LMFDB - Embedded newform 936.2.db.a.61.92

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)

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);

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")

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			61.92
Character	$\chi$	$=$	936.61
Dual form			936.2.db.a.445.92

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.263796 - 1.38939i) q^{2} +(1.42357 + 0.986631i) q^{3} +(-1.86082 - 0.733033i) q^{4} +(-0.715331 + 0.412997i) q^{5} +(1.74635 - 1.71763i) q^{6} -2.35753 q^{7} +(-1.50935 + 2.39204i) q^{8} +(1.05312 + 2.80908i) q^{9} +(0.385113 + 1.10282i) q^{10} +(-0.617926 + 0.356760i) q^{11} +(-1.92578 - 2.87947i) q^{12} +(-3.60386 + 0.110398i) q^{13} +(-0.621909 + 3.27554i) q^{14} +(-1.42580 - 0.117837i) q^{15} +(2.92532 + 2.72809i) q^{16} +(-2.27932 - 3.94789i) q^{17} +(4.18073 - 0.722171i) q^{18} +(-0.636605 + 0.367544i) q^{19} +(1.63385 - 0.244152i) q^{20} +(-3.35612 - 2.32602i) q^{21} +(0.332673 + 0.952654i) q^{22} -4.18348 q^{23} +(-4.50873 + 1.91608i) q^{24} +(-2.15887 + 3.73927i) q^{25} +(-0.797299 + 5.03630i) q^{26} +(-1.27233 + 5.03797i) q^{27} +(4.38695 + 1.72815i) q^{28} +(-6.33702 + 3.65868i) q^{29} +(-0.539843 + 1.94991i) q^{30} +(-1.99094 - 3.44841i) q^{31} +(4.56208 - 3.34476i) q^{32} +(-1.23165 - 0.101791i) q^{33} +(-6.08645 + 2.12543i) q^{34} +(1.68642 - 0.973654i) q^{35} +(0.0994808 - 5.99918i) q^{36} +(3.46950 + 2.00312i) q^{37} +(0.342729 + 0.981451i) q^{38} +(-5.23928 - 3.39852i) q^{39} +(0.0917792 - 2.33446i) q^{40} +3.47908 q^{41} +(-4.11708 + 4.04938i) q^{42} +2.58118i q^{43} +(1.41137 - 0.210906i) q^{44} +(-1.91347 - 1.57449i) q^{45} +(-1.10359 + 5.81249i) q^{46} +(-0.0719052 + 0.124543i) q^{47} +(1.47279 + 6.76985i) q^{48} -1.44203 q^{49} +(4.62581 + 3.98592i) q^{50} +(0.650338 - 7.86896i) q^{51} +(6.78707 + 2.43632i) q^{52} +4.60908i q^{53} +(6.66408 + 3.09677i) q^{54} +(0.294681 - 0.510403i) q^{55} +(3.55834 - 5.63932i) q^{56} +(-1.26888 - 0.104868i) q^{57} +(3.41166 + 9.76975i) q^{58} +(13.0302 + 7.52300i) q^{59} +(2.56679 + 1.26443i) q^{60} -6.48930i q^{61} +(-5.31639 + 1.85652i) q^{62} +(-2.48277 - 6.62251i) q^{63} +(-3.44373 - 7.22085i) q^{64} +(2.53236 - 1.56735i) q^{65} +(-0.466334 + 1.68440i) q^{66} -8.01643i q^{67} +(1.34747 + 9.01714i) q^{68} +(-5.95548 - 4.12755i) q^{69} +(-0.907917 - 2.59994i) q^{70} +(-1.19496 - 2.06973i) q^{71} +(-8.30897 - 1.72078i) 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} +(-6.10398 + 6.38290i) q^{78} +(-6.92208 + 11.9894i) q^{79} +(-3.21927 - 0.743339i) q^{80} +(-6.78188 + 5.91660i) q^{81} +(0.917768 - 4.83380i) q^{82} +(8.70733 + 5.02718i) q^{83} +(4.54010 + 6.78845i) q^{84} +(3.26093 + 1.88270i) q^{85} +(3.58627 + 0.680906i) q^{86} +(-12.6310 - 1.04390i) q^{87} +(0.0792818 - 2.01658i) q^{88} +(8.95021 - 15.5022i) q^{89} +(-2.69235 + 2.24322i) q^{90} +(8.49623 - 0.260267i) q^{91} +(7.78471 + 3.06663i) q^{92} +(0.568058 - 6.87338i) q^{93} +(0.154071 + 0.132759i) q^{94} +(0.303589 - 0.525831i) q^{95} +(9.79450 - 0.260429i) q^{96} -13.8040 q^{97} +(-0.380402 + 2.00355i) 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 $

$2$	0.263796	−	1.38939i	0.186532	−	0.982449i
$2$	0.263796	−	1.38939i	0.186532	−	0.982449i
$3$	1.42357	+	0.986631i	0.821900	+	0.569632i
$3$	1.42357	+	0.986631i	0.821900	+	0.569632i
$4$	−1.86082	−	0.733033i	−0.930411	−	0.366517i
$5$	−0.715331	+	0.412997i	−0.319906	+	0.184698i	−0.651351	−	0.758777i	$-0.725797\pi$
$5$	−0.715331	+	0.412997i	−0.319906	+	0.184698i	0.331445	+	0.943475i	$0.392464\pi$
$6$	1.74635	−	1.71763i	0.712945	−	0.701220i
$7$	−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
$10$	0.385113	+	1.10282i	0.121783	+	0.348743i
$11$	−0.617926	+	0.356760i	−0.186312	+	0.107567i	−0.590255	−	0.807217i	$-0.700973\pi$
$11$	−0.617926	+	0.356760i	−0.186312	+	0.107567i	0.403943	+	0.914784i	$0.367639\pi$
$12$	−1.92578	−	2.87947i	−0.555926	−	0.831232i
$13$	−3.60386	+	0.110398i	−0.999531	+	0.0306189i
$13$	−3.60386	+	0.110398i	−0.999531	+	0.0306189i
$14$	−0.621909	+	3.27554i	−0.166212	+	0.875425i
$15$	−1.42580	−	0.117837i	−0.368140	−	0.0304253i
$16$	2.92532	+	2.72809i	0.731331	+	0.682023i
$17$	−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	$-0.353113\pi$
$18$	4.18073	−	0.722171i	0.985407	−	0.170217i
$19$	−0.636605	+	0.367544i	−0.146047	+	0.0843204i	−0.571243	−	0.820781i	$-0.693539\pi$
$19$	−0.636605	+	0.367544i	−0.146047	+	0.0843204i	0.425196	+	0.905101i	$0.360205\pi$
$20$	1.63385	−	0.244152i	0.365339	−	0.0545941i
$21$	−3.35612	−	2.32602i	−0.732366	−	0.507578i
$22$	0.332673	+	0.952654i	0.0709261	+	0.203106i
$23$	−4.18348			−0.872315			−0.436157	−	0.899870i	$-0.643661\pi$
$23$	−4.18348			−0.872315			−0.436157	+	0.899870i	$0.643661\pi$
$24$	−4.50873	+	1.91608i	−0.920341	+	0.391117i
$25$	−2.15887	+	3.73927i	−0.431773	+	0.747854i
$26$	−0.797299	+	5.03630i	−0.156363	+	0.987700i
$27$	−1.27233	+	5.03797i	−0.244861	+	0.969558i
$28$	4.38695	+	1.72815i	0.829056	+	0.326590i
$29$	−6.33702	+	3.65868i	−1.17675	+	0.679399i	−0.955261	−	0.295763i	$-0.904426\pi$
$29$	−6.33702	+	3.65868i	−1.17675	+	0.679399i	−0.221493	+	0.975162i	$0.571093\pi$
$30$	−0.539843	+	1.94991i	−0.0985614	+	0.356004i
$31$	−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	$0.949732\pi$
$32$	4.56208	−	3.34476i	0.806469	−	0.591276i
$33$	−1.23165	−	0.101791i	−0.214403	−	0.0177196i
$34$	−6.08645	+	2.12543i	−1.04382	+	0.364508i
$35$	1.68642	−	0.973654i	0.285057	−	0.164578i
$36$	0.0994808	−	5.99918i	0.0165801	−	0.999863i
$37$	3.46950	+	2.00312i	0.570383	+	0.329311i	0.757302	−	0.653065i	$-0.226517\pi$
$37$	3.46950	+	2.00312i	0.570383	+	0.329311i	−0.186920	+	0.982375i	$0.559850\pi$
$38$	0.342729	+	0.981451i	0.0555980	+	0.159212i
$39$	−5.23928	−	3.39852i	−0.838956	−	0.544199i
$40$	0.0917792	−	2.33446i	0.0145116	−	0.369110i
$41$	3.47908			0.543341			0.271670	−	0.962390i	$-0.412424\pi$
$41$	3.47908			0.543341			0.271670	+	0.962390i	$0.412424\pi$
$42$	−4.11708	+	4.04938i	−0.635280	+	0.624832i
$43$			2.58118i			0.393626i	0.980441	+	0.196813i	$0.0630592\pi$
$43$			2.58118i			0.393626i	−0.980441	+	0.196813i	$0.936941\pi$
$44$	1.41137	−	0.210906i	0.212772	−	0.0317953i
$45$	−1.91347	−	1.57449i	−0.285243	−	0.234711i
$46$	−1.10359	+	5.81249i	−0.162715	+	0.857005i
$47$	−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	$0.170005\pi$
$48$	1.47279	+	6.76985i	0.212580	+	0.977144i
$49$	−1.44203			−0.206004
$50$	4.62581	+	3.98592i	0.654188	+	0.563694i
$51$	0.650338	−	7.86896i	0.0910656	−	1.10187i
$52$	6.78707	+	2.43632i	0.941198	+	0.337857i
$53$			4.60908i			0.633106i	0.948575	+	0.316553i	$0.102525\pi$
$53$			4.60908i			0.633106i	−0.948575	+	0.316553i	$0.897475\pi$
$54$	6.66408	+	3.09677i	0.906867	+	0.421417i
$55$	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
$58$	3.41166	+	9.76975i	0.447973	+	1.28283i
$59$	13.0302	+	7.52300i	1.69639	+	0.979411i	0.949133	+	0.314877i	$0.101963\pi$
$59$	13.0302	+	7.52300i	1.69639	+	0.979411i	0.747257	+	0.664535i	$0.231370\pi$
$60$	2.56679	+	1.26443i	0.331371	+	0.163238i
$61$		−	6.48930i		−	0.830870i	−0.909623	−	0.415435i	$-0.863629\pi$
$61$		−	6.48930i		−	0.830870i	0.909623	−	0.415435i	$-0.136371\pi$
$62$	−5.31639	+	1.85652i	−0.675182	+	0.235778i
$63$	−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
$66$	−0.466334	+	1.68440i	−0.0574017	+	0.207335i
$67$		−	8.01643i		−	0.979363i	−0.871901	−	0.489681i	$-0.837113\pi$
$67$		−	8.01643i		−	0.979363i	0.871901	−	0.489681i	$-0.162887\pi$
$68$	1.34747	+	9.01714i	0.163405	+	1.09349i
$69$	−5.95548	−	4.12755i	−0.716956	−	0.496898i
$70$	−0.907917	−	2.59994i	−0.108517	−	0.310753i
$71$	−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	$0.878627\pi$
$72$	−8.30897	−	1.72078i	−0.979221	−	0.202796i
$73$	−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
$78$	−6.10398	+	6.38290i	−0.691140	+	0.722721i
$79$	−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	$0.882498\pi$
$80$	−3.21927	−	0.743339i	−0.359925	−	0.0831078i
$81$	−6.78188	+	5.91660i	−0.753542	+	0.657400i
$82$	0.917768	−	4.83380i	0.101350	−	0.533804i
$83$	8.70733	+	5.02718i	0.955753	+	0.551804i	0.894863	−	0.446340i	$-0.147273\pi$
$83$	8.70733	+	5.02718i	0.955753	+	0.551804i	0.0608899	+	0.998144i	$0.480606\pi$
$84$	4.54010	+	6.78845i	0.495366	+	0.740681i
$85$	3.26093	+	1.88270i	0.353698	+	0.204208i
$86$	3.58627	+	0.680906i	0.386718	+	0.0734240i
$87$	−12.6310	−	1.04390i	−1.35418	−	0.111918i
$88$	0.0792818	−	2.01658i	0.00845147	−	0.214968i
$89$	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	$-0.230954\pi$
$90$	−2.69235	+	2.24322i	−0.283799	+	0.236456i
$91$	8.49623	−	0.260267i	0.890647	−	0.0272834i
$92$	7.78471	+	3.06663i	0.811612	+	0.319718i
$93$	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
$96$	9.79450	−	0.260429i	0.999647	−	0.0265799i
$97$	−13.8040			−1.40158			−0.700790	−	0.713368i	$-0.747169\pi$
$97$	−13.8040			−1.40158			−0.700790	+	0.713368i	$0.747169\pi$
$98$	−0.380402	+	2.00355i	−0.0384265	+	0.202389i
$99$	−1.65292	−	1.36009i	−0.166124	−	0.136695i
$100$	6.75828	−	5.37559i	0.675828	−	0.537559i
$101$	10.5504	−	6.09129i	1.04981	−	0.606106i	0.127211	−	0.991876i	$-0.459397\pi$
$101$	10.5504	−	6.09129i	1.04981	−	0.606106i	0.922595	+	0.385770i	$0.126064\pi$
$102$	−10.7615	−	2.97938i	−1.06555	−	0.295002i
$103$	−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	$0.933943\pi$
$104$	5.17541	−	8.78722i	0.507491	−	0.861657i
$105$	3.36138	+	0.277804i	0.328037	+	0.0271109i
$106$	6.40382	+	1.21586i	0.621994	+	0.118095i
$107$	5.20611	+	3.00575i	0.503293	+	0.290577i	0.730073	−	0.683370i	$-0.239486\pi$
$107$	5.20611	+	3.00575i	0.503293	+	0.290577i	−0.226779	+	0.973946i	$0.572820\pi$
$108$	6.06059	−	8.44211i	0.583180	−	0.812343i
$109$			5.73467i			0.549282i	0.961547	+	0.274641i	$0.0885590\pi$
$109$			5.73467i			0.549282i	−0.961547	+	0.274641i	$0.911441\pi$
$110$	−0.631414	−	0.544070i	−0.0602030	−	0.0518751i
$111$	2.96275	+	6.27470i	0.281212	+	0.595568i
$112$	−6.89655	−	6.43157i	−0.651663	−	0.607726i
$113$	−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	$0.981183\pi$
$114$	−0.480430	+	1.73531i	−0.0449964	+	0.162527i
$115$	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
$120$	2.43390	−	3.23272i	0.222184	−	0.295106i
$121$	−5.24544	+	9.08538i	−0.476859	+	0.825943i
$122$	−9.01619	−	1.71185i	−0.816287	−	0.154984i
$123$	4.95272	+	3.43256i	0.446572	+	0.309504i
$124$	1.17699	+	7.87630i	0.105697	+	0.707312i
$125$		−	7.69639i		−	0.688386i
$126$	−9.85621	+	1.70254i	−0.878061	+	0.151675i
$127$	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	$-0.0453074\pi$
$128$	−10.9410	+	2.87986i	−0.967061	+	0.254546i
$129$	−2.54667	+	3.67450i	−0.224222	+	0.323521i
$130$	−1.50964	−	3.93190i	−0.132404	−	0.344851i
$131$	10.8350	−	6.25559i	0.946658	−	0.546553i	0.0546171	−	0.998507i	$-0.482606\pi$
$131$	10.8350	−	6.25559i	0.946658	−	0.546553i	0.892041	+	0.451954i	$0.149273\pi$
$132$	2.21727	+	1.09226i	0.192989	+	0.0950689i
$133$	1.50082	−	0.866498i	0.130137	−	0.0751349i
$134$	−11.1380	−	2.11470i	−0.962174	−	0.182683i
$135$	−1.17053	−	4.12929i	−0.100743	−	0.355393i
$136$	12.8838	+	0.506527i	1.10478	+	0.0434343i
$137$	−2.79017			−0.238380			−0.119190	−	0.992871i	$-0.538030\pi$
$137$	−2.79017			−0.238380			−0.119190	+	0.992871i	$0.538030\pi$
$138$	−7.30581	+	7.18567i	−0.621912	+	0.611685i
$139$	−6.70761	−	3.87264i	−0.568932	−	0.328473i	0.187791	−	0.982209i	$-0.439867\pi$
$139$	−6.70761	−	3.87264i	−0.568932	−	0.328473i	−0.756723	+	0.653736i	$0.773201\pi$
$140$	−3.85185	+	0.575597i	−0.325540	+	0.0486468i
$141$	−0.225241	+	0.106353i	−0.0189687	+	0.00895652i
$142$	−3.19089	+	1.11428i	−0.267774	+	0.0935083i
$143$	2.18753	−	1.35393i	0.182931	−	0.113221i
$144$	−4.58271	+	11.0905i	−0.381893	+	0.924207i
$145$	3.02204	−	5.23433i	0.250967	−	0.434688i
$146$	−2.75900	+	14.5314i	−0.228336	+	1.20263i
$147$	−2.05284	−	1.42275i	−0.169315	−	0.117347i
$148$	−4.98778	−	6.27071i	−0.409993	−	0.515449i
$149$	7.06853	+	4.08102i	0.579077	+	0.334330i	0.760766	−	0.649026i	$-0.224823\pi$
$149$	7.06853	+	4.08102i	0.579077	+	0.334330i	−0.181690	+	0.983356i	$0.558157\pi$
$150$	2.65255	+	10.2382i	0.216580	+	0.835947i
$151$	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	$-0.0456426\pi$
$152$	0.0816784	−	2.07754i	0.00662499	−	0.168511i
$153$	8.68956	−	10.5604i	0.702509	−	0.853757i
$154$	−0.784288	−	2.24591i	−0.0631997	−	0.180981i
$155$	2.84836	+	1.64450i	0.228786	+	0.132090i
$156$	7.25815	+	10.1646i	0.581117	+	0.813820i
$157$	−19.0653	+	11.0073i	−1.52157	+	0.878481i	−0.521898	+	0.853008i	$0.674776\pi$
$157$	−19.0653	+	11.0073i	−1.52157	+	0.878481i	−0.999676	+	0.0254729i	$0.991891\pi$
$158$	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
$162$	6.43144	+	10.9835i	0.505302	+	0.862943i
$163$	−1.95082	+	1.12630i	−0.152800	+	0.0882189i	−0.574450	−	0.818539i	$-0.694784\pi$
$163$	−1.95082	+	1.12630i	−0.152800	+	0.0882189i	0.421651	+	0.906758i	$0.361451\pi$
$164$	−6.47395	−	2.55028i	−0.505530	−	0.199143i
$165$	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	$0.348679\pi$
$168$	10.6295	−	4.51722i	0.820083	−	0.348511i
$169$	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
$172$	1.89209	−	4.80312i	0.144271	−	0.366234i
$173$			9.95921i			0.757185i	0.925563	+	0.378592i	$0.123592\pi$
$173$			9.95921i			0.757185i	−0.925563	+	0.378592i	$0.876408\pi$
$174$	−4.78239	+	17.2740i	−0.362552	+	1.30954i
$175$	5.08960	−	8.81545i	0.384738	−	0.666386i
$176$	−2.78091	−	0.642120i	−0.209619	−	0.0484016i
$177$	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	0.421025	−	0.907049i	$-0.361670\pi$
$179$	−2.06025	−	1.18948i	−0.153990	−	0.0889062i	−0.575015	+	0.818143i	$0.695004\pi$
$180$	2.40648	+	4.33248i	0.179368	+	0.322924i
$181$			20.6555i			1.53531i	0.640861	+	0.767657i	$0.278577\pi$
$181$			20.6555i			1.53531i	−0.640861	+	0.767657i	$0.721423\pi$
$182$	1.87966	−	11.8733i	0.139330	−	0.880104i
$183$	6.40254	−	9.23799i	0.473290	−	0.682892i
$184$	6.31433	−	10.0070i	0.465498	−	0.737729i
$185$	−3.30912			−0.243292
$186$	−9.39997	−	2.60243i	−0.689239	−	0.190819i
$187$	2.81690	+	1.62634i	0.205992	+	0.118930i
$188$	0.225097	−	0.179044i	0.0164169	−	0.0130582i
$189$	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	$0.538194\pi$
$192$	2.22191	−	13.6771i	0.160353	−	0.987060i
$193$	2.69558			0.194032			0.0970162	−	0.995283i	$-0.469070\pi$
$193$	2.69558			0.194032			0.0970162	+	0.995283i	$0.469070\pi$
$194$	−3.64143	+	19.1791i	−0.261440	+	1.37698i
$195$	5.15140	+	0.267262i	0.368899	+	0.0191390i
$196$	2.68336	+	1.05706i	0.191669	+	0.0755040i
$197$	−11.2217	−	6.47885i	−0.799513	−	0.461599i	0.0437880	−	0.999041i	$-0.486057\pi$
$197$	−11.2217	−	6.47885i	−0.799513	−	0.461599i	−0.843301	+	0.537442i	$0.819391\pi$
$198$	−2.32574	+	1.93776i	−0.165283	+	0.137711i
$199$	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	$0.766499\pi$
$200$	−5.68600	−	10.8080i	−0.402061	−	0.764238i
$201$	7.90925	−	11.4120i	0.557876	−	0.804938i
$202$	−5.68003	−	16.2655i	−0.399645	−	1.14444i
$203$	14.9397	−	8.62546i	1.04856	−	0.605389i
$204$	−6.97837	+	14.1660i	−0.488584	+	0.991819i
$205$	−2.48869	+	1.43685i	−0.173818	+	0.100354i
$206$	−8.42385	+	2.94166i	−0.586918	+	0.204955i
$207$	−4.40570	−	11.7517i	−0.306217	−	0.816801i
$208$	−10.8436	−	9.50871i	−0.751871	−	0.659310i
$209$	0.262250	−	0.454230i	0.0181402	−	0.0314197i
$210$	1.27270	−	4.59699i	0.0878245	−	0.317222i
$211$		−	5.11613i		−	0.352209i	−0.984372	−	0.176104i	$-0.943650\pi$
$211$		−	5.11613i		−	0.352209i	0.984372	−	0.176104i	$-0.0563496\pi$
$212$	3.37861	−	8.57668i	0.232044	−	0.589049i
$213$	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
$216$	−10.1306	−	10.6475i	−0.689303	−	0.724473i
$217$	4.69370	+	8.12974i	0.318629	+	0.551882i
$218$	7.96771	+	1.51278i	0.539641	+	0.102459i
$219$	−14.8889	−	10.3190i	−1.00610	−	0.697293i
$220$	−0.922492	+	0.733758i	−0.0621944	+	0.0494700i
$221$	8.65018	+	13.9760i	0.581874	+	0.940129i
$222$	9.49959	−	2.46118i	0.637570	−	0.165184i
$223$	−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	$-0.348354\pi$
$224$	−10.7553	+	7.88540i	−0.718616	+	0.526865i
$225$	−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	$0.0501762\pi$
$227$			4.73032i			0.313962i	−0.987602	+	0.156981i	$0.949824\pi$
$228$	2.28430	+	1.12528i	0.151281	+	0.0745232i
$229$	−20.3569	+	11.7531i	−1.34522	+	0.776665i	−0.987568	−	0.157190i	$-0.949757\pi$
$229$	−20.3569	+	11.7531i	−1.34522	+	0.776665i	−0.357654	+	0.933854i	$0.616423\pi$
$230$	−1.61111	−	4.61363i	−0.106233	−	0.304214i
$231$	2.90366	+	0.239976i	0.191047	+	0.0157893i
$232$	0.813059	−	20.6806i	0.0533799	−	1.35775i
$233$	−9.63844			−0.631436			−0.315718	−	0.948853i	$-0.602245\pi$
$233$	−9.63844			−0.631436			−0.315718	+	0.948853i	$0.602245\pi$
$234$	−14.9870	+	3.06415i	−0.979733	+	0.200310i
$235$		−	0.118786i		−	0.00774877i
$236$	−18.7323	−	23.5506i	−1.21937	−	1.53301i
$237$	−21.6832	+	10.2382i	−1.40848	+	0.665045i
$238$	14.3490	−	5.01077i	0.930108	−	0.324800i
$239$	−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	$-0.336348\pi$
$240$	−3.84946	−	4.23443i	−0.248482	−	0.273331i
$241$	−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
$244$	−4.75687	+	12.0754i	−0.304528	+	0.773051i
$245$	1.03153	−	0.595554i	0.0659020	−	0.0380485i
$246$	6.07569	−	5.97577i	0.387372	−	0.381001i
$247$	2.25366	−	1.39486i	0.143397	−	0.0887526i
$248$	11.2538	+	0.442441i	0.714614	+	0.0280950i
$249$	7.43555	+	15.7475i	0.471209	+	0.997955i
$250$	−10.6933	−	2.03028i	−0.676304	−	0.128406i
$251$	−1.45865	+	0.842153i	−0.0920693	+	0.0531562i	−0.545328	−	0.838223i	$-0.683595\pi$
$251$	−1.45865	+	0.842153i	−0.0920693	+	0.0531562i	0.453258	+	0.891379i	$0.350261\pi$
$252$	−0.234530	+	14.1433i	−0.0147740	+	0.890942i
$253$	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
$256$	1.11505	+	15.9611i	0.0696904	+	0.997569i
$257$	−17.5621			−1.09550			−0.547748	−	0.836643i	$-0.684515\pi$
$257$	−17.5621			−1.09550			−0.547748	+	0.836643i	$0.684515\pi$
$258$	4.43352	+	4.50765i	0.276019	+	0.280634i
$259$	−8.17947	−	4.72242i	−0.508248	−	0.293437i
$260$	−5.86120	+	1.06026i	−0.363496	+	0.0657547i
$261$	−16.9512	−	13.9482i	−1.04925	−	0.863370i
$262$	−5.83324	−	16.7043i	−0.360379	−	1.03199i
$263$	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	$0.510969\pi$
$264$	2.10248	−	2.79253i	0.129399	−	0.171868i
$265$	−1.90353	−	3.29702i	−0.116933	−	0.202534i
$266$	−0.807995	−	2.31380i	−0.0495414	−	0.141868i
$267$	28.0362	−	13.2380i	1.71579	−	0.810152i
$268$	−5.87631	+	14.9172i	−0.358953	+	0.911210i
$269$	−5.91901	+	3.41734i	−0.360888	+	0.208359i	−0.669470	−	0.742839i	$-0.733479\pi$
$269$	−5.91901	+	3.41734i	−0.360888	+	0.208359i	0.308582	+	0.951198i	$0.400146\pi$
$270$	−6.04598	+	0.537029i	−0.367947	+	0.0326826i
$271$	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	$-0.0604498\pi$
$272$	4.10247	−	17.7670i	0.248749	−	1.07729i
$273$	12.3518	+	8.01213i	0.747564	+	0.484916i
$274$	−0.736035	+	3.87663i	−0.0444655	+	0.234196i
$275$		−	3.08079i		−	0.185779i
$276$	8.05647	+	12.0462i	0.484943	+	0.725096i
$277$			9.49422i			0.570452i	0.958460	+	0.285226i	$0.0920687\pi$
$277$			9.49422i			0.570452i	−0.958460	+	0.285226i	$0.907931\pi$
$278$	−7.15006	+	8.29791i	−0.428832	+	0.497676i
$279$	7.59016	−	9.22429i	0.454411	−	0.552244i
$280$	−0.216373	+	5.50357i	−0.0129307	+	0.328901i
$281$	−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	$0.270170\pi$
$282$	0.0883481	+	0.341003i	0.00526105	+	0.0203064i
$283$		−	15.0711i		−	0.895884i	−0.894063	−	0.447942i	$-0.852157\pi$
$283$		−	15.0711i		−	0.895884i	0.894063	−	0.447942i	$-0.147843\pi$
$284$	0.706426	+	4.72734i	0.0419187	+	0.280516i
$285$	0.950982	−	0.449029i	0.0563313	−	0.0265982i
$286$	−1.30408	−	3.39651i	−0.0771117	−	0.200840i
$287$	−8.20204			−0.484151
$288$	14.2001	+	9.29281i	0.836751	+	0.547584i
$289$	−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
$292$	19.4620	+	7.66666i	1.13893	+	0.448657i
$293$	8.58488	+	4.95648i	0.501534	+	0.289561i	0.729347	−	0.684144i	$-0.239824\pi$
$293$	8.58488	+	4.95648i	0.501534	+	0.289561i	−0.227813	+	0.973705i	$0.573157\pi$
$294$	−2.51829	+	2.47688i	−0.146870	+	0.144454i
$295$	−12.4279			−0.723580
$296$	−10.0282	+	5.27579i	−0.582879	+	0.306649i
$297$	−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
$300$	14.9246	−	0.984626i	0.861674	−	0.0568474i
$301$		−	6.08522i		−	0.350746i
$302$	−16.2883	−	14.0352i	−0.937288	−	0.807633i
$303$	21.0291	+	1.73798i	1.20809	+	0.0998441i
$304$	−2.86497	−	0.661530i	−0.164317	−	0.0379414i
$305$	2.68006	+	4.64200i	0.153460	+	0.265800i
$306$	−12.3803	−	14.8590i	−0.707732	−	0.849432i
$307$			11.6413i			0.664402i	0.943209	+	0.332201i	$0.107791\pi$
$307$			11.6413i			0.664402i	−0.943209	+	0.332201i	$0.892209\pi$
$308$	−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	$0.951018\pi$
$312$	16.0373	−	7.40303i	0.907934	−	0.419114i
$313$	−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	$0.230781\pi$
$314$	10.2642	+	29.3928i	0.579240	+	1.65873i
$315$	4.51107	+	3.71191i	0.254170	+	0.209143i
$316$	21.6694	−	17.2360i	1.21900	−	0.969603i
$317$	−26.6192	−	15.3686i	−1.49508	−	0.863187i	−0.495099	−	0.868836i	$-0.664868\pi$
$317$	−26.6192	−	15.3686i	−1.49508	−	0.863187i	−0.999984	+	0.00564972i	$0.998202\pi$
$318$	7.91670	+	8.04907i	0.443947	+	0.451369i
$319$	2.61054	−	4.52158i	0.146162	−	0.253160i
$320$	5.44560	+	3.74305i	0.304418	+	0.209243i
$321$	4.44571	+	9.41540i	0.248135	+	0.525517i
$322$	2.60174	−	13.7031i	0.144989	−	0.763646i
$323$	2.90205	+	1.67550i	0.161474	+	0.0932272i
$324$	16.9569	−	6.03840i	0.942052	−	0.335467i
$325$	7.36745	−	13.7141i	0.408673	−	0.760723i
$326$	1.05026	+	3.00756i	0.0581685	+	0.166573i
$327$	−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
$330$	−0.362068	−	1.39750i	−0.0199312	−	0.0769296i
$331$			27.6723i			1.52101i	0.649332	+	0.760505i	$0.275048\pi$
$331$			27.6723i			1.52101i	−0.649332	+	0.760505i	$0.724952\pi$
$332$	−12.5177	−	15.7374i	−0.686998	−	0.863705i
$333$	−1.97312	+	11.8556i	−0.108126	+	0.649685i
$334$	3.12049	−	16.4353i	0.170745	−	0.899302i
$335$	3.31076	+	5.73440i	0.180886	+	0.313304i
$336$	−3.47216	−	15.9602i	−0.189422	−	0.870698i
$337$	−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	$0.970953\pi$
$338$	2.31736	−	18.2381i	0.126048	−	0.992024i
$339$	−18.3240	+	8.65210i	−0.995221	+	0.469918i
$340$	−4.68794	−	5.89374i	−0.254239	−	0.319633i
$341$	2.46051	+	1.42057i	0.133244	+	0.0769284i
$342$	−2.39604	+	1.99634i	−0.129563	+	0.107950i
$343$	19.9024			1.07463
$344$	−6.17429	−	3.89590i	−0.332895	−	0.210053i
$345$	5.96481	+	0.492968i	0.321134	+	0.0265405i
$346$	13.8373	+	2.62720i	0.743895	+	0.141239i
$347$	−3.94116	−	2.27543i	−0.211573	−	0.122151i	0.390469	−	0.920616i	$-0.372313\pi$
$347$	−3.94116	−	2.27543i	−0.211573	−	0.122151i	−0.602042	+	0.798464i	$0.705646\pi$
$348$	22.7388	+	11.2014i	1.21893	+	0.600460i
$349$	23.6002	−	13.6256i	1.26329	−	0.729360i	0.289579	−	0.957154i	$-0.406485\pi$
$349$	23.6002	−	13.6256i	1.26329	−	0.729360i	0.973709	+	0.227794i	$0.0731514\pi$
$350$	−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	$0.795183\pi$
$354$	35.6771	−	9.24332i	1.89622	−	0.491277i
$355$	1.70958	+	0.987028i	0.0907352	+	0.0523860i
$356$	−28.0184	+	22.2861i	−1.48497	+	1.18116i
$357$	−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	$0.458471\pi$
$360$	6.65434	−	2.20065i	0.350714	−	0.115984i
$361$	−9.22982	+	15.9865i	−0.485780	+	0.841396i
$362$	28.6986	+	5.44885i	1.50837	+	0.286385i
$363$	−16.4312	+	7.75838i	−0.862414	+	0.407209i
$364$	−16.0008	−	5.74371i	−0.838668	−	0.301052i
$365$	7.48152	−	4.31946i	0.391600	−	0.226091i
$366$	−11.1462	−	11.3326i	−0.582623	−	0.592364i
$367$	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	$0.662974\pi$
$368$	−12.2380	−	11.4129i	−0.637951	−	0.594938i
$369$	3.66388	+	9.77301i	0.190734	+	0.508763i
$370$	−0.872935	+	4.59767i	−0.0453817	+	0.239022i
$371$		−	10.8661i		−	0.564138i
$372$	−6.09547	+	12.3737i	−0.316035	+	0.641548i
$373$	5.25090	+	3.03161i	0.271881	+	0.156971i	0.629742	−	0.776804i	$-0.283160\pi$
$373$	5.25090	+	3.03161i	0.271881	+	0.156971i	−0.357861	+	0.933775i	$0.616494\pi$
$374$	3.00271	−	3.48476i	0.155266	−	0.180192i
$375$	7.59349	−	10.9564i	0.392126	−	0.565784i
$376$	−0.189383	−	0.359980i	−0.00976669	−	0.0185645i
$377$	22.4338	−	13.8850i	1.15540	−	0.715112i
$378$	−15.7108	−	7.30074i	−0.808077	−	0.375510i
$379$	−21.0552	−	12.1562i	−1.08153	−	0.624424i	−0.150225	−	0.988652i	$-0.548000\pi$
$379$	−21.0552	−	12.1562i	−1.08153	−	0.624424i	−0.931310	+	0.364228i	$0.881333\pi$
$380$	−0.950377	+	0.755938i	−0.0487533	+	0.0387788i
$381$	21.8089	−	10.2976i	1.11730	−	0.527561i
$382$	−0.872807	+	4.59700i	−0.0446567	+	0.235203i
$383$	−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	$0.204137\pi$
$384$	−18.4167	−	6.69508i	−0.939825	−	0.341657i
$385$	−0.694721	+	1.20329i	−0.0354063	+	0.0613255i
$386$	0.711085	−	3.74522i	0.0361933	−	0.190627i
$387$	−7.25074	+	2.71829i	−0.368576	+	0.138179i
$388$	25.6867	+	10.1188i	1.30405	+	0.513702i
$389$	4.31934	+	2.49377i	0.218999	+	0.126439i	0.605487	−	0.795855i	$-0.292978\pi$
$389$	4.31934	+	2.49377i	0.218999	+	0.126439i	−0.386487	+	0.922295i	$0.626312\pi$
$390$	1.73025	−	7.08681i	0.0876147	−	0.358855i
$391$	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
$396$	2.07879	+	3.74254i	0.104463	+	0.188070i
$397$	−13.3910	+	7.73131i	−0.672076	+	0.388024i	−0.796863	−	0.604160i	$-0.793509\pi$
$397$	−13.3910	+	7.73131i	−0.672076	+	0.388024i	0.124786	+	0.992184i	$0.460175\pi$
$398$	7.85124	−	2.74170i	0.393547	−	0.137429i
$399$	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	$0.658828\pi$
$402$	−13.7693	−	13.9995i	−0.686749	−	0.698231i
$403$	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
$406$	−8.04310	−	23.0325i	−0.399172	−	1.14308i
$407$	−2.85853			−0.141692
$408$	17.8413	+	13.4326i	0.883275	+	0.665015i
$409$	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	$0.0652588\pi$
$410$	1.33984	+	3.83681i	0.0661698	+	0.189486i
$411$	−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
$414$	−17.4900	+	3.02119i	−0.859585	+	0.148483i
$415$	−8.30483			−0.407668
$416$	−16.0718	+	12.5577i	−0.787987	+	0.615692i
$417$	−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	$0.126819\pi$
$419$			15.8826i			0.775914i	−0.921677	+	0.387957i	$0.873181\pi$
$420$	−6.05129	−	2.98095i	−0.295273	−	0.145455i
$421$	−1.19901	−	0.692247i	−0.0584361	−	0.0337381i	0.470497	−	0.882401i	$-0.344075\pi$
$421$	−1.19901	−	0.692247i	−0.0584361	−	0.0337381i	−0.528933	+	0.848663i	$0.677408\pi$
$422$	−7.10831	−	1.34962i	−0.346027	−	0.0656983i
$423$	−0.425577	−	0.0708284i	−0.0206923	−	0.00344379i
$424$	−11.0251	−	6.95671i	−0.535427	−	0.337848i
$425$	19.6830			0.954764
$426$	−5.64185	−	1.56197i	−0.273348	−	0.0756778i
$427$			15.2988i			0.740359i
$428$	−7.48433	−	9.40941i	−0.361769	−	0.454821i
$429$	4.44994	+	0.230870i	0.214845	+	0.0111465i
$430$	−2.84658	+	0.994045i	−0.137274	+	0.0479371i
$431$	−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	$0.918274\pi$
$432$	−17.4660	+	11.2667i	−0.840335	+	0.542068i
$433$	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	$0.441863\pi$
$434$	12.5336	−	4.37680i	0.601631	−	0.210093i
$435$	9.46645	−	4.46981i	0.453882	−	0.214311i
$436$	4.20370	−	10.6712i	0.201321	−	0.511058i
$437$	2.66322	−	1.53761i	0.127399	−	0.0735539i
$438$	−18.2648	+	17.9644i	−0.872724	+	0.858372i
$439$	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	$0.639638\pi$
$440$	0.776128	+	1.47527i	0.0370005	+	0.0703305i
$441$	−1.51863	−	4.05078i	−0.0723158	−	0.192894i
$442$	21.7001	−	8.33167i	1.03217	−	0.396297i
$443$	30.7012	+	17.7254i	1.45866	+	0.842157i	0.998946	−	0.0459103i	$-0.0146188\pi$
$443$	30.7012	+	17.7254i	1.45866	+	0.842157i	0.459713	+	0.888067i	$0.347952\pi$
$444$	−0.913591	−	13.8479i	−0.0433571	−	0.657192i
$445$			14.7856i			0.700906i
$446$	−21.5448	+	7.52359i	−1.02018	+	0.356252i
$447$	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	$0.741487\pi$
$450$	−6.32524	+	17.1919i	−0.298175	+	0.810435i
$451$	−2.14981	+	1.24119i	−0.101231	+	0.0584456i
$452$	18.3123	−	14.5658i	0.861338	−	0.685116i
$453$	23.8123	−	11.2436i	1.11880	−	0.528268i
$454$	6.57227	+	1.24784i	0.308452	+	0.0585641i
$455$	−5.97013	+	3.69509i	−0.279884	+	0.173229i
$456$	2.16604	−	2.87694i	0.101434	−	0.134725i
$457$	−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	$0.864075\pi$
$458$	10.9595	+	31.3842i	0.512106	+	1.46649i
$459$	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	$0.177258\pi$
$461$			22.6963i			1.05707i	−0.848912	+	0.528535i	$0.822742\pi$
$462$	1.09940	−	3.97102i	0.0511486	−	0.184749i
$463$	−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	$0.911792\pi$
$464$	−28.5190	−	6.58513i	−1.32396	−	0.305707i
$465$	2.43233	+	5.15135i	0.112797	+	0.238888i
$466$	−2.54259	+	13.3916i	−0.117783	+	0.620353i
$467$			28.5529i			1.32127i	0.750706	+	0.660636i	$0.229713\pi$
$467$			28.5529i			1.32127i	−0.750706	+	0.660636i	$0.770287\pi$
$468$	0.303781	+	21.6312i	0.0140423	+	0.999901i
$469$			18.8990i			0.872675i
$470$	−0.165041	−	0.0313354i	−0.00761277	−	0.00144540i
$471$	−38.0010	−	3.14063i	−1.75099	−	0.144713i
$472$	−37.6625	+	19.8140i	−1.73356	+	0.912013i
$473$	−0.920861	−	1.59498i	−0.0423412	−	0.0733372i
$474$	8.50499	+	32.8273i	0.390647	+	1.50781i
$475$		−	3.17392i		−	0.145629i
$476$	−3.17670	−	21.2582i	−0.145604	−	0.974369i
$477$	−12.9473	+	4.85391i	−0.592815	+	0.222245i
$478$	−20.9785	+	7.32583i	−0.959534	+	0.335075i
$479$	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	$0.693001\pi$
$480$	−6.89875	+	4.23139i	−0.314884	+	0.193136i
$481$	−12.7247	−	6.83593i	−0.580198	−	0.311692i
$482$	−2.20396	+	11.6081i	−0.100388	+	0.528733i
$483$	14.0403	+	9.73083i	0.638854	+	0.442768i
$484$	16.4207	−	13.0612i	0.746397	−	0.593691i
$485$	9.87440	−	5.70099i	0.448374	−	0.258869i
$486$	−1.68100	+	21.9812i	−0.0762516	+	0.997089i
$487$	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
$490$	−0.555344	−	1.59030i	−0.0250879	−	0.0718426i
$491$		−	34.7450i		−	1.56802i	−0.620749	−	0.784009i	$-0.713171\pi$
$491$		−	34.7450i		−	1.56802i	0.620749	−	0.784009i	$-0.286829\pi$
$492$	−6.69995	−	10.0179i	−0.302057	−	0.451642i
$493$	28.8881	+	16.6786i	1.30106	+	0.751165i
$494$	−1.34350	−	3.49918i	−0.0604468	−	0.157435i
$495$	1.74410	+	0.290268i	0.0783914	+	0.0130466i
$496$	3.58342	−	15.5192i	0.160900	−	0.696831i
$497$	2.81716	+	4.87946i	0.126367	+	0.218874i
$498$	23.8409	−	6.17677i	1.06834	−	0.276788i
$499$	−17.6854	+	10.2107i	−0.791707	+	0.457093i	−0.840563	−	0.541713i	$-0.817776\pi$
$499$	−17.6854	+	10.2107i	−0.791707	+	0.457093i	0.0488559	+	0.998806i	$0.484443\pi$
$500$	−5.64171	+	14.3216i	−0.252305	+	0.640482i
$501$	16.8397	+	11.6710i	0.752341	+	0.521422i
$502$	0.785294	+	2.24880i	0.0350494	+	0.100369i
$503$	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	$0.833252\pi$
$504$	19.5887	+	4.05679i	0.872549	+	0.180704i
$505$	−5.03136	+	8.71458i	−0.223893	+	0.387794i
$506$	−1.39173	−	3.98540i	−0.0618699	−	0.177173i
$507$	19.2568	+	11.6694i	0.855226	+	0.518256i
$508$	−21.7950	+	17.3359i	−0.966996	+	0.769158i
$509$			3.93790i			0.174544i	0.996185	+	0.0872721i	$0.0278150\pi$
$509$			3.93790i			0.174544i	−0.996185	+	0.0872721i	$0.972185\pi$
$510$	8.92852	−	2.31323i	0.395361	−	0.102431i
$511$	24.6570			1.09076
$512$	22.4704	+	2.66124i	0.993060	+	0.117611i
$513$	−1.04170	−	3.67484i	−0.0459923	−	0.162248i
$514$	−4.63283	+	24.4007i	−0.204345	+	1.07627i
$515$	4.51324	+	2.60572i	0.198877	+	0.114822i
$516$	7.43243	−	4.97080i	0.327195	−	0.218827i
$517$		−	0.102612i		−	0.00451285i
$518$	−8.71901	+	10.1187i	−0.383091	+	0.444592i
$519$	−9.82606	+	14.1777i	−0.431316	+	0.622330i
$520$	−0.0730403	+	8.42320i	−0.00320303	+	0.369382i
$521$	19.6482			0.860804			0.430402	−	0.902637i	$-0.358372\pi$
$521$	19.6482			0.860804			0.430402	+	0.902637i	$0.358372\pi$
$522$	−23.8511	+	19.8723i	−1.04394	+	0.869789i
$523$	−15.8740	−	9.16486i	−0.694122	−	0.400751i	0.111033	−	0.993817i	$-0.464584\pi$
$523$	−15.8740	−	9.16486i	−0.694122	−	0.400751i	−0.805154	+	0.593065i	$0.797918\pi$
$524$	−24.7476	+	3.69813i	−1.08110	+	0.161554i
$525$	15.9430	−	7.52788i	0.695810	−	0.328544i
$526$	36.7349	−	12.8281i	1.60172	−	0.559330i
$527$	−9.07596	+	15.7200i	−0.395355	+	0.684775i
$528$	−3.32529	−	3.65783i	−0.144715	−	0.159187i
$529$	−5.49853			−0.239067
$530$	−5.08300	+	1.77502i	−0.220791	+	0.0771017i
$531$	−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
$534$	−10.9969	−	42.4455i	−0.475882	−	1.83680i
$535$	−4.96545			−0.214675
$536$	19.1756	+	12.0996i	0.828261	+	0.522623i
$537$	−1.75933	−	3.72602i	−0.0759207	−	0.160790i
$538$	3.18661	+	9.12531i	0.137385	+	0.393420i
$539$	0.891069	−	0.514459i	0.0383810	−	0.0221593i
$540$	−0.848764	+	8.54191i	−0.0365250	+	0.367585i
$541$			3.83563i			0.164907i	0.996595	+	0.0824534i	$0.0262756\pi$
$541$			3.83563i			0.164907i	−0.996595	+	0.0824534i	$0.973724\pi$
$542$	−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
$546$	14.3903	−	15.0479i	0.615850	−	0.643991i
$547$	−27.6062	−	15.9385i	−1.18036	−	0.681479i	−0.224260	−	0.974529i	$-0.571996\pi$
$547$	−27.6062	−	15.9385i	−1.18036	−	0.681479i	−0.956097	+	0.293050i	$0.905330\pi$
$548$	5.19200	+	2.04528i	0.221791	+	0.0873702i
$549$	18.2290	−	6.83401i	0.777994	−	0.291669i
$550$	−4.28042	−	0.812701i	−0.182518	−	0.0346537i
$551$	2.68945	−	4.65826i	0.114574	−	0.198449i
$552$	18.8622	−	8.01586i	0.802827	−	0.341178i
$553$	16.3190	−	28.2654i	0.693957	−	1.20197i
$554$	13.1912	+	2.50454i	0.560440	+	0.106408i
$555$	−4.71078	−	3.26488i	−0.199961	−	0.138587i
$556$	9.64289	+	12.1232i	0.408950	+	0.514138i
$557$	25.3885	+	14.6580i	1.07574	+	0.621081i	0.929745	−	0.368203i	$-0.120027\pi$
$557$	25.3885	+	14.6580i	1.07574	+	0.621081i	0.145999	+	0.989285i	$0.453360\pi$
$558$	−10.8139	−	12.9790i	−0.457789	−	0.549447i
$559$	−0.284957	−	9.30221i	−0.0120524	−	0.393442i
$560$	7.58954	+	1.75245i	0.320716	+	0.0740544i
$561$	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	−0.117999	−	0.993014i	$-0.537648\pi$
$563$	−24.6049	−	14.2056i	−1.03697	−	0.598697i	−0.918974	+	0.394317i	$0.870981\pi$
$564$	0.497093	−	0.0327948i	0.0209314	−	0.00138091i
$565$		−	9.66361i		−	0.406551i
$566$	−20.9397	−	3.97570i	−0.880160	−	0.167111i
$567$	15.9885	−	13.9486i	0.671454	−	0.585785i
$568$	6.75449	+	0.265553i	0.283412	+	0.0111423i
$569$	−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	$-0.487309\pi$
$570$	−0.373012	−	1.43974i	−0.0156238	−	0.0603041i
$571$	6.34043	−	3.66065i	0.265339	−	0.153193i	−0.361429	−	0.932400i	$-0.617711\pi$
$571$	6.34043	−	3.66065i	0.265339	−	0.153193i	0.626767	+	0.779206i	$0.284378\pi$
$572$	−5.06309	+	0.915889i	−0.211698	+	0.0382953i
$573$	−4.71009	−	3.26441i	−0.196767	−	0.136373i
$574$	−2.16367	+	11.3959i	−0.0903098	+	0.475654i
$575$	9.03157	−	15.6431i	0.376642	−	0.652364i
$576$	16.6573	−	17.2781i	0.694054	−	0.719923i
$577$	−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
$580$	−9.46043	+	7.52491i	−0.392823	+	0.312455i
$581$	−20.5278	−	11.8517i	−0.851638	−	0.491693i
$582$	−24.1065	+	23.7101i	−0.999249	+	0.982816i
$583$	−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	−0.734881	−	0.678196i	$-0.762762\pi$
$587$	−12.4771	+	7.20368i	−0.514987	+	0.297328i	0.219894	+	0.975524i	$0.429429\pi$
$588$	2.77704	+	4.15229i	0.114523	+	0.171237i
$589$	2.53488	+	1.46351i	0.104448	+	0.0603031i
$590$	−3.27843	+	17.2672i	−0.134971	+	0.710881i
$591$	−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	$0.608381\pi$
$594$	−5.22271	+	0.463903i	−0.214291	+	0.0190342i
$595$	−7.68776	−	4.43853i	−0.315168	−	0.181962i
$596$	−10.1618	−	12.7755i	−0.416242	−	0.523306i
$597$	−0.838906	+	10.1506i	−0.0343342	+	0.415436i
$598$	3.33548	−	21.0692i	0.136398	−	0.861585i
$599$	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	$0.755826\pi$
$600$	2.56903	−	20.9959i	0.104880	−	0.857154i
$601$	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	$0.573164\pi$
$602$	−8.45476	−	1.60526i	−0.344590	−	0.0654255i
$603$	22.5188	−	8.44226i	0.917036	−	0.343795i
$604$	−23.7971	+	18.9285i	−0.968292	+	0.770188i
$605$		−	8.66541i		−	0.352299i
$606$	7.96214	−	28.7593i	0.323440	−	1.16827i
$607$	−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
$610$	7.15655	−	2.49911i	0.289760	−	0.101186i
$611$	0.245387	−	0.456775i	0.00992729	−	0.0184792i
$612$	−23.9108	+	13.2813i	−0.966539	+	0.536864i
$613$	0.499668	+	0.288483i	0.0201814	+	0.0116517i	0.510057	−	0.860141i	$-0.329624\pi$
$613$	0.499668	+	0.288483i	0.0201814	+	0.0116517i	−0.489875	+	0.871792i	$0.662958\pi$
$614$	16.1743	+	3.07092i	0.652741	+	0.123932i
$615$	−4.96047	−	0.409964i	−0.200026	−	0.0165313i
$616$	−0.186910	+	4.75416i	−0.00753080	+	0.191550i
$617$	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	$-0.152287\pi$
$618$	−14.8943	−	4.12356i	−0.599137	−	0.165874i
$619$	40.0034	+	23.0960i	1.60787	+	0.928305i	0.989846	+	0.142147i	$0.0454004\pi$
$619$	40.0034	+	23.0960i	1.60787	+	0.928305i	0.618025	+	0.786158i	$0.287933\pi$
$620$	−4.09482	−	5.14807i	−0.164452	−	0.206751i
$621$	5.32278	−	21.0762i	0.213596	−	0.845760i
$622$	−17.0165	+	5.94228i	−0.682301	+	0.238264i
$623$	−21.1004	+	36.5470i	−0.845371	+	1.46423i
$624$	−6.05512	−	24.2350i	−0.242399	−	0.970177i
$625$	−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
$630$	6.34731	−	5.28846i	0.252883	−	0.210697i
$631$	−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	$0.864728\pi$
$632$	−18.2313	−	34.6541i	−0.725202	−	1.37847i
$633$	5.04773	−	7.28318i	0.200629	−	0.289480i
$634$	−28.3751	+	32.9303i	−1.12692	+	1.30783i
$635$			11.5015i			0.456422i
$636$	13.2717	−	8.87609i	0.526258	−	0.351960i
$637$	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
$640$	6.63710	−	6.57867i	0.262354	−	0.260045i
$641$	−14.1088			−0.557263			−0.278631	−	0.960398i	$-0.589881\pi$
$641$	−14.1088			−0.557263			−0.278631	+	0.960398i	$0.589881\pi$
$642$	14.2545	−	3.69309i	0.562578	−	0.145755i
$643$	−15.1607	−	8.75304i	−0.597880	−	0.345186i	0.170327	−	0.985388i	$-0.445518\pi$
$643$	−15.1607	−	8.75304i	−0.597880	−	0.345186i	−0.768207	+	0.640201i	$0.778851\pi$
$644$	−18.3527	−	7.22968i	−0.723198	−	0.284889i
$645$	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	$0.127364\pi$
$648$	−3.91653	−	25.1527i	−0.153856	−	0.988093i
$649$	−10.7356			−0.421410
$650$	−17.1108	−	13.8540i	−0.671141	−	0.543399i
$651$	−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	$-0.928711\pi$
$653$		−	11.3507i		−	0.444187i	0.975025	−	0.222093i	$-0.0712890\pi$
$654$	9.85005	+	10.0147i	0.385167	+	0.391607i
$655$	−5.16708	+	8.94964i	−0.201894	+	0.349691i
$656$	10.1774	+	9.49124i	0.397362	+	0.370571i
$657$	−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	$-0.632232\pi$
$659$		−	46.9752i		−	1.82990i	0.403572	−	0.914948i	$-0.367768\pi$
$660$	−2.03718	+	0.134400i	−0.0792972	+	0.00523149i
$661$			39.1430i			1.52248i	0.648468	+	0.761242i	$0.275410\pi$
$661$			39.1430i			1.52248i	−0.648468	+	0.761242i	$0.724590\pi$
$662$	38.4477	+	7.29986i	1.49431	+	0.283717i
$663$	−1.47501	+	28.4304i	−0.0572847	+	1.10415i
$664$	−25.1676	+	13.2405i	−0.976693	+	0.513832i
$665$	−0.715721	+	1.23967i	−0.0277545	+	0.0480722i
$666$	15.9516	+	5.86891i	0.618113	+	0.227416i
$667$	26.5107	−	15.3060i	1.02650	−	0.592650i
$668$	−22.0120	−	8.67116i	−0.851669	−	0.335497i
$669$	2.30207	−	27.8546i	0.0890032	−	1.07692i
$670$	8.84070	−	3.08723i	0.341546	−	0.119270i
$671$	2.31512	+	4.00991i	0.0893743	+	0.154801i
$672$	−23.0909	+	0.613969i	−0.890749	+	0.0236844i
$673$	−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	$0.979240\pi$
$674$	−20.5394	+	7.17249i	−0.791148	+	0.276274i
$675$	−16.0915	−	15.6339i	−0.619363	−	0.601750i
$676$	−24.7286	−	8.03088i	−0.951101	−	0.308880i
$677$	1.97526	+	1.14042i	0.0759155	+	0.0438298i	0.537477	−	0.843278i	$-0.319377\pi$
$677$	1.97526	+	1.14042i	0.0759155	+	0.0438298i	−0.461562	+	0.887108i	$0.652711\pi$
$678$	7.18737	+	27.7416i	0.276029	+	1.06541i
$679$	32.5433			1.24890
$680$	−9.42539	+	4.95864i	−0.361447	+	0.190155i
$681$	−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	$-0.282342\pi$
$683$	42.3096	−	24.4275i	1.61893	−	0.934691i	0.987197	−	0.159508i	$-0.0509909\pi$
$684$	2.14163	+	3.85567i	0.0818873	+	0.147425i
$685$	1.99589	−	1.15233i	0.0762591	−	0.0440282i
$686$	5.25017	−	27.6522i	0.200453	−	1.05577i
$687$	−40.5755	−	3.35340i	−1.54805	−	0.127940i
$688$	−7.04169	+	7.55079i	−0.268462	+	0.287871i
$689$	−0.508832	−	16.6105i	−0.0193850	−	0.632809i
$690$	2.25842	−	8.15741i	0.0859766	−	0.310547i
$691$	−30.1544	+	17.4097i	−1.14713	+	0.662295i	−0.948186	−	0.317716i	$-0.897084\pi$
$691$	−30.1544	+	17.4097i	−1.14713	+	0.662295i	−0.198943	+	0.980011i	$0.563751\pi$
$692$	7.30043	−	18.5323i	0.277521	−	0.704494i
$693$	3.89681	+	3.20647i	0.148028	+	0.121804i
$694$	−4.20113	+	4.87557i	−0.159473	+	0.185074i
$695$	6.39755			0.242673
$696$	21.5616	−	28.6382i	0.817290	−	1.08553i
$697$	−7.92992	−	13.7350i	−0.300367	−	0.520251i
$698$	−12.7056	−	36.3843i	−0.480915	−	1.37717i
$699$	−13.7210	−	9.50959i	−0.518977	−	0.359686i
$700$	−15.9329	+	12.6731i	−0.602206	+	0.479000i
$701$			28.3660i			1.07137i	0.844418	+	0.535685i	$0.179947\pi$
$701$			28.3660i			1.07137i	−0.844418	+	0.535685i	$0.820053\pi$
$702$	−24.3583	−	10.4246i	−0.919345	−	0.393452i
$703$	−2.94494			−0.111070
$704$	4.70408	+	3.23337i	0.177292	+	0.121862i
$705$	0.117198	−	0.169101i	0.00441394	−	0.00636872i
$706$	5.99873	−	2.09479i	0.225765	−	0.0788386i
$707$	−24.8730	+	14.3604i	−0.935445	+	0.540079i
$708$	−3.43112	−	52.0078i	−0.128950	−	1.95457i
$709$			19.7528i			0.741834i	0.928666	+	0.370917i	$0.120957\pi$
$709$			19.7528i			0.741834i	−0.928666	+	0.370917i	$0.879043\pi$
$710$	1.82235	−	2.11491i	0.0683916	−	0.0793710i
$711$	−40.9690	−	6.81842i	−1.53646	−	0.255711i
$712$	23.5730	+	44.8075i	0.883434	+	1.67923i
$713$	8.32904	+	14.4263i	0.311925	+	0.540270i
$714$	25.3706	+	7.02398i	0.949472	+	0.262866i
$715$	−1.00564	+	1.87195i	−0.0376089	+	0.0700071i
$716$	2.96182	+	3.72365i	0.110688	+	0.139159i
$717$	2.24156	−	27.1224i	0.0837125	−	1.01290i
$718$	1.30050	−	6.84963i	0.0485343	−	0.255626i
$719$	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	$0.581927\pi$
$720$	−1.30218	−	9.82601i	−0.0485292	−	0.366194i
$721$	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
$724$	15.1412	−	38.4363i	0.562718	−	1.42847i
$725$		−	31.5944i		−	1.17339i
$726$	6.44495	+	24.8760i	0.239194	+	0.923235i
$727$	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	$-0.00785195\pi$
$728$	−12.2012	+	20.7162i	−0.452207	+	0.767792i
$729$	−23.7623	−	12.8200i	−0.880087	−	0.474813i
$730$	−4.02782	−	11.5342i	−0.149076	−	0.426901i
$731$	10.1902	−	5.88333i	0.376899	−	0.217603i
$732$	−18.6858	+	12.4970i	−0.690646	+	0.461902i
$733$	18.0106	−	10.3984i	0.665236	−	0.384074i	−0.129033	−	0.991640i	$-0.541187\pi$
$733$	18.0106	−	10.3984i	0.665236	−	0.384074i	0.794269	+	0.607566i	$0.207854\pi$
$734$	26.0900	−	9.11078i	0.962999	−	0.336285i
$735$	2.05605	+	0.169924i	0.0758385	+	0.00626776i
$736$	−19.0853	+	13.9927i	−0.703495	+	0.515779i
$737$	2.85994	+	4.95356i	0.105347	+	0.182467i
$738$	14.5451	−	2.51249i	0.535411	−	0.0924860i
$739$	1.23322	+	0.711998i	0.0453646	+	0.0261913i	0.522511	−	0.852633i	$-0.324995\pi$
$739$	1.23322	+	0.711998i	0.0453646	+	0.0261913i	−0.477146	+	0.878824i	$0.658329\pi$
$740$	6.15769	+	2.42570i	0.226361	+	0.0891704i
$741$	4.58446	+	0.237848i	0.168414	+	0.00873758i
$742$	−15.0972	−	2.86643i	−0.554237	−	0.105230i
$743$	−3.48296			−0.127777			−0.0638886	−	0.997957i	$-0.520350\pi$
$743$	−3.48296			−0.127777			−0.0638886	+	0.997957i	$0.520350\pi$
$744$	15.5840	+	11.7331i	0.571338	+	0.430158i
$745$	−6.74179			−0.247000
$746$	5.59727	−	6.49584i	0.204930	−	0.237830i
$747$	−4.95189	+	29.7538i	−0.181180	+	1.08864i
$748$	−4.04959	−	5.09121i	−0.148068	−	0.186153i
$749$	−12.2736	−	7.08615i	−0.448467	−	0.258922i
$750$	−13.2196	−	13.4406i	−0.482710	−	0.490781i
$751$	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
$754$	−13.3737	−	34.8322i	−0.487041	−	1.26851i
$755$			12.5580i			0.457033i
$756$	−14.2880	+	19.9026i	−0.519651	+	0.723850i
$757$	−38.9868	−	22.5090i	−1.41700	−	0.818104i	−0.420964	−	0.907077i	$-0.638308\pi$
$757$	−38.9868	−	22.5090i	−1.41700	−	0.818104i	−0.996034	+	0.0889732i	$0.971641\pi$
$758$	−22.4441	+	26.0472i	−0.815206	+	0.946077i
$759$	5.15259	+	0.425841i	0.187027	+	0.0154571i
$760$	0.799589	+	1.51986i	0.0290041	+	0.0551311i
$761$	−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	$0.858596\pi$
$762$	−8.55429	−	33.0175i	−0.309889	−	1.19610i
$763$		−	13.5197i		−	0.489445i
$764$	6.15679	+	2.42534i	0.222745	+	0.0877459i
$765$	−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
$768$	−14.1604	+	23.8219i	−0.510968	+	0.859600i
$769$	−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
$772$	−5.01600	−	1.97595i	−0.180530	−	0.0711161i
$773$	13.4159	−	7.74567i	0.482536	−	0.278592i	−0.238937	−	0.971035i	$-0.576799\pi$
$773$	13.4159	−	7.74567i	0.482536	−	0.278592i	0.721473	+	0.692443i	$0.243465\pi$
$774$	1.86405	+	10.7912i	0.0670020	+	0.387882i
$775$	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
$780$	−9.38993	−	4.27347i	−0.336213	−	0.153015i
$781$	1.47679	+	0.852626i	0.0528438	+	0.0305094i
$782$	25.4625	−	8.89167i	0.910537	−	0.317965i
$783$	−10.3695	−	36.5808i	−0.370576	−	1.30729i
$784$	−4.21841	−	3.93399i	−0.150657	−	0.140500i
$785$	9.09198	−	15.7478i	0.324507	−	0.562062i
$786$	8.17691	−	29.5350i	0.291661	−	1.05348i
$787$	−23.5205	−	13.5796i	−0.838415	−	0.484059i	0.0183104	−	0.999832i	$-0.494171\pi$
$787$	−23.5205	−	13.5796i	−0.838415	−	0.484059i	−0.856725	+	0.515773i	$0.827505\pi$
$788$	16.1324	+	20.2819i	0.574692	+	0.722512i
$789$	−3.92513	+	47.4932i	−0.139738	+	1.69080i
$790$	−15.8880	−	3.01656i	−0.565268	−	0.107324i
$791$	13.7908	−	23.8864i	0.490346	−	0.849304i
$792$	5.74823	−	1.90099i	0.204255	−	0.0675488i
$793$	0.716405	+	23.3865i	0.0254403	+	0.830480i
$794$	7.20933	+	20.6449i	0.255849	+	0.732660i
$795$	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	0.146114	−	0.989268i	$-0.453323\pi$
$797$	−17.9991	−	10.3918i	−0.637560	−	0.368095i	−0.783674	+	0.621172i	$0.786657\pi$
$798$	1.13263	−	4.09106i	0.0400947	−	0.144822i
$799$	0.655579			0.0231927
$800$	2.65805	+	24.2797i	0.0939761	+	0.858418i
$801$	52.9726	+	8.81618i	1.87170	+	0.311504i
$802$	−5.05562	+	26.6275i	−0.178520	+	0.940250i
$803$	6.46277	−	3.73128i	0.228066	−	0.131674i
$804$	−23.0831	+	15.4379i	−0.814077	+	0.544453i
$805$	−7.05509	+	4.07326i	−0.248659	+	0.143563i
$806$	18.9546	−	7.27755i	0.667647	−	0.256341i
$807$	−11.7978	−	0.975041i	−0.415302	−	0.0343231i
$808$	−1.35365	+	34.4309i	−0.0476213	+	1.21128i
$809$	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	$-0.102521\pi$
$810$	−9.13675	−	5.20065i	−0.321033	−	0.182732i
$811$		−	35.1214i		−	1.23328i	−0.787245	−	0.616640i	$-0.788493\pi$
$811$		−	35.1214i		−	1.23328i	0.787245	−	0.616640i	$-0.211507\pi$
$812$	−34.1229	+	5.09913i	−1.19748	+	0.178944i
$813$	33.7500	−	15.9359i	1.18366	−	0.558896i
$814$	−0.754069	+	3.97162i	−0.0264301	+	0.139205i
$815$	0.930319	−	1.61136i	0.0325877	−	0.0564435i
$816$	23.3697	−	21.2451i	0.818102	−	0.743726i
$817$	−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	−0.714743	−	0.699387i	$-0.753457\pi$
$821$	−13.3646	+	7.71607i	−0.466428	+	0.269293i	0.248315	+	0.968679i	$0.420123\pi$
$822$	−4.87261	+	4.79248i	−0.169952	+	0.167157i
$823$	−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	$0.827129\pi$
$824$	17.8316	+	0.701051i	0.621194	+	0.0244223i
$825$	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	$0.138100\pi$
$827$			24.1777i			0.840742i	−0.907352	+	0.420371i	$0.861900\pi$
$828$	−0.416176	+	25.0974i	−0.0144631	+	0.872195i
$829$	−19.3485	−	11.1708i	−0.672000	−	0.387979i	0.124834	−	0.992178i	$-0.460160\pi$
$829$	−19.3485	−	11.1708i	−0.672000	−	0.387979i	−0.796834	+	0.604198i	$0.793493\pi$
$830$	−2.19078	+	11.5387i	−0.0760432	+	0.400513i
$831$	−9.36729	+	13.5157i	−0.324948	+	0.468855i
$832$	13.2079	+	25.6428i	0.457901	+	0.889003i
$833$	3.28685	+	5.69298i	0.113882	+	0.197250i
$834$	−18.3656	+	4.75821i	−0.635949	+	0.164763i
$835$	−8.46176	+	4.88540i	−0.292831	+	0.169066i
$836$	−0.820966	+	0.653004i	−0.0283937	+	0.0225846i
$837$	19.9061	−	5.64277i	0.688056	−	0.195043i
$838$	22.0671	+	4.18976i	0.762296	+	0.144733i
$839$	54.9500			1.89708			0.948542	−	0.316651i	$-0.102558\pi$
$839$	54.9500			1.89708			0.948542	+	0.316651i	$0.102558\pi$
$840$	−5.73801	+	7.62125i	−0.197980	+	0.262958i
$841$	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
$844$	−3.75029	+	9.52021i	−0.129090	+	0.327699i
$845$	−8.95324	+	5.92809i	−0.308001	+	0.203933i
$846$	−0.210674	+	0.572610i	−0.00724313	+	0.0196867i
$847$	12.3663	−	21.4191i	0.424912	−	0.735969i
$848$	−12.5740	+	13.4831i	−0.431792	+	0.463010i
$849$	14.8696	−	21.4548i	0.510324	−	0.736327i
$850$	5.19230	−	27.3474i	0.178094	−	0.938007i
$851$	−14.5146	−	8.37999i	−0.497553	−	0.287263i
$852$	−3.65849	+	7.42670i	−0.125338	+	0.254435i
$853$	−38.8568	−	22.4340i	−1.33043	−	0.768124i	−0.345065	−	0.938579i	$-0.612143\pi$
$853$	−38.8568	−	22.4340i	−1.33043	−	0.768124i	−0.985365	+	0.170455i	$0.945476\pi$
$854$	21.2560	+	4.03575i	0.727364	+	0.138101i
$855$	1.79682	+	0.299043i	0.0614499	+	0.0102270i
$856$	−15.0477	+	7.91650i	−0.514320	+	0.270581i
$857$	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	$0.124608\pi$
$858$	1.49465	−	6.12182i	0.0510264	−	0.208995i
$859$	−10.1480	+	5.85897i	−0.346246	+	0.199905i	−0.663031	−	0.748592i	$-0.730730\pi$
$859$	−10.1480	+	5.85897i	−0.346246	+	0.199905i	0.316784	+	0.948498i	$0.397397\pi$
$860$	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	$0.240860\pi$
$864$	11.0463	+	27.2393i	0.375804	+	0.926699i
$865$	−4.11312	−	7.12414i	−0.139850	−	0.242228i
$866$	52.3666	−	18.2868i	1.77949	−	0.621409i
$867$	−5.92215	+	2.79628i	−0.201127	+	0.0949668i
$868$	−2.77479	−	18.5686i	−0.0941824	−	0.630261i
$869$		−	9.87808i		−	0.335091i
$870$	−3.71311	−	14.3317i	−0.125886	−	0.485891i
$871$	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
$874$	−1.43380	−	4.10588i	−0.0484989	−	0.138883i
$875$			18.1445i			0.613396i
$876$	20.1414	+	30.1159i	0.680515	+	1.01752i
$877$	23.2295	+	13.4116i	0.784406	+	0.452877i	0.837989	−	0.545687i	$-0.183731\pi$
$877$	23.2295	+	13.4116i	0.784406	+	0.452877i	−0.0535838	+	0.998563i	$0.517064\pi$
$878$	31.9830	−	11.1687i	1.07937	−	0.376924i
$879$	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	$-0.272218\pi$
$882$	−6.02874	+	1.04139i	−0.202998	+	0.0350655i
$883$			14.0915i			0.474216i	0.971483	+	0.237108i	$0.0761995\pi$
$883$			14.0915i			0.474216i	−0.971483	+	0.237108i	$0.923800\pi$
$884$	−5.85156	−	32.3478i	−0.196809	−	1.08797i
$885$	−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	$0.595637\pi$
$888$	−19.4812	−	2.38369i	−0.653745	−	0.0799914i
$889$	−16.4136	+	28.4292i	−0.550496	+	0.953486i
$890$	20.5430	+	3.90039i	0.688604	+	0.130742i
$891$	2.07989	−	6.07552i	0.0696791	−	0.203538i
$892$	4.76977	+	31.9189i	0.159704	+	1.06872i
$893$		−	0.105713i		−	0.00353756i
$894$	19.3538	−	5.01425i	0.647289	−	0.167702i
$895$	1.96501			0.0656831
$896$	25.7939	−	6.78936i	0.861713	−	0.226817i
$897$	21.9184	+	14.2176i	0.731834	+	0.474713i
$898$	16.1009	−	5.62253i	0.537293	−	0.187626i
$899$	25.2332	+	14.5684i	0.841575	+	0.485883i
$900$	22.2178	+	13.3234i	0.740592	+	0.444114i
$901$	18.1961	−	10.5056i	0.606202	−	0.349991i
$902$	1.15739	+	3.31436i	0.0385370	+	0.110356i
$903$	6.00387	−	8.66276i	0.199796	−	0.288278i
$904$	−15.4068	−	29.2854i	−0.512424	−	0.974017i
$905$	−8.53066	−	14.7755i	−0.283569	−	0.491156i
$906$	−9.34011	−	36.0506i	−0.310304	−	1.19770i
$907$	−8.72926	+	5.03984i	−0.289850	+	0.167345i	−0.637874	−	0.770141i	$-0.720186\pi$
$907$	−8.72926	+	5.03984i	−0.289850	+	0.167345i	0.348024	+	0.937486i	$0.386853\pi$
$908$	3.46748	−	8.80229i	0.115072	−	0.292114i
$909$	28.2218	+	23.2221i	0.936058	+	0.770230i
$910$	3.55903	+	9.26960i	0.117981	+	0.307284i
$911$	−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	$0.908191\pi$
$912$	−3.42581	−	3.76840i	−0.113440	−	0.124784i
$913$	−7.17398			−0.237424
$914$	−5.50450	+	1.92221i	−0.182073	+	0.0635810i
$915$	−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
$918$	−2.96385	−	33.3676i	−0.0978216	−	1.10130i
$919$	−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	$-0.558234\pi$
$920$	−0.383956	+	9.76615i	−0.0126587	+	0.321980i
$921$	−11.4856	+	16.5722i	−0.378464	+	0.546072i
$922$	31.5340	+	5.98719i	1.03852	+	0.197178i
$923$	4.53496	+	7.32709i	0.149270	+	0.241174i
$924$	−5.22730	−	2.57504i	−0.171965	−	0.0847125i
$925$	−14.9804	+	8.64893i	−0.492552	+	0.284375i
$926$	−14.0196	+	4.89573i	−0.460713	+	0.160884i
$927$	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	$0.584660\pi$
$930$	7.79888	−	2.02056i	0.255735	−	0.0662567i
$931$	0.918004	−	0.530010i	0.0300864	−	0.0173704i
$932$	17.9354	+	7.06530i	0.587495	+	0.231432i
$933$	1.81822	−	22.0001i	0.0595259	−	0.720251i
$934$	39.6712	+	7.53216i	1.29808	+	0.246460i
$935$	−2.68669			−0.0878641
$936$	30.1343	+	5.28415i	0.984971	+	0.172718i
$937$	40.0275			1.30764			0.653822	−	0.756649i	$-0.273165\pi$
$937$	40.0275			1.30764			0.653822	+	0.756649i	$0.273165\pi$
$938$	26.2581	+	4.98549i	0.857359	+	0.162782i
$939$	−11.0872	+	5.23510i	−0.361818	+	0.170841i
$940$	−0.0870744	+	0.221040i	−0.00284005	+	0.00720955i
$941$	−5.08240	+	2.93432i	−0.165681	+	0.0956562i	−0.580548	−	0.814226i	$-0.697162\pi$
$941$	−5.08240	+	2.93432i	−0.165681	+	0.0956562i	0.414867	+	0.909882i	$0.363828\pi$
$942$	−14.3881	+	51.9698i	−0.468789	+	1.69327i
$943$	−14.5546			−0.473964
$944$	17.5942	+	57.5548i	0.572642	+	1.87325i
$945$	2.75956	+	9.73494i	0.0897684	+	0.316678i
$946$	−2.45897	+	0.858688i	−0.0799480	+	0.0279184i
$947$	−31.9917	+	18.4704i	−1.03959	+	0.600208i	−0.919718	−	0.392581i	$-0.871582\pi$
$947$	−31.9917	+	18.4704i	−1.03959	+	0.600208i	−0.119874	+	0.992789i	$0.538249\pi$
$948$	47.8536	−	3.15705i	1.55421	−	0.102536i
$949$	37.6921	−	1.15463i	1.22354	−	0.0374809i
$950$	−4.40981	−	0.837267i	−0.143073	−	0.0271645i
$951$	−22.7312	−	48.1416i	−0.737111	−	1.56110i
$952$	−30.3740	−	1.19415i	−0.984428	−	0.0387028i
$953$	−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	$-0.414178\pi$
$954$	3.32854	+	19.2693i	0.107766	+	0.623867i
$955$	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
$958$	24.9387	−	8.70876i	0.805734	−	0.281367i
$959$	6.57791			0.212412
$960$	4.05919	+	10.7013i	0.131010	+	0.345383i
$961$	7.57233	−	13.1157i	0.244269	−	0.423086i
$962$	−12.8545	+	15.8764i	−0.414447	+	0.511875i
$963$	−2.96073	+	17.7898i	−0.0954083	+	0.573268i
$964$	15.5468	+	6.12434i	0.500728	+	0.197252i
$965$	−1.92823	+	1.11327i	−0.0620721	+	0.0358373i
$966$	17.2237	−	16.9405i	0.554164	−	0.545051i
$967$	−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	$0.855861\pi$
$968$	−13.8154	−	26.2603i	−0.444044	−	0.844039i
$969$	2.47818	+	5.24844i	0.0796106	+	0.168604i
$970$	−5.31608	−	15.2233i	−0.170689	−	0.488791i
$971$	−31.2117	+	18.0201i	−1.00163	+	0.578293i	−0.908731	−	0.417383i	$-0.862948\pi$
$971$	−31.2117	+	18.0201i	−1.00163	+	0.578293i	−0.0929015	+	0.995675i	$0.529614\pi$
$972$	30.0971	+	8.13413i	0.965365	+	0.260902i
$973$	15.8134	+	9.12988i	0.506955	+	0.292690i
$974$	19.7234	−	6.88755i	0.631980	−	0.220691i
$975$	24.0189	−	12.2541i	0.769220	−	0.392446i
$976$	17.7034	−	18.9833i	0.566672	−	0.607641i
$977$	−36.2856			−1.16088			−0.580440	−	0.814303i	$-0.697119\pi$
$977$	−36.2856			−1.16088			−0.580440	+	0.814303i	$0.697119\pi$
$978$	−1.47223	+	5.31770i	−0.0470768	+	0.170041i
$979$			12.7723i			0.408204i
$980$	−2.35606	+	0.352075i	−0.0752614	+	0.0112466i
$981$	−16.1092	+	6.03929i	−0.514326	+	0.192820i
$982$	−48.2744	−	9.16560i	−1.54050	−	0.292486i
$983$	−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	$0.813422\pi$
$984$	−15.6862	+	6.66618i	−0.500058	+	0.212510i
$985$	10.7030			0.341025
$986$	30.7937	−	35.7372i	0.980670	−	1.13810i
$987$	0.531013	−	0.250730i	0.0169023	−	0.00798084i
$988$	−5.21614	+	0.943575i	−0.165947	+	0.0300191i
$989$		−	10.7983i		−	0.343366i
$990$	0.863383	−	2.34666i	0.0274401	−	0.0745819i
$991$	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
$994$	7.52264	−	2.62695i	0.238604	−	0.0833219i
$995$	−4.20645	−	2.42860i	−0.133354	−	0.0769917i
$996$	−2.29282	−	34.7538i	−0.0726507	−	1.10121i
$997$		−	16.2202i		−	0.513700i	−0.966451	−	0.256850i	$-0.917315\pi$
$997$		−	16.2202i		−	0.513700i	0.966451	−	0.256850i	$-0.0826847\pi$
$998$	9.52129	+	27.2655i	0.301391	+	0.863075i
$999$	−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.61.92	yes	328
8.5	even	2	inner	936.2.db.a.61.17	yes	328
9.4	even	3		936.2.cj.a.373.126	yes	328
13.3	even	3		936.2.cj.a.133.126	yes	328
72.13	even	6		936.2.cj.a.373.125	yes	328
104.29	even	6		936.2.cj.a.133.125	✓	328
117.94	even	3	inner	936.2.db.a.445.17	yes	328
936.445	even	6	inner	936.2.db.a.445.92	yes	328

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
936.2.cj.a.133.125	✓	328	104.29	even	6
936.2.cj.a.133.126	yes	328	13.3	even	3
936.2.cj.a.373.125	yes	328	72.13	even	6
936.2.cj.a.373.126	yes	328	9.4	even	3
936.2.db.a.61.17	yes	328	8.5	even	2	inner
936.2.db.a.61.92	yes	328	1.1	even	1	trivial
936.2.db.a.445.17	yes	328	117.94	even	3	inner
936.2.db.a.445.92	yes	328	936.445	even	6	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+(0.263796 - 1.38939i) q^{2} +(1.42357 + 0.986631i) q^{3} +(-1.86082 - 0.733033i) q^{4} +(-0.715331 + 0.412997i) q^{5} +(1.74635 - 1.71763i) q^{6} -2.35753 q^{7} +(-1.50935 + 2.39204i) q^{8} +(1.05312 + 2.80908i) q^{9} +(0.385113 + 1.10282i) q^{10} +(-0.617926 + 0.356760i) q^{11} +(-1.92578 - 2.87947i) q^{12} +(-3.60386 + 0.110398i) q^{13} +(-0.621909 + 3.27554i) q^{14} +(-1.42580 - 0.117837i) q^{15} +(2.92532 + 2.72809i) q^{16} +(-2.27932 - 3.94789i) q^{17} +(4.18073 - 0.722171i) q^{18} +(-0.636605 + 0.367544i) q^{19} +(1.63385 - 0.244152i) q^{20} +(-3.35612 - 2.32602i) q^{21} +(0.332673 + 0.952654i) q^{22} -4.18348 q^{23} +(-4.50873 + 1.91608i) q^{24} +(-2.15887 + 3.73927i) q^{25} +(-0.797299 + 5.03630i) q^{26} +(-1.27233 + 5.03797i) q^{27} +(4.38695 + 1.72815i) q^{28} +(-6.33702 + 3.65868i) q^{29} +(-0.539843 + 1.94991i) q^{30} +(-1.99094 - 3.44841i) q^{31} +(4.56208 - 3.34476i) q^{32} +(-1.23165 - 0.101791i) q^{33} +(-6.08645 + 2.12543i) q^{34} +(1.68642 - 0.973654i) q^{35} +(0.0994808 - 5.99918i) q^{36} +(3.46950 + 2.00312i) q^{37} +(0.342729 + 0.981451i) q^{38} +(-5.23928 - 3.39852i) q^{39} +(0.0917792 - 2.33446i) q^{40} +3.47908 q^{41} +(-4.11708 + 4.04938i) q^{42} +2.58118i q^{43} +(1.41137 - 0.210906i) q^{44} +(-1.91347 - 1.57449i) q^{45} +(-1.10359 + 5.81249i) q^{46} +(-0.0719052 + 0.124543i) q^{47} +(1.47279 + 6.76985i) q^{48} -1.44203 q^{49} +(4.62581 + 3.98592i) q^{50} +(0.650338 - 7.86896i) q^{51} +(6.78707 + 2.43632i) q^{52} +4.60908i q^{53} +(6.66408 + 3.09677i) q^{54} +(0.294681 - 0.510403i) q^{55} +(3.55834 - 5.63932i) q^{56} +(-1.26888 - 0.104868i) q^{57} +(3.41166 + 9.76975i) q^{58} +(13.0302 + 7.52300i) q^{59} +(2.56679 + 1.26443i) q^{60} -6.48930i q^{61} +(-5.31639 + 1.85652i) q^{62} +(-2.48277 - 6.62251i) q^{63} +(-3.44373 - 7.22085i) q^{64} +(2.53236 - 1.56735i) q^{65} +(-0.466334 + 1.68440i) q^{66} -8.01643i q^{67} +(1.34747 + 9.01714i) q^{68} +(-5.95548 - 4.12755i) q^{69} +(-0.907917 - 2.59994i) q^{70} +(-1.19496 - 2.06973i) q^{71} +(-8.30897 - 1.72078i) 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} +(-6.10398 + 6.38290i) q^{78} +(-6.92208 + 11.9894i) q^{79} +(-3.21927 - 0.743339i) q^{80} +(-6.78188 + 5.91660i) q^{81} +(0.917768 - 4.83380i) q^{82} +(8.70733 + 5.02718i) q^{83} +(4.54010 + 6.78845i) q^{84} +(3.26093 + 1.88270i) q^{85} +(3.58627 + 0.680906i) q^{86} +(-12.6310 - 1.04390i) q^{87} +(0.0792818 - 2.01658i) q^{88} +(8.95021 - 15.5022i) q^{89} +(-2.69235 + 2.24322i) q^{90} +(8.49623 - 0.260267i) q^{91} +(7.78471 + 3.06663i) q^{92} +(0.568058 - 6.87338i) q^{93} +(0.154071 + 0.132759i) q^{94} +(0.303589 - 0.525831i) q^{95} +(9.79450 - 0.260429i) q^{96} -13.8040 q^{97} +(-0.380402 + 2.00355i) 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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