LMFDB - Embedded newform 207.2.o.a.113.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [207,2,Mod(5,207)] 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("207.5"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(207, base_ring=CyclotomicField(66)) chi = DirichletCharacter(H, H._module([55, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.o (of order $66$, degree $20$, 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:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$22$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			113.19
Character	$\chi$	$=$	207.113
Dual form			207.2.o.a.11.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.02146 + 0.0962939i) q^{2} +(-0.150008 - 1.72554i) q^{3} +(2.08607 + 0.199196i) q^{4} +(1.56283 - 1.49016i) q^{5} +(-0.137076 - 3.50255i) q^{6} +(-0.802915 + 4.16592i) q^{7} +(0.191421 + 0.0275221i) q^{8} +(-2.95499 + 0.517692i) q^{9} +(3.30269 - 2.86180i) q^{10} +(-2.66013 - 1.37139i) q^{11} +(0.0307923 - 3.62949i) q^{12} +(6.74421 - 1.29984i) q^{13} +(-2.02421 + 8.34391i) q^{14} +(-2.80577 - 2.47320i) q^{15} +(-3.73108 - 0.719107i) q^{16} +(-0.615124 + 1.34693i) q^{17} +(-6.02324 + 0.761944i) q^{18} +(-5.21085 + 2.37972i) q^{19} +(3.55701 - 2.79726i) q^{20} +(7.30892 + 0.760542i) q^{21} +(-5.24528 - 3.02837i) q^{22} +(4.46073 + 1.76122i) q^{23} +(0.0187759 - 0.334433i) q^{24} +(-0.0160346 + 0.336607i) q^{25} +(13.7583 - 1.97814i) q^{26} +(1.33657 + 5.02131i) q^{27} +(-2.50477 + 8.53047i) q^{28} +(-0.0825600 - 0.864607i) q^{29} +(-5.43358 - 5.26964i) q^{30} +(1.38242 + 1.08715i) q^{31} +(-7.84885 - 1.90411i) q^{32} +(-1.96735 + 4.79589i) q^{33} +(-1.37315 + 2.66353i) q^{34} +(4.95305 + 7.70710i) q^{35} +(-6.26745 + 0.491320i) q^{36} +(0.388365 + 1.32265i) q^{37} +(-10.7627 + 4.30872i) q^{38} +(-3.25462 - 11.4424i) q^{39} +(0.340170 - 0.242234i) q^{40} +(-8.10406 - 8.49929i) q^{41} +(14.7014 + 2.24121i) q^{42} +(-2.97186 - 3.77903i) q^{43} +(-5.27605 - 3.39071i) q^{44} +(-3.84672 + 5.21247i) q^{45} +(8.84758 + 3.98977i) q^{46} +(4.19556 - 2.42231i) q^{47} +(-0.681156 + 6.54601i) q^{48} +(-10.2116 - 4.08813i) q^{49} +(-0.0648264 + 0.678893i) q^{50} +(2.41646 + 0.859371i) q^{51} +(14.3278 - 1.36814i) q^{52} +(4.97557 - 5.74212i) q^{53} +(2.21830 + 10.2791i) q^{54} +(-6.20093 + 1.82076i) q^{55} +(-0.268349 + 0.775345i) q^{56} +(4.88797 + 8.63457i) q^{57} +(-0.0836350 - 1.75572i) q^{58} +(-0.0115840 - 0.0601035i) q^{59} +(-5.36038 - 5.71816i) q^{60} +(2.53682 + 6.33668i) q^{61} +(2.68982 + 2.33075i) q^{62} +(0.215948 - 12.7259i) q^{63} +(-8.39109 - 2.46385i) q^{64} +(8.60310 - 12.0814i) q^{65} +(-4.43874 + 9.50524i) q^{66} +(-0.497249 - 0.964529i) q^{67} +(-1.55149 + 2.68727i) q^{68} +(2.36991 - 7.96138i) q^{69} +(9.27024 + 16.0565i) q^{70} +(2.81387 - 4.37847i) q^{71} +(-0.579895 + 0.0177691i) q^{72} +(-5.08574 - 11.1362i) q^{73} +(0.657701 + 2.71108i) q^{74} +(0.583236 - 0.0228256i) q^{75} +(-11.3442 + 3.92628i) q^{76} +(7.84897 - 9.98078i) q^{77} +(-5.47723 - 23.4438i) q^{78} +(-4.14873 - 1.43589i) q^{79} +(-6.90264 + 4.43606i) q^{80} +(8.46399 - 3.05955i) q^{81} +(-15.5636 - 17.9613i) q^{82} +(5.35521 + 5.10618i) q^{83} +(15.0954 + 3.04245i) q^{84} +(1.04581 + 3.02166i) q^{85} +(-5.64359 - 7.92531i) q^{86} +(-1.47953 + 0.272159i) q^{87} +(-0.471460 - 0.335725i) q^{88} +(0.911221 + 6.33768i) q^{89} +(-8.27790 + 10.1664i) q^{90} +29.1395i q^{91} +(8.95457 + 4.56259i) q^{92} +(1.66855 - 2.54851i) q^{93} +(8.71440 - 4.49259i) q^{94} +(-4.59753 + 11.4841i) q^{95} +(-2.10823 + 13.8292i) q^{96} +(-4.63139 + 1.12356i) q^{97} +(-20.2487 - 9.24729i) q^{98} +(8.57063 + 2.67533i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23}+ \cdots + 242 q^{99}+O(q^{100}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{13}{22}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	2.02146	+	0.0962939i	1.42939	+	0.0680900i	0.747934	−	0.663773i	$-0.231046\pi$
$2$	2.02146	+	0.0962939i	1.42939	+	0.0680900i	0.681452	+	0.731863i	$0.261349\pi$
$3$	−0.150008	−	1.72554i	−0.0866074	−	0.996243i
$3$	−0.150008	−	1.72554i	−0.0866074	−	0.996243i
$4$	2.08607	+	0.199196i	1.04304	+	0.0995978i
$5$	1.56283	−	1.49016i	0.698920	−	0.666418i	−0.254842	−	0.966983i	$-0.582023\pi$
$5$	1.56283	−	1.49016i	0.698920	−	0.666418i	0.953762	+	0.300564i	$0.0971750\pi$
$6$	−0.137076	−	3.50255i	−0.0559612	−	1.42991i
$7$	−0.802915	+	4.16592i	−0.303474	+	1.57457i	0.435090	+	0.900387i	$0.356716\pi$
$7$	−0.802915	+	4.16592i	−0.303474	+	1.57457i	−0.738564	+	0.674183i	$0.764496\pi$
$8$	0.191421	+	0.0275221i	0.0676774	+	0.00973054i
$9$	−2.95499	+	0.517692i	−0.984998	+	0.172564i
$10$	3.30269	−	2.86180i	1.04440	−	0.904980i
$11$	−2.66013	−	1.37139i	−0.802060	−	0.413490i	0.00790531	−	0.999969i	$-0.497484\pi$
$11$	−2.66013	−	1.37139i	−0.802060	−	0.413490i	−0.809965	+	0.586478i	$0.800514\pi$
$12$	0.0307923	−	3.62949i	0.00888898	−	1.04774i
$13$	6.74421	−	1.29984i	1.87051	−	0.360511i	0.877599	−	0.479395i	$-0.159144\pi$
$13$	6.74421	−	1.29984i	1.87051	−	0.360511i	0.992908	+	0.118884i	$0.0379317\pi$
$14$	−2.02421	+	8.34391i	−0.540993	+	2.23000i
$15$	−2.80577	−	2.47320i	−0.724446	−	0.638577i
$16$	−3.73108	−	0.719107i	−0.932771	−	0.179777i
$17$	−0.615124	+	1.34693i	−0.149189	+	0.326679i	−0.969441	−	0.245323i	$-0.921106\pi$
$17$	−0.615124	+	1.34693i	−0.149189	+	0.326679i	0.820252	+	0.572002i	$0.193833\pi$
$18$	−6.02324	+	0.761944i	−1.41969	+	0.179592i
$19$	−5.21085	+	2.37972i	−1.19545	+	0.545944i	−0.910864	−	0.412706i	$-0.864584\pi$
$19$	−5.21085	+	2.37972i	−1.19545	+	0.545944i	−0.284587	+	0.958650i	$0.591856\pi$
$20$	3.55701	−	2.79726i	0.795372	−	0.625487i
$21$	7.30892	+	0.760542i	1.59494	+	0.165964i
$22$	−5.24528	−	3.02837i	−1.11830	−	0.645650i
$23$	4.46073	+	1.76122i	0.930126	+	0.367240i
$23$	4.46073	+	1.76122i	0.930126	+	0.367240i
$24$	0.0187759	−	0.334433i	0.00383261	−	0.0682658i
$25$	−0.0160346	+	0.336607i	−0.00320692	+	0.0673215i
$26$	13.7583	−	1.97814i	2.69822	−	0.387946i
$27$	1.33657	+	5.02131i	0.257224	+	0.966352i
$28$	−2.50477	+	8.53047i	−0.473357	+	1.61211i
$29$	−0.0825600	−	0.864607i	−0.0153310	−	0.160553i	0.984564	−	0.175023i	$-0.0560000\pi$
$29$	−0.0825600	−	0.864607i	−0.0153310	−	0.160553i	−0.999895	+	0.0144697i	$0.995394\pi$
$30$	−5.43358	−	5.26964i	−0.992032	−	0.962100i
$31$	1.38242	+	1.08715i	0.248291	+	0.195258i	0.734546	−	0.678559i	$-0.237395\pi$
$31$	1.38242	+	1.08715i	0.248291	+	0.195258i	−0.486255	+	0.873817i	$0.661638\pi$
$32$	−7.84885	−	1.90411i	−1.38749	−	0.336602i
$33$	−1.96735	+	4.79589i	−0.342473	+	0.834857i
$34$	−1.37315	+	2.66353i	−0.235493	+	0.456792i
$35$	4.95305	+	7.70710i	0.837219	+	1.30274i
$36$	−6.26745	+	0.491320i	−1.04458	+	0.0818866i
$37$	0.388365	+	1.32265i	0.0638469	+	0.217443i	0.985237	−	0.171197i	$-0.0547634\pi$
$37$	0.388365	+	1.32265i	0.0638469	+	0.217443i	−0.921390	+	0.388639i	$0.872945\pi$
$38$	−10.7627	+	4.30872i	−1.74593	+	0.698967i
$39$	−3.25462	−	11.4424i	−0.521156	−	1.83226i
$40$	0.340170	−	0.242234i	0.0537857	−	0.0383006i
$41$	−8.10406	−	8.49929i	−1.26564	−	1.32737i	−0.921465	−	0.388461i	$-0.873007\pi$
$41$	−8.10406	−	8.49929i	−1.26564	−	1.32737i	−0.344176	−	0.938905i	$-0.611842\pi$
$42$	14.7014	+	2.24121i	2.26848	+	0.345826i
$43$	−2.97186	−	3.77903i	−0.453204	−	0.576296i	0.504732	−	0.863276i	$-0.331591\pi$
$43$	−2.97186	−	3.77903i	−0.453204	−	0.576296i	−0.957937	+	0.286980i	$0.907349\pi$
$44$	−5.27605	−	3.39071i	−0.795394	−	0.511169i
$45$	−3.84672	+	5.21247i	−0.573435	+	0.777029i
$46$	8.84758	+	3.98977i	1.30450	+	0.588260i
$47$	4.19556	−	2.42231i	0.611986	−	0.353330i	−0.161756	−	0.986831i	$-0.551716\pi$
$47$	4.19556	−	2.42231i	0.611986	−	0.353330i	0.773742	+	0.633501i	$0.218383\pi$
$48$	−0.681156	+	6.54601i	−0.0983165	+	0.944836i
$49$	−10.2116	−	4.08813i	−1.45881	−	0.584018i
$50$	−0.0648264	+	0.678893i	−0.00916784	+	0.0960100i
$51$	2.41646	+	0.859371i	0.338373	+	0.120336i
$52$	14.3278	−	1.36814i	1.98691	−	0.189727i
$53$	4.97557	−	5.74212i	0.683447	−	0.788740i	−0.302970	−	0.953000i	$-0.597978\pi$
$53$	4.97557	−	5.74212i	0.683447	−	0.788740i	0.986417	+	0.164260i	$0.0525235\pi$
$54$	2.21830	+	10.2791i	0.301873	+	1.39880i
$55$	−6.20093	+	1.82076i	−0.836133	+	0.245511i
$56$	−0.268349	+	0.775345i	−0.0358597	+	0.103610i
$57$	4.88797	+	8.63457i	0.647428	+	1.14368i
$58$	−0.0836350	−	1.75572i	−0.0109818	−	0.230537i
$59$	−0.0115840	−	0.0601035i	−0.00150811	−	0.00782481i	0.981167	−	0.193162i	$-0.0618743\pi$
$59$	−0.0115840	−	0.0601035i	−0.00150811	−	0.00782481i	−0.982675	+	0.185337i	$0.940662\pi$
$60$	−5.36038	−	5.71816i	−0.692022	−	0.738211i
$61$	2.53682	+	6.33668i	0.324807	+	0.811329i	0.997450	+	0.0713620i	$0.0227345\pi$
$61$	2.53682	+	6.33668i	0.324807	+	0.811329i	−0.672643	+	0.739967i	$0.734841\pi$
$62$	2.68982	+	2.33075i	0.341608	+	0.296005i
$63$	0.215948	−	12.7259i	0.0272069	−	1.60332i
$64$	−8.39109	−	2.46385i	−1.04889	−	0.307981i
$65$	8.60310	−	12.0814i	1.06708	−	1.49851i
$66$	−4.43874	+	9.50524i	−0.546371	+	1.17001i
$67$	−0.497249	−	0.964529i	−0.0607487	−	0.117836i	0.856506	−	0.516137i	$-0.172630\pi$
$67$	−0.497249	−	0.964529i	−0.0607487	−	0.117836i	−0.917255	+	0.398301i	$0.869600\pi$
$68$	−1.55149	+	2.68727i	−0.188146	+	0.325879i
$69$	2.36991	−	7.96138i	0.285304	−	0.958437i
$70$	9.27024	+	16.0565i	1.10801	+	1.91912i
$71$	2.81387	−	4.37847i	0.333945	−	0.519629i	−0.633155	−	0.774025i	$-0.718240\pi$
$71$	2.81387	−	4.37847i	0.333945	−	0.519629i	0.967100	+	0.254396i	$0.0818767\pi$
$72$	−0.579895	+	0.0177691i	−0.0683413	+	0.00209411i
$73$	−5.08574	−	11.1362i	−0.595240	−	1.30339i	−0.932223	−	0.361884i	$-0.882134\pi$
$73$	−5.08574	−	11.1362i	−0.595240	−	1.30339i	0.336983	−	0.941511i	$-0.390594\pi$
$74$	0.657701	+	2.71108i	0.0764562	+	0.315157i
$75$	0.583236	−	0.0228256i	0.0673462	−	0.00263567i
$76$	−11.3442	+	3.92628i	−1.30127	+	0.450375i
$77$	7.84897	−	9.98078i	0.894474	−	1.13742i
$78$	−5.47723	−	23.4438i	−0.620174	−	2.65449i
$79$	−4.14873	−	1.43589i	−0.466769	−	0.161550i	0.0835522	−	0.996503i	$-0.473373\pi$
$79$	−4.14873	−	1.43589i	−0.466769	−	0.161550i	−0.550321	+	0.834953i	$0.685495\pi$
$80$	−6.90264	+	4.43606i	−0.771738	+	0.495966i
$81$	8.46399	−	3.05955i	0.940443	−	0.339950i
$82$	−15.5636	−	17.9613i	−1.71871	−	1.98350i
$83$	5.35521	+	5.10618i	0.587811	+	0.560477i	0.924521	−	0.381132i	$-0.124466\pi$
$83$	5.35521	+	5.10618i	0.587811	+	0.560477i	−0.336710	+	0.941608i	$0.609314\pi$
$84$	15.0954	+	3.04245i	1.64705	+	0.331958i
$85$	1.04581	+	3.02166i	0.113434	+	0.327745i
$86$	−5.64359	−	7.92531i	−0.608564	−	0.854608i
$87$	−1.47953	+	0.272159i	−0.158622	+	0.0291785i
$88$	−0.471460	−	0.335725i	−0.0502578	−	0.0357884i
$89$	0.911221	+	6.33768i	0.0965893	+	0.671793i	0.979380	+	0.202027i	$0.0647528\pi$
$89$	0.911221	+	6.33768i	0.0965893	+	0.671793i	−0.882791	+	0.469766i	$0.844338\pi$
$90$	−8.27790	+	10.1664i	−0.872568	+	1.07163i
$91$			29.1395i			3.05465i
$92$	8.95457	+	4.56259i	0.933578	+	0.475683i
$93$	1.66855	−	2.54851i	0.173020	−	0.264268i
$94$	8.71440	−	4.49259i	0.898822	−	0.463375i
$95$	−4.59753	+	11.4841i	−0.471697	+	1.17824i
$96$	−2.10823	+	13.8292i	−0.215170	+	1.41143i
$97$	−4.63139	+	1.12356i	−0.470246	+	0.114080i	−0.463878	−	0.885899i	$-0.653542\pi$
$97$	−4.63139	+	1.12356i	−0.470246	+	0.114080i	−0.00636838	+	0.999980i	$0.502027\pi$
$98$	−20.2487	−	9.24729i	−2.04543	−	0.934117i
$99$	8.57063	+	2.67533i	0.861381	+	0.268881i
$100$	−0.100500	+	0.698993i	−0.0100500	+	0.0698993i
$101$	1.80468	−	1.89269i	0.179572	−	0.188330i	−0.627796	−	0.778378i	$-0.716043\pi$
$101$	1.80468	−	1.89269i	0.179572	−	0.188330i	0.807368	+	0.590048i	$0.200891\pi$
$102$	4.80203	+	1.96987i	0.475471	+	0.195046i
$103$	−9.60348	+	0.457470i	−0.946259	+	0.0450759i	−0.515035	−	0.857169i	$-0.672221\pi$
$103$	−9.60348	+	0.457470i	−0.946259	+	0.0450759i	−0.431224	+	0.902245i	$0.641918\pi$
$104$	1.32675	−	0.0632011i	0.130099	−	0.00619738i
$105$	12.5559	−	9.70284i	1.22533	−	0.946900i
$106$	10.6108	−	11.1283i	1.03062	−	1.08088i
$107$	−0.273332	+	1.90107i	−0.0264240	+	0.183783i	−0.998759	−	0.0498086i	$-0.984139\pi$
$107$	−0.273332	+	1.90107i	−0.0264240	+	0.183783i	0.972335	+	0.233592i	$0.0750479\pi$
$108$	1.78796	+	10.7411i	0.172047	+	1.03356i
$109$	8.24132	+	3.76368i	0.789375	+	0.360496i	0.768961	−	0.639296i	$-0.220774\pi$
$109$	8.24132	+	3.76368i	0.789375	+	0.360496i	0.0204145	+	0.999792i	$0.493501\pi$
$110$	−12.7102	+	3.08347i	−1.21187	+	0.293997i
$111$	2.22403	−	0.868550i	0.211096	−	0.0824391i
$112$	5.99149	−	14.9660i	0.566142	−	1.41416i
$113$	7.87657	−	4.06066i	0.740966	−	0.381994i	−0.0460404	−	0.998940i	$-0.514660\pi$
$113$	7.87657	−	4.06066i	0.740966	−	0.381994i	0.787006	+	0.616945i	$0.211630\pi$
$114$	9.04937	+	17.9251i	0.847551	+	1.67884i
$115$	9.59586	−	3.89470i	0.894819	−	0.363182i
$116$		−	1.82008i		−	0.168990i
$117$	−19.2562	+	7.33244i	−1.78024	+	0.677885i
$118$	−0.0176290	−	0.122612i	−0.00162288	−	0.0112874i
$119$	−5.11732	−	3.64403i	−0.469104	−	0.334048i
$120$	−0.469014	−	0.550641i	−0.0428149	−	0.0502664i
$121$	−1.18505	−	1.66417i	−0.107732	−	0.151288i
$122$	4.51790	+	13.0536i	0.409031	+	1.18182i
$123$	−13.4502	+	15.2589i	−1.21276	+	1.37585i
$124$	2.66728	+	2.54324i	0.239529	+	0.228390i
$125$	7.54707	+	8.70979i	0.675031	+	0.779027i
$126$	1.66196	−	25.7041i	0.148059	−	2.28991i
$127$	5.51842	−	3.54647i	0.489680	−	0.314698i	−0.272397	−	0.962185i	$-0.587816\pi$
$127$	5.51842	−	3.54647i	0.489680	−	0.314698i	0.762077	+	0.647487i	$0.224180\pi$
$128$	−1.46035	−	0.505433i	−0.129078	−	0.0446744i
$129$	−6.07507	+	5.69495i	−0.534880	+	0.501413i
$130$	18.5542	−	23.5935i	1.62731	−	2.06929i
$131$	1.46665	−	0.507613i	0.128142	−	0.0443503i	−0.262244	−	0.965001i	$-0.584463\pi$
$131$	1.46665	−	0.507613i	0.128142	−	0.0443503i	0.390386	+	0.920651i	$0.372341\pi$
$132$	−5.05936	+	9.61268i	−0.440361	+	0.836676i
$133$	−5.72984	−	23.6187i	−0.496840	−	2.04800i
$134$	−0.912290	−	1.99764i	−0.0788098	−	0.172569i
$135$	9.57138	+	5.85576i	0.823773	+	0.503984i
$136$	−0.154818	+	0.240901i	−0.0132755	+	0.0206571i
$137$	−1.92988	−	3.34266i	−0.164881	−	0.285582i	0.771732	−	0.635948i	$-0.219391\pi$
$137$	−1.92988	−	3.34266i	−0.164881	−	0.285582i	−0.936613	+	0.350366i	$0.886057\pi$
$138$	5.55731	−	15.8654i	0.473070	−	1.35055i
$139$	0.118863	−	0.205877i	0.0100818	−	0.0174622i	−0.860940	−	0.508706i	$-0.830124\pi$
$139$	0.118863	−	0.205877i	0.0100818	−	0.0174622i	0.871022	+	0.491243i	$0.163457\pi$
$140$	8.79720	+	17.0642i	0.743499	+	1.44219i
$141$	−4.80917	−	6.87626i	−0.405005	−	0.579085i
$142$	6.10975	−	8.57994i	0.512718	−	0.720012i
$143$	−19.7231	−	5.79122i	−1.64933	−	0.484286i
$144$	11.3976	+	0.193407i	0.949800	+	0.0161173i
$145$	−1.41743	−	1.22821i	−0.117711	−	0.101997i
$146$	−9.20825	−	23.0011i	−0.762080	−	1.90358i
$147$	−5.52240	+	18.2339i	−0.455480	+	1.50391i
$148$	0.546692	+	2.83651i	0.0449378	+	0.233159i
$149$	−0.413046	−	8.67090i	−0.0338380	−	0.710348i	−0.950508	−	0.310702i	$-0.899436\pi$
$149$	−0.413046	−	8.67090i	−0.0338380	−	0.710348i	0.916669	−	0.399646i	$-0.130867\pi$
$150$	1.18118	+	0.0100211i	0.0964432	+	0.000818219i
$151$	−2.61150	+	7.54542i	−0.212520	+	0.614038i	−0.999997	−	0.00230665i	$-0.999266\pi$
$151$	−2.61150	+	7.54542i	−0.212520	+	0.614038i	0.787477	+	0.616344i	$0.211387\pi$
$152$	−1.06296	+	0.312113i	−0.0862174	+	0.0253157i
$153$	1.12039	−	4.29862i	0.0905783	−	0.347523i
$154$	16.8274	−	19.4199i	1.35599	−	1.56490i
$155$	3.78052	−	0.360996i	0.303659	−	0.0289959i
$156$	−4.51008	−	24.5180i	−0.361095	−	1.96301i
$157$	−1.00194	+	10.4928i	−0.0799637	+	0.837417i	0.863150	+	0.504947i	$0.168488\pi$
$157$	−1.00194	+	10.4928i	−0.0799637	+	0.837417i	−0.943114	+	0.332470i	$0.892118\pi$
$158$	−8.24822	−	3.30209i	−0.656193	−	0.262700i
$159$	−10.6546	−	7.72420i	−0.844968	−	0.612569i
$160$	−15.1039	+	8.72022i	−1.19406	+	0.689394i
$161$	−10.9187	+	17.1689i	−0.860513	+	1.35310i
$162$	17.4042	−	5.36972i	1.36740	−	0.421885i
$163$	−2.89417	−	1.85997i	−0.226689	−	0.145684i	0.422367	−	0.906425i	$-0.361199\pi$
$163$	−2.89417	−	1.85997i	−0.226689	−	0.145684i	−0.649056	+	0.760741i	$0.724836\pi$
$164$	−15.2126	−	19.3444i	−1.18791	−	1.51055i
$165$	4.07198	+	10.4268i	0.317004	+	0.811728i
$166$	10.3336	+	10.8376i	0.802046	+	0.841161i
$167$	−2.65643	+	1.89164i	−0.205561	+	0.146379i	−0.678201	−	0.734876i	$-0.737240\pi$
$167$	−2.65643	+	1.89164i	−0.205561	+	0.146379i	0.472640	+	0.881255i	$0.343301\pi$
$168$	1.37815	+	0.346740i	0.106326	+	0.0267516i
$169$	31.7260	−	12.7012i	2.44046	−	0.977014i
$170$	1.82309	+	6.20886i	0.139824	+	0.476198i
$171$	14.1661	−	9.72966i	1.08331	−	0.744046i
$172$	−5.44674	−	8.47530i	−0.415310	−	0.646235i
$173$	−8.78798	+	17.0463i	−0.668137	+	1.29601i	0.274307	+	0.961642i	$0.411552\pi$
$173$	−8.78798	+	17.0463i	−0.668137	+	1.29601i	−0.942444	+	0.334364i	$0.891479\pi$
$174$	−3.01702	+	0.407688i	−0.228719	+	0.0309067i
$175$	−1.38940	−	0.337066i	−0.105029	−	0.0254798i
$176$	8.93899	+	7.02970i	0.673802	+	0.529883i
$177$	−0.101973	+	0.0290047i	−0.00766479	+	0.00218013i
$178$	1.23171	+	12.8991i	0.0923209	+	0.966828i
$179$	0.202571	−	0.689893i	0.0151409	−	0.0515650i	−0.951576	−	0.307413i	$-0.900537\pi$
$179$	0.202571	−	0.689893i	0.0151409	−	0.0515650i	0.966717	+	0.255848i	$0.0823548\pi$
$180$	−9.06283	+	10.1073i	−0.675503	+	0.753356i
$181$	13.1715	−	1.89378i	0.979030	−	0.140763i	0.365822	−	0.930685i	$-0.380788\pi$
$181$	13.1715	−	1.89378i	0.979030	−	0.140763i	0.613208	+	0.789922i	$0.289879\pi$
$182$	−2.80596	+	58.9043i	−0.207991	+	4.36627i
$183$	10.5537	−	5.32795i	0.780149	−	0.393854i
$184$	0.805403	+	0.459902i	0.0593751	+	0.0339045i
$185$	2.57791	+	1.48836i	0.189532	+	0.109426i
$186$	3.61830	−	4.99104i	0.265307	−	0.365961i
$187$	3.48348	−	2.73944i	0.254738	−	0.200328i
$188$	9.23475	−	4.21737i	0.673514	−	0.307583i
$189$	−21.9915	+	1.53637i	−1.59965	+	0.111755i
$190$	−10.3996	+	22.7719i	−0.754463	+	1.65204i
$191$	−0.368549	−	0.0710320i	−0.0266673	−	0.00513970i	0.175900	−	0.984408i	$-0.443716\pi$
$191$	−0.368549	−	0.0710320i	−0.0266673	−	0.00513970i	−0.202567	+	0.979268i	$0.564929\pi$
$192$	−2.99274	+	14.8488i	−0.215982	+	1.07162i
$193$	−2.92384	+	12.0522i	−0.210462	+	0.867537i	0.764402	+	0.644740i	$0.223034\pi$
$193$	−2.92384	+	12.0522i	−0.210462	+	0.867537i	−0.974865	+	0.222798i	$0.928481\pi$
$194$	−9.47034	+	1.82526i	−0.679931	+	0.131046i
$195$	−22.1374	−	13.0327i	−1.58530	−	0.933292i
$196$	−20.4879	−	10.5622i	−1.46342	−	0.754446i
$197$	−12.1590	+	10.5358i	−0.866293	+	0.750647i	−0.969779	−	0.243983i	$-0.921546\pi$
$197$	−12.1590	+	10.5358i	−0.866293	+	0.750647i	0.103486	+	0.994631i	$0.467000\pi$
$198$	17.0675	+	6.23336i	1.21294	+	0.442986i
$199$	−7.74040	−	1.11290i	−0.548702	−	0.0788915i	−0.137612	−	0.990486i	$-0.543943\pi$
$199$	−7.74040	−	1.11290i	−0.548702	−	0.0788915i	−0.411090	+	0.911595i	$0.634852\pi$
$200$	−0.0123335	+	0.0639922i	−0.000872110	+	0.00452493i
$201$	−1.58974	+	1.00271i	−0.112132	+	0.0707259i
$202$	3.83034	−	3.65222i	0.269502	−	0.256969i
$203$	3.66817	+	0.350268i	0.257455	+	0.0245840i
$204$	4.86973	+	2.27406i	0.340949	+	0.159216i
$205$	−25.3306	−	1.20664i	−1.76916	−	0.0842756i
$206$	−19.4571			−1.35564
$207$	−14.0932	−	2.89511i	−0.979545	−	0.201224i
$208$	−26.0979			−1.80957
$209$	17.1251	+	0.815768i	1.18457	+	0.0564278i
$210$	26.3156	−	18.4048i	1.81595	−	1.27005i
$211$	10.7934	+	1.03065i	0.743051	+	0.0709527i	0.459713	−	0.888068i	$-0.347952\pi$
$211$	10.7934	+	1.03065i	0.743051	+	0.0709527i	0.283338	+	0.959020i	$0.408558\pi$
$212$	11.5232	−	10.9874i	0.791417	−	0.754614i
$213$	−7.97735	−	4.19865i	−0.546599	−	0.287687i
$214$	−0.735591	+	3.81661i	−0.0502839	+	0.260898i
$215$	−10.2759	−	1.47744i	−0.700808	−	0.100761i
$216$	0.117650	+	0.997968i	0.00800510	+	0.0679031i
$217$	−5.63895	+	4.88618i	−0.382797	+	0.331695i
$218$	16.2970	+	8.40171i	1.10378	+	0.569036i
$219$	−18.4531	+	10.4462i	−1.24695	+	0.705888i
$220$	−13.2983	+	2.56303i	−0.896569	+	0.172799i
$221$	−2.39773	+	9.88356i	−0.161289	+	0.664840i
$222$	4.57942	−	1.54158i	0.307351	−	0.103464i
$223$	16.2104	+	3.12430i	1.08553	+	0.209218i	0.700476	−	0.713676i	$-0.252971\pi$
$223$	16.2104	+	3.12430i	1.08553	+	0.209218i	0.385053	+	0.922895i	$0.374183\pi$
$224$	14.2343	−	31.1689i	0.951072	−	2.08256i
$225$	−0.126877	−	1.00297i	−0.00845845	−	0.0668649i
$226$	16.3132	−	7.44997i	1.08514	−	0.495565i
$227$	−1.60612	+	1.26306i	−0.106602	+	0.0838326i	−0.670037	−	0.742328i	$-0.733722\pi$
$227$	−1.60612	+	1.26306i	−0.106602	+	0.0838326i	0.563435	+	0.826160i	$0.309479\pi$
$228$	8.47669	+	18.9860i	0.561383	+	1.25738i
$229$	21.6138	+	12.4788i	1.42828	+	0.824620i	0.996985	−	0.0775900i	$-0.0247225\pi$
$229$	21.6138	+	12.4788i	1.42828	+	0.824620i	0.431298	+	0.902210i	$0.358056\pi$
$230$	19.7727	−	6.94894i	1.30377	−	0.458199i
$231$	−18.3997	−	12.0465i	−1.21061	−	0.792604i
$232$	0.00799215	−	0.167776i	0.000524710	−	0.0110150i
$233$	−3.28025	+	0.471628i	−0.214896	+	0.0308974i	−0.248922	−	0.968524i	$-0.580076\pi$
$233$	−3.28025	+	0.471628i	−0.214896	+	0.0308974i	0.0340258	+	0.999421i	$0.489167\pi$
$234$	−39.6316	+	12.9680i	−2.59080	+	0.847742i
$235$	2.94734	−	10.0377i	0.192263	−	0.654788i
$236$	−0.0121927	−	0.127688i	−0.000793676	−	0.00831175i
$237$	−1.85535	+	7.37421i	−0.120518	+	0.479006i
$238$	−9.99355	−	7.85902i	−0.647786	−	0.509424i
$239$	6.26307	+	1.51940i	0.405124	+	0.0982821i	0.433143	−	0.901325i	$-0.357405\pi$
$239$	6.26307	+	1.51940i	0.405124	+	0.0982821i	−0.0280184	+	0.999607i	$0.508920\pi$
$240$	8.69006	+	11.2453i	0.560941	+	0.725884i
$241$	−9.62377	+	18.6675i	−0.619922	+	1.20248i	0.344668	+	0.938725i	$0.387991\pi$
$241$	−9.62377	+	18.6675i	−0.619922	+	1.20248i	−0.964590	+	0.263755i	$0.915039\pi$
$242$	−2.23527	−	3.47815i	−0.143689	−	0.223584i
$243$	−6.54906	−	14.1460i	−0.420122	−	0.907467i
$244$	4.02976	+	13.7241i	0.257979	+	0.878595i
$245$	−22.0510	+	8.82790i	−1.40879	+	0.563994i
$246$	−28.6584	+	29.5500i	−1.82719	+	1.88404i
$247$	−32.0498	+	22.8226i	−2.03928	+	1.45217i
$248$	0.234704	+	0.246150i	0.0149037	+	0.0156305i
$249$	8.00761	−	10.0066i	0.507462	−	0.634144i
$250$	14.4174	+	18.3332i	0.911835	+	1.15949i
$251$	−10.9766	−	7.05424i	−0.692837	−	0.445260i	0.146256	−	0.989247i	$-0.453278\pi$
$251$	−10.9766	−	7.05424i	−0.692837	−	0.445260i	−0.839094	+	0.543987i	$0.816914\pi$
$252$	2.98543	−	26.5042i	0.188065	−	1.66961i
$253$	−9.45080	−	10.8025i	−0.594167	−	0.679147i
$254$	11.4967	−	6.63765i	0.721370	−	0.416483i
$255$	5.05712	−	2.25786i	0.316689	−	0.141393i
$256$	13.3344	+	5.33830i	0.833401	+	0.333644i
$257$	−0.322599	+	3.37840i	−0.0201231	+	0.210739i	0.979818	+	0.199892i	$0.0640590\pi$
$257$	−0.322599	+	3.37840i	−0.0201231	+	0.210739i	−0.999941	+	0.0108475i	$0.996547\pi$
$258$	−12.8289	+	10.9271i	−0.798691	+	0.680292i
$259$	−5.82189	+	0.555923i	−0.361754	+	0.0345434i
$260$	20.3532	−	23.4889i	1.26225	−	1.45672i
$261$	0.691564	+	2.51217i	0.0428068	+	0.155499i
$262$	3.01365	−	0.884887i	0.186184	−	0.0546685i
$263$	−0.0602179	+	0.173988i	−0.00371320	+	0.0107286i	−0.946842	−	0.321698i	$-0.895746\pi$
$263$	−0.0602179	+	0.173988i	−0.00371320	+	0.0107286i	0.943129	+	0.332427i	$0.107867\pi$
$264$	−0.508585	+	0.863886i	−0.0313013	+	0.0531685i
$265$	−0.780673	−	16.3883i	−0.0479564	−	1.00673i
$266$	−9.30828	−	48.2959i	−0.570727	−	2.96121i
$267$	10.7993	−	2.52306i	0.660904	−	0.154409i
$268$	−0.845167	−	2.11113i	−0.0516268	−	0.128958i
$269$	14.3250	+	12.4127i	0.873409	+	0.756813i	0.971168	−	0.238397i	$-0.0766220\pi$
$269$	14.3250	+	12.4127i	0.873409	+	0.756813i	−0.0977591	+	0.995210i	$0.531167\pi$
$270$	18.7843	+	12.7588i	1.14317	+	0.776478i
$271$	20.3982	+	5.98944i	1.23910	+	0.363833i	0.834677	−	0.550740i	$-0.185654\pi$
$271$	20.3982	+	5.98944i	1.23910	+	0.363833i	0.404423	+	0.914572i	$0.367472\pi$
$272$	3.26367	−	4.58318i	0.197889	−	0.277896i
$273$	50.2815	−	4.37117i	3.04317	−	0.264555i
$274$	−3.57930	−	6.94287i	−0.216233	−	0.419434i
$275$	0.504275	−	0.873430i	0.0304089	−	0.0526698i
$276$	6.52968	−	16.1359i	0.393040	−	0.971268i
$277$	4.12443	+	7.14372i	0.247813	+	0.429225i	0.962919	−	0.269792i	$-0.0869548\pi$
$277$	4.12443	+	7.14372i	0.247813	+	0.429225i	−0.715106	+	0.699016i	$0.753622\pi$
$278$	0.260101	−	0.404725i	0.0155998	−	0.0242738i
$279$	−4.64786	−	2.49685i	−0.278260	−	0.149483i
$280$	0.736001	+	1.61162i	0.0439845	+	0.0963125i
$281$	−4.95355	−	20.4188i	−0.295504	−	1.21809i	−0.905040	−	0.425327i	$-0.860159\pi$
$281$	−4.95355	−	20.4188i	−0.295504	−	1.21809i	0.609536	−	0.792759i	$-0.291356\pi$
$282$	−9.05938	−	14.3631i	−0.539478	−	0.855313i
$283$	−31.3116	+	10.8371i	−1.86128	+	0.644196i	−0.873842	+	0.486210i	$0.838379\pi$
$283$	−31.3116	+	10.8371i	−1.86128	+	0.644196i	−0.987441	+	0.157987i	$0.949500\pi$
$284$	6.74211	−	8.57330i	0.400071	−	0.508732i
$285$	20.5059	+	6.21053i	1.21467	+	0.367880i
$286$	−39.3117	−	13.6059i	−2.32455	−	0.804534i
$287$	41.9142	−	26.9366i	2.47412	−	1.59002i
$288$	24.1791	+	1.56335i	1.42476	+	0.0921214i
$289$	9.69678	+	11.1907i	0.570399	+	0.658275i
$290$	−2.74700	−	2.61926i	−0.161309	−	0.153808i
$291$	2.63350	+	7.82311i	0.154379	+	0.458599i
$292$	−8.39092	−	24.2440i	−0.491042	−	1.41877i
$293$	−11.5593	−	16.2328i	−0.675302	−	0.948329i	−0.999997	−	0.00251049i	$-0.999201\pi$
$293$	−11.5593	−	16.2328i	−0.675302	−	0.948329i	0.324695	−	0.945819i	$-0.394739\pi$
$294$	−12.9191	+	36.3272i	−0.753458	+	2.11865i
$295$	−0.107667	−	0.0766697i	−0.00626864	−	0.00446388i
$296$	0.0379390	+	0.263871i	0.00220516	+	0.0153372i
$297$	3.33073	−	15.1903i	0.193269	−	0.881431i
$298$		−	17.5676i		−	1.01767i
$299$	32.3734	+	6.07981i	1.87220	+	0.351604i
$300$	1.22122	+	0.0685622i	0.0705070	+	0.00395844i
$301$	18.1293	−	9.34629i	1.04495	−	0.538711i
$302$	−6.00560	+	15.0013i	−0.345584	+	0.863226i
$303$	−3.53664	−	2.83013i	−0.203175	−	0.162587i
$304$	21.1534	−	5.13176i	1.21323	−	0.294326i
$305$	13.4073	+	6.12290i	0.767698	+	0.350596i
$306$	2.67875	−	8.58160i	0.153134	−	0.490577i
$307$	−2.10976	+	14.6737i	−0.120410	+	0.837471i	0.836682	+	0.547688i	$0.184492\pi$
$307$	−2.10976	+	14.6737i	−0.120410	+	0.837471i	−0.957093	+	0.289782i	$0.906417\pi$
$308$	18.3616	−	19.2571i	1.04625	−	1.09728i
$309$	2.22999	+	16.5026i	0.126860	+	0.938800i
$310$	7.67692	−	0.365697i	0.436020	−	0.0207702i
$311$	−20.6250	+	0.982492i	−1.16954	+	0.0557120i	−0.623345	−	0.781947i	$-0.714227\pi$
$311$	−20.6250	+	0.982492i	−1.16954	+	0.0557120i	−0.546194	+	0.837659i	$0.683924\pi$
$312$	−0.308081	−	2.27989i	−0.0174416	−	0.129073i
$313$	1.11801	−	1.17253i	0.0631936	−	0.0662755i	−0.691378	−	0.722493i	$-0.742996\pi$
$313$	1.11801	−	1.17253i	0.0631936	−	0.0662755i	0.754572	+	0.656218i	$0.227845\pi$
$314$	−3.03578	+	21.1143i	−0.171319	+	1.19155i
$315$	−18.6262	−	20.2103i	−1.04947	−	1.13872i
$316$	−8.36853	−	3.82178i	−0.470766	−	0.214992i
$317$	−17.3072	+	4.19869i	−0.972072	+	0.235822i	−0.690191	−	0.723627i	$-0.742473\pi$
$317$	−17.3072	+	4.19869i	−0.972072	+	0.235822i	−0.281881	+	0.959449i	$0.590958\pi$
$318$	−20.7941	−	16.6401i	−1.16608	−	0.933131i
$319$	−0.966096	+	2.41319i	−0.0540910	+	0.135113i
$320$	−16.7854	+	8.65347i	−0.938332	+	0.483744i
$321$	3.32138	+	0.186470i	0.185381	+	0.0104078i
$322$	−23.7249	+	33.6549i	−1.32214	+	1.87551i
$323$		−	8.48249i		−	0.471978i
$324$	18.2659	−	4.69646i	1.01477	−	0.260914i
$325$	0.329395	+	2.29099i	0.0182715	+	0.127081i
$326$	−5.67133	−	4.03853i	−0.314106	−	0.223674i
$327$	5.25813	−	14.7853i	0.290775	−	0.817631i
$328$	−1.31736	−	1.84998i	−0.0727393	−	0.102148i
$329$	6.72247	+	19.4233i	0.370622	+	1.07084i
$330$	7.22730	+	21.4695i	0.397850	+	1.18186i
$331$	−18.0857	−	17.2446i	−0.994078	−	0.947851i	0.00456231	−	0.999990i	$-0.498548\pi$
$331$	−18.0857	−	17.2446i	−0.994078	−	0.947851i	−0.998640	+	0.0521386i	$0.983396\pi$
$332$	10.1542	+	11.7186i	0.557285	+	0.643142i
$333$	−1.83234	−	3.70737i	−0.100412	−	0.203163i
$334$	−5.55202	+	3.56807i	−0.303793	+	0.195236i
$335$	−2.21442	−	0.766417i	−0.120987	−	0.0418738i
$336$	−26.7233	−	8.09354i	−1.45787	−	0.441539i
$337$	17.3842	−	22.1058i	0.946976	−	1.20418i	−0.0318522	−	0.999493i	$-0.510141\pi$
$337$	17.3842	−	22.1058i	0.946976	−	1.20418i	0.978828	−	0.204685i	$-0.0656170\pi$
$338$	65.3558	−	22.6199i	3.55489	−	1.23036i
$339$	−8.18839	−	12.9822i	−0.444732	−	0.705098i
$340$	1.57973	+	6.51172i	0.0856727	+	0.353148i
$341$	−2.18652	−	4.78781i	−0.118407	−	0.259274i
$342$	29.5730	−	18.3040i	1.59913	−	0.989766i
$343$	9.17388	−	14.2748i	0.495343	−	0.770769i
$344$	−0.464868	−	0.805175i	−0.0250640	−	0.0434121i
$345$	−8.15992	−	15.9738i	−0.439316	−	0.860002i
$346$	−19.4060	+	33.6121i	−1.04327	+	1.80700i
$347$	0.285766	+	0.554309i	0.0153407	+	0.0297569i	0.896381	−	0.443284i	$-0.146187\pi$
$347$	0.285766	+	0.554309i	0.0153407	+	0.0297569i	−0.881041	+	0.473041i	$0.843156\pi$
$348$	−3.14062	+	0.273027i	−0.168355	+	0.0146358i
$349$	−2.90037	+	4.07300i	−0.155253	+	0.218023i	−0.884875	−	0.465828i	$-0.845757\pi$
$349$	−2.90037	+	4.07300i	−0.155253	+	0.218023i	0.729622	+	0.683851i	$0.239696\pi$
$350$	−2.77616	−	0.815155i	−0.148392	−	0.0435719i
$351$	15.5410	+	32.1275i	0.829519	+	1.71484i
$352$	18.2677	+	15.8290i	0.973671	+	0.843691i
$353$	12.5958	+	31.4627i	0.670406	+	1.67459i	0.736204	+	0.676759i	$0.236616\pi$
$353$	12.5958	+	31.4627i	0.670406	+	1.67459i	−0.0657988	+	0.997833i	$0.520960\pi$
$354$	−0.208928	+	0.0488123i	−0.0111044	+	0.00259435i
$355$	−2.12700	−	11.0359i	−0.112890	−	0.585727i
$356$	0.638434	+	13.4024i	0.0338369	+	0.710324i
$357$	−5.52029	+	9.37680i	−0.292165	+	0.496273i
$358$	0.475921	−	1.37508i	0.0251532	−	0.0726753i
$359$	0.105422	−	0.0309547i	0.00556396	−	0.00163373i	−0.278949	−	0.960306i	$-0.589986\pi$
$359$	0.105422	−	0.0309547i	0.00556396	−	0.00163373i	0.284513	+	0.958672i	$0.408168\pi$
$360$	−0.879799	+	0.891904i	−0.0463695	+	0.0470075i
$361$	9.04757	−	10.4415i	0.476188	−	0.549550i
$362$	26.8080	−	2.55985i	1.40900	−	0.134543i
$363$	−2.69382	+	2.29449i	−0.141389	+	0.120429i
$364$	−5.80446	+	60.7871i	−0.304237	+	3.18611i
$365$	−24.5429	−	9.82548i	−1.28463	−	0.514289i
$366$	21.8468	−	9.75397i	1.14195	−	0.509848i
$367$	18.6924	−	10.7921i	0.975735	−	0.563341i	0.0747554	−	0.997202i	$-0.476182\pi$
$367$	18.6924	−	10.7921i	0.975735	−	0.563341i	0.900980	+	0.433861i	$0.142849\pi$
$368$	−15.3768	−	9.77900i	−0.801573	−	0.509766i
$369$	28.3475	+	20.9200i	1.47571	+	1.08905i
$370$	5.06781	+	3.25688i	0.263463	+	0.169317i
$371$	19.9262	+	25.3383i	1.03452	+	1.31550i
$372$	3.98836	−	4.98401i	0.206787	−	0.258409i
$373$	3.22100	+	3.37808i	0.166777	+	0.174911i	0.801819	−	0.597567i	$-0.203866\pi$
$373$	3.22100	+	3.37808i	0.166777	+	0.174911i	−0.635042	+	0.772477i	$0.719017\pi$
$374$	7.30550	−	5.20223i	0.377759	−	0.269001i
$375$	13.8970	−	14.3293i	0.717637	−	0.739964i
$376$	0.869784	−	0.348209i	0.0448557	−	0.0179575i
$377$	−1.68065	−	5.72378i	−0.0865580	−	0.294790i
$378$	−44.6029	+	0.988056i	−2.29413	+	0.0508201i
$379$	1.29489	+	2.01489i	0.0665141	+	0.103498i	0.872917	−	0.487868i	$-0.162225\pi$
$379$	1.29489	+	2.01489i	0.0665141	+	0.103498i	−0.806403	+	0.591366i	$0.798589\pi$
$380$	−11.8784	+	23.0408i	−0.609347	+	1.18197i
$381$	−6.94739	−	8.99026i	−0.355926	−	0.460585i
$382$	−0.738166	−	0.179077i	−0.0377679	−	0.00916238i
$383$	−14.4916	−	11.3963i	−0.740487	−	0.582325i	0.175050	−	0.984560i	$-0.443991\pi$
$383$	−14.4916	−	11.3963i	−0.740487	−	0.582325i	−0.915537	+	0.402234i	$0.868234\pi$
$384$	−0.653081	+	2.59572i	−0.0333274	+	0.132462i
$385$	−2.60631	−	27.2945i	−0.132830	−	1.39106i
$386$	−7.07096	+	24.0815i	−0.359902	+	1.22572i
$387$	10.7382	+	9.62849i	0.545853	+	0.489444i
$388$	−9.88521	+	1.42128i	−0.501845	+	0.0721545i
$389$	1.07369	−	22.5395i	0.0544382	−	1.14280i	−0.792073	−	0.610427i	$-0.790998\pi$
$389$	1.07369	−	22.5395i	0.0544382	−	1.14280i	0.846511	−	0.532371i	$-0.178699\pi$
$390$	−43.4949	−	28.4768i	−2.20245	−	1.44198i
$391$	−5.11615	+	4.92494i	−0.258735	+	0.249065i
$392$	−1.84221	−	1.06360i	−0.0930454	−	0.0537198i
$393$	−1.09592	−	2.45462i	−0.0552817	−	0.123819i
$394$	−25.5934	+	20.1269i	−1.28938	+	1.01398i
$395$	−8.62347	+	3.93821i	−0.433894	+	0.198153i
$396$	17.3460	+	7.28816i	0.871671	+	0.366244i
$397$	13.4580	−	29.4688i	0.675436	−	1.47900i	−0.191972	−	0.981400i	$-0.561488\pi$
$397$	13.4580	−	29.4688i	0.675436	−	1.47900i	0.867408	−	0.497598i	$-0.165784\pi$
$398$	−15.5397	−	2.99504i	−0.778936	−	0.150128i
$399$	−39.8956	+	13.4301i	−1.99728	+	0.672345i
$400$	0.301883	−	1.24438i	0.0150942	−	0.0622189i
$401$	−33.7904	+	6.51257i	−1.68741	+	0.325222i	−0.940524	−	0.339726i	$-0.889666\pi$
$401$	−33.7904	+	6.51257i	−1.68741	+	0.325222i	−0.746889	+	0.664949i	$0.768453\pi$
$402$	−3.31015	+	1.87386i	−0.165096	+	0.0934595i
$403$	10.7365	+	5.53504i	0.534822	+	0.275720i
$404$	4.14171	−	3.58881i	0.206058	−	0.178550i
$405$	8.66858	−	17.3942i	0.430745	−	0.864327i
$406$	7.38132	+	1.06127i	0.366329	+	0.0526702i
$407$	0.780772	−	4.05103i	0.0387014	−	0.200802i
$408$	0.438909	+	0.231007i	0.0217292	+	0.0114366i
$409$	6.66940	−	6.35926i	0.329781	−	0.314445i	−0.507040	−	0.861923i	$-0.669260\pi$
$409$	6.66940	−	6.35926i	0.329781	−	0.314445i	0.836820	+	0.547477i	$0.184412\pi$
$410$	−51.0884	−	4.87835i	−2.52308	−	0.240925i
$411$	−5.47840	+	3.83152i	−0.270229	+	0.188995i
$412$	−20.1247	−	0.958656i	−0.991471	−	0.0472296i
$413$	0.259687			0.0127784
$414$	−28.2100	−	7.20944i	−1.38645	−	0.354324i
$415$	15.9783			0.784345
$416$	−55.4093	−	2.63947i	−2.71667	−	0.129411i
$417$	−0.373079	−	0.174220i	−0.0182698	−	0.00853158i
$418$	34.5390	+	3.29808i	1.68936	+	0.161314i
$419$	14.5427	−	13.8664i	0.710456	−	0.677418i	−0.246008	−	0.969268i	$-0.579119\pi$
$419$	14.5427	−	13.8664i	0.710456	−	0.677418i	0.956464	+	0.291849i	$0.0942706\pi$
$420$	28.1253	−	17.7397i	1.37238	−	0.865610i
$421$	1.73632	−	9.00889i	0.0846231	−	0.439067i	−0.914762	−	0.403994i	$-0.867622\pi$
$421$	1.73632	−	9.00889i	0.0846231	−	0.439067i	0.999385	−	0.0350725i	$-0.0111662\pi$
$422$	21.7192	+	3.12275i	1.05727	+	0.152013i
$423$	−11.1439	+	9.32992i	−0.541833	+	0.453636i
$424$	1.11046	−	0.962221i	0.0539288	−	0.0467296i
$425$	−0.443524	−	0.228653i	−0.0215141	−	0.0110913i
$426$	−15.7216	−	9.25556i	−0.761712	−	0.448434i
$427$	−28.4350	+	5.48039i	−1.37606	+	0.265215i
$428$	−0.948875	+	3.91132i	−0.0458656	+	0.189061i
$429$	−7.03437	+	34.9017i	−0.339622	+	1.68507i
$430$	−20.6299	−	3.97609i	−0.994863	−	0.191744i
$431$	−14.1326	+	30.9460i	−0.680741	+	1.49062i	0.181115	+	0.983462i	$0.442030\pi$
$431$	−14.1326	+	30.9460i	−0.680741	+	1.49062i	−0.861856	+	0.507153i	$0.830698\pi$
$432$	−1.37600	−	19.6961i	−0.0662030	−	0.947627i
$433$	−15.9313	+	7.27559i	−0.765610	+	0.349642i	−0.759643	−	0.650340i	$-0.774627\pi$
$433$	−15.9313	+	7.27559i	−0.765610	+	0.349642i	−0.00596666	+	0.999982i	$0.501899\pi$
$434$	−11.8694	+	9.33420i	−0.569749	+	0.448056i
$435$	−1.90670	+	2.63007i	−0.0914192	+	0.126102i
$436$	16.4423	+	9.49295i	0.787442	+	0.454630i
$437$	−27.4354	+	1.43781i	−1.31241	+	0.0687799i
$438$	−38.3081	+	19.3396i	−1.83043	+	0.924081i
$439$	−0.585245	+	12.2858i	−0.0279322	+	0.586369i	0.940905	+	0.338671i	$0.109977\pi$
$439$	−0.585245	+	12.2858i	−0.0279322	+	0.586369i	−0.968837	+	0.247698i	$0.920326\pi$
$440$	−1.23710	+	0.177868i	−0.0589762	+	0.00847950i
$441$	32.2918	+	6.79391i	1.53770	+	0.323519i
$442$	−5.79863	+	19.7483i	−0.275813	+	0.939331i
$443$	−3.22444	−	33.7678i	−0.153198	−	1.60436i	−0.666067	−	0.745892i	$-0.732024\pi$
$443$	−3.22444	−	33.7678i	−0.153198	−	1.60436i	0.512869	−	0.858467i	$-0.328583\pi$
$444$	4.81250	−	1.36884i	0.228391	−	0.0649622i
$445$	10.8682	+	8.54687i	0.515204	+	0.405161i
$446$	32.4678	+	7.87660i	1.53739	+	0.372968i
$447$	−14.9000	+	2.01344i	−0.704748	+	0.0952323i
$448$	17.0015	−	32.9784i	0.803247	−	1.55808i
$449$	−1.09526	−	1.70426i	−0.0516887	−	0.0804292i	0.814447	−	0.580237i	$-0.197040\pi$
$449$	−1.09526	−	1.70426i	−0.0516887	−	0.0804292i	−0.866136	+	0.499808i	$0.833404\pi$
$450$	−0.159896	−	2.03969i	−0.00753755	−	0.0961517i
$451$	9.90199	+	33.7231i	0.466266	+	1.58796i
$452$	17.2400	−	6.90184i	0.810899	−	0.324635i
$453$	13.4117	+	3.37437i	0.630136	+	0.158542i
$454$	−3.36832	+	2.39857i	−0.158083	+	0.112571i
$455$	43.4224	+	45.5402i	2.03568	+	2.13496i
$456$	0.698017	+	1.78736i	0.0326876	+	0.0837009i
$457$	−21.1238	−	26.8611i	−0.988128	−	1.25651i	−0.966480	−	0.256742i	$-0.917351\pi$
$457$	−21.1238	−	26.8611i	−0.988128	−	1.25651i	−0.0216484	−	0.999766i	$-0.506891\pi$
$458$	42.4898	+	27.3066i	1.98542	+	1.27595i
$459$	−7.58553	−	1.28845i	−0.354062	−	0.0601398i
$460$	20.7935	−	6.21316i	0.969500	−	0.289690i
$461$	31.8368	−	18.3810i	1.48279	−	0.856089i	0.482980	−	0.875631i	$-0.339554\pi$
$461$	31.8368	−	18.3810i	1.48279	−	0.856089i	0.999809	+	0.0195427i	$0.00622103\pi$
$462$	−36.0341	−	26.1233i	−1.67646	−	1.21537i
$463$	24.9671	+	9.99533i	1.16032	+	0.464522i	0.870312	−	0.492502i	$-0.163917\pi$
$463$	24.9671	+	9.99533i	1.16032	+	0.464522i	0.290009	+	0.957024i	$0.406342\pi$
$464$	−0.313707	+	3.28529i	−0.0145635	+	0.152516i
$465$	−1.19002	−	6.46929i	−0.0551860	−	0.300006i
$466$	−6.67629	+	0.637509i	−0.309273	+	0.0295320i
$467$	26.1811	−	30.2146i	1.21152	−	1.39816i	0.318632	−	0.947879i	$-0.396777\pi$
$467$	26.1811	−	30.2146i	1.21152	−	1.39816i	0.892885	−	0.450285i	$-0.148678\pi$
$468$	−41.6304	+	11.4602i	−1.92436	+	0.529750i
$469$	4.41740	−	1.29707i	0.203977	−	0.0598929i
$470$	6.92448	−	20.0070i	0.319403	−	0.922853i
$471$	18.2561	+	0.154884i	0.841196	+	0.00713666i
$472$	−0.000563240	−	0.0118239i	−2.59252e−5	−	0.000544237i
$473$	2.72300	+	14.1283i	0.125204	+	0.649619i
$474$	−4.46059	+	14.7280i	−0.204882	+	0.676479i
$475$	−0.717476	−	1.79217i	−0.0329201	−	0.0822303i
$476$	−9.94923	−	8.62105i	−0.456022	−	0.395145i
$477$	−11.7301	+	19.5437i	−0.537086	+	0.894846i
$478$	12.5142	+	3.67451i	0.572387	+	0.168068i
$479$	2.70282	−	3.79558i	0.123495	−	0.173425i	−0.748200	−	0.663473i	$-0.769082\pi$
$479$	2.70282	−	3.79558i	0.123495	−	0.173425i	0.871695	+	0.490049i	$0.163021\pi$
$480$	17.3128	+	24.7542i	0.790218	+	1.12987i
$481$	4.33845	+	8.41543i	0.197816	+	0.383710i
$482$	−21.2516	+	36.8089i	−0.967984	+	1.67660i
$483$	31.2636	+	16.2652i	1.42254	+	0.740092i
$484$	−2.14060	−	3.70763i	−0.0972999	−	0.168528i
$485$	−5.56379	+	8.65743i	−0.252639	+	0.393114i
$486$	−11.8765	−	29.2262i	−0.538727	−	1.32573i
$487$	−7.29368	−	15.9709i	−0.330508	−	0.723712i	0.669306	−	0.742987i	$-0.266592\pi$
$487$	−7.29368	−	15.9709i	−0.330508	−	0.723712i	−0.999814	+	0.0192747i	$0.993864\pi$
$488$	0.311201	+	1.28279i	0.0140874	+	0.0580692i
$489$	−2.77530	+	5.27302i	−0.125504	+	0.238454i
$490$	−45.4253	+	15.7218i	−2.05211	+	0.710241i
$491$	9.71567	−	12.3545i	0.438462	−	0.557550i	−0.515727	−	0.856753i	$-0.672478\pi$
$491$	9.71567	−	12.3545i	0.438462	−	0.557550i	0.954190	+	0.299203i	$0.0967207\pi$
$492$	−31.0976	+	29.1518i	−1.40199	+	1.31427i
$493$	1.21535	+	0.420638i	0.0547367	+	0.0189446i
$494$	−66.9850	+	43.0487i	−3.01380	+	1.93685i
$495$	17.3811	−	8.59050i	0.781223	−	0.386114i
$496$	−4.37616	−	5.05036i	−0.196495	−	0.226768i
$497$	15.9811	+	15.2379i	0.716849	+	0.683514i
$498$	17.1506	−	19.4569i	0.768538	−	0.871883i
$499$	−10.2402	−	29.5872i	−0.458416	−	1.32451i	−0.903335	−	0.428935i	$-0.858889\pi$
$499$	−10.2402	−	29.5872i	−0.458416	−	1.32451i	0.444920	−	0.895571i	$-0.353232\pi$
$500$	14.0088	+	19.6726i	0.626491	+	0.879784i
$501$	3.66259	+	4.30003i	0.163632	+	0.192111i
$502$	−21.5095	−	15.3168i	−0.960014	−	0.683623i
$503$	1.00521	+	6.99136i	0.0448199	+	0.311729i	0.999883	+	0.0153254i	$0.00487842\pi$
$503$	1.00521	+	6.99136i	0.0448199	+	0.311729i	−0.955063	+	0.296404i	$0.904212\pi$
$504$	0.391582	−	2.43006i	0.0174424	−	0.108244i
$505$		−	5.64722i		−	0.251298i
$506$	−18.0642	−	22.7468i	−0.803050	−	1.01122i
$507$	−26.6756	−	52.8393i	−1.18470	−	2.34668i
$508$	12.2182	−	6.29894i	0.542097	−	0.279470i
$509$	5.20007	−	12.9892i	0.230489	−	0.575734i	−0.767365	−	0.641211i	$-0.778432\pi$
$509$	5.20007	−	12.9892i	0.230489	−	0.575734i	0.997854	+	0.0654765i	$0.0208567\pi$
$510$	10.4402	−	4.07719i	0.462299	−	0.180541i
$511$	50.4760	−	12.2453i	2.23293	−	0.541702i
$512$	29.2523	+	13.3591i	1.29278	+	0.590393i
$513$	−18.9140	−	22.9846i	−0.835073	−	1.01480i
$514$	−0.977439	+	6.79823i	−0.0431130	+	0.299857i
$515$	−14.3269	+	15.0256i	−0.631320	+	0.662109i
$516$	−13.8074	+	10.6700i	−0.607838	+	0.469718i
$517$	−14.4827	+	0.689895i	−0.636948	+	0.0303416i
$518$	−11.8222	+	0.563162i	−0.519439	+	0.0247439i
$519$	30.7324	+	12.6069i	1.34900	+	0.553383i
$520$	1.97932	−	2.07585i	0.0867987	−	0.0910319i
$521$	1.29676	−	9.01919i	0.0568122	−	0.395138i	−0.941497	−	0.337020i	$-0.890581\pi$
$521$	1.29676	−	9.01919i	0.0568122	−	0.395138i	0.998310	−	0.0581178i	$-0.0185099\pi$
$522$	1.15606	+	5.14483i	0.0505994	+	0.225183i
$523$	29.2603	+	13.3627i	1.27946	+	0.584312i	0.935053	−	0.354507i	$-0.115351\pi$
$523$	29.2603	+	13.3627i	1.27946	+	0.584312i	0.344411	+	0.938819i	$0.388079\pi$
$524$	3.16065	−	0.766766i	0.138074	−	0.0334963i
$525$	−0.373199	+	2.44804i	−0.0162878	+	0.106841i
$526$	−0.138482	+	0.345911i	−0.00603810	+	0.0150824i
$527$	−2.31468	+	1.19330i	−0.100829	+	0.0519810i
$528$	10.7891	−	16.4791i	0.469536	−	0.717162i
$529$	16.7962	+	15.7127i	0.730270	+	0.683159i
$530$		−	33.2035i		−	1.44227i
$531$	0.0653457	+	0.171609i	0.00283576	+	0.00744718i
$532$	−7.24810	−	50.4117i	−0.314245	−	2.18562i
$533$	−65.7032	−	46.7870i	−2.84592	−	2.02657i
$534$	22.0732	−	4.06035i	0.955200	−	0.175709i
$535$	2.40572	+	3.37836i	0.104008	+	0.146059i
$536$	−0.0686378	−	0.198316i	−0.00296470	−	0.00856595i
$537$	−1.22083	−	0.246055i	−0.0526826	−	0.0106180i
$538$	27.7620	+	26.4711i	1.19691	+	1.14125i
$539$	21.5579	+	24.8791i	0.928564	+	1.07162i
$540$	18.8001	+	14.1221i	0.809029	+	0.607719i
$541$	−32.1857	+	20.6845i	−1.38377	+	0.889297i	−0.999425	−	0.0338921i	$-0.989210\pi$
$541$	−32.1857	+	20.6845i	−1.38377	+	0.889297i	−0.384347	+	0.923189i	$0.625573\pi$
$542$	40.6572	+	14.0716i	1.74638	+	0.604427i
$543$	−5.24363	−	22.4439i	−0.225026	−	0.963160i
$544$	7.39272	−	9.40061i	0.316960	−	0.403048i
$545$	18.4883	−	6.39885i	0.791951	−	0.274097i
$546$	102.063	−	3.99434i	4.36788	−	0.170942i
$547$	2.06517	+	8.51274i	0.0883002	+	0.363978i	0.998769	−	0.0495990i	$-0.0157943\pi$
$547$	2.06517	+	8.51274i	0.0883002	+	0.363978i	−0.910469	+	0.413577i	$0.864279\pi$
$548$	−3.36003	−	7.35744i	−0.143533	−	0.314294i
$549$	−10.7767	−	17.4116i	−0.459940	−	0.743107i
$550$	1.10348	−	1.71704i	0.0470524	−	0.0732149i
$551$	2.48773	+	4.30887i	0.105981	+	0.183564i
$552$	0.672764	−	1.45875i	0.0286347	−	0.0620884i
$553$	9.31289	−	16.1304i	0.396024	−	0.685934i
$554$	7.64946	+	14.8379i	0.324994	+	0.630401i
$555$	2.18151	−	4.67156i	0.0926001	−	0.198297i
$556$	0.288966	−	0.405796i	0.0122549	−	0.0172096i
$557$	−15.4086	−	4.52438i	−0.652884	−	0.191704i	−0.0615165	−	0.998106i	$-0.519594\pi$
$557$	−15.4086	−	4.52438i	−0.652884	−	0.191704i	−0.591368	+	0.806402i	$0.701412\pi$
$558$	−9.15502	−	5.49484i	−0.387563	−	0.232615i
$559$	−24.9550	−	21.6236i	−1.05548	−	0.914581i
$560$	−12.9380	−	32.3176i	−0.546731	−	1.36567i
$561$	−5.24958	−	5.59996i	−0.221637	−	0.236431i
$562$	−8.04719	−	41.7528i	−0.339450	−	1.76123i
$563$	1.62996	+	34.2171i	0.0686947	+	1.44208i	0.725606	+	0.688111i	$0.241560\pi$
$563$	1.62996	+	34.2171i	0.0686947	+	1.44208i	−0.656911	+	0.753968i	$0.728137\pi$
$564$	−8.66254	−	15.3023i	−0.364759	−	0.644344i
$565$	6.25874	−	18.0835i	0.263307	−	0.760777i
$566$	−64.3387	+	18.8915i	−2.70436	+	0.794070i
$567$	5.94999	+	37.7169i	0.249876	+	1.58396i
$568$	0.659138	−	0.760686i	0.0276568	−	0.0319177i
$569$	−37.6446	+	3.59463i	−1.57815	+	0.150695i	−0.847025	−	0.531553i	$-0.821609\pi$
$569$	−37.6446	+	3.59463i	−1.57815	+	0.150695i	−0.731121	+	0.682248i	$0.761002\pi$
$570$	40.8538	+	14.5289i	1.71118	+	0.608549i
$571$	0.817573	−	8.56201i	0.0342144	−	0.358309i	−0.962111	−	0.272659i	$-0.912097\pi$
$571$	0.817573	−	8.56201i	0.0342144	−	0.358309i	0.996325	−	0.0856506i	$-0.0272969\pi$
$572$	−39.9901	−	16.0096i	−1.67207	−	0.669397i
$573$	−0.0672833	+	0.646602i	−0.00281080	+	0.0270122i
$574$	87.3217	−	50.4152i	3.64474	−	2.10429i
$575$	−0.664365	+	1.47327i	−0.0277060	+	0.0614397i
$576$	26.0712	+	2.93666i	1.08630	+	0.122361i
$577$	9.08795	+	5.84047i	0.378336	+	0.243142i	0.715963	−	0.698138i	$-0.245988\pi$
$577$	9.08795	+	5.84047i	0.378336	+	0.243142i	−0.337627	+	0.941280i	$0.609624\pi$
$578$	18.5240	+	23.5552i	0.770498	+	0.979768i
$579$	21.2352	+	3.23727i	0.882505	+	0.134536i
$580$	−2.71220	−	2.84447i	−0.112618	−	0.118110i
$581$	−25.5717	+	18.2096i	−1.06089	+	0.755460i
$582$	4.57019	+	16.0677i	0.189441	+	0.666026i
$583$	−21.1104	+	8.45132i	−0.874302	+	0.350018i
$584$	−0.667022	−	2.27167i	−0.0276016	−	0.0940024i
$585$	−19.1677	+	40.1541i	−0.792487	+	1.66017i
$586$	−21.8035	−	33.9270i	−0.900696	−	1.40151i
$587$	10.0429	−	19.4804i	0.414513	−	0.804043i	−0.585465	−	0.810698i	$-0.699088\pi$
$587$	10.0429	−	19.4804i	0.414513	−	0.804043i	0.999978	+	0.00665484i	$0.00211832\pi$
$588$	−15.1522	+	36.9371i	−0.624868	+	1.52326i
$589$	−9.79071	−	2.37520i	−0.403419	−	0.0978684i
$590$	−0.210262	−	0.165352i	−0.00865636	−	0.00680744i
$591$	20.0040	+	19.4004i	0.822854	+	0.798027i
$592$	−0.497896	−	5.21420i	−0.0204634	−	0.214302i
$593$	4.31911	−	14.7095i	0.177364	−	0.604048i	−0.822036	−	0.569435i	$-0.807162\pi$
$593$	4.31911	−	14.7095i	0.177364	−	0.604048i	0.999401	−	0.0346128i	$-0.0110198\pi$
$594$	8.19566	−	30.3858i	0.336272	−	1.24675i
$595$	−13.4277	+	1.93061i	−0.550482	+	0.0791473i
$596$	0.865562	−	18.1704i	0.0354548	−	0.744288i
$597$	−0.759234	+	13.5233i	−0.0310734	+	0.553473i
$598$	64.8560	+	15.4074i	2.65216	+	0.630056i
$599$	−24.7456	−	14.2869i	−1.01108	−	0.583746i	−0.0995713	−	0.995030i	$-0.531747\pi$
$599$	−24.7456	−	14.2869i	−1.01108	−	0.583746i	−0.911507	+	0.411284i	$0.865080\pi$
$600$	0.112271	+	0.0116826i	0.00458346	+	0.000476940i
$601$	−31.5780	+	24.8332i	−1.28809	+	1.01297i	−0.289655	+	0.957131i	$0.593541\pi$
$601$	−31.5780	+	24.8332i	−1.28809	+	1.01297i	−0.998440	+	0.0558378i	$0.982217\pi$
$602$	37.5475	−	17.1474i	1.53032	−	0.698875i
$603$	1.96870	+	2.59276i	0.0801716	+	0.105585i
$604$	−6.95078	+	15.2201i	−0.282823	+	0.619296i
$605$	−4.33190	−	0.834905i	−0.176117	−	0.0339437i
$606$	−6.87664	−	6.06154i	−0.279344	−	0.246233i
$607$	0.686554	−	2.83002i	0.0278664	−	0.114867i	−0.956180	−	0.292780i	$-0.905420\pi$
$607$	0.686554	−	2.83002i	0.0278664	−	0.114867i	0.984046	+	0.177913i	$0.0569347\pi$
$608$	45.4304	−	8.75600i	1.84245	−	0.355103i
$609$	0.0541456	−	6.38213i	0.00219409	−	0.258617i
$610$	26.5126	+	13.6682i	1.07347	+	0.553410i
$611$	25.1471	−	21.7901i	1.01734	−	0.881534i
$612$	3.19348	−	8.74406i	0.129089	−	0.353458i
$613$	9.88185	+	1.42079i	0.399124	+	0.0573854i	0.338954	−	0.940803i	$-0.389927\pi$
$613$	9.88185	+	1.42079i	0.399124	+	0.0573854i	0.0601696	+	0.998188i	$0.480836\pi$
$614$	−5.67776	+	29.4590i	−0.229136	+	1.18887i
$615$	1.71768	+	43.8900i	0.0692636	+	1.76981i
$616$	1.77715	−	1.69451i	0.0716033	−	0.0682736i
$617$	−20.0978	−	1.91910i	−0.809105	−	0.0772602i	−0.317700	−	0.948191i	$-0.602911\pi$
$617$	−20.0978	−	1.91910i	−0.809105	−	0.0772602i	−0.491405	+	0.870931i	$0.663517\pi$
$618$	2.91872	+	33.5740i	0.117408	+	1.35054i
$619$	−13.2473	−	0.631047i	−0.532454	−	0.0253639i	−0.220366	−	0.975417i	$-0.570725\pi$
$619$	−13.2473	−	0.631047i	−0.532454	−	0.0253639i	−0.312088	+	0.950053i	$0.601028\pi$
$620$	7.95834			0.319615
$621$	−2.88154	+	24.7527i	−0.115632	+	0.993292i
$622$	−41.7872			−1.67552
$623$	−27.1339	−	1.29255i	−1.08710	−	0.0517848i
$624$	3.91491	+	45.0331i	0.156722	+	1.80277i
$625$	23.0964	+	2.20544i	0.923857	+	0.0882177i
$626$	2.37291	−	2.26257i	0.0948407	−	0.0904304i
$627$	−1.16126	−	29.6724i	−0.0463764	−	1.18500i
$628$	−4.18024	+	21.6892i	−0.166810	+	0.865492i
$629$	−2.02042	−	0.290492i	−0.0805592	−	0.0115827i
$630$	−35.7058	−	42.6478i	−1.42255	−	1.69913i
$631$	16.6240	−	14.4048i	0.661791	−	0.573445i	−0.257860	−	0.966182i	$-0.583017\pi$
$631$	16.6240	−	14.4048i	0.661791	−	0.573445i	0.919651	+	0.392737i	$0.128472\pi$
$632$	−0.754634	−	0.389041i	−0.0300177	−	0.0154752i
$633$	0.159321	−	18.7791i	0.00633244	−	0.746404i
$634$	−35.3901	+	6.82089i	−1.40552	+	0.270892i
$635$	3.33956	−	13.7658i	0.132526	−	0.546281i
$636$	−20.6877	−	18.2356i	−0.820321	−	0.723088i
$637$	−74.1834	−	14.2977i	−2.93925	−	0.566495i
$638$	−2.18530	+	4.78513i	−0.0865167	+	0.189445i
$639$	−6.04828	+	14.3951i	−0.239266	+	0.569461i
$640$	−3.03546	+	1.38625i	−0.119987	+	0.0547963i
$641$	−6.67746	+	5.25121i	−0.263744	+	0.207410i	−0.741270	−	0.671207i	$-0.765776\pi$
$641$	−6.67746	+	5.25121i	−0.263744	+	0.207410i	0.477526	+	0.878618i	$0.341534\pi$
$642$	6.69606	+	0.696770i	0.264273	+	0.0274993i
$643$	−40.2666	−	23.2480i	−1.58796	−	0.916810i	−0.993643	−	0.112580i	$-0.964089\pi$
$643$	−40.2666	−	23.2480i	−1.58796	−	0.916810i	−0.594318	−	0.804230i	$-0.702578\pi$
$644$	−26.1971	+	33.6407i	−1.03231	+	1.32563i
$645$	−1.00793	+	17.9531i	−0.0396872	+	0.706901i
$646$	0.816811	−	17.1470i	0.0321370	−	0.674639i
$647$	−20.7578	+	2.98452i	−0.816073	+	0.117334i	−0.537697	−	0.843138i	$-0.680705\pi$
$647$	−20.7578	+	2.98452i	−0.816073	+	0.117334i	−0.278377	+	0.960472i	$0.589796\pi$
$648$	1.70439	−	0.352714i	0.0669546	−	0.0138559i
$649$	−0.0516105	+	0.175769i	−0.00202589	+	0.00689955i
$650$	0.445249	+	4.66286i	0.0174641	+	0.182892i
$651$	9.27720	+	8.99728i	0.363602	+	0.352631i
$652$	−5.66694	−	4.45653i	−0.221934	−	0.174531i
$653$	12.4588	+	3.02248i	0.487552	+	0.118279i	0.471997	−	0.881600i	$-0.343533\pi$
$653$	12.4588	+	3.02248i	0.487552	+	0.118279i	0.0155549	+	0.999879i	$0.495049\pi$
$654$	12.0528	−	29.3816i	0.471303	−	1.14891i
$655$	1.53571	−	2.97885i	0.0600050	−	0.116393i
$656$	24.1250	+	37.5392i	0.941923	+	1.46566i
$657$	20.7935	+	30.2746i	0.811230	+	1.18112i
$658$	11.7188	+	39.9107i	0.456848	+	1.55588i
$659$	26.6852	−	10.6831i	1.03951	−	0.416156i	0.211798	−	0.977313i	$-0.432068\pi$
$659$	26.6852	−	10.6831i	1.03951	−	0.416156i	0.827709	+	0.561157i	$0.189644\pi$
$660$	6.41747	+	22.5622i	0.249800	+	0.878234i
$661$	−34.4285	+	24.5164i	−1.33911	+	0.953579i	−0.339197	+	0.940715i	$0.610155\pi$
$661$	−34.4285	+	24.5164i	−1.33911	+	0.953579i	−0.999917	+	0.0128636i	$0.995905\pi$
$662$	−34.8988	−	36.6008i	−1.35638	−	1.42253i
$663$	17.4142	+	2.65476i	0.676311	+	0.103102i
$664$	0.884565	+	1.12482i	0.0343278	+	0.0436513i
$665$	−44.1504	−	28.3737i	−1.71208	−	1.10029i
$666$	−3.34701	−	7.67074i	−0.129694	−	0.297235i
$667$	1.15449	−	4.00218i	0.0447019	−	0.154965i
$668$	−5.91832	+	3.41694i	−0.228987	+	0.132205i
$669$	2.95941	−	28.4404i	0.114418	−	1.09957i
$670$	−4.40255	−	1.76251i	−0.170085	−	0.0680918i
$671$	1.94179	−	20.3354i	0.0749621	−	0.785039i
$672$	−55.9185	−	19.8864i	−2.15710	−	0.767133i
$673$	12.5047	−	1.19405i	0.482019	−	0.0460272i	0.148781	−	0.988870i	$-0.452465\pi$
$673$	12.5047	−	1.19405i	0.482019	−	0.0460272i	0.333238	+	0.942843i	$0.391859\pi$
$674$	37.2700	−	43.0119i	1.43559	−	1.65675i
$675$	−1.71164	+	0.369386i	−0.0658811	+	0.0142177i
$676$	68.7127	−	20.1759i	2.64280	−	0.775995i
$677$	−16.7147	+	48.2939i	−0.642397	+	1.85609i	−0.142976	+	0.989726i	$0.545667\pi$
$677$	−16.7147	+	48.2939i	−0.642397	+	1.85609i	−0.499422	+	0.866359i	$0.666454\pi$
$678$	−15.3024	−	27.0315i	−0.587684	−	1.03814i
$679$	−0.962060	−	20.1961i	−0.0369205	−	0.775056i
$680$	0.117026	+	0.607191i	0.00448776	+	0.0232847i
$681$	2.42040	+	2.58195i	0.0927501	+	0.0989407i
$682$	−3.95892	−	9.88889i	−0.151595	−	0.378665i
$683$	−11.2834	−	9.77713i	−0.431747	−	0.374111i	0.411703	−	0.911318i	$-0.364934\pi$
$683$	−11.2834	−	9.77713i	−0.431747	−	0.374111i	−0.843451	+	0.537207i	$0.819480\pi$
$684$	31.4896	−	17.4749i	1.20403	−	0.668171i
$685$	−7.99717	−	2.34818i	−0.305556	−	0.0897193i
$686$	19.9192	−	27.9726i	0.760518	−	1.06800i
$687$	18.2904	−	39.1675i	0.697821	−	1.49433i
$688$	8.37072	+	16.2369i	0.319131	+	0.619027i
$689$	26.0925	−	45.1935i	0.994044	−	1.72173i
$690$	−14.9568	−	33.0762i	−0.569394	−	1.25919i
$691$	17.1247	+	29.6608i	0.651454	+	1.12835i	0.982770	+	0.184831i	$0.0591739\pi$
$691$	17.1247	+	29.6608i	0.651454	+	1.12835i	−0.331316	+	0.943520i	$0.607493\pi$
$692$	−21.7279	+	33.8093i	−0.825970	+	1.28523i
$693$	−18.0267	+	33.5565i	−0.684778	+	1.27471i
$694$	0.524288	+	1.14803i	0.0199017	+	0.0435786i
$695$	−0.121026	−	0.498875i	−0.00459077	−	0.0189234i
$696$	−0.290703	+	0.0113770i	−0.0110191	+	0.000431244i
$697$	16.4330	−	5.68751i	0.622443	−	0.215430i
$698$	−6.25517	+	7.95410i	−0.236762	+	0.301067i
$699$	1.30588	+	5.58946i	0.0493929	+	0.211413i
$700$	−2.83125	−	0.979907i	−0.107011	−	0.0370370i
$701$	18.1195	−	11.6447i	0.684365	−	0.439815i	−0.151713	−	0.988425i	$-0.548479\pi$
$701$	18.1195	−	11.6447i	0.684365	−	0.439815i	0.836079	+	0.548610i	$0.184843\pi$
$702$	28.3219	+	66.4408i	1.06894	+	2.50764i
$703$	−5.17125	−	5.96794i	−0.195037	−	0.225085i
$704$	18.9425	+	18.0616i	0.713923	+	0.680724i
$705$	−17.7626	−	3.58002i	−0.668979	−	0.134831i
$706$	22.4322	+	64.8134i	0.844245	+	2.43929i
$707$	6.43581	+	9.03782i	0.242043	+	0.339902i
$708$	−0.218501	+	0.0401932i	−0.00821179	+	0.00151055i
$709$	28.6567	+	20.4063i	1.07622	+	0.766376i	0.973581	−	0.228343i	$-0.0733306\pi$
$709$	28.6567	+	20.4063i	1.07622	+	0.766376i	0.102643	+	0.994718i	$0.467270\pi$
$710$	−3.23695	−	22.5135i	−0.121481	−	0.844916i
$711$	13.0028	+	2.09528i	0.487644	+	0.0785793i
$712$			1.23824i			0.0464051i
$713$	4.25191	+	7.28423i	0.159235	+	0.272797i
$714$	−12.0620	+	18.4232i	−0.451407	+	0.689472i
$715$	−39.4537	+	20.3398i	−1.47548	+	0.760665i
$716$	0.560001	−	1.39881i	0.0209282	−	0.0522761i
$717$	1.68228	−	11.0351i	0.0628261	−	0.412114i
$718$	0.216087	−	0.0524220i	0.00806428	−	0.00195637i
$719$	−30.4403	−	13.9016i	−1.13523	−	0.518442i	−0.243001	−	0.970026i	$-0.578132\pi$
$719$	−30.4403	−	13.9016i	−1.13523	−	0.518442i	−0.892229	+	0.451584i	$0.850859\pi$
$720$	18.1007	−	16.6820i	0.674575	−	0.621700i
$721$	5.80500	−	40.3747i	0.216189	−	1.50363i
$722$	19.2947	−	20.2357i	0.718075	−	0.753096i
$723$	33.6552	+	13.8059i	1.25165	+	0.513449i
$724$	27.8539	−	1.32685i	1.03518	−	0.0493118i
$725$	0.292357	−	0.0139267i	0.0108579	−	0.000517224i
$726$	−5.66639	+	4.37881i	−0.210300	+	0.162513i
$727$	6.04569	−	6.34054i	0.224222	−	0.235158i	−0.602008	−	0.798490i	$-0.705632\pi$
$727$	6.04569	−	6.34054i	0.224222	−	0.235158i	0.826230	+	0.563332i	$0.190481\pi$
$728$	−0.801981	+	5.57790i	−0.0297234	+	0.206731i
$729$	−23.4271	+	13.4227i	−0.867672	+	0.497137i
$730$	−48.6662	−	22.2251i	−1.80122	−	0.822588i
$731$	6.91815	−	1.67833i	0.255877	−	0.0620751i
$732$	23.0770	−	9.01224i	0.852951	−	0.333102i
$733$	−1.68756	+	4.21531i	−0.0623313	+	0.155696i	−0.956264	−	0.292505i	$-0.905511\pi$
$733$	−1.68756	+	4.21531i	−0.0623313	+	0.155696i	0.893933	+	0.448202i	$0.147935\pi$
$734$	38.8251	−	20.0157i	1.43306	−	0.738794i
$735$	18.5408	+	36.7257i	0.683887	+	1.35465i
$736$	−31.6580	−	22.3173i	−1.16693	−	0.822626i
$737$			3.24770i			0.119630i
$738$	55.2887	+	45.0185i	2.03521	+	1.65715i
$739$	−1.48672	−	10.3404i	−0.0546898	−	0.380376i	−0.998723	−	0.0505249i	$-0.983911\pi$
$739$	−1.48672	−	10.3404i	−0.0546898	−	0.380376i	0.944033	−	0.329851i	$-0.106999\pi$
$740$	5.08123	+	3.61832i	0.186790	+	0.133012i
$741$	44.1891	+	51.8798i	1.62333	+	1.90585i
$742$	37.8401	+	53.1390i	1.38915	+	1.95079i
$743$	−12.7181	−	36.7466i	−0.466582	−	1.34810i	−0.895622	−	0.444816i	$-0.853269\pi$
$743$	−12.7181	−	36.7466i	−0.466582	−	1.34810i	0.429040	−	0.903286i	$-0.358852\pi$
$744$	0.389535	−	0.441916i	0.0142810	−	0.0162014i
$745$	−13.5665	−	12.9357i	−0.497039	−	0.473926i
$746$	6.18582	+	7.13881i	0.226479	+	0.261371i
$747$	−18.4681	−	12.3164i	−0.675711	−	0.450634i
$748$	7.81248	−	5.02078i	0.285653	−	0.183578i
$749$	−7.70024	−	2.66508i	−0.281361	−	0.0973798i
$750$	29.4720	−	27.6279i	1.07616	−	1.00883i
$751$	−12.4140	+	15.7857i	−0.452993	+	0.576027i	−0.957884	−	0.287156i	$-0.907290\pi$
$751$	−12.4140	+	15.7857i	−0.452993	+	0.576027i	0.504891	+	0.863183i	$0.331533\pi$
$752$	−17.3959	+	6.02078i	−0.634363	+	0.219555i
$753$	−10.5258	+	19.9988i	−0.383582	+	0.728797i
$754$	−2.84620	−	11.7322i	−0.103653	−	0.427262i
$755$	7.16253	+	15.6838i	0.260671	+	0.570790i
$756$	−46.1820	−	1.17564i	−1.67962	−	0.0427576i
$757$	23.4904	−	36.5518i	0.853774	−	1.32850i	−0.0893298	−	0.996002i	$-0.528473\pi$
$757$	23.4904	−	36.5518i	0.853774	−	1.32850i	0.943104	−	0.332497i	$-0.107891\pi$
$758$	2.42355	+	4.19770i	0.0880271	+	0.152467i
$759$	−17.2225	+	17.9282i	−0.625136	+	0.650753i
$760$	−1.19613	+	2.07176i	−0.0433881	+	0.0751505i
$761$	13.1018	+	25.4139i	0.474939	+	0.921254i	0.997635	+	0.0687346i	$0.0218962\pi$
$761$	13.1018	+	25.4139i	0.474939	+	0.921254i	−0.522696	+	0.852519i	$0.675074\pi$
$762$	−13.1782	−	18.8424i	−0.477394	−	0.682589i
$763$	−22.2963	+	31.3108i	−0.807180	+	1.13353i
$764$	−0.754670	−	0.221591i	−0.0273030	−	0.00801689i
$765$	−4.65464	−	8.38759i	−0.168289	−	0.303254i
$766$	−28.1968	−	24.4326i	−1.01879	−	0.882787i
$767$	−0.156250	−	0.390293i	−0.00564185	−	0.0140927i
$768$	7.21118	−	23.8099i	0.260211	−	0.859166i
$769$	−5.49728	−	28.5226i	−0.198237	−	1.02855i	−0.935602	−	0.353056i	$-0.885142\pi$
$769$	−5.49728	−	28.5226i	−0.198237	−	1.02855i	0.737365	−	0.675494i	$-0.236070\pi$
$770$	−2.64025	−	55.4256i	−0.0951479	−	1.99740i
$771$	5.87797	+	0.0498684i	0.211690	+	0.00179597i
$772$	−8.50008	+	24.5594i	−0.305924	+	0.883911i
$773$	−22.6223	+	6.64249i	−0.813666	+	0.238914i	−0.661986	−	0.749516i	$-0.730286\pi$
$773$	−22.6223	+	6.64249i	−0.813666	+	0.238914i	−0.151680	+	0.988430i	$0.548468\pi$
$774$	20.7796	+	20.4976i	0.746909	+	0.736771i
$775$	−0.388109	+	0.447902i	−0.0139413	+	0.0160891i
$776$	−0.917465	+	0.0876073i	−0.0329351	+	0.00314492i
$777$	1.83260	+	9.96252i	0.0657442	+	0.357403i
$778$	4.34083	−	45.4592i	0.155626	−	1.62979i
$779$	62.4549	+	25.0032i	2.23768	+	0.895832i
$780$	−43.5842	−	31.5968i	−1.56057	−	1.13135i
$781$	−13.4899	+	7.78839i	−0.482706	+	0.278690i
$782$	−10.8163	+	9.46289i	−0.386790	+	0.338392i
$783$	4.23111	−	1.57017i	0.151208	−	0.0561133i
$784$	35.1607	+	22.5964i	1.25574	+	0.807015i
$785$	14.0701	+	17.8915i	0.502182	+	0.638577i
$786$	−1.97898	−	5.06744i	−0.0705880	−	0.180750i
$787$	−23.8047	−	24.9656i	−0.848545	−	0.889928i	0.146515	−	0.989209i	$-0.453194\pi$
$787$	−23.8047	−	24.9656i	−0.848545	−	0.889928i	−0.995060	+	0.0992802i	$0.968346\pi$
$788$	−27.4632	+	19.5565i	−0.978337	+	0.696671i
$789$	0.309257	+	0.0778089i	0.0110099	+	0.00277007i
$790$	−17.8112	+	7.13053i	−0.633694	+	0.253693i
$791$	10.5921	+	36.0735i	0.376613	+	1.28263i
$792$	1.56696	+	0.747995i	0.0556797	+	0.0265789i
$793$	25.3455	+	39.4384i	0.900047	+	1.40050i
$794$	30.0424	−	58.2740i	1.06616	−	2.06807i
$795$	−28.1617	+	3.80547i	−0.998792	+	0.134966i
$796$	−15.9253	−	3.86345i	−0.564459	−	0.136936i
$797$	28.6880	+	22.5605i	1.01618	+	0.799133i	0.979754	−	0.200204i	$-0.0641603\pi$
$797$	28.6880	+	22.5605i	1.01618	+	0.799133i	0.0364257	+	0.999336i	$0.488403\pi$
$798$	−81.9404	+	23.3066i	−2.90066	+	0.825046i
$799$	0.681898	+	7.14116i	0.0241238	+	0.252636i
$800$	0.766791	−	2.61145i	0.0271101	−	0.0923287i
$801$	−5.97362	−	18.2561i	−0.211068	−	0.645047i
$802$	−68.9330	+	9.91107i	−2.43411	+	0.349972i
$803$	−1.74339	+	36.5983i	−0.0615230	+	1.29153i
$804$	−3.51606	+	1.77506i	−0.124002	+	0.0626015i
$805$	8.52033	+	43.1027i	0.300302	+	1.51917i
$806$	21.1703	+	12.2227i	0.745693	+	0.430526i
$807$	19.2697	−	26.5803i	0.678326	−	0.935672i
$808$	0.397544	−	0.312632i	0.0139855	−	0.0109983i
$809$	6.95283	−	3.17525i	0.244448	−	0.111636i	−0.289424	−	0.957201i	$-0.593464\pi$
$809$	6.95283	−	3.17525i	0.244448	−	0.111636i	0.533872	+	0.845565i	$0.320736\pi$
$810$	19.1981	−	34.3270i	0.674553	−	1.20613i
$811$	−21.7655	+	47.6598i	−0.764290	+	1.67356i	−0.0254543	+	0.999676i	$0.508103\pi$
$811$	−21.7655	+	47.6598i	−0.764290	+	1.67356i	−0.738836	+	0.673886i	$0.764624\pi$
$812$	7.58230	+	1.46137i	0.266086	+	0.0512840i
$813$	7.27514	−	36.0964i	0.255150	−	1.26595i
$814$	1.96838	−	8.11379i	0.0689919	−	0.284388i
$815$	−7.29474	+	1.40595i	−0.255524	+	0.0492481i
$816$	−8.39805	−	4.94408i	−0.293990	−	0.173077i
$817$	24.4789	+	12.6198i	0.856409	+	0.441510i
$818$	14.0943	−	12.2127i	0.492794	−	0.427009i
$819$	−15.0853	−	86.1071i	−0.527123	−	3.00883i
$820$	−52.6010	−	7.56288i	−1.83691	−	0.264107i
$821$	−2.29770	+	11.9216i	−0.0801904	+	0.416067i	0.919543	+	0.392989i	$0.128559\pi$
$821$	−2.29770	+	11.9216i	−0.0801904	+	0.416067i	−0.999734	+	0.0230784i	$0.992653\pi$
$822$	−11.4433	+	7.21772i	−0.399131	+	0.251747i
$823$	21.3576	−	20.3645i	0.744481	−	0.709861i	−0.219565	−	0.975598i	$-0.570464\pi$
$823$	21.3576	−	20.3645i	0.744481	−	0.709861i	0.964046	+	0.265737i	$0.0856153\pi$
$824$	−1.85089	−	0.176739i	−0.0644790	−	0.00615699i
$825$	−1.58279	−	0.739126i	−0.0551055	−	0.0257331i
$826$	0.524947	+	0.0250063i	0.0182652	+	0.000870080i
$827$	−10.8575			−0.377552			−0.188776	−	0.982020i	$-0.560452\pi$
$827$	−10.8575			−0.377552			−0.188776	+	0.982020i	$0.560452\pi$
$828$	−28.8227	−	8.84672i	−1.00166	−	0.307445i
$829$	−10.9194			−0.379248			−0.189624	−	0.981857i	$-0.560727\pi$
$829$	−10.9194			−0.379248			−0.189624	+	0.981857i	$0.560727\pi$
$830$	32.2995	+	1.53861i	1.12113	+	0.0534060i
$831$	11.7081	−	8.18850i	0.406149	−	0.284056i
$832$	−59.7939	−	5.70963i	−2.07298	−	0.197946i
$833$	11.7879	−	11.2397i	0.408425	−	0.389433i
$834$	−0.737388	−	0.388103i	−0.0255336	−	0.0134389i
$835$	−1.33272	+	6.91482i	−0.0461207	+	0.239297i
$836$	35.5616	+	5.11299i	1.22992	+	0.176836i
$837$	−3.61121	+	8.39463i	−0.124822	+	0.290161i
$838$	30.7326	−	26.6300i	1.06164	−	0.919917i
$839$	−18.3749	−	9.47291i	−0.634371	−	0.327041i	0.110871	−	0.993835i	$-0.464636\pi$
$839$	−18.3749	−	9.47291i	−0.634371	−	0.327041i	−0.745242	+	0.666794i	$0.767666\pi$
$840$	2.67051	−	1.51176i	0.0921412	−	0.0521606i
$841$	27.7352	−	5.34552i	0.956386	−	0.184328i
$842$	4.37740	−	18.0439i	0.150855	−	0.621833i
$843$	−34.4905	+	11.6106i	−1.18792	+	0.399889i
$844$	22.3106	+	4.30001i	0.767961	+	0.148012i
$845$	30.6557	−	67.1265i	1.05459	−	2.30922i
$846$	−23.4252	+	17.7869i	−0.805376	+	0.611528i
$847$	7.88428	−	3.60063i	0.270907	−	0.123719i
$848$	−22.6935	+	17.8463i	−0.779297	+	0.612846i
$849$	23.3968	+	52.4039i	0.802977	+	1.79850i
$850$	−0.874547	−	0.504920i	−0.0299967	−	0.0173186i
$851$	−0.597087	+	6.58399i	−0.0204679	+	0.225696i
$852$	−15.8050	−	10.3477i	−0.541469	−	0.354508i
$853$	1.14006	−	23.9329i	0.0390351	−	0.819447i	−0.891450	−	0.453118i	$-0.850312\pi$
$853$	1.14006	−	23.9329i	0.0390351	−	0.819447i	0.930485	−	0.366329i	$-0.119385\pi$
$854$	−58.0078	+	8.34026i	−1.98499	+	0.285398i
$855$	7.64047	−	36.3155i	0.261299	−	1.24196i
$856$	−0.104643	+	0.356381i	−0.00357662	+	0.0121808i
$857$	−0.0677731	−	0.709752i	−0.00231509	−	0.0242447i	0.994241	−	0.107171i	$-0.0341793\pi$
$857$	−0.0677731	−	0.709752i	−0.00231509	−	0.0242447i	−0.996556	+	0.0829267i	$0.973573\pi$
$858$	−17.5805	+	69.8750i	−0.600188	+	2.38549i
$859$	22.4428	+	17.6492i	0.765738	+	0.602183i	0.922744	−	0.385415i	$-0.125942\pi$
$859$	22.4428	+	17.6492i	0.765738	+	0.602183i	−0.157005	+	0.987598i	$0.550184\pi$
$860$	−21.1419	−	5.12896i	−0.720932	−	0.174896i
$861$	−52.7678	−	68.2841i	−1.79832	−	2.32712i
$862$	−31.5483	+	61.1951i	−1.07454	+	2.08431i
$863$	−28.0881	−	43.7059i	−0.956130	−	1.48777i	−0.870932	−	0.491403i	$-0.836484\pi$
$863$	−28.0881	−	43.7059i	−0.956130	−	1.48777i	−0.0851979	−	0.996364i	$-0.527152\pi$
$864$	−0.929433	−	41.9565i	−0.0316200	−	1.42739i
$865$	11.6675	+	39.7360i	0.396708	+	1.35106i
$866$	−32.9051	+	13.1732i	−1.11816	+	0.447643i
$867$	17.8554	−	18.4109i	0.606401	−	0.625267i
$868$	−12.7366	+	9.06966i	−0.432307	+	0.307844i
$869$	9.06700	+	9.50920i	0.307577	+	0.322577i
$870$	−4.10757	+	5.13298i	−0.139260	+	0.174024i
$871$	−4.60729	−	5.85864i	−0.156112	−	0.198513i
$872$	1.47397	+	0.947265i	0.0499150	+	0.0320784i
$873$	13.1041	−	5.71775i	0.443505	−	0.193517i
$874$	−55.5979	+	0.264615i	−1.88063	+	0.00895072i
$875$	−42.3439	+	24.4473i	−1.43149	+	0.826469i
$876$	−40.5753	+	18.1157i	−1.37091	+	0.612073i
$877$	14.2206	+	5.69308i	0.480196	+	0.192242i	0.599116	−	0.800662i	$-0.295519\pi$
$877$	14.2206	+	5.69308i	0.480196	+	0.192242i	−0.118920	+	0.992904i	$0.537943\pi$
$878$	−2.36609	+	24.7789i	−0.0798518	+	0.836246i
$879$	−26.2764	+	22.3811i	−0.886280	+	0.754897i
$880$	24.4455	−	2.33426i	0.824057	−	0.0786879i
$881$	−33.3778	+	38.5200i	−1.12453	+	1.29777i	−0.174830	+	0.984599i	$0.555938\pi$
$881$	−33.3778	+	38.5200i	−1.12453	+	1.29777i	−0.949696	+	0.313173i	$0.898608\pi$
$882$	64.6222	+	16.8431i	2.17594	+	0.567136i
$883$	−38.3402	+	11.2577i	−1.29025	+	0.378851i	−0.853670	−	0.520814i	$-0.825628\pi$
$883$	−38.3402	+	11.2577i	−1.29025	+	0.378851i	−0.436580	+	0.899666i	$0.643810\pi$
$884$	−6.97059	+	20.1402i	−0.234446	+	0.677388i
$885$	−0.116146	+	0.197286i	−0.00390420	+	0.00663169i
$886$	−3.26643	−	68.5707i	−0.109738	−	2.30368i
$887$	5.89289	+	30.5752i	0.197864	+	1.02662i	0.936010	+	0.351974i	$0.114490\pi$
$887$	5.89289	+	30.5752i	0.197864	+	1.02662i	−0.738146	+	0.674641i	$0.764298\pi$
$888$	0.449630	−	0.105048i	0.0150886	−	0.00352519i
$889$	10.3435	+	25.8368i	0.346910	+	0.866538i
$890$	21.1466	+	18.3237i	0.708837	+	0.614211i
$891$	−26.7112	−	3.46864i	−0.894858	−	0.116204i
$892$	33.1937	+	9.74655i	1.11141	+	0.326339i
$893$	−16.0980	+	22.6065i	−0.538701	+	0.756499i
$894$	−30.3137	+	2.63529i	−1.01384	+	0.0881373i
$895$	−0.711465	−	1.38005i	−0.0237816	−	0.0461299i
$896$	3.27813	−	5.67790i	0.109515	−	0.189685i
$897$	5.63468	−	56.7737i	0.188137	−	1.89562i
$898$	−2.04992	−	3.55056i	−0.0684067	−	0.118484i
$899$	0.825825	−	1.28501i	0.0275428	−	0.0428574i
$900$	−0.0648859	−	2.11755i	−0.00216286	−	0.0705849i
$901$	4.67365	+	10.2339i	0.155702	+	0.340940i
$902$	16.7691	+	69.1232i	0.558350	+	2.30155i
$903$	−18.8470	−	29.8808i	−0.627188	−	0.994371i
$904$	1.61950	−	0.560513i	0.0538636	−	0.0186424i
$905$	17.7628	−	22.5873i	0.590456	−	0.750826i
$906$	26.7862	+	8.11261i	0.889913	+	0.269523i
$907$	50.0117	+	17.3092i	1.66061	+	0.574743i	0.986482	−	0.163872i	$-0.0523983\pi$
$907$	50.0117	+	17.3092i	1.66061	+	0.574743i	0.674128	+	0.738614i	$0.264519\pi$
$908$	−3.60207	+	2.31491i	−0.119539	+	0.0768230i
$909$	−4.35299	+	6.52717i	−0.144379	+	0.216492i
$910$	83.3914	+	96.2388i	2.76440	+	3.19028i
$911$	7.20269	+	6.86775i	0.238636	+	0.227539i	0.799954	−	0.600061i	$-0.204857\pi$
$911$	7.20269	+	6.86775i	0.238636	+	0.227539i	−0.561318	+	0.827600i	$0.689706\pi$
$912$	−12.0283	−	35.7313i	−0.398295	−	1.18318i
$913$	−7.24298	−	20.9272i	−0.239708	−	0.692590i
$914$	−40.1142	−	56.3326i	−1.32686	−	1.86332i
$915$	8.55412	−	24.0533i	0.282790	−	0.795178i
$916$	42.6023	+	30.3370i	1.40762	+	1.00236i
$917$	0.937078	+	6.51752i	0.0309450	+	0.215227i
$918$	−15.2097	−	3.33499i	−0.501996	−	0.110071i
$919$			35.8737i			1.18336i	0.806172	+	0.591682i	$0.201536\pi$
$919$			35.8737i			1.18336i	−0.806172	+	0.591682i	$0.798464\pi$
$920$	1.94404	−	0.481426i	0.0640930	−	0.0158722i
$921$	25.6365	+	1.43930i	0.844752	+	0.0474265i
$922$	66.1268	−	34.0907i	2.17777	−	1.12272i
$923$	13.2860	−	33.1869i	0.437316	−	1.09236i
$924$	−35.9834	−	28.7951i	−1.18377	−	0.947288i
$925$	−0.451441	+	0.109518i	−0.0148433	+	0.00360095i
$926$	49.5075	+	22.6093i	1.62692	+	0.742988i
$927$	28.1414	−	6.32347i	0.924285	−	0.207690i
$928$	−0.998307	+	6.94338i	−0.0327710	+	0.227927i
$929$	−29.4327	+	30.8681i	−0.965656	+	1.01275i	0.0342548	+	0.999413i	$0.489094\pi$
$929$	−29.4327	+	30.8681i	−0.965656	+	1.01275i	−0.999911	+	0.0133380i	$0.995754\pi$
$930$	−1.78263	−	13.1920i	−0.0584547	−	0.432582i
$931$	62.9400	−	2.99820i	2.06277	−	0.0982620i
$932$	−6.93677	+	0.330439i	−0.227222	+	0.0108239i
$933$	4.78926	+	35.4420i	0.156793	+	1.16032i
$934$	55.8334	−	58.5564i	1.82692	−	1.91602i
$935$	1.36190	−	9.47223i	0.0445389	−	0.309775i
$936$	−3.88784	+	0.873609i	−0.127078	+	0.0285548i
$937$	6.75275	+	3.08388i	0.220603	+	0.100746i	0.522651	−	0.852547i	$-0.324943\pi$
$937$	6.75275	+	3.08388i	0.220603	+	0.100746i	−0.302048	+	0.953293i	$0.597670\pi$
$938$	9.05448	−	2.19659i	0.295639	−	0.0717213i
$939$	−2.19097	−	1.75328i	−0.0714995	−	0.0572162i
$940$	8.14782	−	20.3523i	0.265753	−	0.663818i
$941$	−27.7268	+	14.2942i	−0.903868	+	0.465977i	−0.846507	−	0.532377i	$-0.821299\pi$
$941$	−27.7268	+	14.2942i	−0.903868	+	0.465977i	−0.0573611	+	0.998353i	$0.518269\pi$
$942$	36.8890	+	2.07104i	1.20191	+	0.0674781i
$943$	−21.1809	−	52.1861i	−0.689744	−	1.69941i
$944$			0.232581i			0.00756987i
$945$	−32.0796	+	35.1719i	−1.04355	+	1.14414i
$946$	4.14397	+	28.8219i	0.134732	+	0.937082i
$947$	29.5147	+	21.0174i	0.959100	+	0.682972i	0.948435	−	0.316971i	$-0.102666\pi$
$947$	29.5147	+	21.0174i	0.959100	+	0.682972i	0.0106651	+	0.999943i	$0.496605\pi$
$948$	−5.33929	+	15.0135i	−0.173412	+	0.487617i
$949$	−48.7746	−	68.4943i	−1.58329	−	2.22342i
$950$	−1.27777	−	3.69188i	−0.0414564	−	0.119780i
$951$	9.84125	+	29.2345i	0.319124	+	0.947995i
$952$	−0.879270	−	0.838382i	−0.0284973	−	0.0271721i
$953$	2.52669	+	2.91596i	0.0818475	+	0.0944571i	0.795196	−	0.606352i	$-0.207368\pi$
$953$	2.52669	+	2.91596i	0.0818475	+	0.0944571i	−0.713349	+	0.700809i	$0.752822\pi$
$954$	−25.5939	+	38.3773i	−0.828634	+	1.24251i
$955$	−0.681829	+	0.438185i	−0.0220635	+	0.0141793i
$956$	12.7626	+	4.41716i	0.412770	+	0.142861i
$957$	4.30898	+	1.30504i	0.139290	+	0.0421860i
$958$	5.82913	−	7.41234i	0.188331	−	0.239482i
$959$	15.4748	−	5.35587i	0.499707	−	0.172950i
$960$	17.4499	+	27.6658i	0.563192	+	0.892910i
$961$	−6.57933	−	27.1204i	−0.212236	−	0.874850i
$962$	7.95964	+	17.4292i	0.256629	+	0.561940i
$963$	−0.176472	−	5.75915i	−0.00568672	−	0.185586i
$964$	−23.7944	+	37.0247i	−0.766364	+	1.19249i
$965$	13.3902	+	23.1926i	0.431047	+	0.746595i
$966$	61.6318	+	35.8899i	1.98297	+	1.15474i
$967$	16.3061	−	28.2430i	0.524368	−	0.908232i	−0.475229	−	0.879862i	$-0.657635\pi$
$967$	16.3061	−	28.2430i	0.524368	−	0.908232i	0.999597	−	0.0283703i	$-0.00903177\pi$
$968$	−0.181041	−	0.351171i	−0.00581888	−	0.0112871i
$969$	−14.6369	+	1.27244i	−0.470205	+	0.0408768i
$970$	−12.0806	+	16.9649i	−0.387886	+	0.544709i
$971$	−24.0840	−	7.07171i	−0.772893	−	0.226942i	−0.128575	−	0.991700i	$-0.541040\pi$
$971$	−24.0840	−	7.07171i	−0.772893	−	0.226942i	−0.644318	+	0.764758i	$0.722859\pi$
$972$	−10.8440	−	30.8141i	−0.347821	−	0.988364i
$973$	0.762229	+	0.660475i	0.0244359	+	0.0211739i
$974$	−13.2060	−	32.9869i	−0.423146	−	1.05697i
$975$	3.90379	−	0.912053i	0.125021	−	0.0292091i
$976$	−4.90835	−	25.4669i	−0.157112	−	0.815176i
$977$	0.0721500	+	1.51462i	0.00230828	+	0.0484568i	0.999728	−	0.0233395i	$-0.00742987\pi$
$977$	0.0721500	+	1.51462i	0.00230828	+	0.0484568i	−0.997419	+	0.0717963i	$0.977127\pi$
$978$	−6.11792	+	10.3919i	−0.195629	+	0.332297i
$979$	6.26749	−	18.1087i	0.200310	−	0.578757i
$980$	−47.7585	+	14.0232i	−1.52559	+	0.447954i
$981$	−26.3015	−	6.85520i	−0.839742	−	0.218870i
$982$	20.8295	−	24.0385i	0.664695	−	0.767099i
$983$	53.8201	−	5.13920i	1.71660	−	0.163915i	0.810146	−	0.586229i	$-0.199388\pi$
$983$	53.8201	−	5.13920i	1.71660	−	0.163915i	0.906450	+	0.422314i	$0.138782\pi$
$984$	−2.99460	+	2.55068i	−0.0954645	+	0.0813128i
$985$	−3.30243	+	34.5846i	−0.105224	+	1.10196i
$986$	2.41628	+	0.967332i	0.0769500	+	0.0308061i
$987$	32.5073	−	14.5136i	1.03472	−	0.461972i
$988$	−71.4044	+	41.2253i	−2.27168	+	1.31155i
$989$	−6.60096	−	22.0913i	−0.209898	−	0.702463i
$990$	35.9624	−	15.6916i	1.14296	−	0.498712i
$991$	−5.89497	−	3.78847i	−0.187260	−	0.120345i	0.443652	−	0.896199i	$-0.353683\pi$
$991$	−5.89497	−	3.78847i	−0.187260	−	0.120345i	−0.630912	+	0.775855i	$0.717319\pi$
$992$	−8.78038	−	11.1652i	−0.278777	−	0.354494i
$993$	−27.0434	+	33.7944i	−0.858195	+	1.07243i
$994$	30.8377	+	32.3417i	0.978113	+	1.02582i
$995$	−13.7553	+	9.79514i	−0.436074	+	0.310527i
$996$	18.6977	−	19.2794i	0.592460	−	0.610892i
$997$	−24.4391	+	9.78393i	−0.773993	+	0.309860i	−0.724828	−	0.688930i	$-0.758081\pi$
$997$	−24.4391	+	9.78393i	−0.773993	+	0.309860i	−0.0491660	+	0.998791i	$0.515656\pi$
$998$	−17.8511	−	60.7953i	−0.565067	−	1.92444i
$999$	−6.12237	+	3.71792i	−0.193703	+	0.117630i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.o.a.113.19	yes	440
3.2	odd	2		621.2.s.a.44.4		440
9.2	odd	6	inner	207.2.o.a.182.19	yes	440
9.7	even	3		621.2.s.a.251.4		440
23.11	odd	22	inner	207.2.o.a.149.19	yes	440
69.11	even	22		621.2.s.a.287.4		440
207.11	even	66	inner	207.2.o.a.11.19	✓	440
207.34	odd	66		621.2.s.a.494.4		440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.19	✓	440	207.11	even	66	inner
207.2.o.a.113.19	yes	440	1.1	even	1	trivial
207.2.o.a.149.19	yes	440	23.11	odd	22	inner
207.2.o.a.182.19	yes	440	9.2	odd	6	inner
621.2.s.a.44.4		440	3.2	odd	2
621.2.s.a.251.4		440	9.7	even	3
621.2.s.a.287.4		440	69.11	even	22
621.2.s.a.494.4		440	207.34	odd	66

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:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.o (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(2.02146 + 0.0962939i) q^{2} +(-0.150008 - 1.72554i) q^{3} +(2.08607 + 0.199196i) q^{4} +(1.56283 - 1.49016i) q^{5} +(-0.137076 - 3.50255i) q^{6} +(-0.802915 + 4.16592i) q^{7} +(0.191421 + 0.0275221i) q^{8} +(-2.95499 + 0.517692i) q^{9} +(3.30269 - 2.86180i) q^{10} +(-2.66013 - 1.37139i) q^{11} +(0.0307923 - 3.62949i) q^{12} +(6.74421 - 1.29984i) q^{13} +(-2.02421 + 8.34391i) q^{14} +(-2.80577 - 2.47320i) q^{15} +(-3.73108 - 0.719107i) q^{16} +(-0.615124 + 1.34693i) q^{17} +(-6.02324 + 0.761944i) q^{18} +(-5.21085 + 2.37972i) q^{19} +(3.55701 - 2.79726i) q^{20} +(7.30892 + 0.760542i) q^{21} +(-5.24528 - 3.02837i) q^{22} +(4.46073 + 1.76122i) q^{23} +(0.0187759 - 0.334433i) q^{24} +(-0.0160346 + 0.336607i) q^{25} +(13.7583 - 1.97814i) q^{26} +(1.33657 + 5.02131i) q^{27} +(-2.50477 + 8.53047i) q^{28} +(-0.0825600 - 0.864607i) q^{29} +(-5.43358 - 5.26964i) q^{30} +(1.38242 + 1.08715i) q^{31} +(-7.84885 - 1.90411i) q^{32} +(-1.96735 + 4.79589i) q^{33} +(-1.37315 + 2.66353i) q^{34} +(4.95305 + 7.70710i) q^{35} +(-6.26745 + 0.491320i) q^{36} +(0.388365 + 1.32265i) q^{37} +(-10.7627 + 4.30872i) q^{38} +(-3.25462 - 11.4424i) q^{39} +(0.340170 - 0.242234i) q^{40} +(-8.10406 - 8.49929i) q^{41} +(14.7014 + 2.24121i) q^{42} +(-2.97186 - 3.77903i) q^{43} +(-5.27605 - 3.39071i) q^{44} +(-3.84672 + 5.21247i) q^{45} +(8.84758 + 3.98977i) q^{46} +(4.19556 - 2.42231i) q^{47} +(-0.681156 + 6.54601i) q^{48} +(-10.2116 - 4.08813i) q^{49} +(-0.0648264 + 0.678893i) q^{50} +(2.41646 + 0.859371i) q^{51} +(14.3278 - 1.36814i) q^{52} +(4.97557 - 5.74212i) q^{53} +(2.21830 + 10.2791i) q^{54} +(-6.20093 + 1.82076i) q^{55} +(-0.268349 + 0.775345i) q^{56} +(4.88797 + 8.63457i) q^{57} +(-0.0836350 - 1.75572i) q^{58} +(-0.0115840 - 0.0601035i) q^{59} +(-5.36038 - 5.71816i) q^{60} +(2.53682 + 6.33668i) q^{61} +(2.68982 + 2.33075i) q^{62} +(0.215948 - 12.7259i) q^{63} +(-8.39109 - 2.46385i) q^{64} +(8.60310 - 12.0814i) q^{65} +(-4.43874 + 9.50524i) q^{66} +(-0.497249 - 0.964529i) q^{67} +(-1.55149 + 2.68727i) q^{68} +(2.36991 - 7.96138i) q^{69} +(9.27024 + 16.0565i) q^{70} +(2.81387 - 4.37847i) q^{71} +(-0.579895 + 0.0177691i) q^{72} +(-5.08574 - 11.1362i) q^{73} +(0.657701 + 2.71108i) q^{74} +(0.583236 - 0.0228256i) q^{75} +(-11.3442 + 3.92628i) q^{76} +(7.84897 - 9.98078i) q^{77} +(-5.47723 - 23.4438i) q^{78} +(-4.14873 - 1.43589i) q^{79} +(-6.90264 + 4.43606i) q^{80} +(8.46399 - 3.05955i) q^{81} +(-15.5636 - 17.9613i) q^{82} +(5.35521 + 5.10618i) q^{83} +(15.0954 + 3.04245i) q^{84} +(1.04581 + 3.02166i) q^{85} +(-5.64359 - 7.92531i) q^{86} +(-1.47953 + 0.272159i) q^{87} +(-0.471460 - 0.335725i) q^{88} +(0.911221 + 6.33768i) q^{89} +(-8.27790 + 10.1664i) q^{90} +29.1395i q^{91} +(8.95457 + 4.56259i) q^{92} +(1.66855 - 2.54851i) q^{93} +(8.71440 - 4.49259i) q^{94} +(-4.59753 + 11.4841i) q^{95} +(-2.10823 + 13.8292i) q^{96} +(-4.63139 + 1.12356i) q^{97} +(-20.2487 - 9.24729i) q^{98} +(8.57063 + 2.67533i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23}+ \cdots + 242 q^{99}+O(q^{100}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9 - 44 * q^10 - 33 * q^11 - 22 * q^12 - 9 * q^13 - 33 * q^14 + 3 * q^16 - 39 * q^18 - 44 * q^19 - 33 * q^20 - 55 * q^21 - 27 * q^23 + 52 * q^24 + 11 * q^25 - 79 * q^27 - 44 * q^28 + 27 * q^29 - 66 * q^30 - 3 * q^31 - 33 * q^32 - 11 * q^34 + 23 * q^36 - 44 * q^37 - 33 * q^38 - 40 * q^39 - 77 * q^40 + 9 * q^41 - 22 * q^42 - 11 * q^43 - 36 * q^46 - 120 * q^47 - 56 * q^48 + 35 * q^49 - 3 * q^50 - 22 * q^51 - 38 * q^52 + 42 * q^54 - 44 * q^55 + 165 * q^56 + 11 * q^57 - 10 * q^58 - 9 * q^59 + 88 * q^60 - 11 * q^61 + 33 * q^63 - 22 * q^64 + 198 * q^65 + 33 * q^66 - 11 * q^67 + 3 * q^69 - 70 * q^70 + 14 * q^72 - 36 * q^73 + 231 * q^74 - 13 * q^75 - 11 * q^76 + 39 * q^77 + 3 * q^78 - 11 * q^79 + 172 * q^81 - 10 * q^82 + 66 * q^83 - 110 * q^84 + q^85 - 33 * q^86 - 196 * q^87 - 99 * q^88 + 418 * q^90 + 63 * q^92 - 188 * q^93 - 42 * q^94 - 93 * q^95 - 82 * q^96 + 22 * q^97 + 242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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