LMFDB - Embedded newform 189.2.ba.a.5.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(5,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([5, 15]))

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

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

chi := DirichletCharacter("189.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.ba (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			5.3
Character	$\chi$	$=$	189.5
Dual form			189.2.ba.a.38.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.31815 + 0.408753i) q^{2} +(-0.111866 - 1.72843i) q^{3} +(3.32736 - 1.21106i) q^{4} +(-0.175778 + 0.996886i) q^{5} +(0.965825 + 3.96105i) q^{6} +(1.63463 + 2.08038i) q^{7} +(-3.14120 + 1.81358i) q^{8} +(-2.97497 + 0.386707i) q^{9} +O(q^{10})$	\(q+(-2.31815 + 0.408753i) q^{2} +(-0.111866 - 1.72843i) q^{3} +(3.32736 - 1.21106i) q^{4} +(-0.175778 + 0.996886i) q^{5} +(0.965825 + 3.96105i) q^{6} +(1.63463 + 2.08038i) q^{7} +(-3.14120 + 1.81358i) q^{8} +(-2.97497 + 0.386707i) q^{9} -2.38278i q^{10} +(0.972614 - 0.171498i) q^{11} +(-2.46546 - 5.61565i) q^{12} +(3.55093 - 4.23183i) q^{13} +(-4.63968 - 4.15448i) q^{14} +(1.74272 + 0.192303i) q^{15} +(1.11551 - 0.936020i) q^{16} +3.54415 q^{17} +(6.73837 - 2.11247i) q^{18} -0.366602i q^{19} +(0.622412 + 3.52988i) q^{20} +(3.41294 - 3.05808i) q^{21} +(-2.18457 + 0.795117i) q^{22} +(4.11352 - 4.90230i) q^{23} +(3.48604 + 5.22649i) q^{24} +(3.73558 + 1.35964i) q^{25} +(-6.50182 + 11.2615i) q^{26} +(1.00120 + 5.09878i) q^{27} +(7.95847 + 4.94254i) q^{28} +(-0.703413 - 0.838295i) q^{29} +(-4.11848 + 0.266553i) q^{30} +(-2.36457 - 6.49659i) q^{31} +(2.45967 - 2.93132i) q^{32} +(-0.405226 - 1.66191i) q^{33} +(-8.21588 + 1.44868i) q^{34} +(-2.36123 + 1.26385i) q^{35} +(-9.43048 + 4.88958i) q^{36} +(2.23803 + 3.87639i) q^{37} +(0.149849 + 0.849839i) q^{38} +(-7.71168 - 5.66415i) q^{39} +(-1.25577 - 3.45021i) q^{40} +(0.350145 + 0.293807i) q^{41} +(-6.66172 + 8.48413i) q^{42} +(-9.94497 - 3.61967i) q^{43} +(3.02854 - 1.74853i) q^{44} +(0.137431 - 3.03368i) q^{45} +(-7.53193 + 13.0457i) q^{46} +(10.6873 + 3.88985i) q^{47} +(-1.74264 - 1.82337i) q^{48} +(-1.65597 + 6.80131i) q^{49} +(-9.21539 - 1.62492i) q^{50} +(-0.396472 - 6.12584i) q^{51} +(6.69022 - 18.3812i) q^{52} +(-6.67945 + 3.85638i) q^{53} +(-4.40507 - 11.4105i) q^{54} +0.999731i q^{55} +(-8.90764 - 3.57038i) q^{56} +(-0.633647 + 0.0410104i) q^{57} +(1.97327 + 1.65577i) q^{58} +(-0.199348 - 0.167273i) q^{59} +(6.03153 - 1.47067i) q^{60} +(-3.45090 + 9.48126i) q^{61} +(8.13692 + 14.0936i) q^{62} +(-5.66748 - 5.55695i) q^{63} +(-5.95988 + 10.3228i) q^{64} +(3.59448 + 4.28373i) q^{65} +(1.61869 + 3.68693i) q^{66} +(-0.0909855 + 0.516004i) q^{67} +(11.7927 - 4.29218i) q^{68} +(-8.93347 - 6.56154i) q^{69} +(4.95709 - 3.89497i) q^{70} +(-4.17294 - 2.40925i) q^{71} +(8.64367 - 6.61006i) q^{72} +(9.88409 + 5.70658i) q^{73} +(-6.77258 - 8.07125i) q^{74} +(1.93216 - 6.60880i) q^{75} +(-0.443977 - 1.21982i) q^{76} +(1.94665 + 1.74307i) q^{77} +(20.1921 + 9.97819i) q^{78} +(0.918512 + 5.20914i) q^{79} +(0.737024 + 1.27656i) q^{80} +(8.70091 - 2.30089i) q^{81} +(-0.931784 - 0.537966i) q^{82} +(7.16717 - 6.01397i) q^{83} +(7.65258 - 14.3086i) q^{84} +(-0.622984 + 3.53312i) q^{85} +(24.5335 + 4.32592i) q^{86} +(-1.37025 + 1.30958i) q^{87} +(-2.74416 + 2.30262i) q^{88} +2.53472 q^{89} +(0.921439 + 7.08871i) q^{90} +(14.6083 + 0.469805i) q^{91} +(7.75018 - 21.2934i) q^{92} +(-10.9644 + 4.81375i) q^{93} +(-26.3647 - 4.64881i) q^{94} +(0.365460 + 0.0644405i) q^{95} +(-5.34174 - 3.92346i) q^{96} +(0.637350 - 1.75110i) q^{97} +(1.05874 - 16.4433i) q^{98} +(-2.82718 + 0.886319i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−2.31815	+	0.408753i	−1.63918	+	0.289032i	−0.915865	−	0.401486i	$-0.868494\pi$
$2$	−2.31815	+	0.408753i	−1.63918	+	0.289032i	−0.723315	+	0.690518i	$0.757383\pi$
$3$	−0.111866	−	1.72843i	−0.0645861	−	0.997912i
$3$	−0.111866	−	1.72843i	−0.0645861	−	0.997912i
$4$	3.32736	−	1.21106i	1.66368	−	0.605530i
$5$	−0.175778	+	0.996886i	−0.0786102	+	0.445821i	0.919943	+	0.392052i	$0.128235\pi$
$5$	−0.175778	+	0.996886i	−0.0786102	+	0.445821i	−0.998553	+	0.0537691i	$0.982877\pi$
$6$	0.965825	+	3.96105i	0.394296	+	1.61709i
$7$	1.63463	+	2.08038i	0.617832	+	0.786310i
$7$	1.63463	+	2.08038i	0.617832	+	0.786310i
$8$	−3.14120	+	1.81358i	−1.11058	+	0.641196i
$9$	−2.97497	+	0.386707i	−0.991657	+	0.128902i
$10$		−	2.38278i		−	0.753502i
$11$	0.972614	−	0.171498i	0.293254	−	0.0517086i	−0.0250856	−	0.999685i	$-0.507986\pi$
$11$	0.972614	−	0.171498i	0.293254	−	0.0517086i	0.318340	+	0.947977i	$0.396875\pi$
$12$	−2.46546	−	5.61565i	−0.711716	−	1.62110i
$13$	3.55093	−	4.23183i	0.984851	−	1.17370i	5.22189e−5	−	1.00000i	$-0.499983\pi$
$13$	3.55093	−	4.23183i	0.984851	−	1.17370i	0.984799	−	0.173700i	$-0.0555722\pi$
$14$	−4.63968	−	4.15448i	−1.24001	−	1.11033i
$15$	1.74272	+	0.192303i	0.449967	+	0.0496523i
$16$	1.11551	−	0.936020i	0.278876	−	0.234005i
$17$	3.54415			0.859584			0.429792	−	0.902928i	$-0.358587\pi$
$17$	3.54415			0.859584			0.429792	+	0.902928i	$0.358587\pi$
$18$	6.73837	−	2.11247i	1.58825	−	0.497915i
$19$		−	0.366602i		−	0.0841042i	−0.999115	−	0.0420521i	$-0.986610\pi$
$19$		−	0.366602i		−	0.0841042i	0.999115	−	0.0420521i	$-0.0133896\pi$
$20$	0.622412	+	3.52988i	0.139176	+	0.789304i
$21$	3.41294	−	3.05808i	0.744765	−	0.667327i
$22$	−2.18457	+	0.795117i	−0.465751	+	0.169520i
$23$	4.11352	−	4.90230i	0.857728	−	1.02220i	−0.141750	−	0.989902i	$-0.545273\pi$
$23$	4.11352	−	4.90230i	0.857728	−	1.02220i	0.999478	−	0.0322978i	$-0.0102825\pi$
$24$	3.48604	+	5.22649i	0.711585	+	1.06685i
$25$	3.73558	+	1.35964i	0.747116	+	0.271928i
$26$	−6.50182	+	11.2615i	−1.27511	+	2.20856i
$27$	1.00120	+	5.09878i	0.192681	+	0.981262i
$28$	7.95847	+	4.94254i	1.50401	+	0.934053i
$29$	−0.703413	−	0.838295i	−0.130620	−	0.155667i	0.696770	−	0.717295i	$-0.254620\pi$
$29$	−0.703413	−	0.838295i	−0.130620	−	0.155667i	−0.827390	+	0.561627i	$0.810175\pi$
$30$	−4.11848	+	0.266553i	−0.751928	+	0.0486657i
$31$	−2.36457	−	6.49659i	−0.424689	−	1.16682i	−0.948994	−	0.315293i	$-0.897897\pi$
$31$	−2.36457	−	6.49659i	−0.424689	−	1.16682i	0.524306	−	0.851530i	$-0.324325\pi$
$32$	2.45967	−	2.93132i	0.434812	−	0.518188i
$33$	−0.405226	−	1.66191i	−0.0705408	−	0.289302i
$34$	−8.21588	+	1.44868i	−1.40901	+	0.248447i
$35$	−2.36123	+	1.26385i	−0.399121	+	0.213630i
$36$	−9.43048	+	4.88958i	−1.57175	+	0.814931i
$37$	2.23803	+	3.87639i	0.367930	+	0.637274i	0.989242	−	0.146290i	$-0.0467331\pi$
$37$	2.23803	+	3.87639i	0.367930	+	0.637274i	−0.621311	+	0.783564i	$0.713400\pi$
$38$	0.149849	+	0.849839i	0.0243088	+	0.137862i
$39$	−7.71168	−	5.66415i	−1.23486	−	0.906990i
$40$	−1.25577	−	3.45021i	−0.198555	−	0.545526i
$41$	0.350145	+	0.293807i	0.0546835	+	0.0458849i	0.669720	−	0.742614i	$-0.266414\pi$
$41$	0.350145	+	0.293807i	0.0546835	+	0.0458849i	−0.615036	+	0.788499i	$0.710859\pi$
$42$	−6.66172	+	8.48413i	−1.02793	+	1.30913i
$43$	−9.94497	−	3.61967i	−1.51659	−	0.551995i	−0.556299	−	0.830982i	$-0.687779\pi$
$43$	−9.94497	−	3.61967i	−1.51659	−	0.551995i	−0.960295	+	0.278988i	$0.910001\pi$
$44$	3.02854	−	1.74853i	0.456570	−	0.263601i
$45$	0.137431	−	3.03368i	0.0204870	−	0.452235i
$46$	−7.53193	+	13.0457i	−1.11052	+	1.92348i
$47$	10.6873	+	3.88985i	1.55890	+	0.567393i	0.970484	−	0.241165i	$-0.0775296\pi$
$47$	10.6873	+	3.88985i	1.55890	+	0.567393i	0.588416	+	0.808559i	$0.299752\pi$
$48$	−1.74264	−	1.82337i	−0.251528	−	0.263181i
$49$	−1.65597	+	6.80131i	−0.236567	+	0.971615i
$50$	−9.21539	−	1.62492i	−1.30325	−	0.229799i
$51$	−0.396472	−	6.12584i	−0.0555171	−	0.857789i
$52$	6.69022	−	18.3812i	0.927767	−	2.54902i
$53$	−6.67945	+	3.85638i	−0.917493	+	0.529715i	−0.882834	−	0.469684i	$-0.844368\pi$
$53$	−6.67945	+	3.85638i	−0.917493	+	0.529715i	−0.0346586	+	0.999399i	$0.511034\pi$
$54$	−4.40507	−	11.4105i	−0.599454	−	1.55277i
$55$			0.999731i			0.134804i
$56$	−8.90764	−	3.57038i	−1.19033	−	0.477112i
$57$	−0.633647	+	0.0410104i	−0.0839286	+	0.00543196i
$58$	1.97327	+	1.65577i	0.259103	+	0.217414i
$59$	−0.199348	−	0.167273i	−0.0259529	−	0.0217771i	0.629719	−	0.776823i	$-0.283170\pi$
$59$	−0.199348	−	0.167273i	−0.0259529	−	0.0217771i	−0.655672	+	0.755046i	$0.727615\pi$
$60$	6.03153	−	1.47067i	0.778667	−	0.189863i
$61$	−3.45090	+	9.48126i	−0.441842	+	1.21395i	0.496438	+	0.868072i	$0.334641\pi$
$61$	−3.45090	+	9.48126i	−0.441842	+	1.21395i	−0.938279	+	0.345878i	$0.887581\pi$
$62$	8.13692	+	14.0936i	1.03339	+	1.78988i
$63$	−5.66748	−	5.55695i	−0.714035	−	0.700110i
$64$	−5.95988	+	10.3228i	−0.744985	+	1.29035i
$65$	3.59448	+	4.28373i	0.445840	+	0.531332i
$66$	1.61869	+	3.68693i	0.199247	+	0.453830i
$67$	−0.0909855	+	0.516004i	−0.0111156	+	0.0630400i	−0.989861	−	0.142039i	$-0.954634\pi$
$67$	−0.0909855	+	0.516004i	−0.0111156	+	0.0630400i	0.978745	+	0.205079i	$0.0657452\pi$
$68$	11.7927	−	4.29218i	1.43007	−	0.520504i
$69$	−8.93347	−	6.56154i	−1.07546	−	0.789917i
$70$	4.95709	−	3.89497i	0.592486	−	0.465537i
$71$	−4.17294	−	2.40925i	−0.495237	−	0.285925i	0.231507	−	0.972833i	$-0.425634\pi$
$71$	−4.17294	−	2.40925i	−0.495237	−	0.285925i	−0.726745	+	0.686908i	$0.758968\pi$
$72$	8.64367	−	6.61006i	1.01867	−	0.779003i
$73$	9.88409	+	5.70658i	1.15685	+	0.667905i	0.950546	−	0.310584i	$-0.100525\pi$
$73$	9.88409	+	5.70658i	1.15685	+	0.667905i	0.206300	+	0.978489i	$0.433858\pi$
$74$	−6.77258	−	8.07125i	−0.787297	−	0.938264i
$75$	1.93216	−	6.60880i	0.223107	−	0.763119i
$76$	−0.443977	−	1.21982i	−0.0509276	−	0.139923i
$77$	1.94665	+	1.74307i	0.221841	+	0.198641i
$78$	20.1921	+	9.97819i	2.28630	+	1.12981i
$79$	0.918512	+	5.20914i	0.103341	+	0.586074i	0.991870	+	0.127255i	$0.0406165\pi$
$79$	0.918512	+	5.20914i	0.103341	+	0.586074i	−0.888529	+	0.458820i	$0.848272\pi$
$80$	0.737024	+	1.27656i	0.0824018	+	0.142724i
$81$	8.70091	−	2.30089i	0.966768	−	0.255654i
$82$	−0.931784	−	0.537966i	−0.102898	−	0.0594084i
$83$	7.16717	−	6.01397i	0.786699	−	0.660119i	−0.158227	−	0.987403i	$-0.550578\pi$
$83$	7.16717	−	6.01397i	0.786699	−	0.660119i	0.944926	+	0.327284i	$0.106133\pi$
$84$	7.65258	−	14.3086i	0.834964	−	1.56120i
$85$	−0.622984	+	3.53312i	−0.0675721	+	0.383220i
$86$	24.5335	+	4.32592i	2.64551	+	0.466476i
$87$	−1.37025	+	1.30958i	−0.146906	+	0.140402i
$88$	−2.74416	+	2.30262i	−0.292528	+	0.245460i
$89$	2.53472			0.268680			0.134340	−	0.990935i	$-0.457109\pi$
$89$	2.53472			0.268680			0.134340	+	0.990935i	$0.457109\pi$
$90$	0.921439	+	7.08871i	0.0971282	+	0.747215i
$91$	14.6083	+	0.469805i	1.53136	+	0.0492489i
$92$	7.75018	−	21.2934i	0.808012	−	2.21999i
$93$	−10.9644	+	4.81375i	−1.13696	+	0.499163i
$94$	−26.3647	−	4.64881i	−2.71931	−	0.479488i
$95$	0.365460	+	0.0644405i	0.0374954	+	0.00661145i
$96$	−5.34174	−	3.92346i	−0.545189	−	0.400436i
$97$	0.637350	−	1.75110i	0.0647130	−	0.177798i	−0.903122	−	0.429385i	$-0.858730\pi$
$97$	0.637350	−	1.75110i	0.0647130	−	0.177798i	0.967835	+	0.251587i	$0.0809526\pi$
$98$	1.05874	−	16.4433i	0.106948	−	1.66103i
$99$	−2.82718	+	0.886319i	−0.284142	+	0.0890784i
$100$	14.0762			1.40762
$101$	−13.4219	+	11.2623i	−1.33553	+	1.12064i	−0.352783	+	0.935705i	$0.614764\pi$
$101$	−13.4219	+	11.2623i	−1.33553	+	1.12064i	−0.982750	+	0.184940i	$0.940791\pi$
$102$	3.42303	+	14.0386i	0.338931	+	1.39002i
$103$	−2.69840	−	0.475801i	−0.265881	−	0.0468820i	0.0391182	−	0.999235i	$-0.487545\pi$
$103$	−2.69840	−	0.475801i	−0.265881	−	0.0468820i	−0.304999	+	0.952353i	$0.598656\pi$
$104$	−3.47945	+	19.7329i	−0.341188	+	1.93497i
$105$	2.44863	+	3.93986i	0.238962	+	0.384491i
$106$	13.9077	−	11.6699i	1.35083	−	1.13348i
$107$	−16.9866	−	9.80720i	−1.64215	−	0.948098i	−0.980066	−	0.198673i	$-0.936337\pi$
$107$	−16.9866	−	9.80720i	−1.64215	−	0.948098i	−0.662088	−	0.749426i	$-0.730330\pi$
$108$	9.50628	+	15.7530i	0.914742	+	1.51583i
$109$	−8.71121	−	15.0883i	−0.834382	−	1.44519i	−0.894532	−	0.447003i	$-0.852491\pi$
$109$	−8.71121	−	15.0883i	−0.834382	−	1.44519i	0.0601503	−	0.998189i	$-0.480842\pi$
$110$	−0.408643	−	2.31753i	−0.0389625	−	0.220968i
$111$	6.44972	−	4.30193i	0.612181	−	0.408321i
$112$	3.77072	+	0.790629i	0.356299	+	0.0747075i
$113$	3.31029	+	9.09496i	0.311406	+	0.855582i	0.992373	+	0.123268i	$0.0393374\pi$
$113$	3.31029	+	9.09496i	0.311406	+	0.855582i	−0.680967	+	0.732314i	$0.738440\pi$
$114$	1.45213	−	0.354073i	0.136004	−	0.0331620i
$115$	4.16397	+	4.96242i	0.388292	+	0.462748i
$116$	−3.35573	−	1.93743i	−0.311572	−	0.179886i
$117$	−8.92744	+	13.9628i	−0.825342	+	1.29086i
$118$	0.530492	+	0.306280i	0.0488357	+	0.0281953i
$119$	5.79338	+	7.37319i	0.531078	+	0.675899i
$120$	−5.82298	+	2.55648i	−0.531563	+	0.233374i
$121$	−9.42005	+	3.42862i	−0.856368	+	0.311693i
$122$	4.12421	−	23.3895i	0.373388	−	2.11759i
$123$	0.468657	−	0.638071i	0.0422573	−	0.0575329i
$124$	−15.7355	−	18.7529i	−1.41309	−	1.68406i
$125$	−4.54270	+	7.86818i	−0.406311	+	0.703752i
$126$	15.4095	+	10.5653i	1.37279	+	0.941228i
$127$	−7.52166	−	13.0279i	−0.667439	−	1.15604i	−0.978618	−	0.205687i	$-0.934057\pi$
$127$	−7.52166	−	13.0279i	−0.667439	−	1.15604i	0.311178	−	0.950352i	$-0.399276\pi$
$128$	6.97891	−	19.1744i	0.616854	−	1.69479i
$129$	−5.14386	+	17.5941i	−0.452892	+	1.54908i
$130$	−10.0835	−	8.46109i	−0.884385	−	0.742087i
$131$	7.80505	+	6.54921i	0.681930	+	0.572207i	0.916570	−	0.399875i	$-0.130947\pi$
$131$	7.80505	+	6.54921i	0.681930	+	0.572207i	−0.234640	+	0.972082i	$0.575391\pi$
$132$	−3.36101	−	5.03904i	−0.292539	−	0.438592i
$133$	0.762672	−	0.599258i	0.0661320	−	0.0519623i
$134$		−	1.23337i		−	0.106547i
$135$	−5.25889	+	0.101826i	−0.452614	+	0.00876381i
$136$	−11.1329	+	6.42759i	−0.954639	+	0.551161i
$137$	1.02391	−	2.81318i	0.0874788	−	0.240346i	−0.888237	−	0.459385i	$-0.848070\pi$
$137$	1.02391	−	2.81318i	0.0874788	−	0.240346i	0.975716	+	0.219039i	$0.0702921\pi$
$138$	23.3912	+	11.5591i	1.99119	+	0.983974i
$139$	−3.53438	−	0.623206i	−0.299782	−	0.0528596i	0.0217341	−	0.999764i	$-0.493081\pi$
$139$	−3.53438	−	0.623206i	−0.299782	−	0.0528596i	−0.321516	+	0.946904i	$0.604192\pi$
$140$	−6.32607	+	7.06490i	−0.534651	+	0.597093i
$141$	5.52781	−	18.9074i	0.465525	−	1.59229i
$142$	10.6583	+	3.87930i	0.894425	+	0.325544i
$143$	2.72793	−	4.72492i	0.228121	−	0.395118i
$144$	−2.95663	+	3.21601i	−0.246386	+	0.268001i
$145$	0.959329	−	0.553869i	0.0796679	−	0.0459963i
$146$	−25.2454	−	9.18857i	−2.08932	−	0.760452i
$147$	11.9409	+	2.10140i	0.984866	+	0.173320i
$148$	12.1413	+	10.1877i	0.998007	+	0.837428i
$149$	−2.17683	−	5.98079i	−0.178333	−	0.489966i	0.818030	−	0.575175i	$-0.195066\pi$
$149$	−2.17683	−	5.98079i	−0.178333	−	0.489966i	−0.996363	+	0.0852097i	$0.972844\pi$
$150$	−1.77768	+	16.1100i	−0.145147	+	1.31537i
$151$	0.900878	+	5.10913i	0.0733124	+	0.415775i	0.999272	+	0.0381524i	$0.0121472\pi$
$151$	0.900878	+	5.10913i	0.0733124	+	0.415775i	−0.925960	+	0.377623i	$0.876742\pi$
$152$	0.664860	+	1.15157i	0.0539273	+	0.0934048i
$153$	−10.5438	+	1.37055i	−0.852412	+	0.110802i
$154$	−5.22510	−	3.24501i	−0.421051	−	0.261490i
$155$	6.89200	−	1.21525i	0.553579	−	0.0976109i
$156$	−32.5192	−	9.50737i	−2.60362	−	0.761198i
$157$	4.54023	−	5.41084i	0.362350	−	0.431832i	−0.553811	−	0.832642i	$-0.686827\pi$
$157$	4.54023	−	5.41084i	0.362350	−	0.431832i	0.916161	+	0.400811i	$0.131271\pi$
$158$	−4.25850	−	11.7001i	−0.338788	−	0.930813i
$159$	7.41271	+	11.1136i	0.587866	+	0.881365i
$160$	2.48983	+	2.96727i	0.196839	+	0.234583i
$161$	16.9227	+	0.544238i	1.33370	+	0.0428920i
$162$	−19.2295	+	8.89033i	−1.51082	+	0.698490i
$163$	3.91668	−	6.78389i	0.306778	−	0.531355i	−0.670878	−	0.741568i	$-0.734082\pi$
$163$	3.91668	−	6.78389i	0.306778	−	0.531355i	0.977656	+	0.210213i	$0.0674157\pi$
$164$	1.52088	+	0.553554i	0.118761	+	0.0432253i
$165$	1.72797	−	0.111836i	0.134522	−	0.00870644i
$166$	−14.1564	+	16.8709i	−1.09875	+	1.30943i
$167$	−18.9988	+	6.91501i	−1.47017	+	0.535100i	−0.948148	−	0.317829i	$-0.897046\pi$
$167$	−18.9988	+	6.91501i	−1.47017	+	0.535100i	−0.522027	+	0.852929i	$0.674824\pi$
$168$	−5.17470	+	15.7957i	−0.399237	+	1.21866i
$169$	−3.04189	−	17.2514i	−0.233991	−	1.32703i
$170$		−	8.44494i		−	0.647698i
$171$	0.141768	+	1.09063i	0.0108412	+	0.0834026i
$172$	−37.4741			−2.85738
$173$	−0.779539	+	0.654111i	−0.0592672	+	0.0497311i	−0.671940	−	0.740605i	$-0.734539\pi$
$173$	−0.779539	+	0.654111i	−0.0592672	+	0.0497311i	0.612673	+	0.790337i	$0.290094\pi$
$174$	2.64115	−	3.59590i	0.200225	−	0.272604i
$175$	3.27772	+	9.99394i	0.247772	+	0.755471i
$176$	0.924431	−	1.10169i	0.0696816	−	0.0830433i
$177$	−0.266820	+	0.363272i	−0.0200554	+	0.0273052i
$178$	−5.87586	+	1.03607i	−0.440415	+	0.0776570i
$179$			3.77073i			0.281837i	0.990021	+	0.140919i	$0.0450056\pi$
$179$			3.77073i			0.281837i	−0.990021	+	0.140919i	$0.954994\pi$
$180$	−3.21669	−	10.2606i	−0.239758	−	0.764779i
$181$	15.4065	−	8.89497i	1.14516	−	0.661158i	0.197456	−	0.980312i	$-0.436732\pi$
$181$	15.4065	−	8.89497i	1.14516	−	0.661158i	0.947703	+	0.319154i	$0.103399\pi$
$182$	−34.0562	+	4.88210i	−2.52442	+	0.361885i
$183$	16.7738	+	4.90401i	1.23995	+	0.362515i
$184$	−4.03071	+	22.8593i	−0.297148	+	1.68521i
$185$	−4.25771	+	1.54968i	−0.313033	+	0.113935i
$186$	23.4496	−	15.6407i	1.71940	−	1.14683i
$187$	3.44709	−	0.607816i	0.252076	−	0.0444479i
$188$	40.2713			2.93708
$189$	−8.97083	+	10.4175i	−0.652532	+	0.757762i
$190$	−0.873532			−0.0633727
$191$	−17.9877	+	3.17172i	−1.30155	+	0.229498i	−0.781105	−	0.624400i	$-0.785344\pi$
$191$	−17.9877	+	3.17172i	−1.30155	+	0.229498i	−0.520441	+	0.853898i	$0.674232\pi$
$192$	18.5090	+	9.14649i	1.33577	+	0.660091i
$193$	4.71776	−	1.71713i	0.339592	−	0.123601i	−0.166594	−	0.986026i	$-0.553277\pi$
$193$	4.71776	−	1.71713i	0.339592	−	0.123601i	0.506186	+	0.862424i	$0.331055\pi$
$194$	−0.761705	+	4.31984i	−0.0546872	+	0.310147i
$195$	7.00205	−	6.69203i	0.501427	−	0.479226i
$196$	2.72678	+	24.6359i	0.194770	+	1.75971i
$197$	−18.1661	+	10.4882i	−1.29428	+	0.747252i	−0.979410	−	0.201883i	$-0.935294\pi$
$197$	−18.1661	+	10.4882i	−1.29428	+	0.747252i	−0.314869	+	0.949135i	$0.601961\pi$
$198$	6.19155	−	3.21024i	0.440014	−	0.228142i
$199$			5.71686i			0.405257i	0.979256	+	0.202629i	$0.0649484\pi$
$199$			5.71686i			0.405257i	−0.979256	+	0.202629i	$0.935052\pi$
$200$	−14.2000	+	2.50385i	−1.00409	+	0.177049i
$201$	0.902058	+	0.0995390i	0.0636263	+	0.00702094i
$202$	26.5106	−	31.5941i	1.86528	−	2.22295i
$203$	0.594153	−	2.83367i	0.0417013	−	0.198885i
$204$	−8.73796	−	19.9027i	−0.611780	−	1.39347i
$205$	−0.354440	+	0.297410i	−0.0247551	+	0.0207720i
$206$	6.44978			0.449378
$207$	−10.3418	+	16.1749i	−0.718808	+	1.12424i
$208$		−	8.04438i		−	0.557777i
$209$	−0.0628715	−	0.356562i	−0.00434891	−	0.0246639i
$210$	−7.28673	−	8.13229i	−0.502832	−	0.561182i
$211$	21.3830	−	7.78276i	1.47206	−	0.535787i	0.523404	−	0.852085i	$-0.324662\pi$
$211$	21.3830	−	7.78276i	1.47206	−	0.535787i	0.948660	+	0.316297i	$0.102440\pi$
$212$	−17.5546	+	20.9208i	−1.20566	+	1.43685i
$213$	−3.69742	+	7.48217i	−0.253343	+	0.512670i
$214$	43.3862	+	15.7913i	2.96582	+	1.07947i
$215$	5.35650	−	9.27774i	0.365311	−	0.632736i
$216$	−12.3920	−	14.2006i	−0.843169	−	0.966227i
$217$	9.65020	−	15.5387i	0.655098	−	1.05484i
$218$	26.3613	+	31.4161i	1.78541	+	2.12777i
$219$	8.75776	−	17.7224i	0.591795	−	1.19757i
$220$	1.21073	+	3.32646i	0.0816277	+	0.224270i
$221$	12.5850	−	14.9983i	0.846562	−	1.00889i
$222$	−13.1930	+	12.6089i	−0.885456	+	0.846252i
$223$	−1.93428	+	0.341066i	−0.129529	+	0.0228395i	−0.238037	−	0.971256i	$-0.576504\pi$
$223$	−1.93428	+	0.341066i	−0.129529	+	0.0228395i	0.108508	+	0.994096i	$0.465393\pi$
$224$	10.1189	+	0.325425i	0.676097	+	0.0217434i
$225$	−11.6390	−	2.60031i	−0.775935	−	0.173354i
$226$	−11.3913	−	19.7304i	−0.757741	−	1.31245i
$227$	−1.19172	−	6.75861i	−0.0790975	−	0.448584i	−0.998475	−	0.0552076i	$-0.982418\pi$
$227$	−1.19172	−	6.75861i	−0.0790975	−	0.448584i	0.919377	−	0.393377i	$-0.128693\pi$
$228$	−2.05871	+	0.903842i	−0.136341	+	0.0598584i
$229$	7.11726	+	19.5545i	0.470322	+	1.29220i	0.917494	+	0.397750i	$0.130209\pi$
$229$	7.11726	+	19.5545i	0.470322	+	1.29220i	−0.447172	+	0.894448i	$0.647569\pi$
$230$	−11.6811	−	9.80161i	−0.770230	−	0.646299i
$231$	2.79502	−	3.55964i	0.183899	−	0.234207i
$232$	3.72987	+	1.35756i	0.244878	+	0.0891284i
$233$	−17.2391	+	9.95302i	−1.12937	+	0.652044i	−0.943777	−	0.330582i	$-0.892755\pi$
$233$	−17.2391	+	9.95302i	−1.12937	+	0.652044i	−0.185596	+	0.982626i	$0.559421\pi$
$234$	14.9878	−	36.0169i	0.979785	−	2.35450i
$235$	−5.75632	+	9.97025i	−0.375501	+	0.650387i
$236$	−0.865880	−	0.315155i	−0.0563640	−	0.0205148i
$237$	8.90091	−	2.17032i	0.578176	−	0.140977i
$238$	−16.4437	−	14.7241i	−1.06589	−	0.954422i
$239$	0.136444	+	0.0240588i	0.00882584	+	0.00155623i	0.178059	−	0.984020i	$-0.443018\pi$
$239$	0.136444	+	0.0240588i	0.00882584	+	0.00155623i	−0.169234	+	0.985576i	$0.554129\pi$
$240$	2.12401	−	1.41670i	0.137104	−	0.0914477i
$241$	−2.77730	+	7.63057i	−0.178902	+	0.491528i	−0.996436	−	0.0843514i	$-0.973118\pi$
$241$	−2.77730	+	7.63057i	−0.178902	+	0.491528i	0.817534	+	0.575880i	$0.195340\pi$
$242$	20.4356	−	11.7985i	1.31365	−	0.758438i
$243$	−4.95027	−	14.7816i	−0.317560	−	0.948238i
$244$			35.7268i			2.28717i
$245$	−6.48904	−	2.84633i	−0.414570	−	0.181845i
$246$	−0.825604	+	1.67071i	−0.0526386	+	0.106520i
$247$	−1.55140	−	1.30178i	−0.0987131	−	0.0828301i
$248$	19.2097	+	16.1188i	1.21981	+	1.02355i
$249$	−11.1965	−	11.7152i	−0.709550	−	0.742422i
$250$	7.31452	−	20.0965i	0.462611	−	1.27101i
$251$	−10.2480	−	17.7501i	−0.646848	−	1.12037i	−0.983871	−	0.178877i	$-0.942753\pi$
$251$	−10.2480	−	17.7501i	−0.646848	−	1.12037i	0.337023	−	0.941496i	$-0.390580\pi$
$252$	−25.5875	−	11.6263i	−1.61186	−	0.732390i
$253$	3.16013	−	5.47351i	0.198676	−	0.344116i
$254$	22.7615	+	27.1261i	1.42819	+	1.70205i
$255$	6.17645	+	0.681550i	0.386784	+	0.0426803i
$256$	−4.20089	+	23.8244i	−0.262556	+	1.48903i
$257$	3.85987	−	1.40488i	0.240772	−	0.0876340i	−0.218816	−	0.975766i	$-0.570219\pi$
$257$	3.85987	−	1.40488i	0.240772	−	0.0876340i	0.459588	+	0.888132i	$0.347997\pi$
$258$	4.73259	−	42.8885i	0.294638	−	2.67012i
$259$	−4.40601	+	10.9924i	−0.273776	+	0.683036i
$260$	17.1480	+	9.90040i	1.06347	+	0.613997i
$261$	2.41681	+	2.22189i	0.149597	+	0.137531i
$262$	−20.7703	−	11.9917i	−1.28319	−	0.740851i
$263$	15.0074	+	17.8852i	0.925398	+	1.10285i	0.994448	+	0.105234i	$0.0335591\pi$
$263$	15.0074	+	17.8852i	0.925398	+	1.10285i	−0.0690490	+	0.997613i	$0.521996\pi$
$264$	4.28691	+	4.48551i	0.263841	+	0.276064i
$265$	−2.67027	−	7.33651i	−0.164034	−	0.450679i
$266$	−1.52304	+	1.70092i	−0.0933835	+	0.104290i
$267$	−0.283550	−	4.38110i	−0.0173530	−	0.268119i
$268$	0.322171	+	1.82712i	0.0196797	+	0.111609i
$269$	5.04717	+	8.74196i	0.307732	+	0.533007i	0.977866	−	0.209233i	$-0.0670968\pi$
$269$	5.04717	+	8.74196i	0.307732	+	0.533007i	−0.670134	+	0.742240i	$0.733763\pi$
$270$	12.1493	−	2.38564i	0.739382	−	0.145185i
$271$	−19.8563	−	11.4641i	−1.20619	−	0.696392i	−0.244262	−	0.969709i	$-0.578546\pi$
$271$	−19.8563	−	11.4641i	−1.20619	−	0.696392i	−0.961924	+	0.273317i	$0.911879\pi$
$272$	3.95352	−	3.31740i	0.239718	−	0.201147i
$273$	−0.822149	−	25.3020i	−0.0497587	−	1.53135i
$274$	−1.22369	+	6.93990i	−0.0739259	+	0.419255i
$275$	3.86645	+	0.681760i	0.233156	+	0.0411117i
$276$	−37.6713	−	11.0137i	−2.26755	−	0.662944i
$277$	−16.6984	+	14.0116i	−1.00331	+	0.841875i	−0.987439	−	0.157999i	$-0.949496\pi$
$277$	−16.6984	+	14.0116i	−1.00331	+	0.841875i	−0.0158688	+	0.999874i	$0.505051\pi$
$278$	8.44795			0.506675
$279$	9.54680	+	18.4128i	0.571552	+	1.10234i
$280$	5.12502	−	8.25230i	0.306279	−	0.493169i
$281$	−2.93911	+	8.07514i	−0.175333	+	0.481722i	−0.995966	−	0.0897329i	$-0.971399\pi$
$281$	−2.93911	+	8.07514i	−0.175333	+	0.481722i	0.820633	+	0.571455i	$0.193621\pi$
$282$	−5.08584	+	46.0897i	−0.302857	+	2.74460i
$283$	−17.0288	−	3.00264i	−1.01226	−	0.178488i	−0.357168	−	0.934040i	$-0.616258\pi$
$283$	−17.0288	−	3.00264i	−1.01226	−	0.178488i	−0.655089	+	0.755552i	$0.727369\pi$
$284$	−16.8026	−	2.96276i	−0.997053	−	0.175807i
$285$	0.0704985	−	0.638883i	0.00417597	−	0.0378441i
$286$	−4.39244	+	12.0681i	−0.259730	+	0.713603i
$287$	−0.0388721	+	1.20870i	−0.00229454	+	0.0713474i
$288$	−6.18388	+	9.67175i	−0.364388	+	0.569914i
$289$	−4.43897			−0.261116
$290$	−1.99747	+	1.67608i	−0.117296	+	0.0984228i
$291$	−3.09797	−	0.905727i	−0.181606	−	0.0530947i
$292$	39.7990	+	7.01763i	2.32906	+	0.410676i
$293$	−2.36568	+	13.4164i	−0.138205	+	0.783797i	0.834370	+	0.551205i	$0.185832\pi$
$293$	−2.36568	+	13.4164i	−0.138205	+	0.783797i	−0.972574	+	0.232592i	$0.925279\pi$
$294$	−28.5397	+	0.00950028i	−1.66447	+	0.000554067i
$295$	0.201793	−	0.169324i	0.0117488	−	0.00985844i
$296$	−14.0602	−	8.11769i	−0.817235	−	0.471831i
$297$	1.84821	+	4.78745i	0.107244	+	0.277796i
$298$	7.49089	+	12.9746i	0.433936	+	0.751598i
$299$	−6.13890	−	34.8155i	−0.355022	−	2.01343i
$300$	−1.57466	−	24.3298i	−0.0909128	−	1.40468i
$301$	−8.72605	−	26.6061i	−0.502961	−	1.53355i
$302$	−4.17674	−	11.4755i	−0.240344	−	0.660341i
$303$	20.9677	+	21.9391i	1.20456	+	1.26037i
$304$	−0.343147	−	0.408946i	−0.0196808	−	0.0234547i
$305$	−8.84514	−	5.10674i	−0.506471	−	0.292411i
$306$	23.8818	−	7.48693i	1.36523	−	0.427999i
$307$	11.7697	+	6.79523i	0.671731	+	0.387824i	0.796732	−	0.604332i	$-0.206560\pi$
$307$	11.7697	+	6.79523i	0.671731	+	0.387824i	−0.125001	+	0.992157i	$0.539893\pi$
$308$	8.58816	+	3.44232i	0.489356	+	0.196145i
$309$	−0.520530	+	4.71723i	−0.0296119	+	0.268354i
$310$	−15.4800	+	5.63425i	−0.879203	+	0.320004i
$311$	0.691761	−	3.92317i	0.0392262	−	0.222463i	−0.958893	−	0.283768i	$-0.908415\pi$
$311$	0.691761	−	3.92317i	0.0392262	−	0.222463i	0.998119	+	0.0613056i	$0.0195264\pi$
$312$	34.4963	+	3.80655i	1.95297	+	0.215503i
$313$	−4.47317	−	5.33091i	−0.252838	−	0.301321i	0.624664	−	0.780894i	$-0.285236\pi$
$313$	−4.47317	−	5.33091i	−0.252838	−	0.301321i	−0.877502	+	0.479573i	$0.840792\pi$
$314$	−8.31325	+	14.3990i	−0.469144	+	0.812581i
$315$	6.53586	−	4.67304i	0.368254	−	0.263296i
$316$	9.36481	+	16.2203i	0.526811	+	0.912464i
$317$	4.42454	−	12.1563i	0.248507	−	0.682767i	−0.751235	−	0.660035i	$-0.770541\pi$
$317$	4.42454	−	12.1563i	0.248507	−	0.682767i	0.999742	−	0.0227318i	$-0.00723637\pi$
$318$	−21.7265	−	22.7330i	−1.21836	−	1.27480i
$319$	−0.827915	−	0.694703i	−0.0463544	−	0.0388959i
$320$	−9.24306	−	7.75585i	−0.516703	−	0.433565i
$321$	−15.0509	+	30.4573i	−0.840058	+	1.69996i
$322$	−39.4519	+	5.65558i	−2.19857	+	0.315173i
$323$		−	1.29929i		−	0.0722946i
$324$	26.1646	−	18.1932i	1.45359	−	1.01073i
$325$	19.0186	−	10.9804i	1.05496	−	0.609081i
$326$	−6.30653	+	17.3270i	−0.349286	+	0.959656i
$327$	−25.1046	+	16.7446i	−1.38829	+	0.925979i
$328$	−1.63272	−	0.287893i	−0.0901519	−	0.0158962i
$329$	9.37737	+	28.5921i	0.516991	+	1.57633i
$330$	−3.95998	+	0.965565i	−0.217990	+	0.0531526i
$331$	12.6017	+	4.58664i	0.692651	+	0.252104i	0.664270	−	0.747493i	$-0.268743\pi$
$331$	12.6017	+	4.58664i	0.692651	+	0.252104i	0.0283810	+	0.999597i	$0.490965\pi$
$332$	16.5645	−	28.6905i	0.909094	−	1.57460i
$333$	−8.15711	−	10.6667i	−0.447007	−	0.584530i
$334$	41.2157	−	23.7959i	2.25522	−	1.30205i
$335$	−0.498404	−	0.181404i	−0.0272307	−	0.00991118i
$336$	0.944735	−	6.60588i	0.0515395	−	0.360380i
$337$	8.03963	+	6.74605i	0.437947	+	0.367481i	0.834940	−	0.550340i	$-0.185502\pi$
$337$	8.03963	+	6.74605i	0.437947	+	0.367481i	−0.396994	+	0.917821i	$0.629947\pi$
$338$	14.1031	+	38.7480i	0.767108	+	2.10761i
$339$	15.3497	−	6.73905i	0.833683	−	0.366015i
$340$	2.20593	+	12.5104i	0.119633	+	0.678473i
$341$	−3.41397	−	5.91316i	−0.184877	−	0.320216i
$342$	−0.774437	−	2.47030i	−0.0418767	−	0.133578i
$343$	−16.8562	+	7.67257i	−0.910150	+	0.414280i
$344$	37.8037	−	6.66582i	2.03824	−	0.359397i
$345$	8.11142	−	7.75227i	0.436704	−	0.417368i
$346$	1.53972	−	1.83497i	0.0827758	−	0.0986484i
$347$	−6.60110	−	18.1364i	−0.354366	−	0.973612i	−0.980950	−	0.194258i	$-0.937770\pi$
$347$	−6.60110	−	18.1364i	−0.354366	−	0.973612i	0.626585	−	0.779353i	$-0.284452\pi$
$348$	−2.97333	+	6.01690i	−0.159387	+	0.322540i
$349$	−5.74245	−	6.84358i	−0.307386	−	0.366329i	0.590131	−	0.807307i	$-0.299076\pi$
$349$	−5.74245	−	6.84358i	−0.307386	−	0.366329i	−0.897518	+	0.440979i	$0.854631\pi$
$350$	−11.6833	−	21.8277i	−0.624499	−	1.16674i
$351$	25.1324	+	13.8685i	1.34147	+	0.740247i
$352$	1.88959	−	3.27287i	0.100716	−	0.174444i
$353$	27.2321	+	9.91167i	1.44942	+	0.527545i	0.942429	−	0.334407i	$-0.108536\pi$
$353$	27.2321	+	9.91167i	1.44942	+	0.527545i	0.506990	+	0.861952i	$0.330758\pi$
$354$	0.470040	−	0.951183i	0.0249823	−	0.0505548i
$355$	3.13526	−	3.73645i	0.166402	−	0.198310i
$356$	8.43393	−	3.06970i	0.446997	−	0.162694i
$357$	12.0960	−	10.8383i	0.640188	−	0.573623i
$358$	−1.54129	−	8.74111i	−0.0814599	−	0.461982i
$359$		−	6.72303i		−	0.354828i	−0.984136	−	0.177414i	$-0.943227\pi$
$359$		−	6.72303i		−	0.354828i	0.984136	−	0.177414i	$-0.0567732\pi$
$360$	5.07011	+	9.77866i	0.267218	+	0.515380i
$361$	18.8656			0.992926
$362$	−32.0789	+	26.9174i	−1.68603	+	1.41474i
$363$	6.97993	+	15.8984i	0.366351	+	0.834449i
$364$	49.1760	−	16.1283i	2.57752	−	0.845353i
$365$	−7.42622	+	8.85022i	−0.388706	+	0.463242i
$366$	−40.8887	−	4.51192i	−2.13728	−	0.235842i
$367$	10.1307	−	1.78632i	0.528818	−	0.0932449i	0.0971368	−	0.995271i	$-0.469032\pi$
$367$	10.1307	−	1.78632i	0.528818	−	0.0932449i	0.431682	+	0.902026i	$0.357920\pi$
$368$		−	9.31888i		−	0.485780i
$369$	−1.15529	−	0.738664i	−0.0601420	−	0.0384533i
$370$	9.23658	−	5.33274i	0.480187	−	0.277236i
$371$	−18.9412	−	7.59204i	−0.983377	−	0.394159i
$372$	−30.6528	+	29.2957i	−1.58928	+	1.51891i
$373$	−3.06978	+	17.4096i	−0.158947	+	0.901434i	0.796141	+	0.605112i	$0.206872\pi$
$373$	−3.06978	+	17.4096i	−0.158947	+	0.901434i	−0.955088	+	0.296323i	$0.904240\pi$
$374$	−7.74244	+	2.81802i	−0.400352	+	0.145716i
$375$	14.1078	+	6.97157i	0.728525	+	0.360010i
$376$	−40.6255	+	7.16337i	−2.09510	+	0.369422i
$377$	−6.04529			−0.311349
$378$	16.5376	−	27.8162i	0.850600	−	1.43071i
$379$	−23.3651			−1.20018			−0.600092	−	0.799931i	$-0.704869\pi$
$379$	−23.3651			−1.20018			−0.600092	+	0.799931i	$0.704869\pi$
$380$	1.29406	−	0.228178i	0.0663838	−	0.0117053i
$381$	−21.6764	+	14.4581i	−1.11052	+	0.740710i
$382$	40.4018	−	14.7051i	2.06714	−	0.752376i
$383$	2.69264	−	15.2707i	0.137588	−	0.780298i	−0.835435	−	0.549589i	$-0.814784\pi$
$383$	2.69264	−	15.2707i	0.137588	−	0.780298i	0.973023	−	0.230709i	$-0.0741045\pi$
$384$	−33.9224	−	9.91762i	−1.73109	−	0.506106i
$385$	−2.07982	+	1.63419i	−0.105997	+	0.0832860i
$386$	−10.2346	+	5.90896i	−0.520928	+	0.300758i
$387$	30.9858	+	6.92263i	1.57509	+	0.351897i
$388$		−	6.59842i		−	0.334984i
$389$	12.3228	−	2.17285i	0.624792	−	0.110168i	0.147716	−	0.989030i	$-0.452808\pi$
$389$	12.3228	−	2.17285i	0.624792	−	0.110168i	0.477076	+	0.878862i	$0.341697\pi$
$390$	−13.4964	+	18.3752i	−0.683418	+	0.930467i
$391$	14.5789	−	17.3745i	0.737289	−	0.878667i
$392$	−7.13294	−	24.3675i	−0.360268	−	1.23075i
$393$	10.4468	−	14.2231i	0.526969	−	0.717463i
$394$	37.8246	−	31.7386i	1.90558	−	1.59897i
$395$	−5.35437			−0.269408
$396$	−8.33366	+	6.37299i	−0.418782	+	0.320255i
$397$			6.72738i			0.337638i	0.985647	+	0.168819i	$0.0539953\pi$
$397$			6.72738i			0.337638i	−0.985647	+	0.168819i	$0.946005\pi$
$398$	−2.33678	−	13.2525i	−0.117132	−	0.664290i
$399$	−1.12110	−	1.25119i	−0.0561250	−	0.0626379i
$400$	5.43971	−	1.97989i	0.271985	−	0.0989946i
$401$	−1.74561	+	2.08034i	−0.0871718	+	0.103887i	−0.807867	−	0.589365i	$-0.799378\pi$
$401$	−1.74561	+	2.08034i	−0.0871718	+	0.103887i	0.720695	+	0.693252i	$0.243823\pi$
$402$	−2.13179	+	0.137972i	−0.106324	+	0.00688143i
$403$	−35.8889	−	13.0625i	−1.78775	−	0.650690i
$404$	−31.0202	+	53.7286i	−1.54331	+	2.67310i
$405$	0.764293	+	9.07826i	0.0379780	+	0.451103i
$406$	−0.219067	+	6.81173i	−0.0108721	+	0.338061i
$407$	2.84154	+	3.38641i	0.140850	+	0.167858i
$408$	12.3551	+	18.5235i	0.611667	+	0.917049i
$409$	7.93652	+	21.8054i	0.392435	+	1.07821i	0.965886	+	0.258967i	$0.0833822\pi$
$409$	7.93652	+	21.8054i	0.392435	+	1.07821i	−0.573451	+	0.819240i	$0.694396\pi$
$410$	0.700078	−	0.834320i	0.0345744	−	0.0412041i
$411$	−4.97694	−	1.45507i	−0.245494	−	0.0717731i
$412$	−9.55477	+	1.68476i	−0.470730	+	0.0830024i
$413$	0.0221310	−	0.688149i	0.00108899	−	0.0338616i
$414$	17.3624	−	41.7232i	0.853316	−	2.05058i
$415$	4.73541	+	8.20197i	0.232452	+	0.402619i
$416$	−3.67074	−	20.8178i	−0.179973	−	1.02068i
$417$	−0.681793	+	6.17865i	−0.0333875	+	0.302570i
$418$	0.291491	+	0.800866i	0.0142573	+	0.0391716i
$419$	−2.69835	−	2.26418i	−0.131823	−	0.110612i	0.574492	−	0.818510i	$-0.305199\pi$
$419$	−2.69835	−	2.26418i	−0.131823	−	0.110612i	−0.706315	+	0.707897i	$0.749644\pi$
$420$	12.9189	+	10.1439i	0.630377	+	0.494971i
$421$	7.29428	+	2.65490i	0.355501	+	0.129392i	0.513596	−	0.858032i	$-0.328313\pi$
$421$	7.29428	+	2.65490i	0.355501	+	0.129392i	−0.158095	+	0.987424i	$0.550535\pi$
$422$	−46.3877	+	26.7820i	−2.25812	+	1.30373i
$423$	−33.2986	−	7.43935i	−1.61903	−	0.361713i
$424$	13.9877	−	24.2274i	0.679302	−	1.17659i
$425$	13.2395	+	4.81877i	0.642209	+	0.233745i
$426$	5.51282	−	18.8561i	0.267097	−	0.913583i
$427$	−25.3656	+	8.31917i	−1.22753	+	0.402593i
$428$	−68.3976	−	12.0603i	−3.30612	−	0.582958i
$429$	−8.47188	−	4.18649i	−0.409026	−	0.202126i
$430$	−8.62489	+	23.6967i	−0.415929	+	1.14276i
$431$	−24.1151	+	13.9229i	−1.16158	+	0.670641i	−0.951683	−	0.307082i	$-0.900647\pi$
$431$	−24.1151	+	13.9229i	−1.16158	+	0.670641i	−0.209901	+	0.977723i	$0.567314\pi$
$432$	5.88941	+	4.75058i	0.283354	+	0.228562i
$433$		−	12.9718i		−	0.623384i	−0.950183	−	0.311692i	$-0.899104\pi$
$433$		−	12.9718i		−	0.623384i	0.950183	−	0.311692i	$-0.100896\pi$
$434$	−16.0191	+	39.9657i	−0.768943	+	1.91841i
$435$	−1.06464	−	1.59618i	−0.0510457	−	0.0765308i
$436$	−47.2581	−	39.6543i	−2.26325	−	1.89909i
$437$	−1.79719	−	1.50802i	−0.0859714	−	0.0721385i
$438$	−13.0577	+	44.6629i	−0.623923	+	2.13408i
$439$	−1.48780	+	4.08771i	−0.0710090	+	0.195096i	−0.970120	−	0.242625i	$-0.921992\pi$
$439$	−1.48780	+	4.08771i	−0.0710090	+	0.195096i	0.899111	+	0.437720i	$0.144214\pi$
$440$	−1.81309	−	3.14036i	−0.0864355	−	0.149711i
$441$	2.29635	−	20.8741i	0.109350	−	0.994003i
$442$	−23.0435	+	39.9124i	−1.09607	+	1.89844i
$443$	12.6998	+	15.1351i	0.603388	+	0.719090i	0.978120	−	0.208044i	$-0.0667096\pi$
$443$	12.6998	+	15.1351i	0.603388	+	0.719090i	−0.374732	+	0.927133i	$0.622265\pi$
$444$	16.2507	−	22.1251i	0.771222	−	1.05001i
$445$	−0.445548	+	2.52683i	−0.0211210	+	0.119783i
$446$	4.34455	−	1.58129i	0.205720	−	0.0748761i
$447$	−10.0939	+	4.43156i	−0.477425	+	0.209606i
$448$	−31.2176	+	4.47516i	−1.47489	+	0.211432i
$449$	13.7666	+	7.94817i	0.649688	+	0.375097i	0.788337	−	0.615244i	$-0.210943\pi$
$449$	13.7666	+	7.94817i	0.649688	+	0.375097i	−0.138649	+	0.990342i	$0.544276\pi$
$450$	28.0439	+	1.27044i	1.32200	+	0.0598890i
$451$	0.390944	+	0.225711i	0.0184088	+	0.0106283i
$452$	22.0291	+	26.2532i	1.03616	+	1.23485i
$453$	8.73002	−	2.12865i	0.410172	−	0.100013i
$454$	5.52519	+	15.1803i	0.259310	+	0.712449i
$455$	−3.03615	+	14.4802i	−0.142337	+	0.678843i
$456$	1.91604	−	1.27799i	0.0897268	−	0.0598473i
$457$	−6.15554	−	34.9098i	−0.287944	−	1.63301i	−0.694575	−	0.719420i	$-0.744408\pi$
$457$	−6.15554	−	34.9098i	−0.287944	−	1.63301i	0.406631	−	0.913592i	$-0.366703\pi$
$458$	−24.4918	−	42.4211i	−1.14443	−	1.98221i
$459$	3.54840	+	18.0709i	0.165625	+	0.843476i
$460$	19.8648	+	11.4690i	0.926202	+	0.534743i
$461$	15.9132	−	13.3527i	0.741151	−	0.621899i	−0.191996	−	0.981396i	$-0.561496\pi$
$461$	15.9132	−	13.3527i	0.741151	−	0.621899i	0.933146	+	0.359497i	$0.117052\pi$
$462$	−5.02427	+	9.39426i	−0.233750	+	0.437060i
$463$	−2.91569	+	16.5357i	−0.135504	+	0.768480i	0.839004	+	0.544126i	$0.183139\pi$
$463$	−2.91569	+	16.5357i	−0.135504	+	0.768480i	−0.974508	+	0.224355i	$0.927973\pi$
$464$	−1.56932	−	0.276714i	−0.0728539	−	0.0128461i
$465$	−2.87146	−	11.7764i	−0.133161	−	0.546119i
$466$	35.8946	−	30.1191i	1.66278	−	1.39524i
$467$	−3.28103			−0.151828			−0.0759140	−	0.997114i	$-0.524187\pi$
$467$	−3.28103			−0.151828			−0.0759140	+	0.997114i	$0.524187\pi$
$468$	−12.7951	+	57.2708i	−0.591452	+	2.64734i
$469$	−1.22221	+	0.654192i	−0.0564366	+	0.0302078i
$470$	9.26867	−	25.4654i	0.427532	−	1.17463i
$471$	−9.86018	−	7.24220i	−0.454333	−	0.333703i
$472$	0.929555	+	0.163906i	0.0427862	+	0.00754436i
$473$	−10.2934	−	1.81500i	−0.473290	−	0.0834538i
$474$	−19.7465	+	8.66939i	−0.906988	+	0.398198i
$475$	0.498447	−	1.36947i	0.0228703	−	0.0628356i
$476$	28.2060	+	17.5171i	1.29282	+	0.802896i
$477$	18.3799	−	14.0556i	0.841557	−	0.643563i
$478$	−0.326132			−0.0149169
$479$	24.4613	−	20.5255i	1.11767	−	0.937833i	0.119182	−	0.992872i	$-0.461973\pi$
$479$	24.4613	−	20.5255i	1.11767	−	0.937833i	0.998484	+	0.0550390i	$0.0175283\pi$
$480$	4.85020	−	4.63545i	0.221380	−	0.211578i
$481$	24.3513	+	4.29380i	1.11033	+	0.195780i
$482$	3.31919	−	18.8241i	0.151185	−	0.857412i
$483$	−0.952405	−	29.3107i	−0.0433359	−	1.33368i
$484$	−27.1916	+	22.8165i	−1.23598	+	1.03711i
$485$	1.63362	+	0.943170i	0.0741788	+	0.0428271i
$486$	17.5175	+	32.2425i	0.794609	+	1.46255i
$487$	13.3392	+	23.1043i	0.604459	+	1.04695i	0.992137	+	0.125159i	$0.0399440\pi$
$487$	13.3392	+	23.1043i	0.604459	+	1.04695i	−0.387678	+	0.921795i	$0.626723\pi$
$488$	−6.35501	−	36.0410i	−0.287678	−	1.63150i
$489$	−12.1637	−	6.01084i	−0.550059	−	0.271819i
$490$	16.2060	+	3.94581i	0.732114	+	0.178254i
$491$	−5.33517	−	14.6583i	−0.240773	−	0.661519i	−0.999944	−	0.0106267i	$-0.996617\pi$
$491$	−5.33517	−	14.6583i	−0.240773	−	0.661519i	0.759170	−	0.650892i	$-0.225605\pi$
$492$	0.786647	−	2.69066i	0.0354648	−	0.121304i
$493$	−2.49300	−	2.97105i	−0.112279	−	0.133809i
$494$	4.12848	+	2.38358i	0.185749	+	0.107242i
$495$	−0.386603	−	2.97417i	−0.0173765	−	0.133679i
$496$	−8.71863	−	5.03370i	−0.391478	−	0.226020i
$497$	−1.80906	−	12.6195i	−0.0811475	−	0.566064i
$498$	30.7438	+	22.5810i	1.37766	+	1.01188i
$499$	−2.39951	+	0.873349i	−0.107417	+	0.0390965i	−0.395169	−	0.918608i	$-0.629314\pi$
$499$	−2.39951	+	0.873349i	−0.107417	+	0.0390965i	0.287753	+	0.957705i	$0.407092\pi$
$500$	−5.58635	+	31.6818i	−0.249829	+	1.41685i
$501$	14.0775	+	32.0647i	0.628935	+	1.43255i
$502$	31.0118	+	36.9584i	1.38412	+	1.64953i
$503$	18.3905	−	31.8533i	0.819993	−	1.42027i	−0.0856932	−	0.996322i	$-0.527311\pi$
$503$	18.3905	−	31.8533i	0.819993	−	1.42027i	0.905686	−	0.423948i	$-0.139356\pi$
$504$	27.8807	+	7.17712i	1.24190	+	0.319695i
$505$	−8.86799	−	15.3598i	−0.394620	−	0.683502i
$506$	−5.08835	+	13.9801i	−0.226205	+	0.621492i
$507$	−29.4776	+	7.18755i	−1.30915	+	0.319210i
$508$	−40.8048	−	34.2393i	−1.81042	−	1.51912i
$509$	−3.11377	−	2.61276i	−0.138015	−	0.115809i	0.571167	−	0.820834i	$-0.306491\pi$
$509$	−3.11377	−	2.61276i	−0.138015	−	0.115809i	−0.709182	+	0.705026i	$0.750935\pi$
$510$	−14.5965	+	0.944705i	−0.646345	+	0.0418322i
$511$	4.28497	+	29.8908i	0.189556	+	1.32229i
$512$		−	16.1358i		−	0.713110i
$513$	1.86922	−	0.367041i	0.0825283	−	0.0162053i
$514$	−8.37352	+	4.83446i	−0.369340	+	0.213239i
$515$	0.948638	−	2.60636i	0.0418020	−	0.114850i
$516$	4.19210	+	64.7716i	0.184547	+	2.85141i
$517$	11.0617	+	1.95048i	0.486493	+	0.0857818i
$518$	5.72061	−	27.2831i	0.251349	−	1.19875i
$519$	1.21779	+	1.27421i	0.0534551	+	0.0559316i
$520$	−19.0599	−	6.93723i	−0.835831	−	0.304218i
$521$	−5.06650	+	8.77544i	−0.221967	+	0.384459i	−0.955405	−	0.295298i	$-0.904581\pi$
$521$	−5.06650	+	8.77544i	−0.221967	+	0.384459i	0.733438	+	0.679756i	$0.237915\pi$
$522$	−6.51073	−	4.16280i	−0.284967	−	0.182201i
$523$	−0.925908	+	0.534573i	−0.0404871	+	0.0233753i	−0.520107	−	0.854101i	$-0.674108\pi$
$523$	−0.925908	+	0.534573i	−0.0404871	+	0.0233753i	0.479620	+	0.877476i	$0.340775\pi$
$524$	33.9017	+	12.3392i	1.48100	+	0.539041i
$525$	16.9072	−	6.78331i	0.737891	−	0.296048i
$526$	−42.1001	−	35.3262i	−1.83565	−	1.54030i
$527$	−8.38039	−	23.0249i	−0.365056	−	1.00298i
$528$	−2.00762	−	1.47458i	−0.0873703	−	0.0641727i
$529$	−3.11761	−	17.6808i	−0.135548	−	0.768732i
$530$	9.18892	+	15.9157i	0.399141	+	0.691332i
$531$	0.657740	+	0.420543i	0.0285435	+	0.0182500i
$532$	1.81195	−	2.91759i	0.0785578	−	0.126494i
$533$	2.48668	−	0.438470i	0.107710	−	0.0189922i
$534$	2.44810	+	10.0401i	0.105939	+	0.434479i
$535$	12.7625	−	15.2098i	0.551772	−	0.657576i
$536$	−0.650009	−	1.78588i	−0.0280761	−	0.0771385i
$537$	6.51745	−	0.421817i	0.281249	−	0.0182028i
$538$	−15.2734	−	18.2021i	−0.658483	−	0.784750i
$539$	−0.444208	+	6.89904i	−0.0191334	+	0.297163i
$540$	−17.3749	+	6.70765i	−0.747697	+	0.288651i
$541$	1.87506	−	3.24770i	0.0806153	−	0.139630i	−0.822899	−	0.568188i	$-0.807645\pi$
$541$	1.87506	−	3.24770i	0.0806153	−	0.139630i	0.903514	+	0.428558i	$0.140978\pi$
$542$	50.7159	+	18.4591i	2.17844	+	0.792886i
$543$	−17.0979	−	25.6342i	−0.733739	−	1.10007i
$544$	8.71744	−	10.3890i	0.373757	−	0.445426i
$545$	16.5725	−	6.03190i	0.709888	−	0.258378i
$546$	12.2481	+	58.3178i	0.524172	+	2.49577i
$547$	−2.42723	−	13.7655i	−0.103781	−	0.588570i	−0.991700	−	0.128571i	$-0.958961\pi$
$547$	−2.42723	−	13.7655i	−0.103781	−	0.588570i	0.887919	−	0.459999i	$-0.152150\pi$
$548$		−	10.6005i		−	0.452830i
$549$	6.59984	−	29.5410i	0.281674	−	1.26078i
$550$	−9.24169			−0.394067
$551$	−0.307320	+	0.257872i	−0.0130923	+	0.0109857i
$552$	39.9617	+	4.40963i	1.70088	+	0.187687i
$553$	−9.33557	+	10.4259i	−0.396989	+	0.443353i
$554$	32.9821	−	39.3065i	1.40127	−	1.66997i
$555$	3.15482	+	7.18582i	0.133914	+	0.305021i
$556$	−12.5149	+	2.20671i	−0.530749	+	0.0935854i
$557$		−	37.7207i		−	1.59828i	−0.601147	−	0.799139i	$-0.705289\pi$
$557$		−	37.7207i		−	1.59828i	0.601147	−	0.799139i	$-0.294711\pi$
$558$	−29.6572	−	38.7814i	−1.25549	−	1.64175i
$559$	−50.6317	+	29.2322i	−2.14149	+	1.23639i
$560$	−1.45098	+	3.62000i	−0.0613149	+	0.152973i
$561$	−1.43618	−	5.89008i	−0.0606357	−	0.248679i
$562$	3.51257	−	19.9208i	0.148169	−	0.840306i
$563$	9.84586	−	3.58360i	0.414953	−	0.151031i	−0.126103	−	0.992017i	$-0.540247\pi$
$563$	9.84586	−	3.58360i	0.414953	−	0.151031i	0.541056	+	0.840987i	$0.318025\pi$
$564$	−4.50500	−	69.6063i	−0.189695	−	2.93095i
$565$	−9.64851	+	1.70129i	−0.405916	+	0.0715739i
$566$	40.7027			1.71086
$567$	19.0095	+	14.3401i	0.798324	+	0.602228i
$568$	17.4774			0.733336
$569$	−27.4820	+	4.84582i	−1.15211	+	0.203147i	−0.716895	−	0.697181i	$-0.754437\pi$
$569$	−27.4820	+	4.84582i	−1.15211	+	0.203147i	−0.435211	+	0.900328i	$0.643326\pi$
$570$	0.0977189	+	1.50984i	0.00409299	+	0.0632404i
$571$	1.87656	−	0.683010i	0.0785314	−	0.0285831i	−0.302456	−	0.953163i	$-0.597806\pi$
$571$	1.87656	−	0.683010i	0.0785314	−	0.0285831i	0.380987	+	0.924580i	$0.375584\pi$
$572$	3.35466	−	19.0252i	0.140265	−	0.795484i
$573$	7.49433	+	30.7358i	0.313080	+	1.28401i
$574$	−0.403949	−	2.81784i	−0.0168605	−	0.117614i
$575$	22.0317	−	12.7200i	0.918787	−	0.530462i
$576$	13.7386	−	33.0148i	0.572441	−	1.37562i
$577$		−	27.3579i		−	1.13892i	−0.822018	−	0.569462i	$-0.807152\pi$
$577$		−	27.3579i		−	1.13892i	0.822018	−	0.569462i	$-0.192848\pi$
$578$	10.2902	−	1.81444i	0.428016	−	0.0754708i
$579$	−3.49570	−	7.96226i	−0.145276	−	0.330900i
$580$	2.52126	−	3.00473i	0.104690	−	0.124764i
$581$	24.2270	+	5.07983i	1.00511	+	0.210747i
$582$	7.55177	+	0.833312i	0.313031	+	0.0345419i
$583$	−5.83517	+	4.89628i	−0.241668	+	0.202783i
$584$	−41.3973			−1.71303
$585$	−12.3500	−	11.3540i	−0.510611	−	0.469429i
$586$		−	32.0683i		−	1.32473i
$587$	0.974072	+	5.52423i	0.0402042	+	0.228010i	0.998289	−	0.0584759i	$-0.0186241\pi$
$587$	0.974072	+	5.52423i	0.0402042	+	0.228010i	−0.958085	+	0.286485i	$0.907513\pi$
$588$	42.2765	−	7.46899i	1.74345	−	0.308016i
$589$	−2.38166	+	0.866855i	−0.0981348	+	0.0357181i
$590$	−0.398575	+	0.475003i	−0.0164091	+	0.0195555i
$591$	20.1603	+	30.2256i	0.829285	+	1.24331i
$592$	6.12492	+	2.22929i	0.251732	+	0.0916231i
$593$	7.59363	−	13.1526i	0.311833	−	0.540111i	−0.666926	−	0.745124i	$-0.732390\pi$
$593$	7.59363	−	13.1526i	0.311833	−	0.540111i	0.978759	+	0.205013i	$0.0657237\pi$
$594$	−6.24131	−	10.3426i	−0.256084	−	0.424360i
$595$	−8.36858	+	4.47929i	−0.343078	+	0.183633i
$596$	−14.4862	−	17.2640i	−0.593378	−	0.707160i
$597$	9.88121	−	0.639524i	0.404411	−	0.0261740i
$598$	28.4618	+	78.1982i	1.16389	+	3.19776i
$599$	−27.2744	+	32.5043i	−1.11440	+	1.32809i	−0.175274	+	0.984520i	$0.556081\pi$
$599$	−27.2744	+	32.5043i	−1.11440	+	1.32809i	−0.939127	+	0.343571i	$0.888363\pi$
$600$	5.91624	+	24.2637i	0.241530	+	0.990562i
$601$	1.13325	−	0.199822i	0.0462262	−	0.00815092i	−0.150487	−	0.988612i	$-0.548084\pi$
$601$	1.13325	−	0.199822i	0.0462262	−	0.00815092i	0.196713	+	0.980461i	$0.436973\pi$
$602$	31.1036	+	58.1103i	1.26769	+	2.36840i
$603$	0.0711366	−	1.57028i	0.00289691	−	0.0639469i
$604$	9.18501	+	15.9089i	0.373733	+	0.647324i
$605$	−1.76210	−	9.99339i	−0.0716397	−	0.406289i
$606$	−57.5739	−	42.2875i	−2.33878	−	1.71781i
$607$	−5.71360	−	15.6980i	−0.231908	−	0.637161i	0.768087	−	0.640345i	$-0.221209\pi$
$607$	−5.71360	−	15.6980i	−0.231908	−	0.637161i	−0.999995	+	0.00318399i	$0.998987\pi$
$608$	−1.07463	−	0.901718i	−0.0435818	−	0.0365695i
$609$	−4.96428	−	0.709962i	−0.201163	−	0.0287691i
$610$	22.5918	+	8.22273i	0.914714	+	0.332929i
$611$	54.4110	−	31.4142i	2.20123	−	1.27088i
$612$	−33.4231	+	17.3294i	−1.35105	+	0.700501i
$613$	−11.5895	+	20.0735i	−0.468094	+	0.810762i	−0.999335	−	0.0364584i	$-0.988392\pi$
$613$	−11.5895	+	20.0735i	−0.468094	+	0.810762i	0.531242	+	0.847220i	$0.321726\pi$
$614$	−30.0615	−	10.9415i	−1.21318	−	0.441562i
$615$	0.553704	+	0.579356i	0.0223275	+	0.0233619i
$616$	−9.27600	−	1.94496i	−0.373741	−	0.0783646i
$617$	19.1376	+	3.37447i	0.770450	+	0.135851i	0.545037	−	0.838412i	$-0.316516\pi$
$617$	19.1376	+	3.37447i	0.770450	+	0.135851i	0.225413	+	0.974263i	$0.427627\pi$
$618$	−0.721514	−	11.1480i	−0.0290235	−	0.448439i
$619$	−12.3203	+	33.8496i	−0.495193	+	1.36053i	0.400679	+	0.916219i	$0.368774\pi$
$619$	−12.3203	+	33.8496i	−0.495193	+	1.36053i	−0.895872	+	0.444313i	$0.853448\pi$
$620$	21.4604	−	12.3902i	0.861872	−	0.497602i
$621$	29.1142	+	16.0658i	1.16831	+	0.644697i
$622$			9.37727i			0.375994i
$623$	4.14333	+	5.27318i	0.165999	+	0.211266i
$624$	−13.9042	+	0.899895i	−0.556613	+	0.0360246i
$625$	8.18119	+	6.86483i	0.327247	+	0.274593i
$626$	12.5485	+	10.5294i	0.501539	+	0.420841i
$627$	−0.609261	+	0.148557i	−0.0243315	+	0.00593278i
$628$	8.55414	−	23.5023i	0.341347	−	0.937844i
$629$	7.93194	+	13.7385i	0.316267	+	0.547790i
$630$	−13.2410	+	13.5044i	−0.527534	+	0.538027i
$631$	−10.9185	+	18.9114i	−0.434658	+	0.752849i	−0.997268	−	0.0738734i	$-0.976464\pi$
$631$	−10.9185	+	18.9114i	−0.434658	+	0.752849i	0.562610	+	0.826722i	$0.309797\pi$
$632$	−12.3324	−	14.6972i	−0.490557	−	0.584623i
$633$	−15.8440	−	36.0884i	−0.629744	−	1.43439i
$634$	−5.28782	+	29.9887i	−0.210006	+	1.19100i
$635$	14.3095	−	5.20822i	0.567854	−	0.206682i
$636$	38.1240	+	28.0017i	1.51171	+	1.11034i
$637$	22.9018	+	31.1588i	0.907401	+	1.23455i
$638$	2.20319	+	1.27201i	0.0872253	+	0.0503596i
$639$	13.3461	+	5.55374i	0.527962	+	0.219703i
$640$	17.8879	+	10.3276i	0.707083	+	0.408235i
$641$	16.3142	+	19.4425i	0.644373	+	0.767934i	0.985054	−	0.172245i	$-0.0551021\pi$
$641$	16.3142	+	19.4425i	0.644373	+	0.767934i	−0.340681	+	0.940179i	$0.610658\pi$
$642$	22.4407	−	76.7567i	0.885665	−	3.02934i
$643$	4.96013	+	13.6278i	0.195609	+	0.537430i	0.998257	−	0.0590229i	$-0.0187985\pi$
$643$	4.96013	+	13.6278i	0.195609	+	0.537430i	−0.802648	+	0.596453i	$0.796576\pi$
$644$	56.9671	−	18.6836i	2.24482	−	0.736236i
$645$	−16.6352	−	8.22050i	−0.655009	−	0.323682i
$646$	0.531090	+	3.01196i	0.0208954	+	0.118504i
$647$	21.4787	+	37.2021i	0.844414	+	1.46257i	0.886129	+	0.463438i	$0.153384\pi$
$647$	21.4787	+	37.2021i	0.844414	+	1.46257i	−0.0417158	+	0.999130i	$0.513282\pi$
$648$	−23.1585	+	23.0073i	−0.909753	+	0.903813i
$649$	−0.222576	−	0.128504i	−0.00873686	−	0.00504423i
$650$	−39.5996	+	33.2280i	−1.55323	+	1.30331i
$651$	−27.9372	−	14.9415i	−1.09495	−	0.585603i
$652$	4.81651	−	27.3158i	0.188629	−	1.06977i
$653$	17.8826	+	3.15319i	0.699801	+	0.123394i	0.512218	−	0.858855i	$-0.328824\pi$
$653$	17.8826	+	3.15319i	0.699801	+	0.123394i	0.187582	+	0.982249i	$0.439935\pi$
$654$	51.3518	−	49.0781i	2.00801	−	1.91911i
$655$	−7.90077	+	6.62953i	−0.308709	+	0.259037i
$656$	0.665598			0.0259872
$657$	−31.6117	−	13.1547i	−1.23329	−	0.513213i
$658$	−33.4253	−	62.4477i	−1.30305	−	2.43447i
$659$	−14.8897	+	40.9090i	−0.580019	+	1.59359i	0.208129	+	0.978101i	$0.433263\pi$
$659$	−14.8897	+	40.9090i	−0.580019	+	1.59359i	−0.788147	+	0.615487i	$0.788959\pi$
$660$	5.61414	−	2.46479i	0.218530	−	0.0959420i
$661$	−12.5819	−	2.21854i	−0.489381	−	0.0862910i	−0.0764876	−	0.997071i	$-0.524371\pi$
$661$	−12.5819	−	2.21854i	−0.489381	−	0.0862910i	−0.412893	+	0.910780i	$0.635482\pi$
$662$	−31.0874	−	5.48155i	−1.20825	−	0.213046i
$663$	−27.3314	−	20.0746i	−1.06146	−	0.779634i
$664$	−11.6068	+	31.8893i	−0.450430	+	1.23755i
$665$	0.463331	+	0.865633i	0.0179672	+	0.0335678i
$666$	23.2695	+	21.3927i	0.901673	+	0.828952i
$667$	−7.00307			−0.271160
$668$	−54.8415	+	46.0175i	−2.12188	+	1.78047i
$669$	0.805892	+	3.30513i	0.0311576	+	0.127784i
$670$	1.22953	+	0.216799i	0.0475007	+	0.00837566i
$671$	−1.73037	+	9.81343i	−0.0668003	+	0.378843i
$672$	−0.569488	−	17.5263i	−0.0219685	−	0.676090i
$673$	2.75663	−	2.31309i	0.106260	−	0.0891630i	−0.588110	−	0.808781i	$-0.700128\pi$
$673$	2.75663	−	2.31309i	0.106260	−	0.0891630i	0.694370	+	0.719618i	$0.255683\pi$
$674$	−21.3946	−	12.3521i	−0.824087	−	0.475787i
$675$	−3.19246	+	20.4082i	−0.122878	+	0.785511i
$676$	−31.0139	−	53.7177i	−1.19284	−	2.06607i
$677$	−6.25605	−	35.4798i	−0.240439	−	1.36360i	−0.830850	−	0.556496i	$-0.812145\pi$
$677$	−6.25605	−	35.4798i	−0.240439	−	1.36360i	0.590411	−	0.807103i	$-0.298966\pi$
$678$	−32.8284	+	21.8964i	−1.26077	+	0.840925i
$679$	4.68479	−	1.53648i	0.179786	−	0.0589646i
$680$	−4.45065	−	12.2281i	−0.170675	−	0.468925i
$681$	−11.5485	+	2.81588i	−0.442539	+	0.107905i
$682$	10.3311	+	12.3121i	0.395599	+	0.471456i
$683$	22.1117	+	12.7662i	0.846079	+	0.488484i	0.859326	−	0.511428i	$-0.170883\pi$
$683$	22.1117	+	12.7662i	0.846079	+	0.488484i	−0.0132470	+	0.999912i	$0.504217\pi$
$684$	1.79253	+	3.45723i	0.0685391	+	0.132191i
$685$	2.62444	+	1.51522i	0.100275	+	0.0578935i
$686$	35.9390	−	24.6762i	1.37216	−	0.942142i
$687$	33.0025	−	14.4892i	1.25912	−	0.552798i
$688$	−14.4818	+	5.27093i	−0.552112	+	0.200952i
$689$	−7.39869	+	41.9601i	−0.281868	+	1.59855i
$690$	−15.6347	+	21.2865i	−0.595204	+	0.810363i
$691$	−6.41627	−	7.64661i	−0.244086	−	0.290891i	0.630067	−	0.776541i	$-0.283027\pi$
$691$	−6.41627	−	7.64661i	−0.244086	−	0.290891i	−0.874153	+	0.485650i	$0.838583\pi$
$692$	−1.80164	+	3.12053i	−0.0684880	+	0.118625i
$693$	−6.46527	−	4.43281i	−0.245595	−	0.168388i
$694$	22.7156	+	39.3446i	0.862274	+	1.49350i
$695$	1.24253	−	3.41382i	0.0471319	−	0.129494i
$696$	1.92921	−	6.59871i	0.0731266	−	0.250123i
$697$	1.24097	+	1.04130i	0.0470051	+	0.0394419i
$698$	16.1092	+	13.5172i	0.609742	+	0.511634i
$699$	19.1316	+	28.6833i	0.723624	+	1.08490i
$700$	23.0094	+	29.2839i	0.869674	+	1.10683i
$701$		−	15.6794i		−	0.592201i	−0.955157	−	0.296100i	$-0.904314\pi$
$701$		−	15.6794i		−	0.592201i	0.955157	−	0.296100i	$-0.0956863\pi$
$702$	−63.9295	−	21.8764i	−2.41286	−	0.825672i
$703$	1.42109	−	0.820467i	0.0535975	−	0.0309445i
$704$	−4.02632	+	11.0622i	−0.151748	+	0.416923i
$705$	17.8769	+	8.83409i	0.673281	+	0.332711i
$706$	−67.1795	−	11.8456i	−2.52834	−	0.445814i
$707$	−45.3699	−	9.51298i	−1.70631	−	0.357772i
$708$	−0.447861	+	1.53187i	−0.0168317	+	0.0575713i
$709$	−15.8961	−	5.78570i	−0.596990	−	0.217287i	0.0258110	−	0.999667i	$-0.491783\pi$
$709$	−15.8961	−	5.78570i	−0.596990	−	0.217287i	−0.622801	+	0.782380i	$0.714005\pi$
$710$	−5.74072	+	9.94321i	−0.215445	+	0.373162i
$711$	−4.74696	−	15.1419i	−0.178025	−	0.567864i
$712$	−7.96207	+	4.59691i	−0.298391	+	0.172276i
$713$	−41.5749	−	15.1320i	−1.55699	−	0.566700i
$714$	−23.6102	+	30.0691i	−0.883588	+	1.12531i
$715$	4.23069	+	3.54997i	0.158219	+	0.132762i
$716$	4.56658	+	12.5466i	0.170661	+	0.468887i
$717$	0.0263205	−	0.238526i	0.000982958	−	0.00890792i
$718$	2.74806	+	15.5850i	0.102557	+	0.581627i
$719$	−10.0964	−	17.4874i	−0.376530	−	0.652170i	0.614024	−	0.789287i	$-0.289550\pi$
$719$	−10.0964	−	17.4874i	−0.376530	−	0.652170i	−0.990555	+	0.137117i	$0.956216\pi$
$720$	−2.68628	−	3.51273i	−0.100112	−	0.130912i
$721$	−3.42104	−	6.39146i	−0.127406	−	0.238030i
$722$	−43.7333	+	7.71136i	−1.62759	+	0.286987i
$723$	13.4996	+	3.94678i	0.502057	+	0.146782i
$724$	40.4908	−	48.2550i	1.50483	−	1.79338i
$725$	−1.48788	−	4.08791i	−0.0552583	−	0.151821i
$726$	−22.6790	−	34.0018i	−0.841698	−	1.26193i
$727$	3.43878	+	4.09818i	0.127537	+	0.151993i	0.826034	−	0.563620i	$-0.190592\pi$
$727$	3.43878	+	4.09818i	0.127537	+	0.151993i	−0.698497	+	0.715613i	$0.746147\pi$
$728$	−46.7396	+	25.0175i	−1.73229	+	0.927209i
$729$	−24.9952	+	10.2098i	−0.925748	+	0.378140i
$730$	13.5975	−	23.5516i	0.503268	−	0.871685i
$731$	−35.2465	−	12.8287i	−1.30364	−	0.474486i
$732$	61.7514	−	3.99663i	2.28240	−	0.147720i
$733$	−31.2377	+	37.2277i	−1.15379	+	1.37504i	−0.239044	+	0.971009i	$0.576834\pi$
$733$	−31.2377	+	37.2277i	−1.15379	+	1.37504i	−0.914747	+	0.404026i	$0.867610\pi$
$734$	−22.7543	+	8.28190i	−0.839878	+	0.305691i
$735$	−4.19379	+	11.5343i	−0.154690	+	0.425449i
$736$	−4.25231	−	24.1160i	−0.156742	−	0.888929i
$737$			0.517477i			0.0190615i
$738$	2.98007	+	1.24011i	0.109698	+	0.0456489i
$739$	31.1057			1.14424			0.572121	−	0.820169i	$-0.306121\pi$
$739$	31.1057			1.14424			0.572121	+	0.820169i	$0.306121\pi$
$740$	−12.2902	+	10.3127i	−0.451796	+	0.379102i
$741$	−2.07649	+	2.82712i	−0.0762817	+	0.103857i
$742$	47.0118	+	9.85725i	1.72586	+	0.361871i
$743$	−20.4465	+	24.3672i	−0.750110	+	0.893947i	−0.997180	−	0.0750512i	$-0.976088\pi$
$743$	−20.4465	+	24.3672i	−0.750110	+	0.893947i	0.247069	+	0.968998i	$0.420532\pi$
$744$	25.7114	−	35.0058i	0.942626	−	1.28337i
$745$	6.34481	−	1.11876i	0.232456	−	0.0409882i
$746$		−	41.6128i		−	1.52355i
$747$	−18.9965	+	20.6630i	−0.695045	+	0.756019i
$748$	10.7336	−	6.19706i	0.392460	−	0.226587i
$749$	−7.36405	−	51.3697i	−0.269076	−	1.87701i
$750$	−35.5537	−	10.3946i	−1.29824	−	0.379555i
$751$	−4.62079	+	26.2058i	−0.168615	+	0.956263i	0.776643	+	0.629940i	$0.216921\pi$
$751$	−4.62079	+	26.2058i	−0.168615	+	0.956263i	−0.945258	+	0.326323i	$0.894190\pi$
$752$	15.5627	−	5.66436i	0.567513	−	0.206558i
$753$	−29.5334	+	19.6986i	−1.07626	+	0.717858i
$754$	14.0139	−	2.47103i	0.510356	−	0.0899896i
$755$	−5.25157			−0.191124
$756$	−17.2330	+	45.5270i	−0.626757	+	1.65580i
$757$	−36.6889			−1.33348			−0.666741	−	0.745289i	$-0.732311\pi$
$757$	−36.6889			−1.33348			−0.666741	+	0.745289i	$0.732311\pi$
$758$	54.1638	−	9.55054i	1.96732	−	0.346891i
$759$	−9.81411	−	4.84978i	−0.356230	−	0.176036i
$760$	−1.26485	+	0.460369i	−0.0458810	+	0.0166993i
$761$	−0.705348	+	4.00023i	−0.0255688	+	0.145008i	−0.994920	−	0.100673i	$-0.967900\pi$
$761$	−0.705348	+	4.00023i	−0.0255688	+	0.145008i	0.969351	+	0.245681i	$0.0790116\pi$
$762$	44.3395	−	42.3763i	1.60625	−	1.53513i
$763$	17.1497	−	42.7863i	0.620861	−	1.54897i
$764$	−56.0105	+	32.3377i	−2.02639	+	1.16994i
$765$	0.487077	−	10.7518i	0.0176103	−	0.388733i
$766$			36.5005i			1.31882i
$767$	−1.41574	+	0.249633i	−0.0511195	+	0.00901374i
$768$	41.6489	+	4.59581i	1.50288	+	0.165837i
$769$	12.5387	−	14.9430i	0.452157	−	0.538860i	−0.491021	−	0.871148i	$-0.663376\pi$
$769$	12.5387	−	14.9430i	0.452157	−	0.538860i	0.943178	+	0.332288i	$0.107821\pi$
$770$	4.15336	−	4.63843i	0.149677	−	0.167157i
$771$	−2.86003	−	6.51438i	−0.103002	−	0.234610i
$772$	13.6182	−	11.4270i	0.490128	−	0.411266i
$773$	−8.27868			−0.297763			−0.148882	−	0.988855i	$-0.547567\pi$
$773$	−8.27868			−0.297763			−0.148882	+	0.988855i	$0.547567\pi$
$774$	−74.6593	−	3.38220i	−2.68357	−	0.121571i
$775$		−	27.4835i		−	0.987237i
$776$	1.17371	+	6.65646i	0.0421338	+	0.238953i
$777$	19.4926	+	6.38581i	0.699292	+	0.229090i
$778$	−27.6780	+	10.0740i	−0.992305	+	0.361170i
$779$	0.107710	−	0.128364i	0.00385912	−	0.00459912i
$780$	15.1939	−	30.7467i	0.544029	−	1.10091i
$781$	−4.47185	−	1.62762i	−0.160015	−	0.0582408i
$782$	−26.6943	+	46.2359i	−0.954587	+	1.65339i
$783$	3.57003	−	4.42585i	0.127582	−	0.158167i
$784$	4.51892	+	9.13691i	0.161390	+	0.326318i
$785$	4.59591	+	5.47720i	0.164035	+	0.195490i
$786$	−18.4034	+	37.2415i	−0.656428	+	1.32836i
$787$	−1.90387	−	5.23085i	−0.0678657	−	0.186460i	0.901124	−	0.433562i	$-0.142744\pi$
$787$	−1.90387	−	5.23085i	−0.0678657	−	0.186460i	−0.968989	+	0.247103i	$0.920521\pi$
$788$	−47.7432	+	56.8982i	−1.70078	+	2.02691i
$789$	29.2345	−	27.9401i	1.04078	−	0.994695i
$790$	12.4122	−	2.18861i	0.441608	−	0.0778674i
$791$	−13.5099	+	21.7536i	−0.480356	+	0.773468i
$792$	7.27334	−	7.91141i	0.258447	−	0.281120i
$793$	27.8692	+	48.2709i	0.989665	+	1.71415i
$794$	−2.74983	−	15.5951i	−0.0975880	−	0.553449i
$795$	−12.3820	+	5.43610i	−0.439143	+	0.192799i
$796$	6.92346	+	19.0220i	0.245395	+	0.674218i
$797$	−9.46830	−	7.94485i	−0.335384	−	0.281421i	0.459505	−	0.888175i	$-0.348027\pi$
$797$	−9.46830	−	7.94485i	−0.335384	−	0.281421i	−0.794890	+	0.606754i	$0.792471\pi$
$798$	3.11030	+	2.44220i	0.110103	+	0.0864529i
$799$	37.8774	+	13.7862i	1.34000	+	0.487722i
$800$	13.1738	−	7.60590i	0.465765	−	0.268909i
$801$	−7.54072	+	0.980195i	−0.266438	+	0.0346335i
$802$	3.19625	−	5.53607i	0.112864	−	0.195485i
$803$	10.5921	+	3.85520i	0.373786	+	0.136047i
$804$	3.12202	−	0.761245i	0.110105	−	0.0268470i
$805$	−3.51718	+	16.7744i	−0.123964	+	0.591219i
$806$	88.5353	+	15.6112i	3.11852	+	0.549880i
$807$	14.5453	−	9.70164i	0.512019	−	0.341514i
$808$	21.7359	−	59.7190i	0.764668	−	2.10091i
$809$	7.15947	−	4.13352i	0.251713	−	0.145327i	−0.368835	−	0.929495i	$-0.620243\pi$
$809$	7.15947	−	4.13352i	0.251713	−	0.145327i	0.620549	+	0.784168i	$0.286910\pi$
$810$	−5.48251	−	20.7324i	−0.192636	−	0.728462i
$811$		−	27.8163i		−	0.976761i	−0.872631	−	0.488380i	$-0.837588\pi$
$811$		−	27.8163i		−	0.976761i	0.872631	−	0.488380i	$-0.162412\pi$
$812$	−1.45478	−	10.1482i	−0.0510529	−	0.356132i
$813$	−17.5936	+	35.6028i	−0.617035	+	1.24864i
$814$	−7.97131	−	6.68873i	−0.279394	−	0.234440i
$815$	6.07430	+	5.09694i	0.212773	+	0.178538i
$816$	−6.17617	−	6.46230i	−0.216209	−	0.226226i
$817$	−1.32698	+	3.64584i	−0.0464251	+	0.127552i
$818$	−27.3111	−	47.3041i	−0.954909	−	1.65395i
$819$	−43.6409	+	4.25147i	−1.52494	+	0.148559i
$820$	−0.819167	+	1.41884i	−0.0286066	+	0.0495480i
$821$	−20.9336	−	24.9477i	−0.730588	−	0.870681i	0.265026	−	0.964241i	$-0.414620\pi$
$821$	−20.9336	−	24.9477i	−0.730588	−	0.870681i	−0.995614	+	0.0935605i	$0.970175\pi$
$822$	12.1321	+	1.33873i	0.423154	+	0.0466935i
$823$	−5.72231	+	32.4528i	−0.199467	+	1.13123i	0.706445	+	0.707768i	$0.250298\pi$
$823$	−5.72231	+	32.4528i	−0.199467	+	1.13123i	−0.905912	+	0.423466i	$0.860813\pi$
$824$	9.33912	−	3.39916i	0.325344	−	0.118415i
$825$	0.745852	−	6.75918i	0.0259672	−	0.235324i
$826$	0.229980	+	1.60428i	0.00800202	+	0.0558200i
$827$	−1.49761	−	0.864645i	−0.0520769	−	0.0300666i	0.473735	−	0.880667i	$-0.342905\pi$
$827$	−1.49761	−	0.864645i	−0.0520769	−	0.0300666i	−0.525812	+	0.850601i	$0.676239\pi$
$828$	−14.8222	+	66.3444i	−0.515108	+	2.30563i
$829$	13.0052	+	7.50853i	0.451688	+	0.260782i	0.708543	−	0.705668i	$-0.249353\pi$
$829$	13.0052	+	7.50853i	0.451688	+	0.260782i	−0.256855	+	0.966450i	$0.582686\pi$
$830$	−14.3300	−	17.0778i	−0.497401	−	0.592779i
$831$	26.0861	+	27.2946i	0.904917	+	0.946840i
$832$	22.5213	+	61.8769i	0.780787	+	2.14519i
$833$	−5.86901	+	24.1049i	−0.203349	+	0.835184i
$834$	−0.945042	−	14.6017i	−0.0327241	−	0.505617i
$835$	−3.55390	−	20.1552i	−0.122988	−	0.697499i
$836$	−0.641014	−	1.11027i	−0.0221699	−	0.0383995i
$837$	30.7573	−	18.5608i	1.06313	−	0.641555i
$838$	7.18066	+	4.14576i	0.248052	+	0.143213i
$839$	4.20102	−	3.52507i	0.145035	−	0.121699i	−0.567383	−	0.823454i	$-0.692044\pi$
$839$	4.20102	−	3.52507i	0.145035	−	0.121699i	0.712419	+	0.701755i	$0.247600\pi$
$840$	−14.8369	−	7.93511i	−0.511921	−	0.273787i
$841$	4.82785	−	27.3801i	0.166478	−	0.944141i
$842$	−17.9944	−	3.17290i	−0.620129	−	0.109345i
$843$	14.2861	+	4.17672i	0.492041	+	0.143854i
$844$	61.7234	−	51.7921i	2.12461	−	1.78276i
$845$	17.7324			0.610012
$846$	80.2320	+	3.63465i	2.75843	+	0.124962i
$847$	−22.5311	−	13.9928i	−0.774179	−	0.480797i
$848$	−3.84131	+	10.5539i	−0.131911	+	0.362423i
$849$	−3.28491	+	29.7691i	−0.112738	+	1.02167i
$850$	−32.6608	−	5.75898i	−1.12026	−	0.197531i
$851$	28.2094	+	4.97408i	0.967006	+	0.170509i
$852$	−3.24128	+	29.3737i	−0.111045	+	1.00633i
$853$	10.2501	−	28.1620i	0.350957	−	0.964248i	−0.631106	−	0.775697i	$-0.717399\pi$
$853$	10.2501	−	28.1620i	0.350957	−	0.964248i	0.982063	−	0.188551i	$-0.0603791\pi$
$854$	55.4007	−	29.6533i	1.89577	−	1.01472i
$855$	−1.11215	−	0.0503825i	−0.0380348	−	0.00172305i
$856$	71.1444			2.43167
$857$	24.7521	−	20.7695i	0.845515	−	0.709471i	−0.113282	−	0.993563i	$-0.536136\pi$
$857$	24.7521	−	20.7695i	0.845515	−	0.709471i	0.958797	+	0.284092i	$0.0916920\pi$
$858$	21.3503	+	6.24203i	0.728888	+	0.213099i
$859$	−28.4191	−	5.01105i	−0.969646	−	0.170975i	−0.333676	−	0.942688i	$-0.608289\pi$
$859$	−28.4191	−	5.01105i	−0.969646	−	0.170975i	−0.635971	+	0.771713i	$0.719400\pi$
$860$	6.58712	−	37.3574i	0.224619	−	1.27388i
$861$	2.09351	−	0.0680253i	0.0713466	−	0.00231829i
$862$	50.2114	−	42.1324i	1.71021	−	1.43504i
$863$	2.77792	+	1.60383i	0.0945614	+	0.0545951i	0.546535	−	0.837436i	$-0.315947\pi$
$863$	2.77792	+	1.60383i	0.0945614	+	0.0545951i	−0.451974	+	0.892031i	$0.649280\pi$
$864$	17.4088	+	9.60648i	0.592258	+	0.326819i
$865$	−0.515048	−	0.892089i	−0.0175122	−	0.0303319i
$866$	5.30225	+	30.0706i	0.180178	+	1.02184i
$867$	0.496572	+	7.67247i	0.0168645	+	0.260571i
$868$	13.2914	−	63.3899i	0.451138	−	2.15159i
$869$	1.78672	+	4.90896i	0.0606102	+	0.166525i
$870$	3.12044	+	3.26500i	0.105793	+	0.110694i
$871$	1.86056	+	2.21733i	0.0630427	+	0.0751314i
$872$	54.7274	+	31.5969i	1.85330	+	1.07000i
$873$	−1.21893	+	5.45595i	−0.0412546	+	0.184656i
$874$	4.78257	+	2.76122i	0.161773	+	0.0933996i
$875$	−23.7945	+	3.41103i	−0.804399	+	0.115314i
$876$	7.67735	−	69.5749i	0.259394	−	2.35072i
$877$	23.3178	−	8.48699i	0.787387	−	0.286585i	0.0831376	−	0.996538i	$-0.473506\pi$
$877$	23.3178	−	8.48699i	0.787387	−	0.286585i	0.704249	+	0.709953i	$0.251284\pi$
$878$	1.77809	−	10.0841i	0.0600077	−	0.340321i
$879$	23.4541	+	2.58808i	0.791087	+	0.0872936i
$880$	0.935768	+	1.11520i	0.0315447	+	0.0375936i
$881$	−24.2620	+	42.0230i	−0.817408	+	1.41579i	0.0901784	+	0.995926i	$0.471256\pi$
$881$	−24.2620	+	42.0230i	−0.817408	+	1.41579i	−0.907586	+	0.419866i	$0.862077\pi$
$882$	3.20905	+	49.3279i	0.108054	+	1.66096i
$883$	13.3874	+	23.1877i	0.450523	+	0.780329i	0.998419	−	0.0562182i	$-0.0179042\pi$
$883$	13.3874	+	23.1877i	0.450523	+	0.780329i	−0.547896	+	0.836547i	$0.684571\pi$
$884$	23.7112	−	65.1459i	0.797493	−	2.19109i
$885$	−0.315240	−	0.329844i	−0.0105967	−	0.0110876i
$886$	−35.6267	−	29.8943i	−1.19690	−	1.00432i
$887$	4.66762	+	3.91660i	0.156723	+	0.131506i	0.717777	−	0.696273i	$-0.245160\pi$
$887$	4.66762	+	3.91660i	0.156723	+	0.131506i	−0.561054	+	0.827779i	$0.689604\pi$
$888$	−12.4580	+	25.2103i	−0.418064	+	0.846002i
$889$	14.8079	−	36.9437i	0.496640	−	1.23905i
$890$		−	6.03968i		−	0.202451i
$891$	8.06803	−	3.73007i	0.270289	−	0.124962i
$892$	−6.02301	+	3.47738i	−0.201665	+	0.116431i
$893$	1.42603	−	3.91798i	0.0477202	−	0.131110i
$894$	21.5878	−	14.3989i	0.722003	−	0.481572i
$895$	−3.75898	−	0.662810i	−0.125649	−	0.0221553i
$896$	51.2980	−	16.8243i	1.71375	−	0.562059i
$897$	−59.4895	+	14.5054i	−1.98630	+	0.484320i
$898$	−35.1620	−	12.7979i	−1.17337	−	0.427072i
$899$	−3.78279	+	6.55199i	−0.126163	+	0.218521i
$900$	−41.8764	+	5.44338i	−1.39588	+	0.181446i
$901$	−23.6730	+	13.6676i	−0.788662	+	0.455334i
$902$	−0.998527	−	0.363434i	−0.0332473	−	0.0121010i
$903$	−45.0108	+	18.0587i	−1.49787	+	0.600957i
$904$	−26.8927	−	22.5657i	−0.894438	−	0.750523i
$905$	6.15914	+	16.9221i	0.204737	+	0.562510i
$906$	−19.3674	+	8.50294i	−0.643439	+	0.282491i
$907$	−3.84935	−	21.8308i	−0.127816	−	0.724879i	−0.979596	−	0.200979i	$-0.935588\pi$
$907$	−3.84935	−	21.8308i	−0.127816	−	0.724879i	0.851780	−	0.523900i	$-0.175523\pi$
$908$	−12.1504	−	21.0451i	−0.403224	−	0.698405i
$909$	35.5747	−	38.6955i	1.17994	−	1.28345i
$910$	1.11944	−	34.8083i	0.0371092	−	1.15389i
$911$	−50.7920	+	8.95600i	−1.68281	+	0.296725i	−0.931641	−	0.363380i	$-0.881623\pi$
$911$	−50.7920	+	8.95600i	−1.68281	+	0.296725i	−0.751173	+	0.660106i	$0.770511\pi$
$912$	−0.668450	+	0.638854i	−0.0221346	+	0.0211546i
$913$	5.93950	−	7.07843i	0.196569	−	0.234262i
$914$	28.5390	+	78.4101i	0.943985	+	2.59358i
$915$	−7.83720	+	15.8595i	−0.259090	+	0.524299i
$916$	47.3634	+	56.4455i	1.56493	+	1.86501i
$917$	−0.866492	+	26.9430i	−0.0286141	+	0.889736i
$918$	−15.6122	−	40.4406i	−0.515281	−	1.33474i
$919$	−19.1716	+	33.2062i	−0.632413	+	1.09537i	0.354644	+	0.935002i	$0.384602\pi$
$919$	−19.1716	+	33.2062i	−0.632413	+	1.09537i	−0.987057	+	0.160371i	$0.948731\pi$
$920$	−22.0796	−	8.03632i	−0.727943	−	0.264950i
$921$	10.4285	−	21.1033i	0.343630	−	0.695377i
$922$	−31.4312	+	37.4582i	−1.03513	+	1.23362i
$923$	−25.0134	+	9.10412i	−0.823325	+	0.299666i
$924$	4.98911	−	15.2291i	0.164130	−	0.501002i
$925$	3.08986	+	17.5235i	0.101594	+	0.576168i
$926$		−	39.5241i		−	1.29884i
$927$	8.21166	+	0.372002i	0.269706	+	0.0122182i
$928$	−4.18747			−0.137460
$929$	−29.1569	+	24.4655i	−0.956606	+	0.802687i	−0.980398	−	0.197030i	$-0.936871\pi$
$929$	−29.1569	+	24.4655i	−0.956606	+	0.802687i	0.0237920	+	0.999717i	$0.492426\pi$
$930$	11.4701	+	26.1258i	0.376120	+	0.856700i
$931$	2.49337	+	0.607082i	0.0817170	+	0.0198963i
$932$	−45.3071	+	53.9949i	−1.48408	+	1.76866i
$933$	−6.85833	−	0.756793i	−0.224532	−	0.0247763i
$934$	7.60593	−	1.34113i	0.248874	−	0.0438831i
$935$			3.54320i			0.115875i
$936$	2.72039	−	60.0505i	0.0889188	−	1.96281i
$937$	−12.8142	+	7.39826i	−0.418620	+	0.241691i	−0.694487	−	0.719505i	$-0.744369\pi$
$937$	−12.8142	+	7.39826i	−0.418620	+	0.241691i	0.275867	+	0.961196i	$0.411035\pi$
$938$	2.56587	−	2.01610i	0.0837787	−	0.0658279i
$939$	−8.71374	+	8.32793i	−0.284362	+	0.271772i
$940$	−7.07880	+	40.1459i	−0.230885	+	1.30941i
$941$	−27.5378	+	10.0229i	−0.897706	+	0.326738i	−0.749333	−	0.662193i	$-0.769626\pi$
$941$	−27.5378	+	10.0229i	−0.897706	+	0.326738i	−0.148373	+	0.988932i	$0.547404\pi$
$942$	25.8176	+	12.7581i	0.841184	+	0.415683i
$943$	2.88066	−	0.507938i	0.0938072	−	0.0165407i
$944$	−0.378944			−0.0123336
$945$	−8.80818	−	10.7741i	−0.286530	−	0.350480i
$946$	24.6035			0.799929
$947$	18.4789	−	3.25833i	0.600483	−	0.105881i	0.134860	−	0.990865i	$-0.456941\pi$
$947$	18.4789	−	3.25833i	0.600483	−	0.105881i	0.465623	+	0.884983i	$0.345830\pi$
$948$	26.9882	−	18.0010i	0.876534	−	0.584644i
$949$	59.2470	−	21.5642i	1.92324	−	0.700002i
$950$	−0.595700	+	3.37838i	−0.0193271	+	0.109609i
$951$	−21.5064	−	6.28764i	−0.697391	−	0.203891i
$952$	−31.5700	−	12.6540i	−1.02319	−	0.410117i
$953$	15.1037	−	8.72012i	0.489256	−	0.282472i	−0.235010	−	0.971993i	$-0.575512\pi$
$953$	15.1037	−	8.72012i	0.489256	−	0.282472i	0.724266	+	0.689521i	$0.242179\pi$
$954$	−36.8621	+	40.0959i	−1.19345	+	1.29815i
$955$		−	18.4892i		−	0.598297i
$956$	0.483135	−	0.0851898i	0.0156257	−	0.00275524i
$957$	−1.10813	+	1.50871i	−0.0358209	+	0.0487697i
$958$	−48.3152	+	57.5798i	−1.56099	+	1.86032i
$959$	7.52620	−	2.46838i	0.243034	−	0.0797080i
$960$	−12.3715	+	16.8436i	−0.399288	+	0.543626i
$961$	−12.8672	+	10.7969i	−0.415071	+	0.348286i
$962$	−58.2052			−1.87661
$963$	54.3271	+	22.6073i	1.75067	+	0.728511i
$964$			28.7531i			0.926077i
$965$	0.882500	+	5.00490i	0.0284087	+	0.161114i
$966$	14.1886	+	67.5574i	0.456512	+	2.17362i
$967$	8.04417	−	2.92784i	0.258683	−	0.0941529i	−0.209423	−	0.977825i	$-0.567159\pi$
$967$	8.04417	−	2.92784i	0.258683	−	0.0941529i	0.468106	+	0.883672i	$0.344936\pi$
$968$	23.3723	−	27.8540i	0.751213	−	0.895260i
$969$	−2.24574	+	0.145347i	−0.0721437	+	0.00466923i
$970$	−4.17250	−	1.51866i	−0.133971	−	0.0487614i
$971$	3.94677	−	6.83600i	0.126658	−	0.219378i	−0.795722	−	0.605662i	$-0.792908\pi$
$971$	3.94677	−	6.83600i	0.126658	−	0.219378i	0.922380	+	0.386284i	$0.126242\pi$
$972$	−34.3727	−	43.1885i	−1.10251	−	1.38527i
$973$	−4.48089	−	8.37156i	−0.143651	−	0.268380i
$974$	−40.3663	−	48.1067i	−1.29342	−	1.54144i
$975$	−21.1064	−	31.6440i	−0.675945	−	1.01342i
$976$	5.02516	+	13.8065i	0.160851	+	0.441935i
$977$	34.3201	−	40.9011i	1.09800	−	1.30854i	0.150558	−	0.988601i	$-0.451893\pi$
$977$	34.3201	−	40.9011i	1.09800	−	1.30854i	0.947438	−	0.319940i	$-0.103663\pi$
$978$	30.6541	+	8.96210i	0.980211	+	0.286576i
$979$	2.46530	−	0.434700i	0.0787915	−	0.0138931i
$980$	−25.0385	−	1.61215i	−0.799824	−	0.0514982i
$981$	31.7503	+	41.5184i	1.01371	+	1.32558i
$982$	18.3593	+	31.7993i	0.585870	+	1.01476i
$983$	−4.55632	−	25.8402i	−0.145324	−	0.824174i	−0.967106	−	0.254373i	$-0.918131\pi$
$983$	−4.55632	−	25.8402i	−0.145324	−	0.824174i	0.821782	−	0.569802i	$-0.192980\pi$
$984$	−0.314957	+	2.85425i	−0.0100405	+	0.0909903i
$985$	−7.26233	−	19.9531i	−0.231397	−	0.635758i
$986$	6.99358	+	5.86831i	0.222721	+	0.186885i
$987$	48.3705	−	19.4067i	1.53965	−	0.617721i
$988$	−6.73859	−	2.45265i	−0.214383	−	0.0780291i
$989$	−58.6535	+	33.8636i	−1.86507	+	1.07680i
$990$	2.11190	+	6.73655i	0.0671207	+	0.214102i
$991$	3.85870	−	6.68347i	0.122576	−	0.212308i	−0.798207	−	0.602383i	$-0.794218\pi$
$991$	3.85870	−	6.68347i	0.122576	−	0.212308i	0.920783	+	0.390076i	$0.127551\pi$
$992$	−24.8596	−	9.04816i	−0.789294	−	0.287279i
$993$	6.51800	−	22.2943i	0.206842	−	0.707487i
$994$	9.35195	+	28.5145i	0.296626	+	0.904427i
$995$	−5.69905	−	1.00490i	−0.180672	−	0.0318574i
$996$	−51.4427	−	25.4211i	−1.63002	−	0.805499i
$997$	11.4771	−	31.5331i	0.363483	−	0.998662i	−0.614305	−	0.789069i	$-0.710564\pi$
$997$	11.4771	−	31.5331i	0.363483	−	0.998662i	0.977789	−	0.209594i	$-0.0672142\pi$
$998$	5.20543	−	3.00536i	0.164775	−	0.0951330i
$999$	−17.5242	+	15.2923i	−0.554440	+	0.483826i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.ba.a.5.3	✓	132
3.2	odd	2		567.2.ba.a.530.20		132
7.3	odd	6		189.2.bd.a.59.20	yes	132
21.17	even	6		567.2.bd.a.206.3		132
27.11	odd	18		189.2.bd.a.173.20	yes	132
27.16	even	9		567.2.bd.a.278.3		132
189.38	even	18	inner	189.2.ba.a.38.3	yes	132
189.178	odd	18		567.2.ba.a.521.20		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.5.3	✓	132	1.1	even	1	trivial
189.2.ba.a.38.3	yes	132	189.38	even	18	inner
189.2.bd.a.59.20	yes	132	7.3	odd	6
189.2.bd.a.173.20	yes	132	27.11	odd	18
567.2.ba.a.521.20		132	189.178	odd	18
567.2.ba.a.530.20		132	3.2	odd	2
567.2.bd.a.206.3		132	21.17	even	6
567.2.bd.a.278.3		132	27.16	even	9

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.ba (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.31815 + 0.408753i) q^{2} +(-0.111866 - 1.72843i) q^{3} +(3.32736 - 1.21106i) q^{4} +(-0.175778 + 0.996886i) q^{5} +(0.965825 + 3.96105i) q^{6} +(1.63463 + 2.08038i) q^{7} +(-3.14120 + 1.81358i) q^{8} +(-2.97497 + 0.386707i) q^{9} +O(q^{10})\)	\(q+(-2.31815 + 0.408753i) q^{2} +(-0.111866 - 1.72843i) q^{3} +(3.32736 - 1.21106i) q^{4} +(-0.175778 + 0.996886i) q^{5} +(0.965825 + 3.96105i) q^{6} +(1.63463 + 2.08038i) q^{7} +(-3.14120 + 1.81358i) q^{8} +(-2.97497 + 0.386707i) q^{9} -2.38278i q^{10} +(0.972614 - 0.171498i) q^{11} +(-2.46546 - 5.61565i) q^{12} +(3.55093 - 4.23183i) q^{13} +(-4.63968 - 4.15448i) q^{14} +(1.74272 + 0.192303i) q^{15} +(1.11551 - 0.936020i) q^{16} +3.54415 q^{17} +(6.73837 - 2.11247i) q^{18} -0.366602i q^{19} +(0.622412 + 3.52988i) q^{20} +(3.41294 - 3.05808i) q^{21} +(-2.18457 + 0.795117i) q^{22} +(4.11352 - 4.90230i) q^{23} +(3.48604 + 5.22649i) q^{24} +(3.73558 + 1.35964i) q^{25} +(-6.50182 + 11.2615i) q^{26} +(1.00120 + 5.09878i) q^{27} +(7.95847 + 4.94254i) q^{28} +(-0.703413 - 0.838295i) q^{29} +(-4.11848 + 0.266553i) q^{30} +(-2.36457 - 6.49659i) q^{31} +(2.45967 - 2.93132i) q^{32} +(-0.405226 - 1.66191i) q^{33} +(-8.21588 + 1.44868i) q^{34} +(-2.36123 + 1.26385i) q^{35} +(-9.43048 + 4.88958i) q^{36} +(2.23803 + 3.87639i) q^{37} +(0.149849 + 0.849839i) q^{38} +(-7.71168 - 5.66415i) q^{39} +(-1.25577 - 3.45021i) q^{40} +(0.350145 + 0.293807i) q^{41} +(-6.66172 + 8.48413i) q^{42} +(-9.94497 - 3.61967i) q^{43} +(3.02854 - 1.74853i) q^{44} +(0.137431 - 3.03368i) q^{45} +(-7.53193 + 13.0457i) q^{46} +(10.6873 + 3.88985i) q^{47} +(-1.74264 - 1.82337i) q^{48} +(-1.65597 + 6.80131i) q^{49} +(-9.21539 - 1.62492i) q^{50} +(-0.396472 - 6.12584i) q^{51} +(6.69022 - 18.3812i) q^{52} +(-6.67945 + 3.85638i) q^{53} +(-4.40507 - 11.4105i) q^{54} +0.999731i q^{55} +(-8.90764 - 3.57038i) q^{56} +(-0.633647 + 0.0410104i) q^{57} +(1.97327 + 1.65577i) q^{58} +(-0.199348 - 0.167273i) q^{59} +(6.03153 - 1.47067i) q^{60} +(-3.45090 + 9.48126i) q^{61} +(8.13692 + 14.0936i) q^{62} +(-5.66748 - 5.55695i) q^{63} +(-5.95988 + 10.3228i) q^{64} +(3.59448 + 4.28373i) q^{65} +(1.61869 + 3.68693i) q^{66} +(-0.0909855 + 0.516004i) q^{67} +(11.7927 - 4.29218i) q^{68} +(-8.93347 - 6.56154i) q^{69} +(4.95709 - 3.89497i) q^{70} +(-4.17294 - 2.40925i) q^{71} +(8.64367 - 6.61006i) q^{72} +(9.88409 + 5.70658i) q^{73} +(-6.77258 - 8.07125i) q^{74} +(1.93216 - 6.60880i) q^{75} +(-0.443977 - 1.21982i) q^{76} +(1.94665 + 1.74307i) q^{77} +(20.1921 + 9.97819i) q^{78} +(0.918512 + 5.20914i) q^{79} +(0.737024 + 1.27656i) q^{80} +(8.70091 - 2.30089i) q^{81} +(-0.931784 - 0.537966i) q^{82} +(7.16717 - 6.01397i) q^{83} +(7.65258 - 14.3086i) q^{84} +(-0.622984 + 3.53312i) q^{85} +(24.5335 + 4.32592i) q^{86} +(-1.37025 + 1.30958i) q^{87} +(-2.74416 + 2.30262i) q^{88} +2.53472 q^{89} +(0.921439 + 7.08871i) q^{90} +(14.6083 + 0.469805i) q^{91} +(7.75018 - 21.2934i) q^{92} +(-10.9644 + 4.81375i) q^{93} +(-26.3647 - 4.64881i) q^{94} +(0.365460 + 0.0644405i) q^{95} +(-5.34174 - 3.92346i) q^{96} +(0.637350 - 1.75110i) q^{97} +(1.05874 - 16.4433i) q^{98} +(-2.82718 + 0.886319i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} - 18 q^{6} - 6 q^{7} - 18 q^{8} + 3 q^{9} - 9 q^{11} - 9 q^{12} + 3 q^{14} - 24 q^{15} + 3 q^{16} - 18 q^{17} - 3 q^{18} + 18 q^{20} - 21 q^{21} - 12 q^{22} - 6 q^{23} - 9 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} + 51 q^{30} - 9 q^{31} + 3 q^{32} - 9 q^{33} - 18 q^{34} + 18 q^{35} + 3 q^{37} - 99 q^{38} - 36 q^{39} - 54 q^{40} - 45 q^{42} - 12 q^{43} - 9 q^{44} - 9 q^{45} + 3 q^{46} + 45 q^{47} - 24 q^{49} - 9 q^{50} - 48 q^{51} - 9 q^{52} - 45 q^{53} + 171 q^{54} + 3 q^{56} - 3 q^{58} + 36 q^{59} + 57 q^{60} - 9 q^{61} - 99 q^{62} - 33 q^{63} + 18 q^{64} + 69 q^{65} - 9 q^{66} - 3 q^{67} + 36 q^{68} + 108 q^{69} + 66 q^{70} + 18 q^{71} - 129 q^{72} - 9 q^{73} + 75 q^{74} + 36 q^{75} + 36 q^{76} + 15 q^{77} + 66 q^{78} - 21 q^{79} + 72 q^{80} - 33 q^{81} - 18 q^{82} - 90 q^{83} - 120 q^{84} + 9 q^{85} - 105 q^{86} - 54 q^{87} - 63 q^{88} - 18 q^{89} + 81 q^{90} + 6 q^{91} + 150 q^{92} + 21 q^{93} - 9 q^{94} + 45 q^{95} - 81 q^{96} + 27 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 - 18 * q^6 - 6 * q^7 - 18 * q^8 + 3 * q^9 - 9 * q^11 - 9 * q^12 + 3 * q^14 - 24 * q^15 + 3 * q^16 - 18 * q^17 - 3 * q^18 + 18 * q^20 - 21 * q^21 - 12 * q^22 - 6 * q^23 - 9 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 + 51 * q^30 - 9 * q^31 + 3 * q^32 - 9 * q^33 - 18 * q^34 + 18 * q^35 + 3 * q^37 - 99 * q^38 - 36 * q^39 - 54 * q^40 - 45 * q^42 - 12 * q^43 - 9 * q^44 - 9 * q^45 + 3 * q^46 + 45 * q^47 - 24 * q^49 - 9 * q^50 - 48 * q^51 - 9 * q^52 - 45 * q^53 + 171 * q^54 + 3 * q^56 - 3 * q^58 + 36 * q^59 + 57 * q^60 - 9 * q^61 - 99 * q^62 - 33 * q^63 + 18 * q^64 + 69 * q^65 - 9 * q^66 - 3 * q^67 + 36 * q^68 + 108 * q^69 + 66 * q^70 + 18 * q^71 - 129 * q^72 - 9 * q^73 + 75 * q^74 + 36 * q^75 + 36 * q^76 + 15 * q^77 + 66 * q^78 - 21 * q^79 + 72 * q^80 - 33 * q^81 - 18 * q^82 - 90 * q^83 - 120 * q^84 + 9 * q^85 - 105 * q^86 - 54 * q^87 - 63 * q^88 - 18 * q^89 + 81 * q^90 + 6 * q^91 + 150 * q^92 + 21 * q^93 - 9 * q^94 + 45 * q^95 - 81 * q^96 + 27 * q^98 + 96 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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