−1.41327	−	10.1098i	−0.0533406	−	0.381568i
$703$	47.9639	+	5.24172i	1.80899	+	0.197695i
$704$	23.2002	+	21.0751i	0.874392	+	0.794299i
$705$	6.35479	−	7.57335i	0.239335	−	0.285229i
$706$	31.1451	−	16.5309i	1.17216	−	0.622147i
$707$	29.9356	−	5.27845i	1.12584	−	0.198517i
$708$	−0.543729	−	5.24724i	−0.0204346	−	0.197204i
$709$	−28.6122	−	10.4140i	−1.07455	−	0.391105i	−0.256675	−	0.966498i	$-0.582627\pi$
$709$	−28.6122	−	10.4140i	−1.07455	−	0.391105i	−0.817877	+	0.575393i	$0.804849\pi$
$710$	7.91273	+	10.1432i	0.296959	+	0.380666i
$711$	−9.67154	+	16.7516i	−0.362711	+	0.628234i
$712$	1.88869	+	0.926324i	0.0707817	+	0.0347155i
$713$	1.79402	+	2.13802i	0.0671864	+	0.0800697i
$714$	−49.5663	−	20.0684i	−1.85497	−	0.751040i
$715$	1.55001	+	2.68469i	0.0579669	+	0.100402i
$716$	0.734024	+	0.0524098i	0.0274318	+	0.00195865i
$717$	64.8496	+	11.4347i	2.42185	+	0.427038i
$718$	−32.3910	+	10.4982i	−1.20882	+	0.391790i
$719$	2.98701	+	8.20674i	0.111397	+	0.306060i	0.982847	−	0.184425i	$-0.0590421\pi$
$719$	2.98701	+	8.20674i	0.111397	+	0.306060i	−0.871450	+	0.490484i	$0.836820\pi$
$720$	−22.2392	−	3.19206i	−0.828807	−	0.118961i
$721$		−	6.05882i		−	0.225642i
$722$	19.1600	+	18.8387i	0.713060	+	0.701103i
$723$			28.7455i			1.06906i
$724$	−15.4100	+	34.4752i	−0.572707	+	1.28126i
$725$	4.25249	+	11.6836i	0.157933	+	0.433919i
$726$	−5.66088	−	17.4660i	−0.210095	−	0.648223i
$727$	−21.6522	−	3.81787i	−0.803036	−	0.141597i	−0.242958	−	0.970037i	$-0.578118\pi$
$727$	−21.6522	−	3.81787i	−0.803036	−	0.141597i	−0.560078	+	0.828440i	$0.689229\pi$
$728$	−7.24988	+	0.490937i	−0.268698	+	0.0181954i
$729$	14.7074	+	25.4740i	0.544719	+	0.943481i
$730$	1.30980	−	3.23504i	0.0484779	−	0.119734i
$731$	−7.83782	−	9.34075i	−0.289892	−	0.345480i
$732$	33.6360	−	49.7100i	1.24322	−	1.83733i
$733$	10.4654	−	18.1267i	0.386549	−	0.669523i	−0.605433	−	0.795896i	$-0.707000\pi$
$733$	10.4654	−	18.1267i	0.386549	−	0.669523i	0.991983	+	0.126373i	$0.0403335\pi$
$734$	−11.5839	+	9.03669i	−0.427571	+	0.333550i
$735$	6.75485	+	2.45856i	0.249156	+	0.0906855i
$736$	12.2269	−	6.99955i	0.450689	−	0.258007i
$737$	−31.8648	+	5.61863i	−1.17376	+	0.206965i
$738$	−20.0086	−	37.6973i	−0.736526	−	1.38766i
$739$	−9.03080	+	10.7625i	−0.332203	+	0.395905i	−0.906128	−	0.423003i	$-0.860976\pi$
$739$	−9.03080	+	10.7625i	−0.332203	+	0.395905i	0.573925	+	0.818908i	$0.305420\pi$
$740$	5.77296	+	20.2447i	0.212218	+	0.744210i
$741$	−10.7603	−	1.17593i	−0.395288	−	0.0431989i
$742$	−18.7532	+	2.62157i	−0.688452	+	0.0962408i
$743$	−15.7144	−	13.1860i	−0.576506	−	0.483746i	0.307291	−	0.951615i	$-0.400577\pi$
$743$	−15.7144	−	13.1860i	−0.576506	−	0.483746i	−0.883798	+	0.467869i	$0.845022\pi$
$744$	6.81904	−	6.55614i	0.249998	−	0.240360i
$745$	−3.06180	−	17.3644i	−0.112176	−	0.636181i
$746$	−11.5096	−	0.410375i	−0.421398	−	0.0150249i
$747$	24.9800	−	68.6321i	0.913971	−	2.51112i
$748$	−22.3706	+	23.0976i	−0.817951	+	0.844531i
$749$	8.01809	+	4.62925i	0.292975	+	0.169149i
$750$	24.4466	−	27.1107i	0.892664	−	0.989943i
$751$	25.9874	−	21.8061i	0.948295	−	0.795714i	−0.0307144	−	0.999528i	$-0.509778\pi$
$751$	25.9874	−	21.8061i	0.948295	−	0.795714i	0.979010	+	0.203814i	$0.0653338\pi$
$752$	13.9274	−	0.445462i	0.507882	−	0.0162443i
$753$	4.27350	−	2.46731i	0.155735	−	0.0899136i
$754$	3.49360	+	0.745266i	0.127229	+	0.0271410i
$755$	−3.16619	+	17.9564i	−0.115230	+	0.653499i
$756$	−48.1812	+	23.4121i	−1.75233	+	0.851491i
$757$	−26.8038	+	9.75577i	−0.974199	+	0.354580i	−0.779582	−	0.626300i	$-0.784569\pi$
$757$	−26.8038	+	9.75577i	−0.974199	+	0.354580i	−0.194617	+	0.980879i	$0.562346\pi$
$758$	−31.9191	−	19.9778i	−1.15935	−	0.725628i
$759$	−29.1213			−1.05704
$760$	−4.46051	+	10.8420i	−0.161800	+	0.393279i
$761$	16.4874			0.597667			0.298834	−	0.954305i	$-0.403402\pi$
$761$	16.4874			0.597667			0.298834	+	0.954305i	$0.403402\pi$
$762$	5.74253	+	3.59419i	0.208030	+	0.130204i
$763$	−26.8691	+	9.77956i	−0.972727	+	0.354044i
$764$	−26.8257	+	13.0351i	−0.970521	+	0.471594i
$765$	4.00239	−	22.6987i	0.144707	−	0.820673i
$766$	−25.3756	−	5.41319i	−0.916856	−	0.195587i
$767$	0.636879	−	0.367702i	0.0229964	−	0.0132770i
$768$	−26.4691	−	39.7430i	−0.955123	−	1.43410i
$769$	1.90875	−	1.60163i	0.0688314	−	0.0577564i	−0.607723	−	0.794149i	$-0.707917\pi$
$769$	1.90875	−	1.60163i	0.0688314	−	0.0577564i	0.676554	+	0.736393i	$0.263472\pi$
$770$	10.8941	−	12.0813i	0.392596	−	0.435380i
$771$	53.4668	+	30.8691i	1.92556	+	1.11172i
$772$	10.4024	−	10.7404i	0.374389	−	0.386555i
$773$	−0.00136352	+	0.00374623i	−4.90422e−5	+	0.000134742i	−0.939717	−	0.341953i	$-0.888912\pi$
$773$	−0.00136352	+	0.00374623i	−4.90422e−5	+	0.000134742i	0.939668	+	0.342088i	$0.111134\pi$
$774$	−24.8058	−	0.884448i	−0.891625	−	0.0317908i
$775$	0.797020	+	4.52013i	0.0286298	+	0.162368i
$776$	18.6175	+	19.3640i	0.668328	+	0.695127i
$777$	78.1346	+	65.5627i	2.80306	+	2.35205i
$778$	−25.3014	+	3.53696i	−0.907098	+	0.126806i
$779$	−21.6306	+	5.29827i	−0.774998	+	0.189830i
$780$	−1.29511	−	4.54171i	−0.0463723	−	0.162619i
$781$	24.0913	−	28.7109i	0.862055	−	1.02736i
$782$	6.77611	+	12.7666i	0.242313	+	0.456532i
$783$	25.9341	−	4.57288i	0.926809	−	0.163422i
$784$	3.76790	+	9.40520i	0.134568	+	0.335900i
$785$	−7.11590	−	2.58998i	−0.253977	−	0.0924402i
$786$	32.6358	−	25.4593i	1.16408	−	0.908105i
$787$	14.7870	−	25.6119i	0.527100	−	0.912964i	−0.472401	−	0.881384i	$-0.656613\pi$
$787$	14.7870	−	25.6119i	0.527100	−	0.912964i	0.999501	−	0.0315805i	$-0.0100541\pi$
$788$	24.0214	−	35.5008i	0.855729	−	1.26467i
$789$	−28.2977	−	33.7239i	−1.00743	−	1.20060i
$790$	−1.65271	+	4.08199i	−0.0588009	+	0.145231i
$791$	−16.3378	−	28.2979i	−0.580906	−	1.00616i
$792$	4.42233	+	65.3063i	0.157141	+	2.32056i
$793$	8.24000	+	1.45293i	0.292611	+	0.0515952i
$794$	−0.215664	−	0.665405i	−0.00765363	−	0.0236143i
$795$	−4.20921	−	11.5647i	−0.149285	−	0.410158i
$796$	20.9033	−	46.7648i	0.740897	−	1.65753i
$797$			23.5686i			0.834844i	0.908713	+	0.417422i	$0.137066\pi$
$797$			23.5686i			0.834844i	−0.908713	+	0.417422i	$0.862934\pi$
$798$	11.5393	+	55.6177i	0.408488	+	1.96885i
$799$			14.2953i			0.505733i
$800$	23.1690	+	0.0849434i	0.819147	+	0.00300320i
$801$	1.50252	+	4.12815i	0.0530891	+	0.145861i
$802$	38.9954	−	12.6388i	1.37697	−	0.446290i
$803$	−10.0137	−	1.76568i	−0.353376	−	0.0623096i
$804$	49.1686	+	3.51067i	1.73404	+	0.123812i
$805$	−3.65611	−	6.33257i	−0.128861	−	0.223194i
$806$	1.22231	+	0.494888i	0.0430541	+	0.0174317i
$807$	−14.6554	−	17.4657i	−0.515896	−	0.614820i
$808$	−12.2620	+	25.0012i	−0.431377	+	0.879538i
$809$	9.96738	−	17.2640i	0.350434	−	0.606970i	−0.635891	−	0.771779i	$-0.719367\pi$
$809$	9.96738	−	17.2640i	0.350434	−	0.606970i	0.986326	+	0.164809i	$0.0527006\pi$
$810$	−6.75727	−	8.66200i	−0.237426	−	0.304352i
$811$	7.15270	+	2.60337i	0.251165	+	0.0914167i	0.464535	−	0.885555i	$-0.346222\pi$
$811$	7.15270	+	2.60337i	0.251165	+	0.0914167i	−0.213369	+	0.976972i	$0.568444\pi$
$812$	−1.93211	−	18.6458i	−0.0678039	−	0.654340i
$813$	4.41458	−	0.778409i	0.154826	−	0.0273000i
$814$	54.1742	−	28.7540i	1.89880	−	1.00783i
$815$	10.4144	−	12.4114i	0.364800	−	0.434752i
$816$	41.6192	−	25.8372i	1.45696	−	0.904481i
$817$	−3.62154	+	12.4356i	−0.126702	+	0.435066i
$818$	−1.35822	−	9.71591i	−0.0474890	−	0.339709i
$819$	−11.6247	−	9.75424i	−0.406198	−	0.340841i
$820$	−5.69976	−	7.86929i	−0.199044	−	0.274808i
$821$	−3.47380	−	19.7009i	−0.121237	−	0.687567i	−0.983472	−	0.181059i	$-0.942047\pi$
$821$	−3.47380	−	19.7009i	−0.121237	−	0.687567i	0.862236	−	0.506507i	$-0.169064\pi$
$822$	−0.831406	+	23.3181i	−0.0289986	+	0.813312i
$823$	4.87923	−	13.4056i	0.170079	−	0.467289i	−0.825143	−	0.564924i	$-0.808906\pi$
$823$	4.87923	−	13.4056i	0.170079	−	0.467289i	0.995222	+	0.0976351i	$0.0311278\pi$
$824$	4.48312	+	3.27227i	0.156177	+	0.113995i
$825$	−41.4745	−	23.9453i	−1.44396	−	0.833669i
$826$	−2.86601	−	2.58437i	−0.0997211	−	0.0899217i
$827$	−38.9790	+	32.7073i	−1.35543	+	1.13734i	−0.378071	+	0.925777i	$0.623412\pi$
$827$	−38.9790	+	32.7073i	−1.35543	+	1.13734i	−0.977363	+	0.211568i	$0.932143\pi$
$828$	28.5375	+	7.15967i	0.991747	+	0.248816i
$829$	17.8100	−	10.2826i	0.618567	−	0.357130i	−0.157744	−	0.987480i	$-0.550422\pi$
$829$	17.8100	−	10.2826i	0.618567	−	0.357130i	0.776311	+	0.630350i	$0.217089\pi$
$830$	3.46917	−	16.2625i	0.120416	−	0.564479i
$831$	−5.83748	+	33.1060i	−0.202500	+	1.14843i
$832$	3.55228	−	5.62958i	0.123153	−	0.195171i
$833$	−9.76734	+	3.55502i	−0.338418	+	0.123174i
$834$	−20.4557	+	32.6826i	−0.708322	+	1.13170i
$835$	−11.5849			−0.400913
$836$	33.6031	+	6.11933i	1.16219	+	0.211642i
$837$	9.72137			0.336020
$838$	−18.8599	+	30.1329i	−0.651503	+	1.04092i
$839$	17.8217	−	6.48656i	0.615272	−	0.223941i	−0.0155363	−	0.999879i	$-0.504946\pi$
$839$	17.8217	−	6.48656i	0.615272	−	0.223941i	0.630809	+	0.775939i	$0.282723\pi$
$840$	−20.5767	+	13.8134i	−0.709965	+	0.476608i
$841$	3.43556	−	19.4840i	0.118468	−	0.671864i
$842$	−7.02159	+	32.9153i	−0.241980	+	1.13434i
$843$	−59.2005	+	34.1794i	−2.03897	+	1.17720i
$844$	−1.52903	+	6.09450i	−0.0526313	+	0.209781i
$845$	−8.96541	+	7.52287i	−0.308419	+	0.258795i
$846$	21.6113	+	19.4877i	0.743013	+	0.669999i
$847$	−11.6320	−	6.71573i	−0.399680	−	0.230755i
$848$	8.18852	−	15.2920i	0.281195	−	0.525129i
$849$	−18.9970	+	52.1938i	−0.651975	+	1.79129i
$850$	−0.846944	+	23.7539i	−0.0290499	+	0.814752i
$851$	−4.78719	−	27.1495i	−0.164103	−	0.930673i
$852$	−46.2429	+	33.4939i	−1.58425	+	1.14748i
$853$	5.99511	+	5.03049i	0.205269	+	0.172241i	0.739627	−	0.673017i	$-0.235002\pi$
$853$	5.99511	+	5.03049i	0.205269	+	0.172241i	−0.534358	+	0.845258i	$0.679447\pi$
$854$	−6.07887	−	43.4848i	−0.208015	−	1.48802i
$855$	−22.4073	+	9.86562i	−0.766314	+	0.337397i
$856$	−7.75578	+	3.43267i	−0.265087	+	0.117326i
$857$	19.4931	−	23.2309i	0.665871	−	0.793554i	−0.322345	−	0.946622i	$-0.604471\pi$
$857$	19.4931	−	23.2309i	0.665871	−	0.793554i	0.988216	+	0.153068i	$0.0489154\pi$
$858$	−12.1535	+	6.45069i	−0.414913	+	0.220223i
$859$	38.2799	−	6.74979i	1.30609	−	0.230300i	0.523070	−	0.852290i	$-0.324787\pi$
$859$	38.2799	−	6.74979i	1.30609	−	0.230300i	0.783025	+	0.621990i	$0.213676\pi$
$860$	−5.62107	+	0.582465i	−0.191677	+	0.0198619i
$861$	−44.2388	−	16.1016i	−1.50766	−	0.548742i
$862$	−3.57349	−	4.58078i	−0.121714	−	0.156022i
$863$	14.7302	−	25.5135i	0.501423	−	0.868490i	−0.498576	−	0.866846i	$-0.666143\pi$
$863$	14.7302	−	25.5135i	0.501423	−	0.868490i	0.999999	−	0.00164372i	$-0.000523212\pi$
$864$	8.69847	−	48.2954i	0.295928	−	1.64304i
$865$	13.4015	+	15.9713i	0.455666	+	0.543042i
$866$	−14.6671	−	5.93839i	−0.498407	−	0.201795i
$867$	−0.239896	−	0.415513i	−0.00814731	−	0.0141116i
$868$	0.492840	−	6.90246i	0.0167281	−	0.234285i
$869$	12.6353	+	2.22795i	0.428625	+	0.0755781i
$870$	11.5900	−	3.75641i	0.392936	−	0.127354i
$871$	2.35028	+	6.45734i	0.0796362	+	0.218799i
$872$	7.27536	−	25.1631i	0.246375	−	0.852132i
$873$			56.0974i			1.89861i
$874$	7.27356	−	13.5204i	0.246032	−	0.457336i
$875$		−	26.7051i		−	0.902798i
$876$	14.1423	+	6.32144i	0.477825	+	0.213582i
$877$	11.5291	+	31.6760i	0.389311	+	1.06962i	0.967313	+	0.253587i	$0.0816103\pi$
$877$	11.5291	+	31.6760i	0.389311	+	1.06962i	−0.578002	+	0.816035i	$0.696167\pi$
$878$	−10.6087	−	32.7320i	−0.358028	−	1.10465i
$879$	59.9215	+	10.5658i	2.02110	+	0.356375i
$880$	3.05563	+	14.5858i	0.103005	+	0.491688i
$881$	−13.9103	−	24.0933i	−0.468649	−	0.811724i	0.530709	−	0.847554i	$-0.321926\pi$
$881$	−13.9103	−	24.0933i	−0.468649	−	0.811724i	−0.999358	+	0.0358302i	$0.988592\pi$
$882$	−7.94061	+	19.6123i	−0.267374	+	0.660380i
$883$	22.1282	+	26.3714i	0.744673	+	0.887467i	0.996776	−	0.0802332i	$-0.0255665\pi$
$883$	22.1282	+	26.3714i	0.744673	+	0.887467i	−0.252103	+	0.967700i	$0.581122\pi$
$884$	5.65588	+	3.82702i	0.190228	+	0.128717i
$885$	1.25410	−	2.17216i	0.0421561	−	0.0730164i
$886$	−16.6477	+	12.9869i	−0.559289	+	0.436305i
$887$	16.7427	+	6.09383i	0.562163	+	0.204611i	0.607443	−	0.794364i	$-0.292195\pi$
$887$	16.7427	+	6.09383i	0.562163	+	0.204611i	−0.0452791	+	0.998974i	$0.514418\pi$
$888$	−90.7113	+	22.4050i	−3.04407	+	0.751864i
$889$	4.88060	−	0.860582i	0.163690	−	0.0288630i
$890$	0.468909	+	0.883452i	0.0157179	+	0.0296134i
$891$	−20.5734	+	24.5184i	−0.689234	+	0.821397i
$892$	−7.18775	+	2.04965i	−0.240664	+	0.0686274i
$893$	12.6238	−	8.43916i	0.422439	−	0.282406i
$894$	77.5064	−	10.8349i	2.59220	−	0.362372i
$895$	0.268028	+	0.224902i	0.00895918	+	0.00751764i
$896$	−33.8502	−	8.62459i	−1.13086	−	0.288127i
$897$	1.07396	+	6.09074i	0.0358585	+	0.203364i
$898$	−47.5034	−	1.69373i	−1.58521	−	0.0565205i
$899$	−1.16352	+	3.19674i	−0.0388055	+	0.106617i
$900$	34.7560	+	33.6621i	1.15853	+	1.12207i
$901$	15.4114	+	8.89775i	0.513427	+	0.296427i
$902$	−18.9575	+	21.0234i	−0.631216	+	0.700003i
$903$	−20.9746	+	17.5998i	−0.697991	+	0.585684i
$904$	29.7624	+	3.19436i	0.989883	+	0.106243i
$905$	−15.5490	+	8.97722i	−0.516866	+	0.298413i
$906$	−79.1474	−	16.8840i	−2.62949	−	0.560932i
$907$	2.92970	−	16.6152i	0.0972792	−	0.551698i	−0.896746	−	0.442546i	$-0.854075\pi$
$907$	2.92970	−	16.6152i	0.0972792	−	0.551698i	0.994025	−	0.109152i	$-0.0348135\pi$
$908$	−12.3953	−	25.5091i	−0.411354	−	0.846549i
$909$	−54.6456	+	19.8894i	−1.81248	+	0.659689i
$910$	−2.92858	−	1.83297i	−0.0970814	−	0.0607622i
$911$	43.3664			1.43679			0.718396	−	0.695635i	$-0.244877\pi$
$911$	43.3664			1.43679			0.718396	+	0.695635i	$0.244877\pi$
$912$	−47.3856	−	21.4999i	−1.56910	−	0.711933i
$913$	−48.4453			−1.60330
$914$	−50.4472	−	31.5744i	−1.66865	−	1.04439i
$915$	26.8162	−	9.76029i	0.886515	−	0.322665i
$916$	−6.85556	−	14.1085i	−0.226514	−	0.466156i
$917$	5.25803	−	29.8198i	0.173636	−	0.984736i
$918$	49.2352	+	10.5030i	1.62500	+	0.346651i
$919$	10.4580	−	6.03794i	0.344978	−	0.199173i	−0.317493	−	0.948261i	$-0.602841\pi$
$919$	10.4580	−	6.03794i	0.344978	−	0.199173i	0.662471	+	0.749087i	$0.269508\pi$
$920$	6.66030	+	0.714842i	0.219583	+	0.0235676i
$921$	−66.2279	+	55.5718i	−2.18228	+	1.83115i
$922$	−5.86042	+	6.49906i	−0.193003	+	0.214035i
$923$	−6.89337	−	3.97989i	−0.226898	−	0.131000i
$924$	51.8655	+	50.2331i	1.70625	+	1.65255i
$925$	15.5061	−	42.6027i	0.509837	−	1.40077i
$926$	−16.8302	−	0.600081i	−0.553076	−	0.0197199i
$927$	2.01275	+	11.4149i	0.0661075	+	0.374914i
$928$	14.8402	+	8.64068i	0.487153	+	0.283644i
$929$	−17.9287	−	15.0439i	−0.588220	−	0.493575i	0.299415	−	0.954123i	$-0.403209\pi$
$929$	−17.9287	−	15.0439i	−0.588220	−	0.493575i	−0.887635	+	0.460548i	$0.847653\pi$
$930$	4.45428	−	0.622677i	0.146061	−	0.0204184i
$931$	8.90542	+	6.52657i	0.291863	+	0.213900i
$932$	3.93454	−	1.12197i	0.128880	−	0.0367514i
$933$	−17.7288	+	21.1284i	−0.580415	+	0.691712i
$934$	10.6073	+	19.9848i	0.347082	+	0.653922i
$935$	−15.0560	+	2.65479i	−0.492385	+	0.0868208i
$936$	13.4958	−	3.33336i	0.441124	−	0.108954i
$937$	−26.6320	−	9.69324i	−0.870028	−	0.316664i	−0.131849	−	0.991270i	$-0.542092\pi$
$937$	−26.6320	−	9.69324i	−0.870028	−	0.316664i	−0.738178	+	0.674605i	$0.764314\pi$
$938$	28.4324	−	22.1802i	0.928349	−	0.724210i
$939$	−37.6167	+	65.1541i	−1.22758	+	2.12622i
$940$	5.48717	+	3.71286i	0.178972	+	0.121100i
$941$	0.258229	+	0.307745i	0.00841802	+	0.0100322i	0.770237	−	0.637758i	$-0.220138\pi$
$941$	0.258229	+	0.307745i	0.00841802	+	0.0100322i	−0.761819	+	0.647790i	$0.775693\pi$
$942$	12.6136	−	31.1540i	0.410974	−	1.01505i
$943$	6.36223	+	11.0197i	0.207183	+	0.358851i
$944$	3.46015	−	0.724877i	0.112618	−	0.0235927i
$945$	−25.0824	−	4.42271i	−0.815932	−	0.143871i
$946$	5.07621	+	15.6620i	0.165042	+	0.509217i
$947$	−1.37169	−	3.76869i	−0.0445739	−	0.122466i	0.915408	−	0.402526i	$-0.131868\pi$
$947$	−1.37169	−	3.76869i	−0.0445739	−	0.122466i	−0.959982	+	0.280060i	$0.909646\pi$
$948$	−17.8449	−	7.97643i	−0.579575	−	0.259062i
$949$			2.15949i			0.0701000i
$950$	21.4764	−	13.2750i	0.696785	−	0.430699i
$951$		−	90.6032i		−	2.93801i
$952$	9.95351	−	34.4260i	0.322595	−	1.11575i
$953$	12.2206	+	33.5757i	0.395863	+	1.08762i	0.964280	+	0.264884i	$0.0853336\pi$
$953$	12.2206	+	33.5757i	0.395863	+	1.08762i	−0.568417	+	0.822740i	$0.692444\pi$
$954$	34.4604	−	11.1689i	1.11570	−	0.361608i
$955$	−13.9651	−	2.46242i	−0.451900	−	0.0796821i
$956$	−3.14286	+	44.0172i	−0.101647	+	1.42362i
$957$	−17.7477	−	30.7400i	−0.573703	−	0.993682i
$958$	−16.2081	−	6.56235i	−0.523662	−	0.212020i
$959$	10.9718	+	13.0756i	0.354297	+	0.422235i
$960$	0.892150	−	22.6858i	0.0287940	−	0.732182i
$961$	14.8721	−	25.7592i	0.479745	−	0.830942i
$962$	−8.01181	−	10.2702i	−0.258311	−	0.331123i
$963$	−16.6441	−	6.05794i	−0.536347	−	0.195214i
$964$	−19.1612	+	1.98551i	−0.617139	+	0.0639491i
$965$	7.00108	−	1.23448i	0.225373	−	0.0397393i
$966$	28.6673	−	15.2157i	0.922355	−	0.489558i
$967$	−30.5866	+	36.4517i	−0.983598	+	1.17221i	0.00146235	+	0.999999i	$0.499535\pi$
$967$	−30.5866	+	36.4517i	−0.983598	+	1.17221i	−0.985061	+	0.172208i	$0.944910\pi$
$968$	11.2514	−	4.97984i	0.361635	−	0.160058i
$969$	23.5993	−	47.8825i	0.758120	−	1.53821i
$970$	1.76822	+	12.6488i	0.0567740	+	0.406129i
$971$	38.0365	+	31.9164i	1.22065	+	1.02425i	0.998791	+	0.0491676i	$0.0156568\pi$
$971$	38.0365	+	31.9164i	1.22065	+	1.02425i	0.221859	+	0.975079i	$0.428788\pi$
$972$	−2.66328	+	1.92902i	−0.0854247	+	0.0618735i
$973$	4.89784	+	27.7770i	0.157018	+	0.890491i
$974$	−0.525354	+	14.7344i	−0.0168334	+	0.472121i
$975$	−3.47865	+	9.55751i	−0.111406	+	0.306085i
$976$	35.4590	+	18.9875i	1.13501	+	0.607774i
$977$	−0.637676	−	0.368162i	−0.0204011	−	0.0117786i	0.489765	−	0.871855i	$-0.337083\pi$
$977$	−0.637676	−	0.368162i	−0.0204011	−	0.0117786i	−0.510166	+	0.860076i	$0.670416\pi$
$978$	53.4055	+	48.1574i	1.70772	+	1.53991i
$979$	2.23220	−	1.87304i	0.0713415	−	0.0598627i
$980$	−1.17226	+	4.67246i	−0.0374463	+	0.149256i
$981$	47.3730	−	27.3508i	1.51250	−	0.873244i
$982$	−4.47506	+	20.9778i	−0.142805	+	0.669430i
$983$	3.73409	−	21.1771i	0.119099	−	0.675444i	−0.865540	−	0.500840i	$-0.833024\pi$
$983$	3.73409	−	21.1771i	0.119099	−	0.675444i	0.984639	−	0.174604i	$-0.0558644\pi$
$984$	35.8068	−	24.0376i	1.14148	−	0.766290i
$985$	19.1510	−	6.97040i	0.610202	−	0.222095i
$986$	−9.34656	+	14.9332i	−0.297655	+	0.475571i
$987$	32.1001			1.02176
$988$	0.0406169	−	7.25379i	0.00129220	−	0.230774i
$989$	7.40050			0.235322
$990$	−16.5112	+	26.3804i	−0.524761	+	0.838424i
$991$	−37.2349	+	13.5524i	−1.18281	+	0.430506i	−0.857192	−	0.514996i	$-0.827793\pi$
$991$	−37.2349	+	13.5524i	−1.18281	+	0.430506i	−0.325614	+	0.945503i	$0.605571\pi$
$992$	4.84119	+	4.09258i	0.153708	+	0.129940i
$993$	10.4790	−	59.4293i	0.332541	−	1.88593i
$994$	−8.71444	+	40.8509i	−0.276405	+	1.29571i
$995$	21.0919	−	12.1774i	0.668657	−	0.386049i
$996$	71.5860	+	17.9599i	2.26829	+	0.569083i
$997$	−45.3533	+	38.0559i	−1.43635	+	1.20524i	−0.494518	+	0.869167i	$0.664656\pi$
$997$	−45.3533	+	38.0559i	−1.43635	+	1.20524i	−0.941835	+	0.336076i	$0.890900\pi$
$998$	9.02782	+	8.14068i	0.285771	+	0.257689i
$999$	−83.1591	−	48.0119i	−2.63104	−	1.51903i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.2.k.a.3.3	✓	48
3.2	odd	2		684.2.cf.a.307.6		48
4.3	odd	2	inner	76.2.k.a.3.7	yes	48
12.11	even	2		684.2.cf.a.307.2		48
19.13	odd	18	inner	76.2.k.a.51.7	yes	48
57.32	even	18		684.2.cf.a.127.2		48
76.51	even	18	inner	76.2.k.a.51.3	yes	48
228.203	odd	18		684.2.cf.a.127.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.2.k.a.3.3	✓	48	1.1	even	1	trivial
76.2.k.a.3.7	yes	48	4.3	odd	2	inner
76.2.k.a.51.3	yes	48	76.51	even	18	inner
76.2.k.a.51.7	yes	48	19.13	odd	18	inner
684.2.cf.a.127.2		48	57.32	even	18
684.2.cf.a.127.6		48	228.203	odd	18
684.2.cf.a.307.2		48	12.11	even	2
684.2.cf.a.307.6		48	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	76.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19877 - 0.750298i) q^{2} +(2.80443 - 1.02073i) q^{3} +(0.874105 + 1.79887i) q^{4} +(-0.165124 + 0.936467i) q^{5} +(-4.12772 - 0.880539i) q^{6} +(-2.67390 + 1.54378i) q^{7} +(0.301838 - 2.81228i) q^{8} +(4.52481 - 3.79677i) q^{9} +O(q^{10})\)	\(q+(-1.19877 - 0.750298i) q^{2} +(2.80443 - 1.02073i) q^{3} +(0.874105 + 1.79887i) q^{4} +(-0.165124 + 0.936467i) q^{5} +(-4.12772 - 0.880539i) q^{6} +(-2.67390 + 1.54378i) q^{7} +(0.301838 - 2.81228i) q^{8} +(4.52481 - 3.79677i) q^{9} +(0.900576 - 0.998718i) q^{10} +(-3.39303 - 1.95897i) q^{11} +(4.28753 + 4.15259i) q^{12} +(-0.284588 + 0.781900i) q^{13} +(4.36368 + 0.155587i) q^{14} +(0.492800 + 2.79481i) q^{15} +(-2.47188 + 3.14481i) q^{16} +(-3.14351 - 2.63772i) q^{17} +(-8.27293 + 1.15650i) q^{18} +(-0.473541 + 4.33310i) q^{19} +(-1.82892 + 0.521533i) q^{20} +(-5.92298 + 7.05874i) q^{21} +(2.59766 + 4.89414i) q^{22} +(2.45271 - 0.432479i) q^{23} +(-2.02409 - 8.19493i) q^{24} +(3.84876 + 1.40083i) q^{25} +(0.927814 - 0.723793i) q^{26} +(4.33744 - 7.51266i) q^{27} +(-5.11432 - 3.46058i) q^{28} +(1.95130 + 2.32547i) q^{29} +(1.50618 - 3.72008i) q^{30} +(0.560318 + 0.970499i) q^{31} +(5.32276 - 1.91526i) q^{32} +(-11.5151 - 2.03042i) q^{33} +(1.78928 + 5.52059i) q^{34} +(-1.00417 - 2.75893i) q^{35} +(10.7851 + 4.82079i) q^{36} -11.0692i q^{37} +(3.81878 - 4.83910i) q^{38} +2.48327i q^{39} +(2.58376 + 0.747037i) q^{40} +(1.74742 + 4.80099i) q^{41} +(12.3965 - 4.01781i) q^{42} +(2.92630 + 0.515985i) q^{43} +(0.558065 - 7.81597i) q^{44} +(2.80839 + 4.86428i) q^{45} +(-3.26472 - 1.32182i) q^{46} +(-2.23924 - 2.66862i) q^{47} +(-3.72222 + 11.3425i) q^{48} +(1.26648 - 2.19361i) q^{49} +(-3.56274 - 4.56699i) q^{50} +(-11.5082 - 4.18863i) q^{51} +(-1.65530 + 0.171525i) q^{52} +(-4.27071 + 0.753042i) q^{53} +(-10.8363 + 5.75159i) q^{54} +(2.39478 - 2.85399i) q^{55} +(3.53444 + 7.98571i) q^{56} +(3.09491 + 12.6352i) q^{57} +(-0.594368 - 4.25176i) q^{58} +(-0.677042 - 0.568105i) q^{59} +(-4.59674 + 3.32944i) q^{60} +(-1.74615 - 9.90290i) q^{61} +(0.0564707 - 1.58381i) q^{62} +(-6.23753 + 17.1375i) q^{63} +(-7.81779 - 1.69770i) q^{64} +(-0.685231 - 0.395618i) q^{65} +(12.2805 + 11.0738i) q^{66} +(6.32640 - 5.30848i) q^{67} +(1.99716 - 7.96042i) q^{68} +(6.43701 - 3.71641i) q^{69} +(-0.866253 + 4.06076i) q^{70} +(-1.66114 + 9.42079i) q^{71} +(-9.31180 - 13.8710i) q^{72} +(2.43877 - 0.887641i) q^{73} +(-8.30520 + 13.2694i) q^{74} +12.2235 q^{75} +(-8.20862 + 2.93575i) q^{76} +12.0968 q^{77} +(1.86319 - 2.97687i) q^{78} +(-3.07726 + 1.12003i) q^{79} +(-2.53684 - 2.83412i) q^{80} +(1.41857 - 8.04512i) q^{81} +(1.50742 - 7.06637i) q^{82} +(10.7084 - 6.18250i) q^{83} +(-17.8751 - 4.48461i) q^{84} +(2.98921 - 2.50824i) q^{85} +(-3.12082 - 2.81414i) q^{86} +(7.84597 + 4.52987i) q^{87} +(-6.53330 + 8.95084i) q^{88} +(-0.254375 + 0.698890i) q^{89} +(0.283039 - 7.93829i) q^{90} +(-0.446118 - 2.53006i) q^{91} +(2.92190 + 4.03408i) q^{92} +(2.56199 + 2.14976i) q^{93} +(0.682075 + 4.87917i) q^{94} +(-3.97961 - 1.15896i) q^{95} +(12.9724 - 10.8043i) q^{96} +(-6.10468 + 7.27528i) q^{97} +(-3.16409 + 1.67940i) q^{98} +(-22.7906 + 4.01859i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9	\( 48 q - 6 q^{2} - 12 q^{5} - 12 q^{6} - 9 q^{8} - 18 q^{9} - 3 q^{10} - 9 q^{12} - 3 q^{14} - 12 q^{17} - 42 q^{20} - 18 q^{21} - 12 q^{22} + 24 q^{24} - 12 q^{25} + 21 q^{26} - 12 q^{29} + 42 q^{30} + 9 q^{32} - 36 q^{33} + 87 q^{36} + 60 q^{38} + 6 q^{40} + 30 q^{41} + 3 q^{42} + 45 q^{44} - 6 q^{45} + 36 q^{46} + 45 q^{48} - 18 q^{49} + 18 q^{50} - 15 q^{52} - 24 q^{53} - 75 q^{54} - 12 q^{57} + 60 q^{58} + 6 q^{60} - 66 q^{62} - 45 q^{64} + 18 q^{65} - 42 q^{66} - 42 q^{68} + 126 q^{69} - 63 q^{70} - 78 q^{72} - 12 q^{73} - 105 q^{74} - 126 q^{76} - 36 q^{77} + 3 q^{78} - 3 q^{80} + 72 q^{81} - 111 q^{82} - 117 q^{84} + 108 q^{85} - 24 q^{86} - 81 q^{88} - 18 q^{90} + 36 q^{92} + 30 q^{93} - 66 q^{96} - 6 q^{97} + 39 q^{98}+O(q^{100}) \) 48 * q - 6 * q^2 - 12 * q^5 - 12 * q^6 - 9 * q^8 - 18 * q^9 - 3 * q^10 - 9 * q^12 - 3 * q^14 - 12 * q^17 - 42 * q^20 - 18 * q^21 - 12 * q^22 + 24 * q^24 - 12 * q^25 + 21 * q^26 - 12 * q^29 + 42 * q^30 + 9 * q^32 - 36 * q^33 + 87 * q^36 + 60 * q^38 + 6 * q^40 + 30 * q^41 + 3 * q^42 + 45 * q^44 - 6 * q^45 + 36 * q^46 + 45 * q^48 - 18 * q^49 + 18 * q^50 - 15 * q^52 - 24 * q^53 - 75 * q^54 - 12 * q^57 + 60 * q^58 + 6 * q^60 - 66 * q^62 - 45 * q^64 + 18 * q^65 - 42 * q^66 - 42 * q^68 + 126 * q^69 - 63 * q^70 - 78 * q^72 - 12 * q^73 - 105 * q^74 - 126 * q^76 - 36 * q^77 + 3 * q^78 - 3 * q^80 + 72 * q^81 - 111 * q^82 - 117 * q^84 + 108 * q^85 - 24 * q^86 - 81 * q^88 - 18 * q^90 + 36 * q^92 + 30 * q^93 - 66 * q^96 - 6 * q^97 + 39 * q^98

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