LMFDB - Embedded newform 936.2.db.a.61.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [936,2,Mod(61,936)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(936, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 4, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("936.61"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 936 = 2^{3} \cdot 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	936.db (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$7.47399762919$
Analytic rank:	$0$
Dimension:	$328$
Relative dimension:	$164$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			61.17
Character	$\chi$	$=$	936.61
Dual form			936.2.db.a.445.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.33515 - 0.466242i) q^{2} +(-1.42357 - 0.986631i) q^{3} +(1.56524 + 1.24500i) q^{4} +(0.715331 - 0.412997i) q^{5} +(1.44067 + 1.98103i) q^{6} -2.35753 q^{7} +(-1.50935 - 2.39204i) q^{8} +(1.05312 + 2.80908i) q^{9} +(-1.14763 + 0.217894i) q^{10} +(0.617926 - 0.356760i) q^{11} +(-0.999870 - 3.31666i) q^{12} +(3.60386 - 0.110398i) q^{13} +(3.14766 + 1.09918i) q^{14} +(-1.42580 - 0.117837i) q^{15} +(0.899933 + 3.89745i) q^{16} +(-2.27932 - 3.94789i) q^{17} +(-0.0963584 - 4.24155i) q^{18} +(0.636605 - 0.367544i) q^{19} +(1.63385 + 0.244152i) q^{20} +(3.35612 + 2.32602i) q^{21} +(-0.991359 + 0.188224i) q^{22} -4.18348 q^{23} +(-0.211393 + 4.89442i) q^{24} +(-2.15887 + 3.73927i) q^{25} +(-4.86316 - 1.53287i) q^{26} +(1.27233 - 5.03797i) q^{27} +(-3.69010 - 2.93514i) q^{28} +(6.33702 - 3.65868i) q^{29} +(1.84871 + 0.822098i) q^{30} +(-1.99094 - 3.44841i) q^{31} +(0.615611 - 5.62326i) q^{32} +(-1.23165 - 0.101791i) q^{33} +(1.20255 + 6.33373i) q^{34} +(-1.68642 + 0.973654i) q^{35} +(-1.84893 + 5.70802i) q^{36} +(-3.46950 - 2.00312i) q^{37} +(-1.02133 + 0.193914i) q^{38} +(-5.23928 - 3.39852i) q^{39} +(-2.06759 - 1.08775i) q^{40} +3.47908 q^{41} +(-3.39643 - 4.67034i) q^{42} -2.58118i q^{43} +(1.41137 + 0.210906i) q^{44} +(1.91347 + 1.57449i) q^{45} +(5.58556 + 1.95051i) q^{46} +(-0.0719052 + 0.124543i) q^{47} +(2.56422 - 6.43621i) q^{48} -1.44203 q^{49} +(4.62581 - 3.98592i) q^{50} +(-0.650338 + 7.86896i) q^{51} +(5.77834 + 4.31402i) q^{52} -4.60908i q^{53} +(-4.04767 + 6.13322i) q^{54} +(0.294681 - 0.510403i) q^{55} +(3.55834 + 5.63932i) q^{56} +(-1.26888 - 0.104868i) q^{57} +(-10.1667 + 1.93029i) q^{58} +(-13.0302 - 7.52300i) q^{59} +(-2.08501 - 1.95957i) q^{60} +6.48930i q^{61} +(1.05040 + 5.53239i) q^{62} +(-2.48277 - 6.62251i) q^{63} +(-3.44373 + 7.22085i) q^{64} +(2.53236 - 1.56735i) q^{65} +(1.59698 + 0.710155i) q^{66} +8.01643i q^{67} +(1.34747 - 9.01714i) q^{68} +(5.95548 + 4.12755i) q^{69} +(2.70558 - 0.513693i) q^{70} +(-1.19496 - 2.06973i) q^{71} +(5.12992 - 6.75899i) q^{72} -10.4588 q^{73} +(3.69836 + 4.29208i) q^{74} +(6.76258 - 3.19312i) q^{75} +(1.45403 + 0.217282i) q^{76} +(-1.45678 + 0.841074i) q^{77} +(5.41068 + 6.98030i) q^{78} +(-6.92208 + 11.9894i) q^{79} +(2.25338 + 2.41630i) q^{80} +(-6.78188 + 5.91660i) q^{81} +(-4.64508 - 1.62209i) q^{82} +(-8.70733 - 5.02718i) q^{83} +(2.35723 + 7.81915i) q^{84} +(-3.26093 - 1.88270i) q^{85} +(-1.20345 + 3.44626i) q^{86} +(-12.6310 - 1.04390i) q^{87} +(-1.78605 - 0.939630i) q^{88} +(8.95021 - 15.5022i) q^{89} +(-1.82067 - 2.99431i) q^{90} +(-8.49623 + 0.260267i) q^{91} +(-6.54813 - 5.20844i) q^{92} +(-0.568058 + 6.87338i) q^{93} +(0.154071 - 0.132759i) q^{94} +(0.303589 - 0.525831i) q^{95} +(-6.42445 + 7.39774i) q^{96} -13.8040 q^{97} +(1.92532 + 0.672335i) q^{98} +(1.65292 + 1.36009i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 328 q + q^{2} + q^{4} + q^{6} - 4 q^{7} - 2 q^{8} - 2 q^{9} - 4 q^{10} + 5 q^{12} - 6 q^{14} + 4 q^{15} + q^{16} - 4 q^{17} - 12 q^{18} - 18 q^{20} - 7 q^{22} + 44 q^{23} - 6 q^{24} + 144 q^{25} - 16 q^{26}+ \cdots + 39 q^{98}+O(q^{100}) $ 328 * q + q^2 + q^4 + q^6 - 4 * q^7 - 2 * q^8 - 2 * q^9 - 4 * q^10 + 5 * q^12 - 6 * q^14 + 4 * q^15 + q^16 - 4 * q^17 - 12 * q^18 - 18 * q^20 - 7 * q^22 + 44 * q^23 - 6 * q^24 + 144 * q^25 - 16 * q^26 - 10 * q^28 - 5 * q^30 - 4 * q^31 + q^32 - 14 * q^33 - 13 * q^36 + 6 * q^38 + 20 * q^39 + 8 * q^40 - 4 * q^41 - 46 * q^42 - 32 * q^44 - 6 * q^46 - 4 * q^47 - 46 * q^48 + 276 * q^49 + 68 * q^50 + 40 * q^54 - 14 * q^55 - 56 * q^56 - 20 * q^57 - 25 * q^58 - 41 * q^60 + 3 * q^62 - 58 * q^63 - 26 * q^64 - 22 * q^65 - 6 * q^66 - 64 * q^68 - 17 * q^70 - 4 * q^71 - 7 * q^72 - 16 * q^73 - 38 * q^74 - 18 * q^76 - q^78 - 4 * q^79 - 42 * q^80 - 2 * q^81 + 3 * q^82 + 6 * q^84 + 36 * q^86 - 2 * q^87 + 5 * q^88 - 4 * q^89 + 33 * q^90 + 28 * q^92 - 6 * q^94 + 56 * q^95 - 113 * q^96 - 4 * q^97 + 39 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/936\mathbb{Z}\right)^\times$.

$n$	$145$	$209$	$469$	$703$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$-1$	$1$

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 $

$2$	−1.33515	−	0.466242i	−0.944092	−	0.329683i
$2$	−1.33515	−	0.466242i	−0.944092	−	0.329683i
$3$	−1.42357	−	0.986631i	−0.821900	−	0.569632i
$3$	−1.42357	−	0.986631i	−0.821900	−	0.569632i
$4$	1.56524	+	1.24500i	0.782618	+	0.622502i
$5$	0.715331	−	0.412997i	0.319906	−	0.184698i	−0.331445	−	0.943475i	$-0.607536\pi$
$5$	0.715331	−	0.412997i	0.319906	−	0.184698i	0.651351	+	0.758777i	$0.274203\pi$
$6$	1.44067	+	1.98103i	0.588151	+	0.808751i
$7$	−2.35753			−0.891064			−0.445532	−	0.895266i	$-0.646986\pi$
$7$	−2.35753			−0.891064			−0.445532	+	0.895266i	$0.646986\pi$
$8$	−1.50935	−	2.39204i	−0.533636	−	0.845715i
$9$	1.05312	+	2.80908i	0.351040	+	0.936361i
$10$	−1.14763	+	0.217894i	−0.362912	+	0.0689041i
$11$	0.617926	−	0.356760i	0.186312	−	0.107567i	−0.403943	−	0.914784i	$-0.632361\pi$
$11$	0.617926	−	0.356760i	0.186312	−	0.107567i	0.590255	+	0.807217i	$0.299027\pi$
$12$	−0.999870	−	3.31666i	−0.288638	−	0.957438i
$13$	3.60386	−	0.110398i	0.999531	−	0.0306189i
$13$	3.60386	−	0.110398i	0.999531	−	0.0306189i
$14$	3.14766	+	1.09918i	0.841246	+	0.293769i
$15$	−1.42580	−	0.117837i	−0.368140	−	0.0304253i
$16$	0.899933	+	3.89745i	0.224983	+	0.974363i
$17$	−2.27932	−	3.94789i	−0.552816	−	0.957505i	−0.998070	−	0.0621004i	$-0.980220\pi$
$17$	−2.27932	−	3.94789i	−0.552816	−	0.957505i	0.445254	−	0.895404i	$-0.353113\pi$
$18$	−0.0963584	−	4.24155i	−0.0227119	−	0.999742i
$19$	0.636605	−	0.367544i	0.146047	−	0.0843204i	−0.425196	−	0.905101i	$-0.639795\pi$
$19$	0.636605	−	0.367544i	0.146047	−	0.0843204i	0.571243	+	0.820781i	$0.306461\pi$
$20$	1.63385	+	0.244152i	0.365339	+	0.0545941i
$21$	3.35612	+	2.32602i	0.732366	+	0.507578i
$22$	−0.991359	+	0.188224i	−0.211358	+	0.0401295i
$23$	−4.18348			−0.872315			−0.436157	−	0.899870i	$-0.643661\pi$
$23$	−4.18348			−0.872315			−0.436157	+	0.899870i	$0.643661\pi$
$24$	−0.211393	+	4.89442i	−0.0431505	+	0.999069i
$25$	−2.15887	+	3.73927i	−0.431773	+	0.747854i
$26$	−4.86316	−	1.53287i	−0.953744	−	0.300621i
$27$	1.27233	−	5.03797i	0.244861	−	0.969558i
$28$	−3.69010	−	2.93514i	−0.697363	−	0.554689i
$29$	6.33702	−	3.65868i	1.17675	−	0.679399i	0.221493	−	0.975162i	$-0.428907\pi$
$29$	6.33702	−	3.65868i	1.17675	−	0.679399i	0.955261	+	0.295763i	$0.0955738\pi$
$30$	1.84871	+	0.822098i	0.337528	+	0.150094i
$31$	−1.99094	−	3.44841i	−0.357583	−	0.619352i	0.629973	−	0.776617i	$-0.283066\pi$
$31$	−1.99094	−	3.44841i	−0.357583	−	0.619352i	−0.987556	+	0.157265i	$0.949732\pi$
$32$	0.615611	−	5.62326i	0.108826	−	0.994061i
$33$	−1.23165	−	0.101791i	−0.214403	−	0.0177196i
$34$	1.20255	+	6.33373i	0.206236	+	1.08623i
$35$	−1.68642	+	0.973654i	−0.285057	+	0.164578i
$36$	−1.84893	+	5.70802i	−0.308156	+	0.951336i
$37$	−3.46950	−	2.00312i	−0.570383	−	0.329311i	0.186920	−	0.982375i	$-0.440150\pi$
$37$	−3.46950	−	2.00312i	−0.570383	−	0.329311i	−0.757302	+	0.653065i	$0.773483\pi$
$38$	−1.02133	+	0.193914i	−0.165681	+	0.0314569i
$39$	−5.23928	−	3.39852i	−0.838956	−	0.544199i
$40$	−2.06759	−	1.08775i	−0.326915	−	0.171988i
$41$	3.47908			0.543341			0.271670	−	0.962390i	$-0.412424\pi$
$41$	3.47908			0.543341			0.271670	+	0.962390i	$0.412424\pi$
$42$	−3.39643	−	4.67034i	−0.524081	−	0.720649i
$43$		−	2.58118i		−	0.393626i	−0.980441	−	0.196813i	$-0.936941\pi$
$43$		−	2.58118i		−	0.393626i	0.980441	−	0.196813i	$-0.0630592\pi$
$44$	1.41137	+	0.210906i	0.212772	+	0.0317953i
$45$	1.91347	+	1.57449i	0.285243	+	0.234711i
$46$	5.58556	+	1.95051i	0.823545	+	0.287587i
$47$	−0.0719052	+	0.124543i	−0.0104884	+	0.0181665i	−0.871222	−	0.490889i	$-0.836672\pi$
$47$	−0.0719052	+	0.124543i	−0.0104884	+	0.0181665i	0.860734	+	0.509056i	$0.170005\pi$
$48$	2.56422	−	6.43621i	0.370114	−	0.928986i
$49$	−1.44203			−0.206004
$50$	4.62581	−	3.98592i	0.654188	−	0.563694i
$51$	−0.650338	+	7.86896i	−0.0910656	+	1.10187i
$52$	5.77834	+	4.31402i	0.801312	+	0.598247i
$53$		−	4.60908i		−	0.633106i	−0.948575	−	0.316553i	$-0.897475\pi$
$53$		−	4.60908i		−	0.633106i	0.948575	−	0.316553i	$-0.102525\pi$
$54$	−4.04767	+	6.13322i	−0.550818	+	0.834626i
$55$	0.294681	−	0.510403i	0.0397348	−	0.0688227i
$56$	3.55834	+	5.63932i	0.475504	+	0.753586i
$57$	−1.26888	−	0.104868i	−0.168068	−	0.0138901i
$58$	−10.1667	+	1.93029i	−1.33495	+	0.253460i
$59$	−13.0302	−	7.52300i	−1.69639	−	0.979411i	−0.949133	−	0.314877i	$-0.898037\pi$
$59$	−13.0302	−	7.52300i	−1.69639	−	0.979411i	−0.747257	−	0.664535i	$-0.768630\pi$
$60$	−2.08501	−	1.95957i	−0.269174	−	0.252979i
$61$			6.48930i			0.830870i	0.909623	+	0.415435i	$0.136371\pi$
$61$			6.48930i			0.830870i	−0.909623	+	0.415435i	$0.863629\pi$
$62$	1.05040	+	5.53239i	0.133401	+	0.702614i
$63$	−2.48277	−	6.62251i	−0.312799	−	0.834357i
$64$	−3.44373	+	7.22085i	−0.430466	+	0.902607i
$65$	2.53236	−	1.56735i	0.314101	−	0.194406i
$66$	1.59698	+	0.710155i	0.196575	+	0.0874140i
$67$			8.01643i			0.979363i	0.871901	+	0.489681i	$0.162887\pi$
$67$			8.01643i			0.979363i	−0.871901	+	0.489681i	$0.837113\pi$
$68$	1.34747	−	9.01714i	0.163405	−	1.09349i
$69$	5.95548	+	4.12755i	0.716956	+	0.496898i
$70$	2.70558	−	0.513693i	0.323378	−	0.0613980i
$71$	−1.19496	−	2.06973i	−0.141815	−	0.245632i	0.786365	−	0.617762i	$-0.211961\pi$
$71$	−1.19496	−	2.06973i	−0.141815	−	0.245632i	−0.928180	+	0.372131i	$0.878627\pi$
$72$	5.12992	−	6.75899i	0.604566	−	0.796555i
$73$	−10.4588			−1.22411			−0.612056	−	0.790815i	$-0.709657\pi$
$73$	−10.4588			−1.22411			−0.612056	+	0.790815i	$0.709657\pi$
$74$	3.69836	+	4.29208i	0.429925	+	0.498945i
$75$	6.76258	−	3.19312i	0.780876	−	0.368709i
$76$	1.45403	+	0.217282i	0.166789	+	0.0249239i
$77$	−1.45678	+	0.841074i	−0.166016	+	0.0958492i
$78$	5.41068	+	6.98030i	0.612639	+	0.790363i
$79$	−6.92208	+	11.9894i	−0.778795	+	1.34891i	0.153841	+	0.988096i	$0.450835\pi$
$79$	−6.92208	+	11.9894i	−0.778795	+	1.34891i	−0.932637	+	0.360817i	$0.882498\pi$
$80$	2.25338	+	2.41630i	0.251936	+	0.270150i
$81$	−6.78188	+	5.91660i	−0.753542	+	0.657400i
$82$	−4.64508	−	1.62209i	−0.512963	−	0.179130i
$83$	−8.70733	−	5.02718i	−0.955753	−	0.551804i	−0.0608899	−	0.998144i	$-0.519394\pi$
$83$	−8.70733	−	5.02718i	−0.955753	−	0.551804i	−0.894863	+	0.446340i	$0.852727\pi$
$84$	2.35723	+	7.81915i	0.257195	+	0.853139i
$85$	−3.26093	−	1.88270i	−0.353698	−	0.204208i
$86$	−1.20345	+	3.44626i	−0.129772	+	0.371619i
$87$	−12.6310	−	1.04390i	−1.35418	−	0.111918i
$88$	−1.78605	−	0.939630i	−0.190394	−	0.100165i
$89$	8.95021	−	15.5022i	0.948720	−	1.64323i	0.200595	−	0.979674i	$-0.435712\pi$
$89$	8.95021	−	15.5022i	0.948720	−	1.64323i	0.748125	−	0.663557i	$-0.230954\pi$
$90$	−1.82067	−	2.99431i	−0.191916	−	0.315629i
$91$	−8.49623	+	0.260267i	−0.890647	+	0.0272834i
$92$	−6.54813	−	5.20844i	−0.682690	−	0.543018i
$93$	−0.568058	+	6.87338i	−0.0589048	+	0.712736i
$94$	0.154071	−	0.132759i	0.0158913	−	0.0136930i
$95$	0.303589	−	0.525831i	0.0311476	−	0.0539492i
$96$	−6.42445	+	7.39774i	−0.655692	+	0.755028i
$97$	−13.8040			−1.40158			−0.700790	−	0.713368i	$-0.747169\pi$
$97$	−13.8040			−1.40158			−0.700790	+	0.713368i	$0.747169\pi$
$98$	1.92532	+	0.672335i	0.194487	+	0.0679161i
$99$	1.65292	+	1.36009i	0.166124	+	0.136695i
$100$	−8.03454	+	3.16504i	−0.803454	+	0.316504i
$101$	−10.5504	+	6.09129i	−1.04981	+	0.606106i	−0.922595	−	0.385770i	$-0.873936\pi$
$101$	−10.5504	+	6.09129i	−1.04981	+	0.606106i	−0.127211	+	0.991876i	$0.540603\pi$
$102$	4.53713	−	10.2030i	0.449243	−	1.01025i
$103$	−3.15465	−	5.46402i	−0.310837	−	0.538386i	0.667707	−	0.744424i	$-0.267276\pi$
$103$	−3.15465	−	5.46402i	−0.310837	−	0.538386i	−0.978544	+	0.206039i	$0.933943\pi$
$104$	−5.70356	−	8.45396i	−0.559280	−	0.828979i
$105$	3.36138	+	0.277804i	0.328037	+	0.0271109i
$106$	−2.14895	+	6.15380i	−0.208724	+	0.597710i
$107$	−5.20611	−	3.00575i	−0.503293	−	0.290577i	0.226779	−	0.973946i	$-0.427180\pi$
$107$	−5.20611	−	3.00575i	−0.503293	−	0.290577i	−0.730073	+	0.683370i	$0.760514\pi$
$108$	8.26380	−	6.30156i	0.795184	−	0.606368i
$109$		−	5.73467i		−	0.549282i	−0.961547	−	0.274641i	$-0.911441\pi$
$109$		−	5.73467i		−	0.549282i	0.961547	−	0.274641i	$-0.0885590\pi$
$110$	−0.631414	+	0.544070i	−0.0602030	+	0.0518751i
$111$	2.96275	+	6.27470i	0.281212	+	0.595568i
$112$	−2.12162	−	9.18837i	−0.200475	−	0.868220i
$113$	−5.84969	+	10.1320i	−0.550292	+	0.953135i	0.447961	+	0.894053i	$0.352150\pi$
$113$	−5.84969	+	10.1320i	−0.550292	+	0.953135i	−0.998253	+	0.0590813i	$0.981183\pi$
$114$	1.64525	+	0.731621i	0.154092	+	0.0685226i
$115$	−2.99257	+	1.72776i	−0.279059	+	0.161115i
$116$	14.4740	+	2.16291i	1.34388	+	0.200821i
$117$	4.10541	+	10.0073i	0.379546	+	0.925173i
$118$	13.8897	+	16.1195i	1.27865	+	1.48392i
$119$	5.37357	+	9.30729i	0.492594	+	0.853198i
$120$	1.87016	+	3.58843i	0.170722	+	0.327578i
$121$	−5.24544	+	9.08538i	−0.476859	+	0.825943i
$122$	3.02558	−	8.66417i	0.273924	−	0.784417i
$123$	−4.95272	−	3.43256i	−0.446572	−	0.309504i
$124$	1.17699	−	7.87630i	0.105697	−	0.707312i
$125$			7.69639i			0.688386i
$126$	0.227168	+	9.99959i	0.0202378	+	0.890834i
$127$	6.96220	−	12.0589i	0.617796	−	1.07005i	−0.372092	−	0.928196i	$-0.621359\pi$
$127$	6.96220	−	12.0589i	0.617796	−	1.07005i	0.989887	−	0.141857i	$-0.0453074\pi$
$128$	7.96455	−	8.03529i	0.703974	−	0.710226i
$129$	−2.54667	+	3.67450i	−0.224222	+	0.323521i
$130$	−4.11184	+	0.911955i	−0.360632	+	0.0799838i
$131$	−10.8350	+	6.25559i	−0.946658	+	0.546553i	−0.892041	−	0.451954i	$-0.850727\pi$
$131$	−10.8350	+	6.25559i	−0.946658	+	0.546553i	−0.0546171	+	0.998507i	$0.517394\pi$
$132$	−1.80110	−	1.69274i	−0.156765	−	0.147334i
$133$	−1.50082	+	0.866498i	−0.130137	+	0.0751349i
$134$	3.73760	−	10.7031i	0.322879	−	0.924608i
$135$	−1.17053	−	4.12929i	−0.100743	−	0.355393i
$136$	−6.00324	+	11.4110i	−0.514774	+	0.978483i
$137$	−2.79017			−0.238380			−0.119190	−	0.992871i	$-0.538030\pi$
$137$	−2.79017			−0.238380			−0.119190	+	0.992871i	$0.538030\pi$
$138$	−6.02701	−	8.28758i	−0.513053	−	0.705485i
$139$	6.70761	+	3.87264i	0.568932	+	0.328473i	0.756723	−	0.653736i	$-0.226799\pi$
$139$	6.70761	+	3.87264i	0.568932	+	0.328473i	−0.187791	+	0.982209i	$0.560133\pi$
$140$	−3.85185	−	0.575597i	−0.325540	−	0.0486468i
$141$	0.225241	−	0.106353i	0.0189687	−	0.00895652i
$142$	0.630451	+	3.32053i	0.0529063	+	0.278653i
$143$	2.18753	−	1.35393i	0.182931	−	0.113221i
$144$	−10.0005	+	6.63247i	−0.833377	+	0.552706i
$145$	3.02204	−	5.23433i	0.250967	−	0.434688i
$146$	13.9641	+	4.87634i	1.15567	+	0.403569i
$147$	2.05284	+	1.42275i	0.169315	+	0.117347i
$148$	−2.93670	−	7.45490i	−0.241396	−	0.612789i
$149$	−7.06853	−	4.08102i	−0.579077	−	0.334330i	0.181690	−	0.983356i	$-0.441843\pi$
$149$	−7.06853	−	4.08102i	−0.579077	−	0.334330i	−0.760766	+	0.649026i	$0.775177\pi$
$150$	−10.5178	+	1.11028i	−0.858775	+	0.0906541i
$151$	7.60177	−	13.1667i	0.618623	−	1.07149i	−0.371114	−	0.928587i	$-0.621024\pi$
$151$	7.60177	−	13.1667i	0.618623	−	1.07149i	0.989737	−	0.142900i	$-0.0456426\pi$
$152$	−1.84004	−	0.968033i	−0.149247	−	0.0785179i
$153$	8.68956	−	10.5604i	0.702509	−	0.853757i
$154$	2.33716	−	0.443744i	0.188334	−	0.0357579i
$155$	−2.84836	−	1.64450i	−0.228786	−	0.132090i
$156$	−3.96955	−	11.8424i	−0.317818	−	0.948152i
$157$	19.0653	−	11.0073i	1.52157	−	0.878481i	0.521898	−	0.853008i	$-0.325224\pi$
$157$	19.0653	−	11.0073i	1.52157	−	0.878481i	0.999676	−	0.0254729i	$-0.00810917\pi$
$158$	14.8320	−	12.7802i	1.17997	−	1.01674i
$159$	−4.54746	+	6.56136i	−0.360637	+	0.520350i
$160$	−1.88202	−	4.27674i	−0.148787	−	0.338106i
$161$	9.86269			0.777289
$162$	11.8134	−	4.73753i	0.928146	−	0.372216i
$163$	1.95082	−	1.12630i	0.152800	−	0.0882189i	−0.421651	−	0.906758i	$-0.638549\pi$
$163$	1.95082	−	1.12630i	0.152800	−	0.0882189i	0.574450	+	0.818539i	$0.305216\pi$
$164$	5.44558	+	4.33146i	0.425228	+	0.338230i
$165$	−0.923079	+	0.435854i	−0.0718616	+	0.0339312i
$166$	9.28168	+	10.7717i	0.720398	+	0.836049i
$167$	11.8292			0.915368			0.457684	−	0.889115i	$-0.348679\pi$
$167$	11.8292			0.915368			0.457684	+	0.889115i	$0.348679\pi$
$168$	0.498367	−	11.5388i	0.0384499	−	0.890234i
$169$	12.9756	−	0.795717i	0.998125	−	0.0612090i
$170$	3.47603	+	4.03407i	0.266599	+	0.309399i
$171$	1.70288	+	1.40121i	0.130223	+	0.107153i
$172$	3.21358	−	4.04016i	0.245033	−	0.308059i
$173$		−	9.95921i		−	0.757185i	−0.925563	−	0.378592i	$-0.876408\pi$
$173$		−	9.95921i		−	0.757185i	0.925563	−	0.378592i	$-0.123592\pi$
$174$	16.3775	+	7.28285i	1.24157	+	0.552111i
$175$	5.08960	−	8.81545i	0.384738	−	0.666386i
$176$	1.94655	+	2.08728i	0.146726	+	0.157334i
$177$	11.1270	+	23.5656i	0.836360	+	1.77130i
$178$	−19.1776	+	16.5248i	−1.43742	+	1.23858i
$179$	2.06025	+	1.18948i	0.153990	+	0.0889062i	0.575015	−	0.818143i	$-0.304996\pi$
$179$	2.06025	+	1.18948i	0.153990	+	0.0889062i	−0.421025	+	0.907049i	$0.638330\pi$
$180$	1.03479	+	4.84673i	0.0771288	+	0.361254i
$181$		−	20.6555i		−	1.53531i	−0.640861	−	0.767657i	$-0.721423\pi$
$181$		−	20.6555i		−	1.53531i	0.640861	−	0.767657i	$-0.278577\pi$
$182$	11.4651	+	3.61380i	0.849847	+	0.267873i
$183$	6.40254	−	9.23799i	0.473290	−	0.682892i
$184$	6.31433	+	10.0070i	0.465498	+	0.737729i
$185$	−3.30912			−0.243292
$186$	3.96310	−	8.91212i	0.290588	−	0.653468i
$187$	−2.81690	−	1.62634i	−0.205992	−	0.118930i
$188$	−0.267606	+	0.105418i	−0.0195171	+	0.00768838i
$189$	−2.99957	+	11.8772i	−0.218187	+	0.863939i
$190$	−0.650501	+	0.560517i	−0.0471923	+	0.0406641i
$191$	−3.30864			−0.239405			−0.119702	−	0.992810i	$-0.538194\pi$
$191$	−3.30864			−0.239405			−0.119702	+	0.992810i	$0.538194\pi$
$192$	12.0267	−	6.88172i	0.867953	−	0.496645i
$193$	2.69558			0.194032			0.0970162	−	0.995283i	$-0.469070\pi$
$193$	2.69558			0.194032			0.0970162	+	0.995283i	$0.469070\pi$
$194$	18.4303	+	6.43598i	1.32322	+	0.462077i
$195$	−5.15140	−	0.267262i	−0.368899	−	0.0191390i
$196$	−2.25712	−	1.79533i	−0.161223	−	0.128238i
$197$	11.2217	+	6.47885i	0.799513	+	0.461599i	0.843301	−	0.537442i	$-0.180609\pi$
$197$	11.2217	+	6.47885i	0.799513	+	0.461599i	−0.0437880	+	0.999041i	$0.513943\pi$
$198$	−1.57276	−	2.58659i	−0.111771	−	0.183821i
$199$	2.94021	+	5.09260i	0.208426	+	0.361005i	0.951219	−	0.308517i	$-0.0998326\pi$
$199$	2.94021	+	5.09260i	0.208426	+	0.361005i	−0.742793	+	0.669521i	$0.766499\pi$
$200$	12.2030	−	0.479760i	0.862880	−	0.0339241i
$201$	7.90925	−	11.4120i	0.557876	−	0.804938i
$202$	16.9264	−	3.21372i	1.19094	−	0.226117i
$203$	−14.9397	+	8.62546i	−1.04856	+	0.605389i
$204$	−10.8148	+	11.5071i	−0.757188	+	0.805659i
$205$	2.48869	−	1.43685i	0.173818	−	0.100354i
$206$	1.66437	+	8.76610i	0.115962	+	0.610763i
$207$	−4.40570	−	11.7517i	−0.306217	−	0.816801i
$208$	3.67350	+	13.9465i	0.254712	+	0.967017i
$209$	0.262250	−	0.454230i	0.0181402	−	0.0314197i
$210$	−4.35841	−	1.93812i	−0.300759	−	0.133743i
$211$			5.11613i			0.352209i	0.984372	+	0.176104i	$0.0563496\pi$
$211$			5.11613i			0.352209i	−0.984372	+	0.176104i	$0.943650\pi$
$212$	5.73832	−	7.21430i	0.394109	−	0.495480i
$213$	−0.340947	+	4.12539i	−0.0233613	+	0.282667i
$214$	5.54951	+	6.44042i	0.379357	+	0.440258i
$215$	−1.06602	−	1.84640i	−0.0727019	−	0.125923i
$216$	−13.9714	+	4.56059i	−0.950636	+	0.310309i
$217$	4.69370	+	8.12974i	0.318629	+	0.551882i
$218$	−2.67374	+	7.65663i	−0.181089	+	0.518572i
$219$	14.8889	+	10.3190i	1.00610	+	0.697293i
$220$	1.09670	−	0.432022i	0.0739394	−	0.0291269i
$221$	−8.65018	−	13.9760i	−0.581874	−	0.940129i
$222$	−1.03018	−	9.75901i	−0.0691412	−	0.654982i
$223$	−8.06833	−	13.9748i	−0.540296	−	0.935819i	−0.998887	−	0.0471721i	$-0.984979\pi$
$223$	−8.06833	−	13.9748i	−0.540296	−	0.935819i	0.458591	−	0.888647i	$-0.348354\pi$
$224$	−1.45132	+	13.2570i	−0.0969707	+	0.885772i
$225$	−12.7775	−	2.12654i	−0.851830	−	0.141769i
$226$	12.5341	−	10.8003i	0.833759	−	0.718424i
$227$		−	4.73032i		−	0.313962i	−0.987602	−	0.156981i	$-0.949824\pi$
$227$		−	4.73032i		−	0.313962i	0.987602	−	0.156981i	$-0.0501762\pi$
$228$	−1.85554	−	1.74391i	−0.122886	−	0.115493i
$229$	20.3569	−	11.7531i	1.34522	−	0.776665i	0.357654	−	0.933854i	$-0.383577\pi$
$229$	20.3569	−	11.7531i	1.34522	−	0.776665i	0.987568	+	0.157190i	$0.0502434\pi$
$230$	4.80108	−	0.911554i	0.316574	−	0.0601061i
$231$	2.90366	+	0.239976i	0.191047	+	0.0157893i
$232$	−18.3165	−	9.63618i	−1.20254	−	0.632647i
$233$	−9.63844			−0.631436			−0.315718	−	0.948853i	$-0.602245\pi$
$233$	−9.63844			−0.631436			−0.315718	+	0.948853i	$0.602245\pi$
$234$	−0.815520	−	15.2753i	−0.0533122	−	0.998578i
$235$			0.118786i			0.00774877i
$236$	−11.0292	−	27.9979i	−0.717941	−	1.82251i
$237$	21.6832	−	10.2382i	1.40848	−	0.665045i
$238$	−2.83505	−	14.9320i	−0.183769	−	0.967897i
$239$	−7.85625	−	13.6074i	−0.508179	−	0.880191i	−0.999955	−	0.00946968i	$-0.996986\pi$
$239$	−7.85625	−	13.6074i	−0.508179	−	0.880191i	0.491777	−	0.870721i	$-0.336348\pi$
$240$	−0.823863	−	5.66304i	−0.0531801	−	0.365547i
$241$	−8.35478			−0.538179			−0.269090	−	0.963115i	$-0.586723\pi$
$241$	−8.35478			−0.538179			−0.269090	+	0.963115i	$0.586723\pi$
$242$	11.2394	−	9.68467i	0.722498	−	0.622554i
$243$	15.4920	−	1.73150i	0.993812	−	0.111076i
$244$	−8.07920	+	10.1573i	−0.517218	+	0.650254i
$245$	−1.03153	+	0.595554i	−0.0659020	+	0.0380485i
$246$	5.01221	+	6.89214i	0.319567	+	0.439427i
$247$	2.25366	−	1.39486i	0.143397	−	0.0887526i
$248$	−5.24371	+	9.96726i	−0.332976	+	0.632921i
$249$	7.43555	+	15.7475i	0.471209	+	0.997955i
$250$	3.58838	−	10.2758i	0.226949	−	0.649899i
$251$	1.45865	−	0.842153i	0.0920693	−	0.0531562i	−0.453258	−	0.891379i	$-0.649739\pi$
$251$	1.45865	−	0.842153i	0.0920693	−	0.0531562i	0.545328	+	0.838223i	$0.316405\pi$
$252$	4.35893	−	13.4568i	0.274587	−	0.847701i
$253$	−2.58508	+	1.49250i	−0.162523	+	0.0938324i
$254$	−14.9179	+	12.8543i	−0.936034	+	0.806552i
$255$	2.78465	+	5.89750i	0.174381	+	0.369316i
$256$	−14.3802	+	7.01489i	−0.898765	+	0.438431i
$257$	−17.5621			−1.09550			−0.547748	−	0.836643i	$-0.684515\pi$
$257$	−17.5621			−1.09550			−0.547748	+	0.836643i	$0.684515\pi$
$258$	5.11339	−	3.71863i	0.318346	−	0.231512i
$259$	8.17947	+	4.72242i	0.508248	+	0.293437i
$260$	5.91510	+	0.699517i	0.366839	+	0.0433822i
$261$	16.9512	+	13.9482i	1.04925	+	0.863370i
$262$	17.3829	−	3.30040i	1.07392	−	0.203900i
$263$	13.7569	+	23.8276i	0.848284	+	1.46927i	0.882738	+	0.469865i	$0.155698\pi$
$263$	13.7569	+	23.8276i	0.848284	+	1.46927i	−0.0344536	+	0.999406i	$0.510969\pi$
$264$	1.61551	+	3.09980i	0.0994275	+	0.190780i
$265$	−1.90353	−	3.29702i	−0.116933	−	0.202534i
$266$	2.40781	−	0.457158i	0.147632	−	0.0280301i
$267$	−28.0362	+	13.2380i	−1.71579	+	0.810152i
$268$	−9.98048	+	12.5476i	−0.609655	+	0.766467i
$269$	5.91901	−	3.41734i	0.360888	−	0.208359i	−0.308582	−	0.951198i	$-0.599854\pi$
$269$	5.91901	−	3.41734i	0.360888	−	0.208359i	0.669470	+	0.742839i	$0.266521\pi$
$270$	−0.362423	+	6.05896i	−0.0220563	+	0.368736i
$271$	10.7743	−	18.6616i	0.654490	−	1.13361i	−0.327532	−	0.944840i	$-0.606217\pi$
$271$	10.7743	−	18.6616i	0.654490	−	1.13361i	0.982021	−	0.188769i	$-0.0604498\pi$
$272$	13.3355	−	12.4364i	0.808582	−	0.754065i
$273$	12.3518	+	8.01213i	0.747564	+	0.484916i
$274$	3.72528	+	1.30089i	0.225052	+	0.0785898i
$275$			3.08079i			0.185779i
$276$	4.18293	+	13.8752i	0.251783	+	0.835188i
$277$		−	9.49422i		−	0.570452i	−0.958460	−	0.285226i	$-0.907931\pi$
$277$		−	9.49422i		−	0.570452i	0.958460	−	0.285226i	$-0.0920687\pi$
$278$	−7.15006	−	8.29791i	−0.428832	−	0.497676i
$279$	7.59016	−	9.22429i	0.454411	−	0.552244i
$280$	4.87442	+	2.56440i	0.291302	+	0.153252i
$281$	−5.35523	+	9.27554i	−0.319466	+	0.553332i	−0.980377	−	0.197133i	$-0.936837\pi$
$281$	−5.35523	+	9.27554i	−0.319466	+	0.553332i	0.660910	+	0.750465i	$0.270170\pi$
$282$	−0.350316	+	0.0369800i	−0.0208610	+	0.00220213i
$283$			15.0711i			0.895884i	0.894063	+	0.447942i	$0.147843\pi$
$283$			15.0711i			0.895884i	−0.894063	+	0.447942i	$0.852157\pi$
$284$	0.706426	−	4.72734i	0.0419187	−	0.280516i
$285$	−0.950982	+	0.449029i	−0.0563313	+	0.0265982i
$286$	−3.55194	+	0.787776i	−0.210031	+	0.0465822i
$287$	−8.20204			−0.484151
$288$	16.4445	−	4.19266i	0.969001	−	0.247055i
$289$	−1.89057	+	3.27456i	−0.111210	+	0.192621i
$290$	−6.47534	+	5.57960i	−0.380245	+	0.327646i
$291$	19.6509	+	13.6194i	1.15196	+	0.798384i
$292$	−16.3705	−	13.0213i	−0.958012	−	0.762012i
$293$	−8.58488	−	4.95648i	−0.501534	−	0.289561i	0.227813	−	0.973705i	$-0.426843\pi$
$293$	−8.58488	−	4.95648i	−0.501534	−	0.289561i	−0.729347	+	0.684144i	$0.760176\pi$
$294$	−2.07749	−	2.85670i	−0.121162	−	0.166606i
$295$	−12.4279			−0.723580
$296$	0.445148	+	11.3226i	0.0258737	+	0.658113i
$297$	−1.01114	−	3.56701i	−0.0586722	−	0.206979i
$298$	7.53479	+	8.74441i	0.436479	+	0.506550i
$299$	−15.0767	+	0.461847i	−0.871906	+	0.0267093i
$300$	14.5605	+	3.42145i	0.840650	+	0.197538i
$301$			6.08522i			0.350746i
$302$	−16.2883	+	14.0352i	−0.937288	+	0.807633i
$303$	21.0291	+	1.73798i	1.20809	+	0.0998441i
$304$	2.00539	+	2.15037i	0.115017	+	0.123332i
$305$	2.68006	+	4.64200i	0.153460	+	0.265800i
$306$	−16.5255	+	10.0482i	−0.944702	+	0.574420i
$307$		−	11.6413i		−	0.664402i	−0.943209	−	0.332201i	$-0.892209\pi$
$307$		−	11.6413i		−	0.664402i	0.943209	−	0.332201i	$-0.107791\pi$
$308$	−3.32735	−	0.497219i	−0.189593	−	0.0283317i
$309$	−0.900091	+	10.8909i	−0.0512044	+	0.619562i
$310$	3.03625	+	3.52368i	0.172447	+	0.200131i
$311$	−6.37253	−	11.0375i	−0.361353	−	0.625882i	0.626831	−	0.779156i	$-0.284352\pi$
$311$	−6.37253	−	11.0375i	−0.361353	−	0.625882i	−0.988184	+	0.153274i	$0.951018\pi$
$312$	−0.221500	+	17.6621i	−0.0125399	+	0.999921i
$313$	−3.53945	+	6.13051i	−0.200062	+	0.346517i	−0.948548	−	0.316633i	$-0.897448\pi$
$313$	−3.53945	+	6.13051i	−0.200062	+	0.346517i	0.748486	+	0.663150i	$0.230781\pi$
$314$	−30.5870	+	5.80739i	−1.72613	+	0.327730i
$315$	−4.51107	−	3.71191i	−0.254170	−	0.209143i
$316$	−25.7615	+	10.1482i	−1.44920	+	0.570883i
$317$	26.6192	+	15.3686i	1.49508	+	0.863187i	0.999984	−	0.00564972i	$-0.00179837\pi$
$317$	26.6192	+	15.3686i	1.49508	+	0.863187i	0.495099	+	0.868836i	$0.335132\pi$
$318$	9.13071	−	6.64017i	0.512025	−	0.372362i
$319$	2.61054	−	4.52158i	0.146162	−	0.253160i
$320$	0.518781	+	6.58755i	0.0290007	+	0.368255i
$321$	4.44571	+	9.41540i	0.248135	+	0.525517i
$322$	−13.1681	−	4.59840i	−0.733832	−	0.256259i
$323$	−2.90205	−	1.67550i	−0.161474	−	0.0932272i
$324$	−17.9814	+	0.817417i	−0.998968	+	0.0454121i
$325$	−7.36745	+	13.7141i	−0.408673	+	0.760723i
$326$	−3.12976	+	0.594230i	−0.173341	+	0.0329113i
$327$	−5.65800	+	8.16372i	−0.312888	+	0.451455i
$328$	−5.25114	−	8.32210i	−0.289946	−	0.459511i
$329$	0.169519	−	0.293615i	0.00934588	−	0.0161875i
$330$	1.43566	−	0.151551i	0.0790305	−	0.00834262i
$331$		−	27.6723i		−	1.52101i	−0.649332	−	0.760505i	$-0.724952\pi$
$331$		−	27.6723i		−	1.52101i	0.649332	−	0.760505i	$-0.275048\pi$
$332$	−7.37018	−	18.7094i	−0.404491	−	1.02681i
$333$	1.97312	−	11.8556i	0.108126	−	0.649685i
$334$	−15.7937	−	5.51525i	−0.864191	−	0.301781i
$335$	3.31076	+	5.73440i	0.180886	+	0.313304i
$336$	−6.04525	+	15.1736i	−0.329795	+	0.827787i
$337$	−7.69181	−	13.3226i	−0.419000	−	0.725729i	0.576839	−	0.816858i	$-0.304286\pi$
$337$	−7.69181	−	13.3226i	−0.419000	−	0.725729i	−0.995839	+	0.0911288i	$0.970953\pi$
$338$	−17.6954	−	4.98738i	−0.962501	−	0.271278i
$339$	18.3240	−	8.65210i	0.995221	−	0.469918i
$340$	−2.76016	−	7.00674i	−0.149691	−	0.379994i
$341$	−2.46051	−	1.42057i	−0.133244	−	0.0769284i
$342$	−1.62030	−	2.66477i	−0.0876156	−	0.144094i
$343$	19.9024			1.07463
$344$	−6.17429	+	3.89590i	−0.332895	+	0.210053i
$345$	5.96481	+	0.492968i	0.321134	+	0.0265405i
$346$	−4.64340	+	13.2970i	−0.249631	+	0.714852i
$347$	3.94116	+	2.27543i	0.211573	+	0.122151i	0.602042	−	0.798464i	$-0.294354\pi$
$347$	3.94116	+	2.27543i	0.211573	+	0.122151i	−0.390469	+	0.920616i	$0.627687\pi$
$348$	−18.4708	−	17.3595i	−0.990139	−	0.930569i
$349$	−23.6002	+	13.6256i	−1.26329	+	0.729360i	−0.973709	−	0.227794i	$-0.926849\pi$
$349$	−23.6002	+	13.6256i	−1.26329	+	0.729360i	−0.289579	+	0.957154i	$0.593515\pi$
$350$	−10.9055	+	9.39694i	−0.582924	+	0.502288i
$351$	4.02913	−	18.2966i	0.215059	−	0.976601i
$352$	−1.62575	−	3.69438i	−0.0866528	−	0.196911i
$353$	2.24647	+	3.89099i	0.119567	+	0.207097i	0.919596	−	0.392865i	$-0.128516\pi$
$353$	2.24647	+	3.89099i	0.119567	+	0.207097i	−0.800029	+	0.599961i	$0.795183\pi$
$354$	−3.86899	−	36.6514i	−0.205635	−	1.94800i
$355$	−1.70958	−	0.987028i	−0.0907352	−	0.0523860i
$356$	33.3095	−	13.1216i	1.76540	−	0.695444i
$357$	1.53319	−	18.5513i	0.0811453	−	0.981841i
$358$	−2.19614	−	2.54871i	−0.116070	−	0.134703i
$359$	4.92994			0.260192			0.130096	−	0.991501i	$-0.458471\pi$
$359$	4.92994			0.260192			0.130096	+	0.991501i	$0.458471\pi$
$360$	0.878148	−	6.95356i	0.0462825	−	0.366485i
$361$	−9.22982	+	15.9865i	−0.485780	+	0.841396i
$362$	−9.63047	+	27.5782i	−0.506166	+	1.44948i
$363$	16.4312	−	7.75838i	0.862414	−	0.407209i
$364$	−13.6226	−	10.1705i	−0.714020	−	0.533076i
$365$	−7.48152	+	4.31946i	−0.391600	+	0.226091i
$366$	−12.8555	+	9.34895i	−0.671967	+	0.488677i
$367$	9.77045	+	16.9229i	0.510013	+	0.883369i	0.999933	+	0.0116011i	$0.00369284\pi$
$367$	9.77045	+	16.9229i	0.510013	+	0.883369i	−0.489919	+	0.871768i	$0.662974\pi$
$368$	−3.76485	−	16.3049i	−0.196256	−	0.849951i
$369$	3.66388	+	9.77301i	0.190734	+	0.508763i
$370$	4.41817	+	1.54285i	0.229690	+	0.0802091i
$371$			10.8661i			0.564138i
$372$	−9.44652	+	10.0512i	−0.489779	+	0.521132i
$373$	−5.25090	−	3.03161i	−0.271881	−	0.156971i	0.357861	−	0.933775i	$-0.383506\pi$
$373$	−5.25090	−	3.03161i	−0.271881	−	0.156971i	−0.629742	+	0.776804i	$0.716840\pi$
$374$	3.00271	+	3.48476i	0.155266	+	0.180192i
$375$	7.59349	−	10.9564i	0.392126	−	0.565784i
$376$	0.406443	−	0.0159793i	0.0209607	−	0.000824070i
$377$	22.4338	−	13.8850i	1.15540	−	0.715112i
$378$	9.54251	−	14.4593i	0.490814	−	0.743705i
$379$	21.0552	+	12.1562i	1.08153	+	0.624424i	0.931310	−	0.364228i	$-0.118667\pi$
$379$	21.0552	+	12.1562i	1.08153	+	0.624424i	0.150225	+	0.988652i	$0.452000\pi$
$380$	1.12985	−	0.445082i	0.0579601	−	0.0228322i
$381$	−21.8089	+	10.2976i	−1.11730	+	0.527561i
$382$	4.41752	+	1.54263i	0.226020	+	0.0789277i
$383$	−2.29844	+	3.98101i	−0.117445	+	0.203420i	−0.918754	−	0.394830i	$-0.870804\pi$
$383$	−2.29844	+	3.98101i	−0.117445	+	0.203420i	0.801310	+	0.598250i	$0.204137\pi$
$384$	−19.2660	+	3.58075i	−0.983163	+	0.182730i
$385$	−0.694721	+	1.20329i	−0.0354063	+	0.0613255i
$386$	−3.59900	−	1.25679i	−0.183184	−	0.0639691i
$387$	7.25074	−	2.71829i	0.368576	−	0.138179i
$388$	−21.6065	−	17.1860i	−1.09690	−	0.872486i
$389$	−4.31934	−	2.49377i	−0.218999	−	0.126439i	0.386487	−	0.922295i	$-0.373688\pi$
$389$	−4.31934	−	2.49377i	−0.218999	−	0.126439i	−0.605487	+	0.795855i	$0.707022\pi$
$390$	6.75327	+	2.75863i	0.341965	+	0.139689i
$391$	9.53547	+	16.5159i	0.482229	+	0.835246i
$392$	2.17653	+	3.44940i	0.109931	+	0.174221i
$393$	21.5964	+	1.78485i	1.08939	+	0.0900340i
$394$	−11.9619	−	13.8822i	−0.602632	−	0.699377i
$395$			11.4352i			0.575367i
$396$	0.893886	+	4.18676i	0.0449195	+	0.210392i
$397$	13.3910	−	7.73131i	0.672076	−	0.388024i	−0.124786	−	0.992184i	$-0.539825\pi$
$397$	13.3910	−	7.73131i	0.672076	−	0.388024i	0.796863	+	0.604160i	$0.206491\pi$
$398$	−1.55124	−	8.17022i	−0.0777564	−	0.409536i
$399$	2.99144	+	0.247230i	0.149759	+	0.0123770i
$400$	−16.5164	−	5.04899i	−0.825822	−	0.252449i
$401$	−19.1649			−0.957047			−0.478524	−	0.878075i	$-0.658828\pi$
$401$	−19.1649			−0.957047			−0.478524	+	0.878075i	$0.658828\pi$
$402$	−15.8808	+	11.5490i	−0.792060	+	0.576014i
$403$	−7.55576	−	12.2078i	−0.376379	−	0.608113i
$404$	−24.0976	−	3.60100i	−1.19890	−	0.179156i
$405$	−2.40775	+	7.03322i	−0.119642	+	0.349484i
$406$	23.9683	−	4.55073i	1.18953	−	0.225849i
$407$	−2.85853			−0.141692
$408$	19.8045	−	10.3214i	0.980467	−	0.510984i
$409$	6.33449	−	10.9717i	0.313220	−	0.542514i	−0.665837	−	0.746097i	$-0.731925\pi$
$409$	6.33449	−	10.9717i	0.313220	−	0.542514i	0.979058	+	0.203583i	$0.0652588\pi$
$410$	−3.99269	+	0.758070i	−0.197185	+	0.0374384i
$411$	3.97200	+	2.75286i	0.195924	+	0.135789i
$412$	1.86494	−	12.4800i	0.0918791	−	0.614847i
$413$	30.7192	+	17.7357i	1.51159	+	0.872718i
$414$	0.403113	+	17.7444i	0.0198119	+	0.872090i
$415$	−8.30483			−0.407668
$416$	1.59778	−	20.3334i	0.0783377	−	0.996927i
$417$	−5.72790	−	12.1309i	−0.280497	−	0.594053i
$418$	−0.561923	+	0.484192i	−0.0274846	+	0.0236826i
$419$		−	15.8826i		−	0.775914i	−0.921677	−	0.387957i	$-0.873181\pi$
$419$		−	15.8826i		−	0.775914i	0.921677	−	0.387957i	$-0.126819\pi$
$420$	4.91548	+	4.61975i	0.239851	+	0.225421i
$421$	1.19901	+	0.692247i	0.0584361	+	0.0337381i	0.528933	−	0.848663i	$-0.322592\pi$
$421$	1.19901	+	0.692247i	0.0584361	+	0.0337381i	−0.470497	+	0.882401i	$0.655925\pi$
$422$	2.38535	−	6.83078i	0.116117	−	0.332517i
$423$	−0.425577	−	0.0708284i	−0.0206923	−	0.00344379i
$424$	−11.0251	+	6.95671i	−0.535427	+	0.337848i
$425$	19.6830			0.954764
$426$	2.37865	−	5.34904i	0.115246	−	0.259162i
$427$		−	15.2988i		−	0.740359i
$428$	−4.40663	−	11.1863i	−0.213002	−	0.540711i
$429$	−4.44994	−	0.230870i	−0.214845	−	0.0111465i
$430$	0.562424	+	2.96224i	0.0271225	+	0.142852i
$431$	−14.6056	+	25.2976i	−0.703526	+	1.21854i	0.263695	+	0.964606i	$0.415059\pi$
$431$	−14.6056	+	25.2976i	−0.703526	+	1.21854i	−0.967221	+	0.253937i	$0.918274\pi$
$432$	20.7803	+	0.425017i	0.999791	+	0.0204486i
$433$	19.6108	+	33.9669i	0.942435	+	1.63235i	0.760807	+	0.648978i	$0.224803\pi$
$433$	19.6108	+	33.9669i	0.942435	+	1.63235i	0.181628	+	0.983367i	$0.441863\pi$
$434$	−2.47636	−	13.0428i	−0.118869	−	0.626074i
$435$	−9.46645	+	4.46981i	−0.453882	+	0.214311i
$436$	7.13968	−	8.97612i	0.341929	−	0.429878i
$437$	−2.66322	+	1.53761i	−0.127399	+	0.0735539i
$438$	−15.0677	−	20.7192i	−0.719963	−	0.990001i
$439$	11.9773	+	20.7454i	0.571647	+	0.990122i	0.996397	+	0.0848111i	$0.0270287\pi$
$439$	11.9773	+	20.7454i	0.571647	+	0.990122i	−0.424750	+	0.905311i	$0.639638\pi$
$440$	−1.66568	+	0.0654863i	−0.0794083	+	0.00312194i
$441$	−1.51863	−	4.05078i	−0.0723158	−	0.192894i
$442$	5.03306	+	22.6931i	0.239398	+	1.07940i
$443$	−30.7012	−	17.7254i	−1.45866	−	0.842157i	−0.459713	−	0.888067i	$-0.652048\pi$
$443$	−30.7012	−	17.7254i	−1.45866	−	0.842157i	−0.998946	+	0.0459103i	$0.985381\pi$
$444$	−3.17462	+	13.5100i	−0.150661	+	0.641158i
$445$		−	14.7856i		−	0.700906i
$446$	4.25679	+	22.4202i	0.201565	+	1.06163i
$447$	6.03611	+	12.7837i	0.285498	+	0.604647i
$448$	8.11871	−	17.0234i	0.383573	−	0.804281i
$449$	6.02963	+	10.4436i	0.284556	+	0.492865i	0.972501	−	0.232897i	$-0.0748206\pi$
$449$	6.02963	+	10.4436i	0.284556	+	0.492865i	−0.687946	+	0.725762i	$0.741487\pi$
$450$	16.0683	+	8.79663i	0.757467	+	0.414677i
$451$	2.14981	−	1.24119i	0.101231	−	0.0584456i
$452$	−21.7705	+	8.57603i	−1.02400	+	0.403383i
$453$	−23.8123	+	11.2436i	−1.11880	+	0.528268i
$454$	−2.20547	+	6.31567i	−0.103508	+	0.296409i
$455$	−5.97013	+	3.69509i	−0.279884	+	0.173229i
$456$	1.66434	+	3.19351i	0.0779398	+	0.149550i
$457$	−2.06138	−	3.57042i	−0.0964275	−	0.167017i	0.813776	−	0.581179i	$-0.197408\pi$
$457$	−2.06138	−	3.57042i	−0.0964275	−	0.167017i	−0.910203	+	0.414161i	$0.864075\pi$
$458$	−32.6592	+	6.20083i	−1.52607	+	0.289746i
$459$	−22.7894	+	6.46010i	−1.06372	+	0.301532i
$460$	−6.83515	−	1.02140i	−0.318691	−	0.0476232i
$461$		−	22.6963i		−	1.05707i	−0.848912	−	0.528535i	$-0.822742\pi$
$461$		−	22.6963i		−	1.05707i	0.848912	−	0.528535i	$-0.177258\pi$
$462$	−3.76493	−	1.67421i	−0.175161	−	0.0778915i
$463$	−5.25021	−	9.09363i	−0.243998	−	0.422617i	0.717852	−	0.696196i	$-0.245126\pi$
$463$	−5.25021	−	9.09363i	−0.243998	−	0.422617i	−0.961849	+	0.273580i	$0.911792\pi$
$464$	19.9624	+	21.4056i	0.926731	+	0.993732i
$465$	2.43233	+	5.15135i	0.112797	+	0.238888i
$466$	12.8687	+	4.49385i	0.596133	+	0.208173i
$467$		−	28.5529i		−	1.32127i	−0.750706	−	0.660636i	$-0.770287\pi$
$467$		−	28.5529i		−	1.32127i	0.750706	−	0.660636i	$-0.229713\pi$
$468$	−6.03315	+	20.7750i	−0.278882	+	0.960325i
$469$		−	18.8990i		−	0.872675i
$470$	0.0553832	−	0.158597i	0.00255464	−	0.00731555i
$471$	−38.0010	−	3.14063i	−1.75099	−	0.144713i
$472$	1.67182	+	42.5237i	0.0769516	+	1.95731i
$473$	−0.920861	−	1.59498i	−0.0423412	−	0.0733372i
$474$	−33.7238	+	3.55995i	−1.54898	+	0.163514i
$475$			3.17392i			0.145629i
$476$	−3.17670	+	21.2582i	−0.145604	+	0.974369i
$477$	12.9473	−	4.85391i	0.592815	−	0.222245i
$478$	4.14490	+	21.8308i	0.189583	+	0.998519i
$479$	9.33932	+	16.1762i	0.426724	+	0.739108i	0.996580	−	0.0826368i	$-0.0263341\pi$
$479$	9.33932	+	16.1762i	0.426724	+	0.739108i	−0.569855	+	0.821745i	$0.693001\pi$
$480$	−1.54037	+	7.94511i	−0.0703078	+	0.362643i
$481$	−12.7247	−	6.83593i	−0.580198	−	0.311692i
$482$	11.1549	+	3.89535i	0.508090	+	0.177428i
$483$	−14.0403	−	9.73083i	−0.638854	−	0.442768i
$484$	−19.5217	+	7.69017i	−0.887349	+	0.349553i
$485$	−9.87440	+	5.70099i	−0.448374	+	0.258869i
$486$	−21.4914	−	4.91121i	−0.974869	−	0.222777i
$487$	7.38624	+	12.7933i	0.334702	+	0.579722i	0.983428	−	0.181301i	$-0.0580309\pi$
$487$	7.38624	+	12.7933i	0.334702	+	0.579722i	−0.648725	+	0.761023i	$0.724698\pi$
$488$	15.5227	−	9.79462i	0.702679	−	0.443382i
$489$	−3.88837	−	0.321359i	−0.175838	−	0.0145323i
$490$	1.65492	−	0.314210i	0.0747615	−	0.0141946i
$491$			34.7450i			1.56802i	0.620749	+	0.784009i	$0.286829\pi$
$491$			34.7450i			1.56802i	−0.620749	+	0.784009i	$0.713171\pi$
$492$	−3.47863	−	11.5389i	−0.156829	−	0.520215i
$493$	−28.8881	−	16.6786i	−1.30106	−	0.751165i
$494$	−3.65931	+	0.811589i	−0.164640	+	0.0365151i
$495$	1.74410	+	0.290268i	0.0783914	+	0.0130466i
$496$	11.6483	−	10.8629i	0.523023	−	0.487759i
$497$	2.81716	+	4.87946i	0.126367	+	0.218874i
$498$	−2.58542	−	24.4920i	−0.115855	−	1.09751i
$499$	17.6854	−	10.2107i	0.791707	−	0.457093i	−0.0488559	−	0.998806i	$-0.515557\pi$
$499$	17.6854	−	10.2107i	0.791707	−	0.457093i	0.840563	+	0.541713i	$0.182224\pi$
$500$	−9.58203	+	12.0467i	−0.428521	+	0.538743i
$501$	−16.8397	−	11.6710i	−0.752341	−	0.521422i
$502$	−2.34016	+	0.444314i	−0.104447	+	0.0198307i
$503$	0.00569642	+	0.00986649i	0.000253991	+	0.000439925i	0.866152	−	0.499780i	$-0.166586\pi$
$503$	0.00569642	+	0.00986649i	0.000253991	+	0.000439925i	−0.865898	+	0.500220i	$0.833252\pi$
$504$	−12.0940	+	15.9346i	−0.538707	+	0.709782i
$505$	−5.03136	+	8.71458i	−0.223893	+	0.387794i
$506$	4.14733	−	0.787430i	0.184371	−	0.0350055i
$507$	−19.2568	−	11.6694i	−0.855226	−	0.518256i
$508$	25.9109	−	10.2071i	1.14961	−	0.452865i
$509$		−	3.93790i		−	0.174544i	−0.996185	−	0.0872721i	$-0.972185\pi$
$509$		−	3.93790i		−	0.174544i	0.996185	−	0.0872721i	$-0.0278150\pi$
$510$	−0.968252	−	9.17235i	−0.0428749	−	0.406158i
$511$	24.6570			1.09076
$512$	22.4704	−	2.66124i	0.993060	−	0.117611i
$513$	−1.04170	−	3.67484i	−0.0459923	−	0.162248i
$514$	23.4481	+	8.18821i	1.03425	+	0.361166i
$515$	−4.51324	−	2.60572i	−0.198877	−	0.114822i
$516$	−8.56091	+	2.58085i	−0.376873	+	0.113615i
$517$			0.102612i			0.00451285i
$518$	−8.71901	−	10.1187i	−0.383091	−	0.444592i
$519$	−9.82606	+	14.1777i	−0.431316	+	0.622330i
$520$	−7.57139	−	3.69183i	−0.332027	−	0.161897i
$521$	19.6482			0.860804			0.430402	−	0.902637i	$-0.358372\pi$
$521$	19.6482			0.860804			0.430402	+	0.902637i	$0.358372\pi$
$522$	−16.1291	−	26.5262i	−0.705950	−	1.16102i
$523$	15.8740	+	9.16486i	0.694122	+	0.400751i	0.805154	−	0.593065i	$-0.202082\pi$
$523$	15.8740	+	9.16486i	0.694122	+	0.400751i	−0.111033	+	0.993817i	$0.535416\pi$
$524$	−24.7476	−	3.69813i	−1.08110	−	0.161554i
$525$	−15.9430	+	7.52788i	−0.695810	+	0.328544i
$526$	−7.25802	−	38.2274i	−0.316465	−	1.66679i
$527$	−9.07596	+	15.7200i	−0.395355	+	0.684775i
$528$	−0.711679	−	4.89191i	−0.0309719	−	0.212893i
$529$	−5.49853			−0.239067
$530$	1.00429	+	5.28951i	0.0436236	+	0.229762i
$531$	7.41034	−	44.5256i	0.321581	−	1.93225i
$532$	−3.42793	−	0.512249i	−0.148620	−	0.0222088i
$533$	12.5381	−	0.384083i	0.543086	−	0.0166365i
$534$	43.6046	−	4.60299i	1.88696	−	0.199191i
$535$	−4.96545			−0.214675
$536$	19.1756	−	12.0996i	0.828261	−	0.522623i
$537$	−1.75933	−	3.72602i	−0.0759207	−	0.160790i
$538$	−9.49605	+	1.80296i	−0.409404	+	0.0777313i
$539$	−0.891069	+	0.514459i	−0.0383810	+	0.0221593i
$540$	3.30883	−	7.92062i	0.142389	−	0.340849i
$541$		−	3.83563i		−	0.164907i	−0.996595	−	0.0824534i	$-0.973724\pi$
$541$		−	3.83563i		−	0.164907i	0.996595	−	0.0824534i	$-0.0262756\pi$
$542$	−23.0860	+	19.8925i	−0.991630	+	0.854457i
$543$	−20.3794	+	29.4046i	−0.874563	+	1.26187i
$544$	−23.6032	+	10.3868i	−1.01198	+	0.445331i
$545$	−2.36840	−	4.10219i	−0.101451	−	0.175718i
$546$	−12.7559	−	16.4563i	−0.545901	−	0.704264i
$547$	27.6062	+	15.9385i	1.18036	+	0.681479i	0.956097	−	0.293050i	$-0.0946702\pi$
$547$	27.6062	+	15.9385i	1.18036	+	0.681479i	0.224260	+	0.974529i	$0.428004\pi$
$548$	−4.36727	−	3.47376i	−0.186561	−	0.148392i
$549$	−18.2290	+	6.83401i	−0.777994	+	0.291669i
$550$	1.43639	−	4.11331i	0.0612480	−	0.175392i
$551$	2.68945	−	4.65826i	0.114574	−	0.198449i
$552$	0.884359	−	20.4757i	0.0376408	−	0.871502i
$553$	16.3190	−	28.2654i	0.693957	−	1.20197i
$554$	−4.42660	+	12.6762i	−0.188068	+	0.538559i
$555$	4.71078	+	3.26488i	0.199961	+	0.138587i
$556$	5.67754	+	14.4126i	0.240782	+	0.611230i
$557$	−25.3885	−	14.6580i	−1.07574	−	0.621081i	−0.145999	−	0.989285i	$-0.546640\pi$
$557$	−25.3885	−	14.6580i	−1.07574	−	0.621081i	−0.929745	+	0.368203i	$0.879973\pi$
$558$	−14.4347	+	8.77694i	−0.611071	+	0.371557i
$559$	−0.284957	−	9.30221i	−0.0120524	−	0.393442i
$560$	−5.31243	−	5.69651i	−0.224491	−	0.240721i
$561$	2.40547	+	5.09445i	0.101559	+	0.215088i
$562$	11.4747	−	9.88737i	0.484030	−	0.417074i
$563$	24.6049	+	14.2056i	1.03697	+	0.598697i	0.918974	−	0.394317i	$-0.129019\pi$
$563$	24.6049	+	14.2056i	1.03697	+	0.598697i	0.117999	+	0.993014i	$0.462352\pi$
$564$	0.484965	+	0.113958i	0.0204207	+	0.00479850i
$565$			9.66361i			0.406551i
$566$	7.02678	−	20.1221i	0.295358	−	0.845797i
$567$	15.9885	−	13.9486i	0.671454	−	0.585785i
$568$	−3.14727	+	5.98233i	−0.132056	+	0.251013i
$569$	−20.1661	−	34.9288i	−0.845408	−	1.46429i	−0.885266	−	0.465084i	$-0.846024\pi$
$569$	−20.1661	−	34.9288i	−0.845408	−	1.46429i	0.0398584	−	0.999205i	$-0.487309\pi$
$570$	1.47906	−	0.156132i	0.0619509	−	0.00653966i
$571$	−6.34043	+	3.66065i	−0.265339	+	0.153193i	−0.626767	−	0.779206i	$-0.715622\pi$
$571$	−6.34043	+	3.66065i	−0.265339	+	0.153193i	0.361429	+	0.932400i	$0.382289\pi$
$572$	5.10966	+	0.604265i	0.213645	+	0.0252656i
$573$	4.71009	+	3.26441i	0.196767	+	0.136373i
$574$	10.9509	+	3.82414i	0.457083	+	0.159616i
$575$	9.03157	−	15.6431i	0.376642	−	0.652364i
$576$	−23.9106	−	2.06930i	−0.996276	−	0.0862206i
$577$	−23.2087			−0.966193			−0.483096	−	0.875567i	$-0.660488\pi$
$577$	−23.2087			−0.966193			−0.483096	+	0.875567i	$0.660488\pi$
$578$	4.05093	−	3.49056i	0.168496	−	0.145188i
$579$	−3.83736	−	2.65955i	−0.159475	−	0.110527i
$580$	11.2470	−	4.43052i	0.467005	−	0.183967i
$581$	20.5278	+	11.8517i	0.851638	+	0.491693i
$582$	−19.8870	−	27.3460i	−0.824341	−	1.13353i
$583$	−1.64433	−	2.84807i	−0.0681014	−	0.117955i
$584$	15.7860	+	25.0179i	0.653229	+	1.03525i
$585$	7.06970	+	5.46300i	0.292296	+	0.225867i
$586$	9.15116	+	10.6203i	0.378031	+	0.438719i
$587$	12.4771	−	7.20368i	0.514987	−	0.297328i	−0.219894	−	0.975524i	$-0.570571\pi$
$587$	12.4771	−	7.20368i	0.514987	−	0.297328i	0.734881	+	0.678196i	$0.237238\pi$
$588$	1.44184	+	4.78273i	0.0594606	+	0.197237i
$589$	−2.53488	−	1.46351i	−0.104448	−	0.0603031i
$590$	16.5931	+	5.79441i	0.683126	+	0.238552i
$591$	−9.58267	−	20.2948i	−0.394178	−	0.834816i
$592$	4.68473	−	15.3249i	0.192541	−	0.629849i
$593$	−16.2644			−0.667899			−0.333949	−	0.942591i	$-0.608381\pi$
$593$	−16.2644			−0.667899			−0.333949	+	0.942591i	$0.608381\pi$
$594$	−0.313072	+	5.23392i	−0.0128455	+	0.214750i
$595$	7.68776	+	4.43853i	0.315168	+	0.181962i
$596$	−5.98305	−	15.1881i	−0.245075	−	0.622129i
$597$	0.838906	−	10.1506i	0.0343342	−	0.415436i
$598$	20.3449	+	6.41274i	0.831965	+	0.262236i
$599$	5.90076	+	10.2204i	0.241098	+	0.417595i	0.961027	−	0.276453i	$-0.0891590\pi$
$599$	5.90076	+	10.2204i	0.241098	+	0.417595i	−0.719929	+	0.694048i	$0.755826\pi$
$600$	−17.8452	−	11.3569i	−0.728526	−	0.463642i
$601$	17.8798	+	30.9688i	0.729333	+	1.26324i	0.957165	+	0.289542i	$0.0935030\pi$
$601$	17.8798	+	30.9688i	0.729333	+	1.26324i	−0.227832	+	0.973700i	$0.573164\pi$
$602$	2.83719	−	8.12467i	0.115635	−	0.331137i
$603$	−22.5188	+	8.44226i	−0.917036	+	0.343795i
$604$	28.2911	−	11.1447i	1.15115	−	0.453471i
$605$			8.66541i			0.352299i
$606$	−27.2667	−	12.1251i	−1.10763	−	0.492550i
$607$	−13.3707	+	23.1587i	−0.542699	+	0.939982i	0.456049	+	0.889955i	$0.349264\pi$
$607$	−13.3707	+	23.1587i	−0.542699	+	0.939982i	−0.998748	+	0.0500271i	$0.984069\pi$
$608$	−1.67489	−	3.80606i	−0.0679259	−	0.154356i
$609$	29.7779	+	2.46103i	1.20666	+	0.0997259i
$610$	−1.41398	−	7.44731i	−0.0572504	−	0.301533i
$611$	−0.245387	+	0.456775i	−0.00992729	+	0.0184792i
$612$	26.7489	−	5.71098i	1.08126	−	0.230853i
$613$	−0.499668	−	0.288483i	−0.0201814	−	0.0116517i	0.489875	−	0.871792i	$-0.337042\pi$
$613$	−0.499668	−	0.288483i	−0.0201814	−	0.0116517i	−0.510057	+	0.860141i	$0.670376\pi$
$614$	−5.42764	+	15.5428i	−0.219042	+	0.627256i
$615$	−4.96047	−	0.409964i	−0.200026	−	0.0165313i
$616$	4.21068	+	2.21521i	0.169653	+	0.0892534i
$617$	20.9288	−	36.2498i	0.842562	−	1.45936i	−0.0451591	−	0.998980i	$-0.514379\pi$
$617$	20.9288	−	36.2498i	0.842562	−	1.45936i	0.887721	−	0.460381i	$-0.152287\pi$
$618$	6.27955	−	14.1213i	0.252601	−	0.568042i
$619$	−40.0034	−	23.0960i	−1.60787	−	0.928305i	−0.989846	−	0.142147i	$-0.954600\pi$
$619$	−40.0034	−	23.0960i	−1.60787	−	0.928305i	−0.618025	−	0.786158i	$-0.712067\pi$
$620$	−2.41095	−	6.12025i	−0.0968260	−	0.245795i
$621$	−5.32278	+	21.0762i	−0.213596	+	0.845760i
$622$	3.36210	+	17.7079i	0.134808	+	0.710022i
$623$	−21.1004	+	36.5470i	−0.845371	+	1.46423i
$624$	8.53056	−	23.4783i	0.341496	−	0.939883i
$625$	−7.61575	−	13.1909i	−0.304630	−	0.527635i
$626$	7.58399	−	6.53489i	0.303117	−	0.261187i
$627$	−0.821489	+	0.387886i	−0.0328071	+	0.0154907i
$628$	43.5458	+	6.50723i	1.73767	+	0.259667i
$629$			18.2630i			0.728192i
$630$	4.29230	+	7.05920i	0.171009	+	0.281245i
$631$	−2.47356	−	4.28432i	−0.0984707	−	0.170556i	0.812581	−	0.582848i	$-0.198062\pi$
$631$	−2.47356	−	4.28432i	−0.0984707	−	0.170556i	−0.911052	+	0.412292i	$0.864728\pi$
$632$	39.1270	−	1.53828i	1.55639	−	0.0611894i
$633$	5.04773	−	7.28318i	0.200629	−	0.289480i
$634$	−28.3751	−	32.9303i	−1.12692	−	1.30783i
$635$		−	11.5015i		−	0.456422i
$636$	−15.2868	+	4.60848i	−0.606160	+	0.182738i
$637$	−5.19688	+	0.159197i	−0.205908	+	0.00630762i
$638$	−5.59361	+	4.81984i	−0.221453	+	0.190819i
$639$	4.55560	−	5.53641i	0.180217	−	0.219017i
$640$	2.37874	−	9.03723i	0.0940281	−	0.357228i
$641$	−14.1088			−0.557263			−0.278631	−	0.960398i	$-0.589881\pi$
$641$	−14.1088			−0.557263			−0.278631	+	0.960398i	$0.589881\pi$
$642$	−1.54582	−	14.6437i	−0.0610087	−	0.577942i
$643$	15.1607	+	8.75304i	0.597880	+	0.345186i	0.768207	−	0.640201i	$-0.221149\pi$
$643$	15.1607	+	8.75304i	0.597880	+	0.345186i	−0.170327	+	0.985388i	$0.554482\pi$
$644$	15.4374	+	12.2791i	0.608320	+	0.483864i
$645$	−0.304158	+	3.68025i	−0.0119762	+	0.144910i
$646$	3.09347	+	3.59009i	0.121711	+	0.141250i
$647$	3.13270	−	5.42600i	0.123159	−	0.213318i	−0.797853	−	0.602852i	$-0.794031\pi$
$647$	3.13270	−	5.42600i	0.123159	−	0.213318i	0.921012	+	0.389534i	$0.127364\pi$
$648$	24.3890	+	7.29232i	0.958089	+	0.286470i
$649$	−10.7356			−0.421410
$650$	16.2307	−	14.8754i	0.636622	−	0.583460i
$651$	1.33922	−	16.2042i	0.0524880	−	0.635094i
$652$	4.45574	+	0.665839i	0.174500	+	0.0260763i
$653$			11.3507i			0.444187i	0.975025	+	0.222093i	$0.0712890\pi$
$653$			11.3507i			0.444187i	−0.975025	+	0.222093i	$0.928711\pi$
$654$	11.3605	−	8.26177i	0.444232	−	0.323061i
$655$	−5.16708	+	8.94964i	−0.201894	+	0.349691i
$656$	3.13094	+	13.5595i	0.122243	+	0.529411i
$657$	−11.0144	−	29.3797i	−0.429712	−	1.14621i
$658$	−0.363229	+	0.312983i	−0.0141601	+	0.0122013i
$659$			46.9752i			1.82990i	0.403572	+	0.914948i	$0.367768\pi$
$659$			46.9752i			1.82990i	−0.403572	+	0.914948i	$0.632232\pi$
$660$	−1.98748	−	0.467022i	−0.0773625	−	0.0181788i
$661$		−	39.1430i		−	1.52248i	−0.648468	−	0.761242i	$-0.724590\pi$
$661$		−	39.1430i		−	1.52248i	0.648468	−	0.761242i	$-0.275410\pi$
$662$	−12.9020	+	36.9466i	−0.501451	+	1.43597i
$663$	−1.47501	+	28.4304i	−0.0572847	+	1.10415i
$664$	1.11718	+	28.4161i	0.0433549	+	1.10276i
$665$	−0.715721	+	1.23967i	−0.0277545	+	0.0480722i
$666$	−8.16200	+	14.9091i	−0.316271	+	0.577715i
$667$	−26.5107	+	15.3060i	−1.02650	+	0.592650i
$668$	18.5154	+	14.7273i	0.716384	+	0.569818i
$669$	−2.30207	+	27.8546i	−0.0890032	+	1.07692i
$670$	−1.74673	−	9.19989i	−0.0674821	−	0.355423i
$671$	2.31512	+	4.00991i	0.0893743	+	0.154801i
$672$	15.1459	−	17.4404i	0.584264	−	0.672779i
$673$	−11.4793	−	19.8828i	−0.442495	−	0.766424i	0.555379	−	0.831597i	$-0.312573\pi$
$673$	−11.4793	−	19.8828i	−0.442495	−	0.766424i	−0.997874	+	0.0651734i	$0.979240\pi$
$674$	4.05814	+	21.3739i	0.156314	+	0.823292i
$675$	16.0915	+	15.6339i	0.619363	+	0.601750i
$676$	21.3006	+	14.9092i	0.819254	+	0.573431i
$677$	−1.97526	−	1.14042i	−0.0759155	−	0.0438298i	0.461562	−	0.887108i	$-0.347289\pi$
$677$	−1.97526	−	1.14042i	−0.0759155	−	0.0438298i	−0.537477	+	0.843278i	$0.680623\pi$
$678$	−28.4992	+	3.00843i	−1.09450	+	0.115538i
$679$	32.5433			1.24890
$680$	0.418388	+	10.6419i	0.0160444	+	0.408100i
$681$	−4.66708	+	6.73395i	−0.178843	+	0.258046i
$682$	2.62281	+	3.04387i	0.100432	+	0.116556i
$683$	−42.3096	+	24.4275i	−1.61893	+	0.934691i	−0.631737	+	0.775183i	$0.717658\pi$
$683$	−42.3096	+	24.4275i	−1.61893	+	0.934691i	−0.987197	+	0.159508i	$0.949009\pi$
$684$	0.920906	+	4.31332i	0.0352117	+	0.164924i
$685$	−1.99589	+	1.15233i	−0.0762591	+	0.0440282i
$686$	−26.5726	−	9.27932i	−1.01455	−	0.354286i
$687$	−40.5755	−	3.35340i	−1.54805	−	0.127940i
$688$	10.0600	−	2.32289i	0.383535	−	0.0885593i
$689$	−0.508832	−	16.6105i	−0.0193850	−	0.632809i
$690$	−7.73405	−	3.43923i	−0.294430	−	0.130929i
$691$	30.1544	−	17.4097i	1.14713	−	0.662295i	0.198943	−	0.980011i	$-0.436249\pi$
$691$	30.1544	−	17.4097i	1.14713	−	0.662295i	0.948186	+	0.317716i	$0.102916\pi$
$692$	12.3993	−	15.5885i	0.471349	−	0.592587i
$693$	−3.89681	−	3.20647i	−0.148028	−	0.121804i
$694$	−4.20113	−	4.87557i	−0.159473	−	0.185074i
$695$	6.39755			0.242673
$696$	16.5675	+	31.7894i	0.627989	+	1.20497i
$697$	−7.92992	−	13.7350i	−0.300367	−	0.520251i
$698$	37.8625	−	7.18875i	1.43312	−	0.272098i
$699$	13.7210	+	9.50959i	0.518977	+	0.359686i
$700$	18.9417	−	7.46170i	0.715929	−	0.282026i
$701$		−	28.3660i		−	1.07137i	−0.844418	−	0.535685i	$-0.820053\pi$
$701$		−	28.3660i		−	1.07137i	0.844418	−	0.535685i	$-0.179947\pi$
$702$	−13.9101	+	22.5501i	−0.525004	+	0.851100i
$703$	−2.94494			−0.111070
$704$	0.448140	+	5.69054i	0.0168899	+	0.214470i
$705$	0.117198	−	0.169101i	0.00441394	−	0.00636872i
$706$	−1.18522	−	6.24245i	−0.0446063	−	0.234938i
$707$	24.8730	−	14.3604i	0.935445	−	0.540079i
$708$	−11.9227	+	50.7389i	−0.448084	+	1.90688i
$709$		−	19.7528i		−	0.741834i	−0.928666	−	0.370917i	$-0.879043\pi$
$709$		−	19.7528i		−	0.741834i	0.928666	−	0.370917i	$-0.120957\pi$
$710$	1.82235	+	2.11491i	0.0683916	+	0.0793710i
$711$	−40.9690	−	6.81842i	−1.53646	−	0.255711i
$712$	−50.5909	+	1.98898i	−1.89598	+	0.0745403i
$713$	8.32904	+	14.4263i	0.311925	+	0.540270i
$714$	−10.6965	+	24.0539i	−0.400305	+	0.900196i
$715$	1.00564	−	1.87195i	0.0376089	−	0.0700071i
$716$	1.74386	+	4.42684i	0.0651712	+	0.165439i
$717$	−2.24156	+	27.1224i	−0.0837125	+	1.01290i
$718$	−6.58220	−	2.29855i	−0.245646	−	0.0857810i
$719$	19.0440	+	32.9853i	0.710223	+	1.23014i	0.964773	+	0.263083i	$0.0847393\pi$
$719$	19.0440	+	32.9853i	0.710223	+	1.23014i	−0.254550	+	0.967060i	$0.581927\pi$
$720$	−4.41450	+	8.87459i	−0.164519	+	0.330737i
$721$	7.43720	+	12.8816i	0.276976	+	0.479736i
$722$	19.7768	−	17.0410i	0.736015	−	0.634202i
$723$	11.8936	+	8.24309i	0.442329	+	0.306564i
$724$	25.7162	−	32.3308i	0.955735	−	1.20156i
$725$			31.5944i			1.17339i
$726$	−25.5553	+	2.69767i	−0.948447	+	0.100120i
$727$	14.0533	−	24.3411i	0.521209	−	0.902760i	−0.478487	−	0.878094i	$-0.658815\pi$
$727$	14.0533	−	24.3411i	0.521209	−	0.902760i	0.999696	−	0.0246651i	$-0.00785195\pi$
$728$	13.4463	+	19.9305i	0.498355	+	0.738673i
$729$	−23.7623	−	12.8200i	−0.880087	−	0.474813i
$730$	12.0028	−	2.27891i	0.444245	−	0.0843464i
$731$	−10.1902	+	5.88333i	−0.376899	+	0.217603i
$732$	21.5228	−	6.48846i	0.795507	−	0.239820i
$733$	−18.0106	+	10.3984i	−0.665236	+	0.384074i	−0.794269	−	0.607566i	$-0.792146\pi$
$733$	−18.0106	+	10.3984i	−0.665236	+	0.384074i	0.129033	+	0.991640i	$0.458813\pi$
$734$	−5.15482	−	27.1500i	−0.190268	−	1.00212i
$735$	2.05605	+	0.169924i	0.0758385	+	0.00626776i
$736$	−2.57539	+	23.5248i	−0.0949303	+	0.867134i
$737$	2.85994	+	4.95356i	0.105347	+	0.182467i
$738$	−0.335238	−	14.7567i	−0.0123403	−	0.543200i
$739$	−1.23322	−	0.711998i	−0.0453646	−	0.0261913i	0.477146	−	0.878824i	$-0.341671\pi$
$739$	−1.23322	−	0.711998i	−0.0453646	−	0.0261913i	−0.522511	+	0.852633i	$0.675005\pi$
$740$	−5.17956	−	4.11987i	−0.190405	−	0.151449i
$741$	−4.58446	−	0.237848i	−0.168414	−	0.00873758i
$742$	5.06621	−	14.5078i	0.185987	−	0.532598i
$743$	−3.48296			−0.127777			−0.0638886	−	0.997957i	$-0.520350\pi$
$743$	−3.48296			−0.127777			−0.0638886	+	0.997957i	$0.520350\pi$
$744$	17.2988	−	9.01551i	0.634205	−	0.330525i
$745$	−6.74179			−0.247000
$746$	5.59727	+	6.49584i	0.204930	+	0.237830i
$747$	4.95189	−	29.7538i	0.181180	−	1.08864i
$748$	−2.38432	−	6.05265i	−0.0871793	−	0.221307i
$749$	12.2736	+	7.08615i	0.448467	+	0.258922i
$750$	−15.2467	+	11.0880i	−0.556733	+	0.404875i
$751$	11.0247			0.402298			0.201149	−	0.979561i	$-0.435533\pi$
$751$	11.0247			0.402298			0.201149	+	0.979561i	$0.435533\pi$
$752$	−0.550112	−	0.168166i	−0.0200605	−	0.00613239i
$753$	−2.90739	−	0.240284i	−0.105951	−	0.00875645i
$754$	−36.4262	+	8.07888i	−1.32656	+	0.294215i
$755$		−	12.5580i		−	0.457033i
$756$	−19.4822	+	14.8561i	−0.708560	+	0.540313i
$757$	38.9868	+	22.5090i	1.41700	+	0.818104i	0.996034	−	0.0889732i	$-0.0283585\pi$
$757$	38.9868	+	22.5090i	1.41700	+	0.818104i	0.420964	+	0.907077i	$0.361692\pi$
$758$	−22.4441	−	26.0472i	−0.815206	−	0.946077i
$759$	5.15259	+	0.425841i	0.187027	+	0.0154571i
$760$	−1.71603	+	0.0674658i	−0.0622470	+	0.00244724i
$761$	−22.7217	+	39.3551i	−0.823659	+	1.42662i	0.0792804	+	0.996852i	$0.474738\pi$
$761$	−22.7217	+	39.3551i	−0.823659	+	1.42662i	−0.902940	+	0.429767i	$0.858596\pi$
$762$	33.9192	−	3.58058i	1.22876	−	0.129711i
$763$			13.5197i			0.489445i
$764$	−5.17881	−	4.11927i	−0.187363	−	0.149030i
$765$	1.85451	−	11.1429i	0.0670498	−	0.402874i
$766$	4.92487	−	4.24361i	0.177943	−	0.153328i
$767$	−47.7896	−	25.6733i	−1.72558	−	0.927011i
$768$	27.3924	+	4.20178i	0.988439	+	0.151619i
$769$	−7.10764			−0.256308			−0.128154	−	0.991754i	$-0.540905\pi$
$769$	−7.10764			−0.256308			−0.128154	+	0.991754i	$0.540905\pi$
$770$	1.48858	−	1.28266i	0.0536447	−	0.0462240i
$771$	25.0010	+	17.3274i	0.900389	+	0.624029i
$772$	4.21923	+	3.35601i	0.151853	+	0.120785i
$773$	−13.4159	+	7.74567i	−0.482536	+	0.278592i	−0.721473	−	0.692443i	$-0.756535\pi$
$773$	−13.4159	+	7.74567i	−0.482536	+	0.278592i	0.238937	+	0.971035i	$0.423201\pi$
$774$	−10.9482	+	0.248718i	−0.393525	+	0.00894000i
$775$	17.1927			0.617579
$776$	20.8350	+	33.0196i	0.747933	+	1.18534i
$777$	−6.98479	−	14.7928i	−0.250578	−	0.530690i
$778$	4.60426	+	5.34341i	0.165071	+	0.191571i
$779$	2.21480	−	1.27871i	0.0793533	−	0.0458147i
$780$	−7.73042	−	6.83184i	−0.276793	−	0.244619i
$781$	−1.47679	−	0.852626i	−0.0528438	−	0.0305094i
$782$	−5.03084	−	26.4970i	−0.179903	−	0.947531i
$783$	−10.3695	−	36.5808i	−0.370576	−	1.30729i
$784$	−1.29773	−	5.62024i	−0.0463476	−	0.200723i
$785$	9.09198	−	15.7478i	0.324507	−	0.562062i
$786$	−28.0022	−	12.4522i	−0.998804	−	0.444154i
$787$	23.5205	+	13.5796i	0.838415	+	0.484059i	0.856725	−	0.515773i	$-0.172495\pi$
$787$	23.5205	+	13.5796i	0.838415	+	0.484059i	−0.0183104	+	0.999832i	$0.505829\pi$
$788$	9.49842	+	24.1120i	0.338367	+	0.858954i
$789$	3.92513	−	47.4932i	0.139738	−	1.69080i
$790$	5.33156	−	15.2677i	0.189689	−	0.543199i
$791$	13.7908	−	23.8864i	0.490346	−	0.849304i
$792$	0.758572	−	6.00670i	0.0269547	−	0.213439i
$793$	0.716405	+	23.3865i	0.0254403	+	0.830480i
$794$	−21.4837	+	4.07898i	−0.762427	+	0.144758i
$795$	−0.543119	+	6.57163i	−0.0192625	+	0.233072i
$796$	−1.73817	+	11.6317i	−0.0616079	+	0.412275i
$797$	17.9991	+	10.3918i	0.637560	+	0.368095i	0.783674	−	0.621172i	$-0.213343\pi$
$797$	17.9991	+	10.3918i	0.637560	+	0.368095i	−0.146114	+	0.989268i	$0.546677\pi$
$798$	−3.87874	−	1.72482i	−0.137306	−	0.0610581i
$799$	0.655579			0.0231927
$800$	19.6978	+	14.4418i	0.696424	+	0.510595i
$801$	52.9726	+	8.81618i	1.87170	+	0.311504i
$802$	25.5879	+	8.93546i	0.903540	+	0.315522i
$803$	−6.46277	+	3.73128i	−0.228066	+	0.131674i
$804$	26.5878	−	8.01539i	0.937679	−	0.282681i
$805$	7.05509	−	4.07326i	0.248659	−	0.143563i
$806$	4.39627	+	19.8220i	0.154852	+	0.698200i
$807$	−11.7978	−	0.975041i	−0.415302	−	0.0343231i
$808$	30.4949	+	16.0432i	1.07281	+	0.564397i
$809$	21.2873	−	36.8706i	0.748420	−	1.29630i	−0.200160	−	0.979763i	$-0.564146\pi$
$809$	21.2873	−	36.8706i	0.748420	−	1.29630i	0.948580	−	0.316538i	$-0.102521\pi$
$810$	6.49389	−	8.26779i	0.228172	−	0.290501i
$811$			35.1214i			1.23328i	0.787245	+	0.616640i	$0.211507\pi$
$811$			35.1214i			1.23328i	−0.787245	+	0.616640i	$0.788493\pi$
$812$	−34.1229	−	5.09913i	−1.19748	−	0.178944i
$813$	−33.7500	+	15.9359i	−1.18366	+	0.558896i
$814$	3.81656	+	1.33277i	0.133770	+	0.0467134i
$815$	0.930319	−	1.61136i	0.0325877	−	0.0564435i
$816$	−31.2541	+	4.54688i	−1.09411	+	0.159172i
$817$	−0.948697	−	1.64319i	−0.0331907	−	0.0574880i
$818$	−13.5729	+	11.6954i	−0.474566	+	0.408919i
$819$	−9.67865	−	23.5925i	−0.338200	−	0.824389i
$820$	5.68427	+	0.849424i	0.198503	+	0.0296632i
$821$	13.3646	−	7.71607i	0.466428	−	0.269293i	−0.248315	−	0.968679i	$-0.579877\pi$
$821$	13.3646	−	7.71607i	0.466428	−	0.269293i	0.714743	+	0.699387i	$0.246543\pi$
$822$	−4.01971	−	5.52739i	−0.140203	−	0.192790i
$823$	−25.1194	+	43.5080i	−0.875606	+	1.51659i	−0.0194910	+	0.999810i	$0.506205\pi$
$823$	−25.1194	+	43.5080i	−0.875606	+	1.51659i	−0.856115	+	0.516785i	$0.827129\pi$
$824$	−8.30869	+	15.7932i	−0.289447	+	0.550181i
$825$	3.03960	−	4.38573i	0.105825	−	0.152691i
$826$	−32.7455	−	38.0024i	−1.13936	−	1.32227i
$827$		−	24.1777i		−	0.840742i	−0.907352	−	0.420371i	$-0.861900\pi$
$827$		−	24.1777i		−	0.840742i	0.907352	−	0.420371i	$-0.138100\pi$
$828$	7.73497	−	23.8793i	0.268809	−	0.829865i
$829$	19.3485	+	11.1708i	0.672000	+	0.387979i	0.796834	−	0.604198i	$-0.206507\pi$
$829$	19.3485	+	11.1708i	0.672000	+	0.387979i	−0.124834	+	0.992178i	$0.539840\pi$
$830$	11.0882	+	3.87206i	0.384876	+	0.134401i
$831$	−9.36729	+	13.5157i	−0.324948	+	0.468855i
$832$	−11.6136	+	26.4031i	−0.402628	+	0.915364i
$833$	3.28685	+	5.69298i	0.113882	+	0.197250i
$834$	1.99165	+	18.8671i	0.0689653	+	0.653316i
$835$	8.46176	−	4.88540i	0.292831	−	0.169066i
$836$	0.976001	−	0.384476i	0.0337557	−	0.0132974i
$837$	−19.9061	+	5.64277i	−0.688056	+	0.195043i
$838$	−7.40512	+	21.2056i	−0.255806	+	0.732534i
$839$	54.9500			1.89708			0.948542	−	0.316651i	$-0.102558\pi$
$839$	54.9500			1.89708			0.948542	+	0.316651i	$0.102558\pi$
$840$	−4.40897	−	8.45986i	−0.152124	−	0.291893i
$841$	12.2718	−	21.2555i	0.423167	−	0.732947i
$842$	−1.27810	−	1.48328i	−0.0440461	−	0.0511172i
$843$	16.7751	−	7.92077i	0.577765	−	0.272806i
$844$	−6.36960	+	8.00795i	−0.219251	+	0.275645i
$845$	8.95324	−	5.92809i	0.308001	−	0.203933i
$846$	0.535185	+	0.292988i	0.0184001	+	0.0100731i
$847$	12.3663	−	21.4191i	0.424912	−	0.735969i
$848$	17.9637	−	4.14786i	0.616875	−	0.142438i
$849$	14.8696	−	21.4548i	0.510324	−	0.736327i
$850$	−26.2797	−	9.17703i	−0.901385	−	0.314769i
$851$	14.5146	+	8.37999i	0.497553	+	0.287263i
$852$	−5.66979	+	6.03274i	−0.194244	+	0.206678i
$853$	38.8568	+	22.4340i	1.33043	+	0.768124i	0.985365	−	0.170455i	$-0.0545237\pi$
$853$	38.8568	+	22.4340i	1.33043	+	0.768124i	0.345065	+	0.938579i	$0.387857\pi$
$854$	−7.13292	+	20.4261i	−0.244083	+	0.698966i
$855$	1.79682	+	0.299043i	0.0614499	+	0.0102270i
$856$	0.667960	+	16.9899i	0.0228304	+	0.580704i
$857$	3.85683	−	6.68022i	0.131747	−	0.228192i	−0.792603	−	0.609738i	$-0.791275\pi$
$857$	3.85683	−	6.68022i	0.131747	−	0.228192i	0.924350	+	0.381546i	$0.124608\pi$
$858$	5.83369	+	2.38300i	0.199159	+	0.0813541i
$859$	10.1480	−	5.85897i	0.346246	−	0.199905i	−0.316784	−	0.948498i	$-0.602603\pi$
$859$	10.1480	−	5.85897i	0.346246	−	0.199905i	0.663031	+	0.748592i	$0.269270\pi$
$860$	0.630201	−	4.21725i	0.0214897	−	0.143807i
$861$	11.6762	+	8.09239i	0.397924	+	0.275788i
$862$	31.2954	−	26.9663i	1.06593	−	0.918476i
$863$	42.7208			1.45423			0.727117	−	0.686513i	$-0.240860\pi$
$863$	42.7208			1.45423			0.727117	+	0.686513i	$0.240860\pi$
$864$	−27.5466	−	10.2561i	−0.937153	−	0.348919i
$865$	−4.11312	−	7.12414i	−0.139850	−	0.242228i
$866$	−10.3465	−	54.4942i	−0.351589	−	1.85179i
$867$	5.92215	−	2.79628i	0.201127	−	0.0949668i
$868$	−2.77479	+	18.5686i	−0.0941824	+	0.630261i
$869$			9.87808i			0.335091i
$870$	14.7231	−	1.55420i	0.499161	−	0.0526924i
$871$	0.884996	+	28.8901i	0.0299870	+	0.978903i
$872$	−13.7176	+	8.65562i	−0.464536	+	0.293116i
$873$	−14.5372	−	38.7764i	−0.492010	−	1.31238i
$874$	4.27269	−	0.811232i	0.144526	−	0.0274403i
$875$		−	18.1445i		−	0.613396i
$876$	10.4575	+	34.6884i	0.353325	+	1.17201i
$877$	−23.2295	−	13.4116i	−0.784406	−	0.452877i	0.0535838	−	0.998563i	$-0.482936\pi$
$877$	−23.2295	−	13.4116i	−0.784406	−	0.452877i	−0.837989	+	0.545687i	$0.816269\pi$
$878$	−6.31915	−	33.2824i	−0.213261	−	1.12323i
$879$	7.33099	+	15.5260i	0.247268	+	0.523680i
$880$	2.25446	+	0.689177i	0.0759979	+	0.0232322i
$881$	29.1362	−	50.4654i	0.981624	−	1.70022i	0.325555	−	0.945523i	$-0.394449\pi$
$881$	29.1362	−	50.4654i	0.981624	−	1.70022i	0.656070	−	0.754700i	$-0.272218\pi$
$882$	0.138952	+	6.11644i	0.00467875	+	0.205951i
$883$		−	14.0915i		−	0.474216i	−0.971483	−	0.237108i	$-0.923800\pi$
$883$		−	14.0915i		−	0.474216i	0.971483	−	0.237108i	$-0.0761995\pi$
$884$	3.86062	−	32.6453i	0.129847	−	1.09798i
$885$	17.6920	+	12.2617i	0.594711	+	0.412174i
$886$	32.7263	+	37.9802i	1.09946	+	1.27597i
$887$	−17.6285			−0.591907			−0.295953	−	0.955202i	$-0.595637\pi$
$887$	−17.6285			−0.591907			−0.295953	+	0.955202i	$0.595637\pi$
$888$	10.5375	−	16.5577i	0.353616	−	0.555641i
$889$	−16.4136	+	28.4292i	−0.550496	+	0.953486i
$890$	−6.89368	+	19.7410i	−0.231077	+	0.661720i
$891$	−2.07989	+	6.07552i	−0.0696791	+	0.203538i
$892$	4.76977	−	31.9189i	0.159704	−	1.06872i
$893$			0.105713i			0.00353756i
$894$	−2.09882	−	19.8824i	−0.0701951	−	0.664966i
$895$	1.96501			0.0656831
$896$	−18.7767	+	18.9435i	−0.627286	+	0.632857i
$897$	21.9184	+	14.2176i	0.731834	+	0.474713i
$898$	−3.18119	−	16.7550i	−0.106158	−	0.559123i
$899$	−25.2332	−	14.5684i	−0.841575	−	0.485883i
$900$	−17.3522	−	19.2365i	−0.578407	−	0.641217i
$901$	−18.1961	+	10.5056i	−0.606202	+	0.349991i
$902$	−3.44901	+	0.654845i	−0.114840	+	0.0218040i
$903$	6.00387	−	8.66276i	0.199796	−	0.288278i
$904$	33.0653	−	1.29996i	1.09974	−	0.0432361i
$905$	−8.53066	−	14.7755i	−0.283569	−	0.491156i
$906$	37.0351	−	3.90950i	1.23041	−	0.129885i
$907$	8.72926	−	5.03984i	0.289850	−	0.167345i	−0.348024	−	0.937486i	$-0.613147\pi$
$907$	8.72926	−	5.03984i	0.289850	−	0.167345i	0.637874	+	0.770141i	$0.279814\pi$
$908$	5.88926	−	7.40407i	0.195442	−	0.245713i
$909$	−28.2218	−	23.2221i	−0.936058	−	0.770230i
$910$	9.69381	−	2.14997i	0.321347	−	0.0712707i
$911$	−21.9031	+	37.9373i	−0.725682	+	1.25692i	0.233010	+	0.972474i	$0.425142\pi$
$911$	−21.9031	+	37.9373i	−0.725682	+	1.25692i	−0.958693	+	0.284444i	$0.908191\pi$
$912$	−0.733192	−	5.03979i	−0.0242784	−	0.166884i
$913$	−7.17398			−0.237424
$914$	1.08757	+	5.72814i	0.0359736	+	0.189470i
$915$	0.764679	−	9.25246i	0.0252795	−	0.305877i
$916$	46.4960	+	6.94809i	1.53627	+	0.229571i
$917$	25.5439	−	14.7478i	0.843533	−	0.487014i
$918$	33.4392	+	2.00020i	1.10366	+	0.0660164i
$919$	−28.5730	−	49.4900i	−0.942538	−	1.63252i	−0.760608	−	0.649211i	$-0.775099\pi$
$919$	−28.5730	−	49.4900i	−0.942538	−	1.63252i	−0.181930	−	0.983312i	$-0.558234\pi$
$920$	8.64971	+	4.55056i	0.285173	+	0.150028i
$921$	−11.4856	+	16.5722i	−0.378464	+	0.546072i
$922$	−10.5819	+	30.3028i	−0.348498	+	0.997971i
$923$	−4.53496	−	7.32709i	−0.149270	−	0.241174i
$924$	4.24615	+	3.99069i	0.139688	+	0.131284i
$925$	14.9804	−	8.64893i	0.492552	−	0.284375i
$926$	2.76997	+	14.5892i	0.0910269	+	0.479431i
$927$	12.0266	−	14.6159i	0.395007	−	0.480051i
$928$	−16.6725	−	37.8870i	−0.547303	−	1.24370i
$929$	−16.0226			−0.525686			−0.262843	−	0.964839i	$-0.584660\pi$
$929$	−16.0226			−0.525686			−0.262843	+	0.964839i	$0.584660\pi$
$930$	−0.845748	−	8.01186i	−0.0277332	−	0.262719i
$931$	−0.918004	+	0.530010i	−0.0300864	+	0.0173704i
$932$	−15.0864	−	11.9999i	−0.494173	−	0.393070i
$933$	−1.81822	+	22.0001i	−0.0595259	+	0.720251i
$934$	−13.3126	+	38.1224i	−0.435601	+	1.24740i
$935$	−2.68669			−0.0878641
$936$	17.7413	−	24.9248i	0.579893	−	0.814692i
$937$	40.0275			1.30764			0.653822	−	0.756649i	$-0.273165\pi$
$937$	40.0275			1.30764			0.653822	+	0.756649i	$0.273165\pi$
$938$	−8.81151	+	25.2330i	−0.287706	+	0.823885i
$939$	11.0872	−	5.23510i	0.361818	−	0.170841i
$940$	−0.147889	+	0.185929i	−0.00482362	+	0.00606433i
$941$	5.08240	−	2.93432i	0.165681	−	0.0956562i	−0.414867	−	0.909882i	$-0.636172\pi$
$941$	5.08240	−	2.93432i	0.165681	−	0.0956562i	0.580548	+	0.814226i	$0.302838\pi$
$942$	49.2726	+	21.9108i	1.60539	+	0.713894i
$943$	−14.5546			−0.473964
$944$	17.5942	−	57.5548i	0.572642	−	1.87325i
$945$	2.75956	+	9.73494i	0.0897684	+	0.316678i
$946$	0.485840	+	2.55888i	0.0157960	+	0.0831962i
$947$	31.9917	−	18.4704i	1.03959	−	0.600208i	0.119874	−	0.992789i	$-0.461751\pi$
$947$	31.9917	−	18.4704i	1.03959	−	0.600208i	0.919718	+	0.392581i	$0.128418\pi$
$948$	46.6860	+	10.9704i	1.51629	+	0.356301i
$949$	−37.6921	+	1.15463i	−1.22354	+	0.0374809i
$950$	1.47981	−	4.23764i	0.0480114	−	0.137487i
$951$	−22.7312	−	48.1416i	−0.737111	−	1.56110i
$952$	14.1528	−	26.9018i	0.458696	−	0.871891i
$953$	−21.6575	−	37.5119i	−0.701556	−	1.21513i	−0.967920	−	0.251258i	$-0.919156\pi$
$953$	−21.6575	−	37.5119i	−0.701556	−	1.21513i	0.266364	−	0.963872i	$-0.414178\pi$
$954$	−19.5496	+	0.444124i	−0.632942	+	0.0143790i
$955$	−2.36677	+	1.36646i	−0.0765870	+	0.0442175i
$956$	4.64440	−	31.0799i	0.150210	−	1.00520i
$957$	−8.17743	+	3.86117i	−0.264339	+	0.124814i
$958$	−4.92736	−	25.9520i	−0.159196	−	0.838470i
$959$	6.57791			0.212412
$960$	5.76096	−	9.88970i	0.185934	−	0.319189i
$961$	7.57233	−	13.1157i	0.244269	−	0.423086i
$962$	13.8022	+	15.0598i	0.445001	+	0.485547i
$963$	2.96073	−	17.7898i	0.0954083	−	0.573268i
$964$	−13.0772	−	10.4017i	−0.421189	−	0.335017i
$965$	1.92823	−	1.11327i	0.0620721	−	0.0358373i
$966$	14.2089	+	19.5382i	0.457163	+	0.628633i
$967$	−2.19892	−	3.80864i	−0.0707124	−	0.122478i	0.828501	−	0.559987i	$-0.189194\pi$
$967$	−2.19892	−	3.80864i	−0.0707124	−	0.122478i	−0.899214	+	0.437510i	$0.855861\pi$
$968$	29.6498	−	1.16568i	0.952981	−	0.0374664i
$969$	2.47818	+	5.24844i	0.0796106	+	0.168604i
$970$	15.8418	−	3.00780i	0.508650	−	0.0965746i
$971$	31.2117	−	18.0201i	1.00163	−	0.578293i	0.0929015	−	0.995675i	$-0.470386\pi$
$971$	31.2117	−	18.0201i	1.00163	−	0.578293i	0.908731	+	0.417383i	$0.137052\pi$
$972$	26.4044	+	16.5774i	0.846920	+	0.531720i
$973$	−15.8134	−	9.12988i	−0.506955	−	0.292690i
$974$	−3.89693	−	20.5248i	−0.124866	−	0.657656i
$975$	24.0189	−	12.2541i	0.769220	−	0.392446i
$976$	−25.2917	+	5.83994i	−0.809569	+	0.186932i
$977$	−36.2856			−1.16088			−0.580440	−	0.814303i	$-0.697119\pi$
$977$	−36.2856			−1.16088			−0.580440	+	0.814303i	$0.697119\pi$
$978$	5.04172	+	2.24198i	0.161216	+	0.0716907i
$979$		−	12.7723i		−	0.408204i
$980$	−2.35606	−	0.352075i	−0.0752614	−	0.0112466i
$981$	16.1092	−	6.03929i	0.514326	−	0.192820i
$982$	16.1996	−	46.3897i	0.516949	−	1.48035i
$983$	−28.0792	+	48.6346i	−0.895588	+	1.55120i	−0.0625117	+	0.998044i	$0.519911\pi$
$983$	−28.0792	+	48.6346i	−0.895588	+	1.55120i	−0.833076	+	0.553159i	$0.813422\pi$
$984$	−0.735454	+	17.0281i	−0.0234454	+	0.542834i
$985$	10.7030			0.341025
$986$	30.7937	+	35.7372i	0.980670	+	1.13810i
$987$	−0.531013	+	0.250730i	−0.0169023	+	0.00798084i
$988$	5.26411	+	0.622531i	0.167474	+	0.0198054i
$989$			10.7983i			0.343366i
$990$	−2.19329	−	1.20072i	−0.0697074	−	0.0381615i
$991$	30.5236	−	52.8684i	0.969613	−	1.67942i	0.272938	−	0.962032i	$-0.412005\pi$
$991$	30.5236	−	52.8684i	0.969613	−	1.67942i	0.696675	−	0.717387i	$-0.254662\pi$
$992$	−20.6169	+	9.07268i	−0.654588	+	0.288058i
$993$	−27.3024	+	39.3936i	−0.866415	+	1.25012i
$994$	−1.48631	−	7.82827i	−0.0471429	−	0.248298i
$995$	4.20645	+	2.42860i	0.133354	+	0.0769917i
$996$	−7.96726	+	33.9058i	−0.252452	+	1.07435i
$997$			16.2202i			0.513700i	0.966451	+	0.256850i	$0.0826847\pi$
$997$			16.2202i			0.513700i	−0.966451	+	0.256850i	$0.917315\pi$
$998$	−28.3733	+	5.38708i	−0.898140	+	0.170525i
$999$	−14.5060	+	14.9306i	−0.458950	+	0.472384i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	936.2.db.a.61.17	yes	328
8.5	even	2	inner	936.2.db.a.61.92	yes	328
9.4	even	3		936.2.cj.a.373.125	yes	328
13.3	even	3		936.2.cj.a.133.125	✓	328
72.13	even	6		936.2.cj.a.373.126	yes	328
104.29	even	6		936.2.cj.a.133.126	yes	328
117.94	even	3	inner	936.2.db.a.445.92	yes	328
936.445	even	6	inner	936.2.db.a.445.17	yes	328

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.cj.a.133.125	✓	328	13.3	even	3
936.2.cj.a.133.126	yes	328	104.29	even	6
936.2.cj.a.373.125	yes	328	9.4	even	3
936.2.cj.a.373.126	yes	328	72.13	even	6
936.2.db.a.61.17	yes	328	1.1	even	1	trivial
936.2.db.a.61.92	yes	328	8.5	even	2	inner
936.2.db.a.445.17	yes	328	936.445	even	6	inner
936.2.db.a.445.92	yes	328	117.94	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 936 = 2^{3} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	936.db (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33515 - 0.466242i) q^{2} +(-1.42357 - 0.986631i) q^{3} +(1.56524 + 1.24500i) q^{4} +(0.715331 - 0.412997i) q^{5} +(1.44067 + 1.98103i) q^{6} -2.35753 q^{7} +(-1.50935 - 2.39204i) q^{8} +(1.05312 + 2.80908i) q^{9} +(-1.14763 + 0.217894i) q^{10} +(0.617926 - 0.356760i) q^{11} +(-0.999870 - 3.31666i) q^{12} +(3.60386 - 0.110398i) q^{13} +(3.14766 + 1.09918i) q^{14} +(-1.42580 - 0.117837i) q^{15} +(0.899933 + 3.89745i) q^{16} +(-2.27932 - 3.94789i) q^{17} +(-0.0963584 - 4.24155i) q^{18} +(0.636605 - 0.367544i) q^{19} +(1.63385 + 0.244152i) q^{20} +(3.35612 + 2.32602i) q^{21} +(-0.991359 + 0.188224i) q^{22} -4.18348 q^{23} +(-0.211393 + 4.89442i) q^{24} +(-2.15887 + 3.73927i) q^{25} +(-4.86316 - 1.53287i) q^{26} +(1.27233 - 5.03797i) q^{27} +(-3.69010 - 2.93514i) q^{28} +(6.33702 - 3.65868i) q^{29} +(1.84871 + 0.822098i) q^{30} +(-1.99094 - 3.44841i) q^{31} +(0.615611 - 5.62326i) q^{32} +(-1.23165 - 0.101791i) q^{33} +(1.20255 + 6.33373i) q^{34} +(-1.68642 + 0.973654i) q^{35} +(-1.84893 + 5.70802i) q^{36} +(-3.46950 - 2.00312i) q^{37} +(-1.02133 + 0.193914i) q^{38} +(-5.23928 - 3.39852i) q^{39} +(-2.06759 - 1.08775i) q^{40} +3.47908 q^{41} +(-3.39643 - 4.67034i) q^{42} -2.58118i q^{43} +(1.41137 + 0.210906i) q^{44} +(1.91347 + 1.57449i) q^{45} +(5.58556 + 1.95051i) q^{46} +(-0.0719052 + 0.124543i) q^{47} +(2.56422 - 6.43621i) q^{48} -1.44203 q^{49} +(4.62581 - 3.98592i) q^{50} +(-0.650338 + 7.86896i) q^{51} +(5.77834 + 4.31402i) q^{52} -4.60908i q^{53} +(-4.04767 + 6.13322i) q^{54} +(0.294681 - 0.510403i) q^{55} +(3.55834 + 5.63932i) q^{56} +(-1.26888 - 0.104868i) q^{57} +(-10.1667 + 1.93029i) q^{58} +(-13.0302 - 7.52300i) q^{59} +(-2.08501 - 1.95957i) q^{60} +6.48930i q^{61} +(1.05040 + 5.53239i) q^{62} +(-2.48277 - 6.62251i) q^{63} +(-3.44373 + 7.22085i) q^{64} +(2.53236 - 1.56735i) q^{65} +(1.59698 + 0.710155i) q^{66} +8.01643i q^{67} +(1.34747 - 9.01714i) q^{68} +(5.95548 + 4.12755i) q^{69} +(2.70558 - 0.513693i) q^{70} +(-1.19496 - 2.06973i) q^{71} +(5.12992 - 6.75899i) q^{72} -10.4588 q^{73} +(3.69836 + 4.29208i) q^{74} +(6.76258 - 3.19312i) q^{75} +(1.45403 + 0.217282i) q^{76} +(-1.45678 + 0.841074i) q^{77} +(5.41068 + 6.98030i) q^{78} +(-6.92208 + 11.9894i) q^{79} +(2.25338 + 2.41630i) q^{80} +(-6.78188 + 5.91660i) q^{81} +(-4.64508 - 1.62209i) q^{82} +(-8.70733 - 5.02718i) q^{83} +(2.35723 + 7.81915i) q^{84} +(-3.26093 - 1.88270i) q^{85} +(-1.20345 + 3.44626i) q^{86} +(-12.6310 - 1.04390i) q^{87} +(-1.78605 - 0.939630i) q^{88} +(8.95021 - 15.5022i) q^{89} +(-1.82067 - 2.99431i) q^{90} +(-8.49623 + 0.260267i) q^{91} +(-6.54813 - 5.20844i) q^{92} +(-0.568058 + 6.87338i) q^{93} +(0.154071 - 0.132759i) q^{94} +(0.303589 - 0.525831i) q^{95} +(-6.42445 + 7.39774i) q^{96} -13.8040 q^{97} +(1.92532 + 0.672335i) q^{98} +(1.65292 + 1.36009i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 328 q + q^{2} + q^{4} + q^{6} - 4 q^{7} - 2 q^{8} - 2 q^{9} - 4 q^{10} + 5 q^{12} - 6 q^{14} + 4 q^{15} + q^{16} - 4 q^{17} - 12 q^{18} - 18 q^{20} - 7 q^{22} + 44 q^{23} - 6 q^{24} + 144 q^{25} - 16 q^{26}+ \cdots + 39 q^{98}+O(q^{100}) \) 328 * q + q^2 + q^4 + q^6 - 4 * q^7 - 2 * q^8 - 2 * q^9 - 4 * q^10 + 5 * q^12 - 6 * q^14 + 4 * q^15 + q^16 - 4 * q^17 - 12 * q^18 - 18 * q^20 - 7 * q^22 + 44 * q^23 - 6 * q^24 + 144 * q^25 - 16 * q^26 - 10 * q^28 - 5 * q^30 - 4 * q^31 + q^32 - 14 * q^33 - 13 * q^36 + 6 * q^38 + 20 * q^39 + 8 * q^40 - 4 * q^41 - 46 * q^42 - 32 * q^44 - 6 * q^46 - 4 * q^47 - 46 * q^48 + 276 * q^49 + 68 * q^50 + 40 * q^54 - 14 * q^55 - 56 * q^56 - 20 * q^57 - 25 * q^58 - 41 * q^60 + 3 * q^62 - 58 * q^63 - 26 * q^64 - 22 * q^65 - 6 * q^66 - 64 * q^68 - 17 * q^70 - 4 * q^71 - 7 * q^72 - 16 * q^73 - 38 * q^74 - 18 * q^76 - q^78 - 4 * q^79 - 42 * q^80 - 2 * q^81 + 3 * q^82 + 6 * q^84 + 36 * q^86 - 2 * q^87 + 5 * q^88 - 4 * q^89 + 33 * q^90 + 28 * q^92 - 6 * q^94 + 56 * q^95 - 113 * q^96 - 4 * q^97 + 39 * q^98

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