LMFDB - Embedded newform 207.2.o.a.11.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(5,207)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			11.19
Character	$\chi$	$=$	207.11
Dual form			207.2.o.a.113.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.02146 - 0.0962939i) q^{2} +(-0.150008 + 1.72554i) q^{3} +(2.08607 - 0.199196i) q^{4} +(1.56283 + 1.49016i) q^{5} +(-0.137076 + 3.50255i) q^{6} +(-0.802915 - 4.16592i) q^{7} +(0.191421 - 0.0275221i) q^{8} +(-2.95499 - 0.517692i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{9}{22}\right)$	$e\left(\frac{1}{6}\right)$

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	0.681452	−	0.731863i	$-0.261349\pi$
$2$	2.02146	−	0.0962939i	1.42939	−	0.0680900i	0.747934	+	0.663773i	$0.231046\pi$
$3$	−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	0.953762	−	0.300564i	$-0.0971750\pi$
$5$	1.56283	+	1.49016i	0.698920	+	0.666418i	−0.254842	+	0.966983i	$0.582023\pi$
$6$	−0.137076	+	3.50255i	−0.0559612	+	1.42991i
$7$	−0.802915	−	4.16592i	−0.303474	−	1.57457i	−0.738564	−	0.674183i	$-0.764496\pi$
$7$	−0.802915	−	4.16592i	−0.303474	−	1.57457i	0.435090	−	0.900387i	$-0.356716\pi$
$8$	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	−0.809965	−	0.586478i	$-0.800514\pi$
$11$	−2.66013	+	1.37139i	−0.802060	+	0.413490i	0.00790531	+	0.999969i	$0.497484\pi$
$12$	0.0307923	+	3.62949i	0.00888898	+	1.04774i
$13$	6.74421	+	1.29984i	1.87051	+	0.360511i	0.992908	−	0.118884i	$-0.0379317\pi$
$13$	6.74421	+	1.29984i	1.87051	+	0.360511i	0.877599	+	0.479395i	$0.159144\pi$
$14$	−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	0.820252	−	0.572002i	$-0.193833\pi$
$17$	−0.615124	−	1.34693i	−0.149189	−	0.326679i	−0.969441	+	0.245323i	$0.921106\pi$
$18$	−6.02324	−	0.761944i	−1.41969	−	0.179592i
$19$	−5.21085	−	2.37972i	−1.19545	−	0.545944i	−0.284587	−	0.958650i	$-0.591856\pi$
$19$	−5.21085	−	2.37972i	−1.19545	−	0.545944i	−0.910864	+	0.412706i	$0.864584\pi$
$20$	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	−0.999895	−	0.0144697i	$-0.995394\pi$
$29$	−0.0825600	+	0.864607i	−0.0153310	+	0.160553i	0.984564	+	0.175023i	$0.0560000\pi$
$30$	−5.43358	+	5.26964i	−0.992032	+	0.962100i
$31$	1.38242	−	1.08715i	0.248291	−	0.195258i	−0.486255	−	0.873817i	$-0.661638\pi$
$31$	1.38242	−	1.08715i	0.248291	−	0.195258i	0.734546	+	0.678559i	$0.237395\pi$
$32$	−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	−0.921390	−	0.388639i	$-0.872945\pi$
$37$	0.388365	−	1.32265i	0.0638469	−	0.217443i	0.985237	+	0.171197i	$0.0547634\pi$
$38$	−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	−0.344176	+	0.938905i	$0.611842\pi$
$41$	−8.10406	+	8.49929i	−1.26564	+	1.32737i	−0.921465	+	0.388461i	$0.873007\pi$
$42$	14.7014	−	2.24121i	2.26848	−	0.345826i
$43$	−2.97186	+	3.77903i	−0.453204	+	0.576296i	−0.957937	−	0.286980i	$-0.907349\pi$
$43$	−2.97186	+	3.77903i	−0.453204	+	0.576296i	0.504732	+	0.863276i	$0.331591\pi$
$44$	−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	0.773742	−	0.633501i	$-0.218383\pi$
$47$	4.19556	+	2.42231i	0.611986	+	0.353330i	−0.161756	+	0.986831i	$0.551716\pi$
$48$	−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	0.986417	−	0.164260i	$-0.0525235\pi$
$53$	4.97557	+	5.74212i	0.683447	+	0.788740i	−0.302970	+	0.953000i	$0.597978\pi$
$54$	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	−0.982675	−	0.185337i	$-0.940662\pi$
$59$	−0.0115840	+	0.0601035i	−0.00150811	+	0.00782481i	0.981167	+	0.193162i	$0.0618743\pi$
$60$	−5.36038	+	5.71816i	−0.692022	+	0.738211i
$61$	2.53682	−	6.33668i	0.324807	−	0.811329i	−0.672643	−	0.739967i	$-0.734841\pi$
$61$	2.53682	−	6.33668i	0.324807	−	0.811329i	0.997450	−	0.0713620i	$-0.0227345\pi$
$62$	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	−0.917255	−	0.398301i	$-0.869600\pi$
$67$	−0.497249	+	0.964529i	−0.0607487	+	0.117836i	0.856506	+	0.516137i	$0.172630\pi$
$68$	−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	0.967100	−	0.254396i	$-0.0818767\pi$
$71$	2.81387	+	4.37847i	0.333945	+	0.519629i	−0.633155	+	0.774025i	$0.718240\pi$
$72$	−0.579895	−	0.0177691i	−0.0683413	−	0.00209411i
$73$	−5.08574	+	11.1362i	−0.595240	+	1.30339i	0.336983	+	0.941511i	$0.390594\pi$
$73$	−5.08574	+	11.1362i	−0.595240	+	1.30339i	−0.932223	+	0.361884i	$0.882134\pi$
$74$	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	−0.550321	−	0.834953i	$-0.685495\pi$
$79$	−4.14873	+	1.43589i	−0.466769	+	0.161550i	0.0835522	+	0.996503i	$0.473373\pi$
$80$	−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	−0.336710	−	0.941608i	$-0.609314\pi$
$83$	5.35521	−	5.10618i	0.587811	−	0.560477i	0.924521	+	0.381132i	$0.124466\pi$
$84$	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	−0.882791	−	0.469766i	$-0.844338\pi$
$89$	0.911221	−	6.33768i	0.0965893	−	0.671793i	0.979380	−	0.202027i	$-0.0647528\pi$
$90$	−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	−0.00636838	−	0.999980i	$-0.502027\pi$
$97$	−4.63139	−	1.12356i	−0.470246	−	0.114080i	−0.463878	+	0.885899i	$0.653542\pi$
$98$	−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	0.807368	−	0.590048i	$-0.200891\pi$
$101$	1.80468	+	1.89269i	0.179572	+	0.188330i	−0.627796	+	0.778378i	$0.716043\pi$
$102$	4.80203	−	1.96987i	0.475471	−	0.195046i
$103$	−9.60348	−	0.457470i	−0.946259	−	0.0450759i	−0.431224	−	0.902245i	$-0.641918\pi$
$103$	−9.60348	−	0.457470i	−0.946259	−	0.0450759i	−0.515035	+	0.857169i	$0.672221\pi$
$104$	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	0.972335	−	0.233592i	$-0.0750479\pi$
$107$	−0.273332	−	1.90107i	−0.0264240	−	0.183783i	−0.998759	+	0.0498086i	$0.984139\pi$
$108$	1.78796	−	10.7411i	0.172047	−	1.03356i
$109$	8.24132	−	3.76368i	0.789375	−	0.360496i	0.0204145	−	0.999792i	$-0.493501\pi$
$109$	8.24132	−	3.76368i	0.789375	−	0.360496i	0.768961	+	0.639296i	$0.220774\pi$
$110$	−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	0.787006	−	0.616945i	$-0.211630\pi$
$113$	7.87657	+	4.06066i	0.740966	+	0.381994i	−0.0460404	+	0.998940i	$0.514660\pi$
$114$	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	0.762077	−	0.647487i	$-0.224180\pi$
$127$	5.51842	+	3.54647i	0.489680	+	0.314698i	−0.272397	+	0.962185i	$0.587816\pi$
$128$	−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	0.390386	−	0.920651i	$-0.372341\pi$
$131$	1.46665	+	0.507613i	0.128142	+	0.0443503i	−0.262244	+	0.965001i	$0.584463\pi$
$132$	−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	−0.936613	−	0.350366i	$-0.886057\pi$
$137$	−1.92988	+	3.34266i	−0.164881	+	0.285582i	0.771732	+	0.635948i	$0.219391\pi$
$138$	5.55731	+	15.8654i	0.473070	+	1.35055i
$139$	0.118863	+	0.205877i	0.0100818	+	0.0174622i	0.871022	−	0.491243i	$-0.163457\pi$
$139$	0.118863	+	0.205877i	0.0100818	+	0.0174622i	−0.860940	+	0.508706i	$0.830124\pi$
$140$	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	0.916669	+	0.399646i	$0.130867\pi$
$149$	−0.413046	+	8.67090i	−0.0338380	+	0.710348i	−0.950508	+	0.310702i	$0.899436\pi$
$150$	1.18118	−	0.0100211i	0.0964432	−	0.000818219i
$151$	−2.61150	−	7.54542i	−0.212520	−	0.614038i	0.787477	−	0.616344i	$-0.211387\pi$
$151$	−2.61150	−	7.54542i	−0.212520	−	0.614038i	−0.999997	+	0.00230665i	$0.999266\pi$
$152$	−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	−0.943114	−	0.332470i	$-0.892118\pi$
$157$	−1.00194	−	10.4928i	−0.0799637	−	0.837417i	0.863150	−	0.504947i	$-0.168488\pi$
$158$	−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	−0.649056	−	0.760741i	$-0.724836\pi$
$163$	−2.89417	+	1.85997i	−0.226689	+	0.145684i	0.422367	+	0.906425i	$0.361199\pi$
$164$	−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	0.472640	−	0.881255i	$-0.343301\pi$
$167$	−2.65643	−	1.89164i	−0.205561	−	0.146379i	−0.678201	+	0.734876i	$0.737240\pi$
$168$	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	−0.942444	−	0.334364i	$-0.891479\pi$
$173$	−8.78798	−	17.0463i	−0.668137	−	1.29601i	0.274307	−	0.961642i	$-0.411552\pi$
$174$	−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	0.966717	−	0.255848i	$-0.0823548\pi$
$179$	0.202571	+	0.689893i	0.0151409	+	0.0515650i	−0.951576	+	0.307413i	$0.900537\pi$
$180$	−9.06283	−	10.1073i	−0.675503	−	0.753356i
$181$	13.1715	+	1.89378i	0.979030	+	0.140763i	0.613208	−	0.789922i	$-0.289879\pi$
$181$	13.1715	+	1.89378i	0.979030	+	0.140763i	0.365822	+	0.930685i	$0.380788\pi$
$182$	−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	−0.202567	−	0.979268i	$-0.564929\pi$
$191$	−0.368549	+	0.0710320i	−0.0266673	+	0.00513970i	0.175900	+	0.984408i	$0.443716\pi$
$192$	−2.99274	−	14.8488i	−0.215982	−	1.07162i
$193$	−2.92384	−	12.0522i	−0.210462	−	0.867537i	−0.974865	−	0.222798i	$-0.928481\pi$
$193$	−2.92384	−	12.0522i	−0.210462	−	0.867537i	0.764402	−	0.644740i	$-0.223034\pi$
$194$	−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	0.103486	−	0.994631i	$-0.467000\pi$
$197$	−12.1590	−	10.5358i	−0.866293	−	0.750647i	−0.969779	+	0.243983i	$0.921546\pi$
$198$	17.0675	−	6.23336i	1.21294	−	0.442986i
$199$	−7.74040	+	1.11290i	−0.548702	+	0.0788915i	−0.411090	−	0.911595i	$-0.634852\pi$
$199$	−7.74040	+	1.11290i	−0.548702	+	0.0788915i	−0.137612	+	0.990486i	$0.543943\pi$
$200$	−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	0.283338	−	0.959020i	$-0.408558\pi$
$211$	10.7934	−	1.03065i	0.743051	−	0.0709527i	0.459713	+	0.888068i	$0.347952\pi$
$212$	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	0.385053	−	0.922895i	$-0.374183\pi$
$223$	16.2104	−	3.12430i	1.08553	−	0.209218i	0.700476	+	0.713676i	$0.252971\pi$
$224$	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	0.563435	−	0.826160i	$-0.309479\pi$
$227$	−1.60612	−	1.26306i	−0.106602	−	0.0838326i	−0.670037	+	0.742328i	$0.733722\pi$
$228$	8.47669	−	18.9860i	0.561383	−	1.25738i
$229$	21.6138	−	12.4788i	1.42828	−	0.824620i	0.431298	−	0.902210i	$-0.358056\pi$
$229$	21.6138	−	12.4788i	1.42828	−	0.824620i	0.996985	+	0.0775900i	$0.0247225\pi$
$230$	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	0.0340258	−	0.999421i	$-0.489167\pi$
$233$	−3.28025	−	0.471628i	−0.214896	−	0.0308974i	−0.248922	+	0.968524i	$0.580076\pi$
$234$	−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	−0.0280184	−	0.999607i	$-0.508920\pi$
$239$	6.26307	−	1.51940i	0.405124	−	0.0982821i	0.433143	+	0.901325i	$0.357405\pi$
$240$	8.69006	−	11.2453i	0.560941	−	0.725884i
$241$	−9.62377	−	18.6675i	−0.619922	−	1.20248i	−0.964590	−	0.263755i	$-0.915039\pi$
$241$	−9.62377	−	18.6675i	−0.619922	−	1.20248i	0.344668	−	0.938725i	$-0.387991\pi$
$242$	−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	−0.839094	−	0.543987i	$-0.816914\pi$
$251$	−10.9766	+	7.05424i	−0.692837	+	0.445260i	0.146256	+	0.989247i	$0.453278\pi$
$252$	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	−0.999941	−	0.0108475i	$-0.996547\pi$
$257$	−0.322599	−	3.37840i	−0.0201231	−	0.210739i	0.979818	−	0.199892i	$-0.0640590\pi$
$258$	−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	0.943129	−	0.332427i	$-0.107867\pi$
$263$	−0.0602179	−	0.173988i	−0.00371320	−	0.0107286i	−0.946842	+	0.321698i	$0.895746\pi$
$264$	−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	−0.0977591	−	0.995210i	$-0.531167\pi$
$269$	14.3250	−	12.4127i	0.873409	−	0.756813i	0.971168	+	0.238397i	$0.0766220\pi$
$270$	18.7843	−	12.7588i	1.14317	−	0.776478i
$271$	20.3982	−	5.98944i	1.23910	−	0.363833i	0.404423	−	0.914572i	$-0.367472\pi$
$271$	20.3982	−	5.98944i	1.23910	−	0.363833i	0.834677	+	0.550740i	$0.185654\pi$
$272$	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	−0.715106	−	0.699016i	$-0.753622\pi$
$277$	4.12443	−	7.14372i	0.247813	−	0.429225i	0.962919	+	0.269792i	$0.0869548\pi$
$278$	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	0.609536	+	0.792759i	$0.291356\pi$
$281$	−4.95355	+	20.4188i	−0.295504	+	1.21809i	−0.905040	+	0.425327i	$0.860159\pi$
$282$	−9.05938	+	14.3631i	−0.539478	+	0.855313i
$283$	−31.3116	−	10.8371i	−1.86128	−	0.644196i	−0.987441	−	0.157987i	$-0.949500\pi$
$283$	−31.3116	−	10.8371i	−1.86128	−	0.644196i	−0.873842	−	0.486210i	$-0.838379\pi$
$284$	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	0.324695	+	0.945819i	$0.394739\pi$
$293$	−11.5593	+	16.2328i	−0.675302	+	0.948329i	−0.999997	+	0.00251049i	$0.999201\pi$
$294$	−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	−0.957093	−	0.289782i	$-0.906417\pi$
$307$	−2.10976	−	14.6737i	−0.120410	−	0.837471i	0.836682	−	0.547688i	$-0.184492\pi$
$308$	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	−0.546194	−	0.837659i	$-0.683924\pi$
$311$	−20.6250	−	0.982492i	−1.16954	−	0.0557120i	−0.623345	+	0.781947i	$0.714227\pi$
$312$	−0.308081	+	2.27989i	−0.0174416	+	0.129073i
$313$	1.11801	+	1.17253i	0.0631936	+	0.0662755i	0.754572	−	0.656218i	$-0.227845\pi$
$313$	1.11801	+	1.17253i	0.0631936	+	0.0662755i	−0.691378	+	0.722493i	$0.742996\pi$
$314$	−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	−0.281881	−	0.959449i	$-0.590958\pi$
$317$	−17.3072	−	4.19869i	−0.972072	−	0.235822i	−0.690191	+	0.723627i	$0.742473\pi$
$318$	−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	−0.998640	−	0.0521386i	$-0.983396\pi$
$331$	−18.0857	+	17.2446i	−0.994078	+	0.947851i	0.00456231	+	0.999990i	$0.498548\pi$
$332$	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	0.978828	+	0.204685i	$0.0656170\pi$
$337$	17.3842	+	22.1058i	0.946976	+	1.20418i	−0.0318522	+	0.999493i	$0.510141\pi$
$338$	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	−0.881041	−	0.473041i	$-0.843156\pi$
$347$	0.285766	−	0.554309i	0.0153407	−	0.0297569i	0.896381	+	0.443284i	$0.146187\pi$
$348$	−3.14062	−	0.273027i	−0.168355	−	0.0146358i
$349$	−2.90037	−	4.07300i	−0.155253	−	0.218023i	0.729622	−	0.683851i	$-0.239696\pi$
$349$	−2.90037	−	4.07300i	−0.155253	−	0.218023i	−0.884875	+	0.465828i	$0.845757\pi$
$350$	−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	−0.0657988	−	0.997833i	$-0.520960\pi$
$353$	12.5958	−	31.4627i	0.670406	−	1.67459i	0.736204	−	0.676759i	$-0.236616\pi$
$354$	−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	0.284513	−	0.958672i	$-0.408168\pi$
$359$	0.105422	+	0.0309547i	0.00556396	+	0.00163373i	−0.278949	+	0.960306i	$0.589986\pi$
$360$	−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	0.900980	−	0.433861i	$-0.142849\pi$
$367$	18.6924	+	10.7921i	0.975735	+	0.563341i	0.0747554	+	0.997202i	$0.476182\pi$
$368$	−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	−0.635042	−	0.772477i	$-0.719017\pi$
$373$	3.22100	−	3.37808i	0.166777	−	0.174911i	0.801819	+	0.597567i	$0.203866\pi$
$374$	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	−0.806403	−	0.591366i	$-0.798589\pi$
$379$	1.29489	−	2.01489i	0.0665141	−	0.103498i	0.872917	+	0.487868i	$0.162225\pi$
$380$	−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	−0.915537	−	0.402234i	$-0.868234\pi$
$383$	−14.4916	+	11.3963i	−0.740487	+	0.582325i	0.175050	+	0.984560i	$0.443991\pi$
$384$	−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	0.846511	+	0.532371i	$0.178699\pi$
$389$	1.07369	+	22.5395i	0.0544382	+	1.14280i	−0.792073	+	0.610427i	$0.790998\pi$
$390$	−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	0.867408	+	0.497598i	$0.165784\pi$
$397$	13.4580	+	29.4688i	0.675436	+	1.47900i	−0.191972	+	0.981400i	$0.561488\pi$
$398$	−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	−0.746889	−	0.664949i	$-0.768453\pi$
$401$	−33.7904	−	6.51257i	−1.68741	−	0.325222i	−0.940524	+	0.339726i	$0.889666\pi$
$402$	−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	0.836820	−	0.547477i	$-0.184412\pi$
$409$	6.66940	+	6.35926i	0.329781	+	0.314445i	−0.507040	+	0.861923i	$0.669260\pi$
$410$	−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	0.956464	−	0.291849i	$-0.0942706\pi$
$419$	14.5427	+	13.8664i	0.710456	+	0.677418i	−0.246008	+	0.969268i	$0.579119\pi$
$420$	28.1253	+	17.7397i	1.37238	+	0.865610i
$421$	1.73632	+	9.00889i	0.0846231	+	0.439067i	0.999385	+	0.0350725i	$0.0111662\pi$
$421$	1.73632	+	9.00889i	0.0846231	+	0.439067i	−0.914762	+	0.403994i	$0.867622\pi$
$422$	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	−0.861856	−	0.507153i	$-0.830698\pi$
$431$	−14.1326	−	30.9460i	−0.680741	−	1.49062i	0.181115	−	0.983462i	$-0.442030\pi$
$432$	−1.37600	+	19.6961i	−0.0662030	+	0.947627i
$433$	−15.9313	−	7.27559i	−0.765610	−	0.349642i	−0.00596666	−	0.999982i	$-0.501899\pi$
$433$	−15.9313	−	7.27559i	−0.765610	−	0.349642i	−0.759643	+	0.650340i	$0.774627\pi$
$434$	−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	−0.968837	−	0.247698i	$-0.920326\pi$
$439$	−0.585245	−	12.2858i	−0.0279322	−	0.586369i	0.940905	−	0.338671i	$-0.109977\pi$
$440$	−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	0.512869	+	0.858467i	$0.328583\pi$
$443$	−3.22444	+	33.7678i	−0.153198	+	1.60436i	−0.666067	+	0.745892i	$0.732024\pi$
$444$	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	−0.866136	−	0.499808i	$-0.833404\pi$
$449$	−1.09526	+	1.70426i	−0.0516887	+	0.0804292i	0.814447	+	0.580237i	$0.197040\pi$
$450$	−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	−0.0216484	+	0.999766i	$0.506891\pi$
$457$	−21.1238	+	26.8611i	−0.988128	+	1.25651i	−0.966480	+	0.256742i	$0.917351\pi$
$458$	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	0.999809	−	0.0195427i	$-0.00622103\pi$
$461$	31.8368	+	18.3810i	1.48279	+	0.856089i	0.482980	+	0.875631i	$0.339554\pi$
$462$	−36.0341	+	26.1233i	−1.67646	+	1.21537i
$463$	24.9671	−	9.99533i	1.16032	−	0.464522i	0.290009	−	0.957024i	$-0.406342\pi$
$463$	24.9671	−	9.99533i	1.16032	−	0.464522i	0.870312	+	0.492502i	$0.163917\pi$
$464$	−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	0.892885	+	0.450285i	$0.148678\pi$
$467$	26.1811	+	30.2146i	1.21152	+	1.39816i	0.318632	+	0.947879i	$0.396777\pi$
$468$	−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	0.871695	−	0.490049i	$-0.163021\pi$
$479$	2.70282	+	3.79558i	0.123495	+	0.173425i	−0.748200	+	0.663473i	$0.769082\pi$
$480$	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	−0.999814	−	0.0192747i	$-0.993864\pi$
$487$	−7.29368	+	15.9709i	−0.330508	+	0.723712i	0.669306	+	0.742987i	$0.266592\pi$
$488$	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	0.954190	−	0.299203i	$-0.0967207\pi$
$491$	9.71567	+	12.3545i	0.438462	+	0.557550i	−0.515727	+	0.856753i	$0.672478\pi$
$492$	−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	0.444920	+	0.895571i	$0.353232\pi$
$499$	−10.2402	+	29.5872i	−0.458416	+	1.32451i	−0.903335	+	0.428935i	$0.858889\pi$
$500$	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	−0.955063	−	0.296404i	$-0.904212\pi$
$503$	1.00521	−	6.99136i	0.0448199	−	0.311729i	0.999883	−	0.0153254i	$-0.00487842\pi$
$504$	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	0.997854	−	0.0654765i	$-0.0208567\pi$
$509$	5.20007	+	12.9892i	0.230489	+	0.575734i	−0.767365	+	0.641211i	$0.778432\pi$
$510$	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	0.998310	+	0.0581178i	$0.0185099\pi$
$521$	1.29676	+	9.01919i	0.0568122	+	0.395138i	−0.941497	+	0.337020i	$0.890581\pi$
$522$	1.15606	−	5.14483i	0.0505994	−	0.225183i
$523$	29.2603	−	13.3627i	1.27946	−	0.584312i	0.344411	−	0.938819i	$-0.388079\pi$
$523$	29.2603	−	13.3627i	1.27946	−	0.584312i	0.935053	+	0.354507i	$0.115351\pi$
$524$	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	−0.384347	−	0.923189i	$-0.625573\pi$
$541$	−32.1857	−	20.6845i	−1.38377	−	0.889297i	−0.999425	+	0.0338921i	$0.989210\pi$
$542$	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	−0.910469	−	0.413577i	$-0.864279\pi$
$547$	2.06517	−	8.51274i	0.0883002	−	0.363978i	0.998769	+	0.0495990i	$0.0157943\pi$
$548$	−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	−0.591368	−	0.806402i	$-0.701412\pi$
$557$	−15.4086	+	4.52438i	−0.652884	+	0.191704i	−0.0615165	+	0.998106i	$0.519594\pi$
$558$	−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	−0.656911	−	0.753968i	$-0.728137\pi$
$563$	1.62996	−	34.2171i	0.0686947	−	1.44208i	0.725606	−	0.688111i	$-0.241560\pi$
$564$	−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	−0.731121	−	0.682248i	$-0.761002\pi$
$569$	−37.6446	−	3.59463i	−1.57815	−	0.150695i	−0.847025	+	0.531553i	$0.821609\pi$
$570$	40.8538	−	14.5289i	1.71118	−	0.608549i
$571$	0.817573	+	8.56201i	0.0342144	+	0.358309i	0.996325	+	0.0856506i	$0.0272969\pi$
$571$	0.817573	+	8.56201i	0.0342144	+	0.358309i	−0.962111	+	0.272659i	$0.912097\pi$
$572$	−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	−0.337627	−	0.941280i	$-0.609624\pi$
$577$	9.08795	−	5.84047i	0.378336	−	0.243142i	0.715963	+	0.698138i	$0.245988\pi$
$578$	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	0.999978	−	0.00665484i	$-0.00211832\pi$
$587$	10.0429	+	19.4804i	0.414513	+	0.804043i	−0.585465	+	0.810698i	$0.699088\pi$
$588$	−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	0.999401	+	0.0346128i	$0.0110198\pi$
$593$	4.31911	+	14.7095i	0.177364	+	0.604048i	−0.822036	+	0.569435i	$0.807162\pi$
$594$	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	−0.911507	−	0.411284i	$-0.865080\pi$
$599$	−24.7456	+	14.2869i	−1.01108	+	0.583746i	−0.0995713	+	0.995030i	$0.531747\pi$
$600$	0.112271	−	0.0116826i	0.00458346	−	0.000476940i
$601$	−31.5780	−	24.8332i	−1.28809	−	1.01297i	−0.998440	−	0.0558378i	$-0.982217\pi$
$601$	−31.5780	−	24.8332i	−1.28809	−	1.01297i	−0.289655	−	0.957131i	$-0.593541\pi$
$602$	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	0.984046	−	0.177913i	$-0.0569347\pi$
$607$	0.686554	+	2.83002i	0.0278664	+	0.114867i	−0.956180	+	0.292780i	$0.905420\pi$
$608$	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	0.0601696	−	0.998188i	$-0.480836\pi$
$613$	9.88185	−	1.42079i	0.399124	−	0.0573854i	0.338954	+	0.940803i	$0.389927\pi$
$614$	−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	−0.491405	−	0.870931i	$-0.663517\pi$
$617$	−20.0978	+	1.91910i	−0.809105	+	0.0772602i	−0.317700	+	0.948191i	$0.602911\pi$
$618$	2.91872	−	33.5740i	0.117408	−	1.35054i
$619$	−13.2473	+	0.631047i	−0.532454	+	0.0253639i	−0.312088	−	0.950053i	$-0.601028\pi$
$619$	−13.2473	+	0.631047i	−0.532454	+	0.0253639i	−0.220366	+	0.975417i	$0.570725\pi$
$620$	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	0.919651	−	0.392737i	$-0.128472\pi$
$631$	16.6240	+	14.4048i	0.661791	+	0.573445i	−0.257860	+	0.966182i	$0.583017\pi$
$632$	−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	0.477526	−	0.878618i	$-0.341534\pi$
$641$	−6.67746	−	5.25121i	−0.263744	−	0.207410i	−0.741270	+	0.671207i	$0.765776\pi$
$642$	6.69606	−	0.696770i	0.264273	−	0.0274993i
$643$	−40.2666	+	23.2480i	−1.58796	+	0.916810i	−0.594318	+	0.804230i	$0.702578\pi$
$643$	−40.2666	+	23.2480i	−1.58796	+	0.916810i	−0.993643	+	0.112580i	$0.964089\pi$
$644$	−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	−0.278377	−	0.960472i	$-0.589796\pi$
$647$	−20.7578	−	2.98452i	−0.816073	−	0.117334i	−0.537697	+	0.843138i	$0.680705\pi$
$648$	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	0.0155549	−	0.999879i	$-0.495049\pi$
$653$	12.4588	−	3.02248i	0.487552	−	0.118279i	0.471997	+	0.881600i	$0.343533\pi$
$654$	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	0.827709	−	0.561157i	$-0.189644\pi$
$659$	26.6852	+	10.6831i	1.03951	+	0.416156i	0.211798	+	0.977313i	$0.432068\pi$
$660$	6.41747	−	22.5622i	0.249800	−	0.878234i
$661$	−34.4285	−	24.5164i	−1.33911	−	0.953579i	−0.999917	−	0.0128636i	$-0.995905\pi$
$661$	−34.4285	−	24.5164i	−1.33911	−	0.953579i	−0.339197	−	0.940715i	$-0.610155\pi$
$662$	−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	0.333238	−	0.942843i	$-0.391859\pi$
$673$	12.5047	+	1.19405i	0.482019	+	0.0460272i	0.148781	+	0.988870i	$0.452465\pi$
$674$	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	−0.499422	−	0.866359i	$-0.666454\pi$
$677$	−16.7147	−	48.2939i	−0.642397	−	1.85609i	−0.142976	−	0.989726i	$-0.545667\pi$
$678$	−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	−0.843451	−	0.537207i	$-0.819480\pi$
$683$	−11.2834	+	9.77713i	−0.431747	+	0.374111i	0.411703	+	0.911318i	$0.364934\pi$
$684$	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	−0.331316	−	0.943520i	$-0.607493\pi$
$691$	17.1247	−	29.6608i	0.651454	−	1.12835i	0.982770	−	0.184831i	$-0.0591739\pi$
$692$	−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	0.836079	−	0.548610i	$-0.184843\pi$
$701$	18.1195	+	11.6447i	0.684365	+	0.439815i	−0.151713	+	0.988425i	$0.548479\pi$
$702$	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	0.102643	−	0.994718i	$-0.467270\pi$
$709$	28.6567	−	20.4063i	1.07622	−	0.766376i	0.973581	+	0.228343i	$0.0733306\pi$
$710$	−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	−0.892229	−	0.451584i	$-0.850859\pi$
$719$	−30.4403	+	13.9016i	−1.13523	+	0.518442i	−0.243001	+	0.970026i	$0.578132\pi$
$720$	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	0.826230	−	0.563332i	$-0.190481\pi$
$727$	6.04569	+	6.34054i	0.224222	+	0.235158i	−0.602008	+	0.798490i	$0.705632\pi$
$728$	−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	0.893933	−	0.448202i	$-0.147935\pi$
$733$	−1.68756	−	4.21531i	−0.0623313	−	0.155696i	−0.956264	+	0.292505i	$0.905511\pi$
$734$	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	0.944033	+	0.329851i	$0.106999\pi$
$739$	−1.48672	+	10.3404i	−0.0546898	+	0.380376i	−0.998723	+	0.0505249i	$0.983911\pi$
$740$	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	0.429040	+	0.903286i	$0.358852\pi$
$743$	−12.7181	+	36.7466i	−0.466582	+	1.34810i	−0.895622	+	0.444816i	$0.853269\pi$
$744$	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	0.504891	−	0.863183i	$-0.331533\pi$
$751$	−12.4140	−	15.7857i	−0.452993	−	0.576027i	−0.957884	+	0.287156i	$0.907290\pi$
$752$	−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	0.943104	+	0.332497i	$0.107891\pi$
$757$	23.4904	+	36.5518i	0.853774	+	1.32850i	−0.0893298	+	0.996002i	$0.528473\pi$
$758$	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	−0.522696	−	0.852519i	$-0.675074\pi$
$761$	13.1018	−	25.4139i	0.474939	−	0.921254i	0.997635	−	0.0687346i	$-0.0218962\pi$
$762$	−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	0.737365	+	0.675494i	$0.236070\pi$
$769$	−5.49728	+	28.5226i	−0.198237	+	1.02855i	−0.935602	+	0.353056i	$0.885142\pi$
$770$	−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	−0.151680	−	0.988430i	$-0.548468\pi$
$773$	−22.6223	−	6.64249i	−0.813666	−	0.238914i	−0.661986	+	0.749516i	$0.730286\pi$
$774$	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	−0.995060	−	0.0992802i	$-0.968346\pi$
$787$	−23.8047	+	24.9656i	−0.848545	+	0.889928i	0.146515	+	0.989209i	$0.453194\pi$
$788$	−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	0.0364257	−	0.999336i	$-0.488403\pi$
$797$	28.6880	−	22.5605i	1.01618	−	0.799133i	0.979754	+	0.200204i	$0.0641603\pi$
$798$	−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	0.533872	−	0.845565i	$-0.320736\pi$
$809$	6.95283	+	3.17525i	0.244448	+	0.111636i	−0.289424	+	0.957201i	$0.593464\pi$
$810$	19.1981	+	34.3270i	0.674553	+	1.20613i
$811$	−21.7655	−	47.6598i	−0.764290	−	1.67356i	−0.738836	−	0.673886i	$-0.764624\pi$
$811$	−21.7655	−	47.6598i	−0.764290	−	1.67356i	−0.0254543	−	0.999676i	$-0.508103\pi$
$812$	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	−0.999734	−	0.0230784i	$-0.992653\pi$
$821$	−2.29770	−	11.9216i	−0.0801904	−	0.416067i	0.919543	−	0.392989i	$-0.128559\pi$
$822$	−11.4433	−	7.21772i	−0.399131	−	0.251747i
$823$	21.3576	+	20.3645i	0.744481	+	0.709861i	0.964046	−	0.265737i	$-0.0856153\pi$
$823$	21.3576	+	20.3645i	0.744481	+	0.709861i	−0.219565	+	0.975598i	$0.570464\pi$
$824$	−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	−0.745242	−	0.666794i	$-0.767666\pi$
$839$	−18.3749	+	9.47291i	−0.634371	+	0.327041i	0.110871	+	0.993835i	$0.464636\pi$
$840$	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	0.930485	+	0.366329i	$0.119385\pi$
$853$	1.14006	+	23.9329i	0.0390351	+	0.819447i	−0.891450	+	0.453118i	$0.850312\pi$
$854$	−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	−0.996556	−	0.0829267i	$-0.973573\pi$
$857$	−0.0677731	+	0.709752i	−0.00231509	+	0.0242447i	0.994241	+	0.107171i	$0.0341793\pi$
$858$	−17.5805	−	69.8750i	−0.600188	−	2.38549i
$859$	22.4428	−	17.6492i	0.765738	−	0.602183i	−0.157005	−	0.987598i	$-0.550184\pi$
$859$	22.4428	−	17.6492i	0.765738	−	0.602183i	0.922744	+	0.385415i	$0.125942\pi$
$860$	−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	−0.0851979	+	0.996364i	$0.527152\pi$
$863$	−28.0881	+	43.7059i	−0.956130	+	1.48777i	−0.870932	+	0.491403i	$0.836484\pi$
$864$	−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	−0.118920	−	0.992904i	$-0.537943\pi$
$877$	14.2206	−	5.69308i	0.480196	−	0.192242i	0.599116	+	0.800662i	$0.295519\pi$
$878$	−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	−0.949696	−	0.313173i	$-0.898608\pi$
$881$	−33.3778	−	38.5200i	−1.12453	−	1.29777i	−0.174830	−	0.984599i	$-0.555938\pi$
$882$	64.6222	−	16.8431i	2.17594	−	0.567136i
$883$	−38.3402	−	11.2577i	−1.29025	−	0.378851i	−0.436580	−	0.899666i	$-0.643810\pi$
$883$	−38.3402	−	11.2577i	−1.29025	−	0.378851i	−0.853670	+	0.520814i	$0.825628\pi$
$884$	−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	−0.738146	−	0.674641i	$-0.764298\pi$
$887$	5.89289	−	30.5752i	0.197864	−	1.02662i	0.936010	−	0.351974i	$-0.114490\pi$
$888$	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	0.674128	−	0.738614i	$-0.264519\pi$
$907$	50.0117	−	17.3092i	1.66061	−	0.574743i	0.986482	+	0.163872i	$0.0523983\pi$
$908$	−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	−0.561318	−	0.827600i	$-0.689706\pi$
$911$	7.20269	−	6.86775i	0.238636	−	0.227539i	0.799954	+	0.600061i	$0.204857\pi$
$912$	−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	$-0.798464\pi$
$919$		−	35.8737i		−	1.18336i	0.806172	−	0.591682i	$-0.201536\pi$
$920$	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	−0.999911	−	0.0133380i	$-0.995754\pi$
$929$	−29.4327	−	30.8681i	−0.965656	−	1.01275i	0.0342548	−	0.999413i	$-0.489094\pi$
$930$	−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	−0.302048	−	0.953293i	$-0.597670\pi$
$937$	6.75275	−	3.08388i	0.220603	−	0.100746i	0.522651	+	0.852547i	$0.324943\pi$
$938$	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	−0.0573611	−	0.998353i	$-0.518269\pi$
$941$	−27.7268	−	14.2942i	−0.903868	−	0.465977i	−0.846507	+	0.532377i	$0.821299\pi$
$942$	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	0.0106651	−	0.999943i	$-0.496605\pi$
$947$	29.5147	−	21.0174i	0.959100	−	0.682972i	0.948435	+	0.316971i	$0.102666\pi$
$948$	−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	−0.713349	−	0.700809i	$-0.752822\pi$
$953$	2.52669	−	2.91596i	0.0818475	−	0.0944571i	0.795196	+	0.606352i	$0.207368\pi$
$954$	−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	0.999597	+	0.0283703i	$0.00903177\pi$
$967$	16.3061	+	28.2430i	0.524368	+	0.908232i	−0.475229	+	0.879862i	$0.657635\pi$
$968$	−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	−0.644318	−	0.764758i	$-0.722859\pi$
$971$	−24.0840	+	7.07171i	−0.772893	+	0.226942i	−0.128575	+	0.991700i	$0.541040\pi$
$972$	−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	−0.997419	−	0.0717963i	$-0.977127\pi$
$977$	0.0721500	−	1.51462i	0.00230828	−	0.0484568i	0.999728	+	0.0233395i	$0.00742987\pi$
$978$	−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	0.906450	−	0.422314i	$-0.138782\pi$
$983$	53.8201	+	5.13920i	1.71660	+	0.163915i	0.810146	+	0.586229i	$0.199388\pi$
$984$	−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	−0.630912	−	0.775855i	$-0.717319\pi$
$991$	−5.89497	+	3.78847i	−0.187260	+	0.120345i	0.443652	+	0.896199i	$0.353683\pi$
$992$	−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	−0.0491660	−	0.998791i	$-0.515656\pi$
$997$	−24.4391	−	9.78393i	−0.773993	−	0.309860i	−0.724828	+	0.688930i	$0.758081\pi$
$998$	−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.11.19	✓	440
3.2	odd	2		621.2.s.a.494.4		440
9.4	even	3		621.2.s.a.287.4		440
9.5	odd	6	inner	207.2.o.a.149.19	yes	440
23.21	odd	22	inner	207.2.o.a.182.19	yes	440
69.44	even	22		621.2.s.a.251.4		440
207.67	odd	66		621.2.s.a.44.4		440
207.113	even	66	inner	207.2.o.a.113.19	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
207.2.o.a.11.19	✓	440	1.1	even	1	trivial
207.2.o.a.113.19	yes	440	207.113	even	66	inner
207.2.o.a.149.19	yes	440	9.5	odd	6	inner
207.2.o.a.182.19	yes	440	23.21	odd	22	inner
621.2.s.a.44.4		440	207.67	odd	66
621.2.s.a.251.4		440	69.44	even	22
621.2.s.a.287.4		440	9.4	even	3
621.2.s.a.494.4		440	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(2.02146 - 0.0962939i) q^{2} +(-0.150008 + 1.72554i) q^{3} +(2.08607 - 0.199196i) q^{4} +(1.56283 + 1.49016i) q^{5} +(-0.137076 + 3.50255i) q^{6} +(-0.802915 - 4.16592i) q^{7} +(0.191421 - 0.0275221i) q^{8} +(-2.95499 - 0.517692i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9}+O(q^{10}) \) 440 * q - 27 * q^2 - 16 * q^3 - 29 * q^4 - 33 * q^5 - 25 * q^6 - 11 * q^7 - 16 * q^9	\( 440 q - 27 q^{2} - 16 q^{3} - 29 q^{4} - 33 q^{5} - 25 q^{6} - 11 q^{7} - 16 q^{9} - 44 q^{10} - 33 q^{11} - 22 q^{12} - 9 q^{13} - 33 q^{14} + 3 q^{16} - 39 q^{18} - 44 q^{19} - 33 q^{20} - 55 q^{21} - 27 q^{23} + 52 q^{24} + 11 q^{25} - 79 q^{27} - 44 q^{28} + 27 q^{29} - 66 q^{30} - 3 q^{31} - 33 q^{32} - 11 q^{34} + 23 q^{36} - 44 q^{37} - 33 q^{38} - 40 q^{39} - 77 q^{40} + 9 q^{41} - 22 q^{42} - 11 q^{43} - 36 q^{46} - 120 q^{47} - 56 q^{48} + 35 q^{49} - 3 q^{50} - 22 q^{51} - 38 q^{52} + 42 q^{54} - 44 q^{55} + 165 q^{56} + 11 q^{57} - 10 q^{58} - 9 q^{59} + 88 q^{60} - 11 q^{61} + 33 q^{63} - 22 q^{64} + 198 q^{65} + 33 q^{66} - 11 q^{67} + 3 q^{69} - 70 q^{70} + 14 q^{72} - 36 q^{73} + 231 q^{74} - 13 q^{75} - 11 q^{76} + 39 q^{77} + 3 q^{78} - 11 q^{79} + 172 q^{81} - 10 q^{82} + 66 q^{83} - 110 q^{84} + q^{85} - 33 q^{86} - 196 q^{87} - 99 q^{88} + 418 q^{90} + 63 q^{92} - 188 q^{93} - 42 q^{94} - 93 q^{95} - 82 q^{96} + 22 q^{97} + 242 q^{99}+O(q^{100}) \) 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

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Representations

Groups

Database

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