LMFDB - Embedded newform 93.2.m.b.19.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [93,2,Mod(7,93)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(93, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 28]))

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

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

chi := DirichletCharacter("93.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 93 = 3 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	93.m (of order $15$, degree $8$, 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:	$0.742608738798$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			19.3
Character	$\chi$	$=$	93.19
Dual form			93.2.m.b.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.927656 + 0.673982i) q^{2} +(0.913545 + 0.406737i) q^{3} +(-0.211739 - 0.651666i) q^{4} +(0.430729 - 0.746045i) q^{5} +(0.573323 + 0.993025i) q^{6} +(-2.45397 + 2.72541i) q^{7} +(0.951456 - 2.92828i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})$	\(q+(0.927656 + 0.673982i) q^{2} +(0.913545 + 0.406737i) q^{3} +(-0.211739 - 0.651666i) q^{4} +(0.430729 - 0.746045i) q^{5} +(0.573323 + 0.993025i) q^{6} +(-2.45397 + 2.72541i) q^{7} +(0.951456 - 2.92828i) q^{8} +(0.669131 + 0.743145i) q^{9} +(0.902389 - 0.401770i) q^{10} +(-5.09115 - 1.08216i) q^{11} +(0.0716231 - 0.681448i) q^{12} +(0.427448 + 4.06690i) q^{13} +(-4.11332 + 0.874313i) q^{14} +(0.696934 - 0.506352i) q^{15} +(1.74755 - 1.26967i) q^{16} +(2.06695 - 0.439344i) q^{17} +(0.119857 + 1.14036i) q^{18} +(0.612639 - 5.82887i) q^{19} +(-0.577374 - 0.122725i) q^{20} +(-3.35034 + 1.49167i) q^{21} +(-3.99348 - 4.43521i) q^{22} +(1.39837 - 4.30373i) q^{23} +(2.06024 - 2.28813i) q^{24} +(2.12894 + 3.68744i) q^{25} +(-2.34449 + 4.06078i) q^{26} +(0.309017 + 0.951057i) q^{27} +(2.29566 + 1.02209i) q^{28} +(-1.03064 - 0.748801i) q^{29} +0.987788 q^{30} +(0.955875 + 5.48510i) q^{31} -3.68109 q^{32} +(-4.21084 - 3.05936i) q^{33} +(2.21353 + 0.985527i) q^{34} +(0.976281 + 3.00469i) q^{35} +(0.342601 - 0.593402i) q^{36} +(-1.20935 - 2.09465i) q^{37} +(4.49687 - 4.99428i) q^{38} +(-1.26366 + 3.88916i) q^{39} +(-1.77481 - 1.97112i) q^{40} +(3.45263 - 1.53721i) q^{41} +(-4.11332 - 0.874313i) q^{42} +(-0.814196 + 7.74656i) q^{43} +(0.372790 + 3.54686i) q^{44} +(0.842633 - 0.179107i) q^{45} +(4.19784 - 3.04991i) q^{46} +(4.60370 - 3.34478i) q^{47} +(2.11289 - 0.449109i) q^{48} +(-0.674191 - 6.41450i) q^{49} +(-0.510339 + 4.85555i) q^{50} +(2.06695 + 0.439344i) q^{51} +(2.55975 - 1.13968i) q^{52} +(9.00616 + 10.0024i) q^{53} +(-0.354333 + 1.09053i) q^{54} +(-3.00024 + 3.33211i) q^{55} +(5.64592 + 9.77903i) q^{56} +(2.93049 - 5.07575i) q^{57} +(-0.451398 - 1.38926i) q^{58} +(-7.65834 - 3.40971i) q^{59} +(-0.477541 - 0.346954i) q^{60} -2.01339 q^{61} +(-2.81013 + 5.73253i) q^{62} -3.66740 q^{63} +(-6.90989 - 5.02033i) q^{64} +(3.21820 + 1.43284i) q^{65} +(-1.84427 - 5.67606i) q^{66} +(4.11611 - 7.12931i) q^{67} +(-0.723960 - 1.25393i) q^{68} +(3.02796 - 3.36289i) q^{69} +(-1.11945 + 3.44531i) q^{70} +(-0.187855 - 0.208634i) q^{71} +(2.81279 - 1.25233i) q^{72} +(-2.52645 - 0.537013i) q^{73} +(0.289898 - 2.75819i) q^{74} +(0.445071 + 4.23456i) q^{75} +(-3.92819 + 0.834964i) q^{76} +(15.4429 - 11.2199i) q^{77} +(-3.79347 + 2.75612i) q^{78} +(-4.45142 + 0.946179i) q^{79} +(-0.194510 - 1.85064i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(4.23891 + 0.901007i) q^{82} +(-7.76429 + 3.45689i) q^{83} +(1.68147 + 1.86746i) q^{84} +(0.562525 - 1.73128i) q^{85} +(-5.97634 + 6.63739i) q^{86} +(-0.636968 - 1.10326i) q^{87} +(-8.01287 + 13.8787i) q^{88} +(-1.07901 - 3.32084i) q^{89} +(0.902389 + 0.401770i) q^{90} +(-12.1329 - 8.81508i) q^{91} -3.10069 q^{92} +(-1.35775 + 5.39968i) q^{93} +6.52498 q^{94} +(-4.08471 - 2.96772i) q^{95} +(-3.36284 - 1.49723i) q^{96} +(-5.49168 - 16.9017i) q^{97} +(3.69784 - 6.40485i) q^{98} +(-2.60244 - 4.50757i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9	\( 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9} + 24 q^{10} - 22 q^{11} + 12 q^{12} - 8 q^{13} + 10 q^{14} - 8 q^{15} - 2 q^{16} - 17 q^{17} + 5 q^{19} - 22 q^{20} - 11 q^{21} - 37 q^{22} + 26 q^{23} + 26 q^{24} - 8 q^{25} + 4 q^{26} - 6 q^{27} - 36 q^{28} + 2 q^{29} + 42 q^{30} + 36 q^{32} + 14 q^{33} + 40 q^{34} + 9 q^{35} - 13 q^{36} - 13 q^{37} - q^{38} - 19 q^{39} - 27 q^{40} + 36 q^{41} + 10 q^{42} - 11 q^{43} - 38 q^{44} - q^{45} - 23 q^{46} - 13 q^{47} - 14 q^{48} - 22 q^{49} + 71 q^{50} - 17 q^{51} + 9 q^{52} - 20 q^{53} - 5 q^{54} + 26 q^{55} + 28 q^{56} - 15 q^{57} + 40 q^{58} - 16 q^{59} - 61 q^{60} + 70 q^{61} - 2 q^{62} + 12 q^{63} + 34 q^{64} + 94 q^{65} - 16 q^{66} + 4 q^{67} + 51 q^{68} - 13 q^{69} - 43 q^{70} - 5 q^{71} + q^{72} - 12 q^{73} + 74 q^{74} - 8 q^{75} + 71 q^{76} + 25 q^{77} + 17 q^{78} - 29 q^{79} - 113 q^{80} + 3 q^{81} - 60 q^{82} - 11 q^{83} - 41 q^{84} + 16 q^{85} - 144 q^{86} + 14 q^{87} + 26 q^{88} - 27 q^{89} + 24 q^{90} - 81 q^{91} + 28 q^{92} - 36 q^{93} - 80 q^{94} - 56 q^{95} - 43 q^{96} - 21 q^{97} - 14 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9 + 24 * q^10 - 22 * q^11 + 12 * q^12 - 8 * q^13 + 10 * q^14 - 8 * q^15 - 2 * q^16 - 17 * q^17 + 5 * q^19 - 22 * q^20 - 11 * q^21 - 37 * q^22 + 26 * q^23 + 26 * q^24 - 8 * q^25 + 4 * q^26 - 6 * q^27 - 36 * q^28 + 2 * q^29 + 42 * q^30 + 36 * q^32 + 14 * q^33 + 40 * q^34 + 9 * q^35 - 13 * q^36 - 13 * q^37 - q^38 - 19 * q^39 - 27 * q^40 + 36 * q^41 + 10 * q^42 - 11 * q^43 - 38 * q^44 - q^45 - 23 * q^46 - 13 * q^47 - 14 * q^48 - 22 * q^49 + 71 * q^50 - 17 * q^51 + 9 * q^52 - 20 * q^53 - 5 * q^54 + 26 * q^55 + 28 * q^56 - 15 * q^57 + 40 * q^58 - 16 * q^59 - 61 * q^60 + 70 * q^61 - 2 * q^62 + 12 * q^63 + 34 * q^64 + 94 * q^65 - 16 * q^66 + 4 * q^67 + 51 * q^68 - 13 * q^69 - 43 * q^70 - 5 * q^71 + q^72 - 12 * q^73 + 74 * q^74 - 8 * q^75 + 71 * q^76 + 25 * q^77 + 17 * q^78 - 29 * q^79 - 113 * q^80 + 3 * q^81 - 60 * q^82 - 11 * q^83 - 41 * q^84 + 16 * q^85 - 144 * q^86 + 14 * q^87 + 26 * q^88 - 27 * q^89 + 24 * q^90 - 81 * q^91 + 28 * q^92 - 36 * q^93 - 80 * q^94 - 56 * q^95 - 43 * q^96 - 21 * q^97 - 14 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/93\mathbb{Z}\right)^\times$.

$n$	$32$	$34$
$\chi(n)$	$1$	$e\left(\frac{2}{15}\right)$

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 $

$2$	0.927656	+	0.673982i	0.655952	+	0.476577i	0.865294	−	0.501265i	$-0.167132\pi$
$2$	0.927656	+	0.673982i	0.655952	+	0.476577i	−0.209341	+	0.977843i	$0.567132\pi$
$3$	0.913545	+	0.406737i	0.527436	+	0.234830i
$3$	0.913545	+	0.406737i	0.527436	+	0.234830i
$4$	−0.211739	−	0.651666i	−0.105870	−	0.325833i
$5$	0.430729	−	0.746045i	0.192628	−	0.333641i	−0.753492	−	0.657457i	$-0.771632\pi$
$5$	0.430729	−	0.746045i	0.192628	−	0.333641i	0.946120	+	0.323815i	$0.104966\pi$
$6$	0.573323	+	0.993025i	0.234058	+	0.405401i
$7$	−2.45397	+	2.72541i	−0.927514	+	1.03011i	0.0719515	+	0.997408i	$0.477077\pi$
$7$	−2.45397	+	2.72541i	−0.927514	+	1.03011i	−0.999465	+	0.0327002i	$0.989589\pi$
$8$	0.951456	−	2.92828i	0.336391	−	1.03530i
$9$	0.669131	+	0.743145i	0.223044	+	0.247715i
$10$	0.902389	−	0.401770i	0.285360	−	0.127051i
$11$	−5.09115	−	1.08216i	−1.53504	−	0.326283i	−0.638632	−	0.769513i	$-0.720499\pi$
$11$	−5.09115	−	1.08216i	−1.53504	−	0.326283i	−0.896408	+	0.443230i	$0.853833\pi$
$12$	0.0716231	−	0.681448i	0.0206758	−	0.196717i
$13$	0.427448	+	4.06690i	0.118553	+	1.12796i	0.878424	+	0.477882i	$0.158595\pi$
$13$	0.427448	+	4.06690i	0.118553	+	1.12796i	−0.759871	+	0.650074i	$0.774738\pi$
$14$	−4.11332	+	0.874313i	−1.09933	+	0.233670i
$15$	0.696934	−	0.506352i	0.179948	−	0.130740i
$16$	1.74755	−	1.26967i	0.436888	−	0.317418i
$17$	2.06695	−	0.439344i	0.501309	−	0.106557i	0.0496851	−	0.998765i	$-0.484178\pi$
$17$	2.06695	−	0.439344i	0.501309	−	0.106557i	0.451624	+	0.892208i	$0.350845\pi$
$18$	0.119857	+	1.14036i	0.0282506	+	0.268787i
$19$	0.612639	−	5.82887i	0.140549	−	1.33723i	−0.665949	−	0.745997i	$-0.731973\pi$
$19$	0.612639	−	5.82887i	0.140549	−	1.33723i	0.806498	−	0.591237i	$-0.201360\pi$
$20$	−0.577374	−	0.122725i	−0.129105	−	0.0274421i
$21$	−3.35034	+	1.49167i	−0.731104	+	0.325508i
$22$	−3.99348	−	4.43521i	−0.851414	−	0.945591i
$23$	1.39837	−	4.30373i	0.291580	−	0.897391i	−0.692769	−	0.721160i	$-0.743609\pi$
$23$	1.39837	−	4.30373i	0.291580	−	0.897391i	0.984349	−	0.176231i	$-0.0563906\pi$
$24$	2.06024	−	2.28813i	0.420544	−	0.467062i
$25$	2.12894	+	3.68744i	0.425789	+	0.737488i
$26$	−2.34449	+	4.06078i	−0.459793	+	0.796384i
$27$	0.309017	+	0.951057i	0.0594703	+	0.183031i
$28$	2.29566	+	1.02209i	0.433839	+	0.193157i
$29$	−1.03064	−	0.748801i	−0.191384	−	0.139049i	0.487967	−	0.872862i	$-0.337739\pi$
$29$	−1.03064	−	0.748801i	−0.191384	−	0.139049i	−0.679351	+	0.733813i	$0.737739\pi$
$30$	0.987788			0.180345
$31$	0.955875	+	5.48510i	0.171680	+	0.985153i
$31$	0.955875	+	5.48510i	0.171680	+	0.985153i
$32$	−3.68109			−0.650731
$33$	−4.21084	−	3.05936i	−0.733014	−	0.532566i
$34$	2.21353	+	0.985527i	0.379617	+	0.169016i
$35$	0.976281	+	3.00469i	0.165022	+	0.507884i
$36$	0.342601	−	0.593402i	0.0571002	−	0.0989004i
$37$	−1.20935	−	2.09465i	−0.198815	−	0.344359i	0.749329	−	0.662198i	$-0.230376\pi$
$37$	−1.20935	−	2.09465i	−0.198815	−	0.344359i	−0.948145	+	0.317839i	$0.897043\pi$
$38$	4.49687	−	4.99428i	0.729489	−	0.810179i
$39$	−1.26366	+	3.88916i	−0.202348	+	0.622764i
$40$	−1.77481	−	1.97112i	−0.280622	−	0.311662i
$41$	3.45263	−	1.53721i	0.539210	−	0.240072i	−0.119016	−	0.992892i	$-0.537974\pi$
$41$	3.45263	−	1.53721i	0.539210	−	0.240072i	0.658226	+	0.752820i	$0.271307\pi$
$42$	−4.11332	−	0.874313i	−0.634699	−	0.134909i
$43$	−0.814196	+	7.74656i	−0.124164	+	1.18134i	0.738033	+	0.674765i	$0.235755\pi$
$43$	−0.814196	+	7.74656i	−0.124164	+	1.18134i	−0.862196	+	0.506574i	$0.830912\pi$
$44$	0.372790	+	3.54686i	0.0562003	+	0.534710i
$45$	0.842633	−	0.179107i	0.125612	−	0.0266997i
$46$	4.19784	−	3.04991i	0.618938	−	0.449685i
$47$	4.60370	−	3.34478i	0.671519	−	0.487887i	−0.199014	−	0.979997i	$-0.563774\pi$
$47$	4.60370	−	3.34478i	0.671519	−	0.487887i	0.870533	+	0.492110i	$0.163774\pi$
$48$	2.11289	−	0.449109i	0.304969	−	0.0648233i
$49$	−0.674191	−	6.41450i	−0.0963130	−	0.916357i
$50$	−0.510339	+	4.85555i	−0.0721728	+	0.686678i
$51$	2.06695	+	0.439344i	0.289431	+	0.0615204i
$52$	2.55975	−	1.13968i	0.354974	−	0.158045i
$53$	9.00616	+	10.0024i	1.23709	+	1.37393i	0.901995	+	0.431745i	$0.142102\pi$
$53$	9.00616	+	10.0024i	1.23709	+	1.37393i	0.335096	+	0.942184i	$0.391231\pi$
$54$	−0.354333	+	1.09053i	−0.0482186	+	0.148402i
$55$	−3.00024	+	3.33211i	−0.404553	+	0.449301i
$56$	5.64592	+	9.77903i	0.754468	+	1.30678i
$57$	2.93049	−	5.07575i	0.388153	−	0.672300i
$58$	−0.451398	−	1.38926i	−0.0592714	−	0.182419i
$59$	−7.65834	−	3.40971i	−0.997031	−	0.443907i	−0.157676	−	0.987491i	$-0.550400\pi$
$59$	−7.65834	−	3.40971i	−0.997031	−	0.443907i	−0.839355	+	0.543584i	$0.817067\pi$
$60$	−0.477541	−	0.346954i	−0.0616503	−	0.0447915i
$61$	−2.01339			−0.257789			−0.128894	−	0.991658i	$-0.541143\pi$
$61$	−2.01339			−0.257789			−0.128894	+	0.991658i	$0.541143\pi$
$62$	−2.81013	+	5.73253i	−0.356887	+	0.728032i
$63$	−3.66740			−0.462049
$64$	−6.90989	−	5.02033i	−0.863737	−	0.627541i
$65$	3.21820	+	1.43284i	0.399169	+	0.177722i
$66$	−1.84427	−	5.67606i	−0.227013	−	0.698675i
$67$	4.11611	−	7.12931i	0.502863	−	0.870984i	−0.497132	−	0.867675i	$-0.665613\pi$
$67$	4.11611	−	7.12931i	0.502863	−	0.870984i	0.999995	−	0.00330886i	$-0.00105325\pi$
$68$	−0.723960	−	1.25393i	−0.0877930	−	0.152062i
$69$	3.02796	−	3.36289i	0.364523	−	0.404844i
$70$	−1.11945	+	3.44531i	−0.133800	+	0.411793i
$71$	−0.187855	−	0.208634i	−0.0222942	−	0.0247602i	0.731895	−	0.681418i	$-0.238636\pi$
$71$	−0.187855	−	0.208634i	−0.0222942	−	0.0247602i	−0.754189	+	0.656658i	$0.771970\pi$
$72$	2.81279	−	1.25233i	0.331490	−	0.147589i
$73$	−2.52645	−	0.537013i	−0.295698	−	0.0628526i	0.0576738	−	0.998335i	$-0.481632\pi$
$73$	−2.52645	−	0.537013i	−0.295698	−	0.0628526i	−0.353372	+	0.935483i	$0.614965\pi$
$74$	0.289898	−	2.75819i	0.0336999	−	0.320634i
$75$	0.445071	+	4.23456i	0.0513923	+	0.488965i
$76$	−3.92819	+	0.834964i	−0.450595	+	0.0957769i
$77$	15.4429	−	11.2199i	1.75988	−	1.27863i
$78$	−3.79347	+	2.75612i	−0.429526	+	0.312069i
$79$	−4.45142	+	0.946179i	−0.500824	+	0.106453i	−0.451395	−	0.892324i	$-0.649073\pi$
$79$	−4.45142	+	0.946179i	−0.500824	+	0.106453i	−0.0494290	+	0.998778i	$0.515740\pi$
$80$	−0.194510	−	1.85064i	−0.0217469	−	0.206907i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	4.23891	+	0.901007i	0.468109	+	0.0994996i
$83$	−7.76429	+	3.45689i	−0.852242	+	0.379442i	−0.785899	−	0.618354i	$-0.787800\pi$
$83$	−7.76429	+	3.45689i	−0.852242	+	0.379442i	−0.0663424	+	0.997797i	$0.521133\pi$
$84$	1.68147	+	1.86746i	0.183463	+	0.203756i
$85$	0.562525	−	1.73128i	0.0610145	−	0.187783i
$86$	−5.97634	+	6.63739i	−0.644445	+	0.715728i
$87$	−0.636968	−	1.10326i	−0.0682901	−	0.118282i
$88$	−8.01287	+	13.8787i	−0.854175	+	1.47947i
$89$	−1.07901	−	3.32084i	−0.114375	−	0.352009i	0.877441	−	0.479684i	$-0.159249\pi$
$89$	−1.07901	−	3.32084i	−0.114375	−	0.352009i	−0.991816	+	0.127675i	$0.959249\pi$
$90$	0.902389	+	0.401770i	0.0951202	+	0.0423502i
$91$	−12.1329	−	8.81508i	−1.27188	−	0.924072i
$92$	−3.10069			−0.323269
$93$	−1.35775	+	5.39968i	−0.140793	+	0.559920i
$94$	6.52498			0.673000
$95$	−4.08471	−	2.96772i	−0.419083	−	0.304482i
$96$	−3.36284	−	1.49723i	−0.343219	−	0.152811i
$97$	−5.49168	−	16.9017i	−0.557596	−	1.71610i	−0.688988	−	0.724773i	$-0.741945\pi$
$97$	−5.49168	−	16.9017i	−0.557596	−	1.71610i	0.131392	−	0.991330i	$-0.458055\pi$
$98$	3.69784	−	6.40485i	0.373538	−	0.646987i
$99$	−2.60244	−	4.50757i	−0.261556	−	0.453027i
$100$	1.95220	−	2.16814i	0.195220	−	0.216814i
$101$	0.543810	−	1.67368i	0.0541112	−	0.166537i	−0.920349	−	0.391099i	$-0.872095\pi$
$101$	0.543810	−	1.67368i	0.0541112	−	0.166537i	0.974460	+	0.224562i	$0.0720951\pi$
$102$	1.62131	+	1.80065i	0.160534	+	0.178291i
$103$	9.57271	−	4.26205i	0.943227	−	0.419952i	0.123268	−	0.992373i	$-0.460663\pi$
$103$	9.57271	−	4.26205i	0.943227	−	0.419952i	0.819959	+	0.572422i	$0.193996\pi$
$104$	12.3157	+	2.61779i	1.20766	+	0.256695i
$105$	−0.330238	+	3.14201i	−0.0322279	+	0.306628i
$106$	1.61322	+	15.3487i	0.156690	+	1.49080i
$107$	−15.8220	+	3.36307i	−1.52957	+	0.325120i	−0.894405	−	0.447258i	$-0.852401\pi$
$107$	−15.8220	+	3.36307i	−1.52957	+	0.325120i	−0.635164	+	0.772378i	$0.719067\pi$
$108$	0.554340	−	0.402752i	0.0533414	−	0.0387548i
$109$	−2.65874	+	1.93169i	−0.254661	+	0.185022i	−0.707790	−	0.706423i	$-0.750308\pi$
$109$	−2.65874	+	1.93169i	−0.254661	+	0.185022i	0.453129	+	0.891445i	$0.350308\pi$
$110$	−5.02898	+	1.06894i	−0.479494	+	0.101920i
$111$	−0.252822	−	2.40544i	−0.0239968	−	0.228315i
$112$	−0.828067	+	7.87853i	−0.0782450	+	0.744452i
$113$	−8.18463	−	1.73970i	−0.769946	−	0.163657i	−0.193841	−	0.981033i	$-0.562095\pi$
$113$	−8.18463	−	1.73970i	−0.769946	−	0.163657i	−0.576105	+	0.817376i	$0.695428\pi$
$114$	6.13945	−	2.73346i	0.575012	−	0.256012i
$115$	−2.60846	−	2.89699i	−0.243240	−	0.270146i
$116$	−0.269742	+	0.830181i	−0.0250449	+	0.0770803i
$117$	−2.73628	+	3.03894i	−0.252969	+	0.280950i
$118$	−4.80622	−	8.32462i	−0.442449	−	0.766343i
$119$	−3.87484	+	6.71142i	−0.355206	+	0.615235i
$120$	−0.819640	−	2.52259i	−0.0748225	−	0.230280i
$121$	14.6997	+	6.54475i	1.33634	+	0.594977i
$122$	−1.86774	−	1.35699i	−0.169097	−	0.122856i
$123$	3.77937			0.340775
$124$	3.37206	−	1.78432i	0.302820	−	0.160237i
$125$	7.97528			0.713331
$126$	−3.40209	−	2.47176i	−0.303082	−	0.220202i
$127$	13.3575	+	5.94715i	1.18529	+	0.527724i	0.902178	−	0.431363i	$-0.141967\pi$
$127$	13.3575	+	5.94715i	1.18529	+	0.527724i	0.283110	+	0.959087i	$0.408634\pi$
$128$	−0.751355	−	2.31243i	−0.0664110	−	0.204392i
$129$	−3.89462	+	6.74567i	−0.342902	+	0.593923i
$130$	2.01968	+	3.49819i	0.177138	+	0.306812i
$131$	1.79889	−	1.99787i	0.157170	−	0.174555i	−0.659417	−	0.751777i	$-0.729197\pi$
$131$	1.79889	−	1.99787i	0.157170	−	0.174555i	0.816587	+	0.577222i	$0.195863\pi$
$132$	−1.10208	+	3.39185i	−0.0959236	+	0.295223i
$133$	14.3827	+	15.9736i	1.24713	+	1.38508i
$134$	8.62336	−	3.83937i	0.744945	−	0.331671i
$135$	0.842633	+	0.179107i	0.0725223	+	0.0154151i
$136$	0.680090	−	6.47063i	0.0583173	−	0.554852i
$137$	−0.561177	−	5.33925i	−0.0479446	−	0.456163i	−0.991987	−	0.126339i	$-0.959677\pi$
$137$	−0.561177	−	5.33925i	−0.0479446	−	0.456163i	0.944043	−	0.329824i	$-0.106989\pi$
$138$	5.07543	−	1.07882i	0.432049	−	0.0918350i
$139$	−1.43881	+	1.04535i	−0.122038	+	0.0886658i	−0.647130	−	0.762380i	$-0.724031\pi$
$139$	−1.43881	+	1.04535i	−0.122038	+	0.0886658i	0.525092	+	0.851045i	$0.324031\pi$
$140$	1.75133	−	1.27242i	0.148015	−	0.107539i
$141$	5.56614	−	1.18312i	0.468753	−	0.0996366i
$142$	−0.0336492	−	0.320151i	−0.00282378	−	0.0268665i
$143$	2.22482	−	21.1678i	0.186049	−	1.77014i
$144$	2.11289	+	0.449109i	0.176074	+	0.0374257i
$145$	−1.00256	+	0.446370i	−0.0832584	+	0.0370690i
$146$	−1.98174	−	2.20094i	−0.164010	−	0.182151i
$147$	1.99311	−	6.13416i	0.164389	−	0.505937i
$148$	−1.10895	+	1.23161i	−0.0911548	+	0.101238i
$149$	2.13548	+	3.69876i	0.174945	+	0.303014i	0.940142	−	0.340782i	$-0.110692\pi$
$149$	2.13548	+	3.69876i	0.174945	+	0.303014i	−0.765197	+	0.643796i	$0.777358\pi$
$150$	−2.44115	+	4.22819i	−0.199319	+	0.345230i
$151$	7.13975	+	21.9739i	0.581025	+	1.78821i	0.614681	+	0.788776i	$0.289285\pi$
$151$	7.13975	+	21.9739i	0.581025	+	1.78821i	−0.0336560	+	0.999433i	$0.510715\pi$
$152$	−16.4857	−	7.33989i	−1.33716	−	0.595344i
$153$	1.70956	+	1.24206i	0.138209	+	0.100415i
$154$	21.8877			1.76376
$155$	4.50385	+	1.64947i	0.361758	+	0.132488i
$156$	2.80200			0.224339
$157$	−6.72058	−	4.88279i	−0.536361	−	0.389689i	0.286371	−	0.958119i	$-0.407551\pi$
$157$	−6.72058	−	4.88279i	−0.536361	−	0.389689i	−0.822732	+	0.568430i	$0.807551\pi$
$158$	−4.76710	−	2.12245i	−0.379250	−	0.168853i
$159$	4.15921	+	12.8007i	0.329847	+	1.01517i
$160$	−1.58555	+	2.74626i	−0.125349	+	0.217111i
$161$	8.29789	+	14.3724i	0.653965	+	1.13270i
$162$	−0.767256	+	0.852124i	−0.0602813	+	0.0669492i
$163$	7.25154	−	22.3180i	0.567985	−	1.74808i	−0.0909274	−	0.995858i	$-0.528983\pi$
$163$	7.25154	−	22.3180i	0.567985	−	1.74808i	0.658912	−	0.752220i	$-0.271017\pi$
$164$	−1.73280	−	1.92447i	−0.135309	−	0.150276i
$165$	−4.09615	+	1.82372i	−0.318885	+	0.141977i
$166$	−9.53247	−	2.02619i	−0.739863	−	0.157263i
$167$	−2.51234	+	23.9033i	−0.194411	+	1.84969i	0.268488	+	0.963283i	$0.413476\pi$
$167$	−2.51234	+	23.9033i	−0.194411	+	1.84969i	−0.462898	+	0.886411i	$0.653191\pi$
$168$	1.18032	+	11.2300i	0.0910636	+	0.866412i
$169$	−3.64105	+	0.773929i	−0.280081	+	0.0595330i
$170$	1.68868	−	1.22690i	0.129516	−	0.0940987i
$171$	4.74163	−	3.44500i	0.362601	−	0.263445i
$172$	5.22057	−	1.10967i	0.398064	−	0.0846112i
$173$	−2.10296	−	20.0083i	−0.159885	−	1.52120i	−0.720692	−	0.693255i	$-0.756176\pi$
$173$	−2.10296	−	20.0083i	−0.159885	−	1.52120i	0.560807	−	0.827946i	$-0.310491\pi$
$174$	0.152690	−	1.45275i	0.0115754	−	0.110133i
$175$	−15.2742	−	3.24662i	−1.15462	−	0.245422i
$176$	−10.2710	+	4.57296i	−0.774209	+	0.344700i
$177$	−5.60938	−	6.22985i	−0.421627	−	0.468264i
$178$	1.23724	−	3.80783i	0.0927351	−	0.285409i
$179$	−3.97171	+	4.41103i	−0.296860	+	0.329696i	−0.873060	−	0.487612i	$-0.837868\pi$
$179$	−3.97171	+	4.41103i	−0.296860	+	0.329696i	0.576201	+	0.817308i	$0.304535\pi$
$180$	−0.295136	−	0.511191i	−0.0219982	−	0.0381020i
$181$	−2.23887	+	3.87784i	−0.166414	+	0.288238i	−0.937157	−	0.348909i	$-0.886552\pi$
$181$	−2.23887	+	3.87784i	−0.166414	+	0.288238i	0.770742	+	0.637147i	$0.219886\pi$
$182$	−5.31398	−	16.3547i	−0.393898	−	1.21229i
$183$	−1.83933	−	0.818921i	−0.135967	−	0.0605364i
$184$	−11.2721	−	8.18963i	−0.830987	−	0.603748i
$185$	−2.08360			−0.153190
$186$	−4.89881	+	4.09394i	−0.359198	+	0.300182i
$187$	−10.9986			−0.804297
$188$	−3.15447	−	2.29185i	−0.230063	−	0.167151i
$189$	−3.35034	−	1.49167i	−0.243701	−	0.108503i
$190$	−1.78902	−	5.50605i	−0.129789	−	0.399451i
$191$	−11.9046	+	20.6194i	−0.861390	+	1.49197i	0.00919781	+	0.999958i	$0.497072\pi$
$191$	−11.9046	+	20.6194i	−0.861390	+	1.49197i	−0.870588	+	0.492013i	$0.836261\pi$
$192$	−4.27055	−	7.39681i	−0.308200	−	0.533819i
$193$	−10.4128	+	11.5646i	−0.749531	+	0.832438i	−0.990416	−	0.138116i	$-0.955895\pi$
$193$	−10.4128	+	11.5646i	−0.749531	+	0.832438i	0.240886	+	0.970554i	$0.422562\pi$
$194$	6.29702	−	19.3802i	0.452099	−	1.39142i
$195$	2.35719	+	2.61792i	0.168802	+	0.187473i
$196$	−4.03736	+	1.79755i	−0.288383	+	0.128396i
$197$	−10.6972	−	2.27376i	−0.762145	−	0.161999i	−0.189588	−	0.981864i	$-0.560715\pi$
$197$	−10.6972	−	2.27376i	−0.762145	−	0.161999i	−0.572557	+	0.819865i	$0.694048\pi$
$198$	0.623843	−	5.93547i	0.0443346	−	0.421816i
$199$	0.481657	+	4.58266i	0.0341438	+	0.324856i	0.998240	+	0.0593032i	$0.0188879\pi$
$199$	0.481657	+	4.58266i	0.0341438	+	0.324856i	−0.964096	+	0.265553i	$0.914445\pi$
$200$	12.8235	−	2.72571i	0.906756	−	0.192737i
$201$	6.66001	−	4.83878i	0.469761	−	0.341301i
$202$	1.63250	−	1.18608i	0.114862	−	0.0834522i
$203$	4.56994	−	0.971371i	0.320747	−	0.0681769i
$204$	−0.151349	−	1.43999i	−0.0105965	−	0.100819i
$205$	0.340321	−	3.23794i	0.0237690	−	0.226147i
$206$	11.7527	+	2.49812i	0.818851	+	0.174052i
$207$	4.13399	−	1.84057i	0.287332	−	0.127928i
$208$	5.91062	+	6.56440i	0.409827	+	0.455159i
$209$	−9.42679	+	29.0127i	−0.652065	+	2.00685i
$210$	−2.42400	+	2.69213i	−0.167272	+	0.185774i
$211$	8.01200	+	13.8772i	0.551569	+	0.955345i	0.998162	+	0.0606077i	$0.0193039\pi$
$211$	8.01200	+	13.8772i	0.551569	+	0.955345i	−0.446593	+	0.894737i	$0.647363\pi$
$212$	4.61124	−	7.98690i	0.316701	−	0.548543i
$213$	−0.0867547	−	0.267004i	−0.00594434	−	0.0182948i
$214$	−16.9440	−	7.54396i	−1.15827	−	0.515694i
$215$	5.42858	+	3.94410i	0.370226	+	0.268985i
$216$	3.07898			0.209498
$217$	−17.2948	−	10.8551i	−1.17405	−	0.736893i
$218$	−3.76832			−0.255223
$219$	−2.08960	−	1.51818i	−0.141202	−	0.102589i
$220$	2.80669	+	1.24962i	0.189227	+	0.0842493i
$221$	2.67028	+	8.21828i	0.179623	+	0.552822i
$222$	1.38669	−	2.40182i	0.0930688	−	0.161200i
$223$	−0.702071	−	1.21602i	−0.0470141	−	0.0814309i	0.841561	−	0.540163i	$-0.181637\pi$
$223$	−0.702071	−	1.21602i	−0.0470141	−	0.0814309i	−0.888575	+	0.458732i	$0.848304\pi$
$224$	9.03329	−	10.0325i	0.603562	−	0.670323i
$225$	−1.31576	+	4.04949i	−0.0877174	+	0.269966i
$226$	−6.42000	−	7.13014i	−0.427052	−	0.474290i
$227$	25.7423	−	11.4612i	1.70858	−	0.760707i	0.710184	−	0.704016i	$-0.248612\pi$
$227$	25.7423	−	11.4612i	1.70858	−	0.760707i	0.998392	−	0.0566911i	$-0.0180550\pi$
$228$	−3.92819	−	0.834964i	−0.260151	−	0.0552968i
$229$	2.43770	−	23.1931i	0.161088	−	1.53265i	−0.553351	−	0.832948i	$-0.686651\pi$
$229$	2.43770	−	23.1931i	0.161088	−	1.53265i	0.714439	−	0.699698i	$-0.246682\pi$
$230$	−0.467237	−	4.44546i	−0.0308087	−	0.293125i
$231$	18.6713	−	3.96871i	1.22848	−	0.261122i
$232$	−3.17330	+	2.30554i	−0.208338	+	0.151366i
$233$	1.08785	−	0.790370i	0.0712675	−	0.0517789i	−0.551581	−	0.834121i	$-0.685975\pi$
$233$	1.08785	−	0.790370i	0.0712675	−	0.0517789i	0.622849	+	0.782342i	$0.285975\pi$
$234$	−4.58652	+	0.974894i	−0.299830	+	0.0637308i
$235$	−0.512411	−	4.87526i	−0.0334260	−	0.318027i
$236$	−0.600423	+	5.71265i	−0.0390842	+	0.371862i
$237$	−4.45142	−	0.946179i	−0.289151	−	0.0614609i
$238$	−8.11790	+	3.61432i	−0.526205	+	0.234282i
$239$	−4.99797	−	5.55081i	−0.323292	−	0.359052i	0.559488	−	0.828838i	$-0.310998\pi$
$239$	−4.99797	−	5.55081i	−0.323292	−	0.359052i	−0.882780	+	0.469786i	$0.844331\pi$
$240$	0.575028	−	1.76975i	0.0371179	−	0.114237i
$241$	6.80665	−	7.55955i	0.438455	−	0.486954i	−0.482900	−	0.875675i	$-0.660417\pi$
$241$	6.80665	−	7.55955i	0.438455	−	0.486954i	0.921355	+	0.388722i	$0.127083\pi$
$242$	9.22527	+	15.9786i	0.593023	+	1.02715i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	0.426314	+	1.31206i	0.0272920	+	0.0839960i
$245$	−5.07590	−	2.25994i	−0.324287	−	0.144382i
$246$	3.50596	+	2.54723i	0.223532	+	0.162405i
$247$	23.9673			1.52500
$248$	16.9714	+	2.41976i	1.07768	+	0.153655i
$249$	−8.49908			−0.538607
$250$	7.39832	+	5.37520i	0.467911	+	0.339957i
$251$	−26.9950	−	12.0190i	−1.70391	−	0.758630i	−0.998771	−	0.0495616i	$-0.984218\pi$
$251$	−26.9950	−	12.0190i	−1.70391	−	0.758630i	−0.705140	−	0.709068i	$-0.749116\pi$
$252$	0.776532	+	2.38992i	0.0489169	+	0.150551i
$253$	−11.7766	+	20.3977i	−0.740390	+	1.28239i
$254$	8.38292	+	14.5196i	0.525991	+	0.911043i
$255$	1.21807	−	1.35280i	0.0762782	−	0.0847156i
$256$	−4.41715	+	13.5946i	−0.276072	+	0.849662i
$257$	16.3528	+	18.1616i	1.02006	+	1.13289i	0.991075	+	0.133309i	$0.0425602\pi$
$257$	16.3528	+	18.1616i	1.02006	+	1.13289i	0.0289828	+	0.999580i	$0.490773\pi$
$258$	−8.15933	+	3.63277i	−0.507977	+	0.226166i
$259$	8.67649	+	1.84424i	0.539131	+	0.114596i
$260$	0.252311	−	2.40058i	0.0156477	−	0.148878i
$261$	−0.133163	−	1.26696i	−0.00824256	−	0.0784227i
$262$	3.01528	−	0.640918i	0.186285	−	0.0395961i
$263$	−0.0821009	+	0.0596498i	−0.00506256	+	0.00367816i	−0.590314	−	0.807174i	$-0.700996\pi$
$263$	−0.0821009	+	0.0596498i	−0.00506256	+	0.00367816i	0.585251	+	0.810852i	$0.300996\pi$
$264$	−12.9651	+	9.41969i	−0.797946	+	0.579742i
$265$	11.3414	−	2.41069i	0.696698	−	0.148088i
$266$	2.57628	+	24.5116i	0.157962	+	1.50290i
$267$	0.364986	−	3.47261i	0.0223368	−	0.212521i
$268$	−5.51747	−	1.17277i	−0.337033	−	0.0716386i
$269$	−3.11464	+	1.38673i	−0.189903	+	0.0845503i	−0.499485	−	0.866322i	$-0.666477\pi$
$269$	−3.11464	+	1.38673i	−0.189903	+	0.0845503i	0.309582	+	0.950873i	$0.399811\pi$
$270$	0.660959	+	0.734069i	0.0402247	+	0.0446740i
$271$	4.19601	−	12.9140i	0.254889	−	0.784469i	−0.738962	−	0.673747i	$-0.764684\pi$
$271$	4.19601	−	12.9140i	0.254889	−	0.784469i	0.993851	−	0.110722i	$-0.0353163\pi$
$272$	3.05428	−	3.39212i	0.185193	−	0.205678i
$273$	−7.49856	−	12.9879i	−0.453833	−	0.786062i
$274$	3.07798	−	5.33121i	0.185947	−	0.322070i
$275$	−6.84839	−	21.0772i	−0.412973	−	1.27100i
$276$	−2.83262	−	1.26116i	−0.170504	−	0.0759131i
$277$	−0.153293	−	0.111374i	−0.00921050	−	0.00669182i	0.583170	−	0.812350i	$-0.301812\pi$
$277$	−0.153293	−	0.111374i	−0.00921050	−	0.00669182i	−0.592381	+	0.805658i	$0.701812\pi$
$278$	−2.03927			−0.122307
$279$	−3.43662	+	4.38060i	−0.205745	+	0.262260i
$280$	9.72745			0.581326
$281$	14.9423	+	10.8562i	0.891382	+	0.647627i	0.936238	−	0.351367i	$-0.114283\pi$
$281$	14.9423	+	10.8562i	0.891382	+	0.647627i	−0.0448563	+	0.998993i	$0.514283\pi$
$282$	5.96086	+	2.65395i	0.354964	+	0.158040i
$283$	1.76031	+	5.41768i	0.104640	+	0.322048i	0.989646	−	0.143532i	$-0.0458460\pi$
$283$	1.76031	+	5.41768i	0.104640	+	0.322048i	−0.885006	+	0.465579i	$0.845846\pi$
$284$	−0.0961832	+	0.166594i	−0.00570743	+	0.00988555i
$285$	−2.52449	−	4.37255i	−0.149538	−	0.259007i
$286$	16.3306	−	18.1369i	0.965646	−	1.07246i
$287$	−4.28313	+	13.1821i	−0.252825	+	0.778115i
$288$	−2.46313	−	2.73558i	−0.145141	−	0.161196i
$289$	−11.4510	+	5.09832i	−0.673589	+	0.299901i
$290$	−1.23088	−	0.261632i	−0.0722798	−	0.0153635i
$291$	1.85762	−	17.6741i	0.108896	−	1.03607i
$292$	0.184995	+	1.76011i	0.0108260	+	0.103002i
$293$	−15.1667	+	3.22378i	−0.886049	+	0.188335i	−0.628388	−	0.777900i	$-0.716285\pi$
$293$	−15.1667	+	3.22378i	−0.886049	+	0.188335i	−0.257661	+	0.966235i	$0.582952\pi$
$294$	5.98323	−	4.34707i	0.348949	−	0.253526i
$295$	−5.84246	+	4.24480i	−0.340161	+	0.247142i
$296$	−7.28437	+	1.54834i	−0.423395	+	0.0899955i
$297$	−0.544059	−	5.17638i	−0.0315695	−	0.300364i
$298$	−0.511905	+	4.87045i	−0.0296539	+	0.282138i
$299$	18.1006	+	3.84740i	1.04678	+	0.222501i
$300$	2.66528	−	1.18666i	0.153880	−	0.0685119i
$301$	−19.1145	−	21.2289i	−1.10174	−	1.22361i
$302$	−8.18677	+	25.1963i	−0.471096	+	1.44988i
$303$	1.17754	−	1.30779i	0.0676480	−	0.0751307i
$304$	−6.33013	−	10.9641i	−0.363058	−	0.628835i
$305$	−0.867227	+	1.50208i	−0.0496573	+	0.0860089i
$306$	0.748751	+	2.30442i	0.0428033	+	0.131735i
$307$	12.5746	+	5.59855i	0.717668	+	0.319526i	0.732880	−	0.680358i	$-0.238176\pi$
$307$	12.5746	+	5.59855i	0.717668	+	0.319526i	−0.0152123	+	0.999884i	$0.504842\pi$
$308$	−10.5815	−	7.68789i	−0.602936	−	0.438058i
$309$	10.4786			0.596109
$310$	3.06632	+	4.56565i	0.174155	+	0.259312i
$311$	19.6781			1.11584			0.557920	−	0.829895i	$-0.311600\pi$
$311$	19.6781			1.11584			0.557920	+	0.829895i	$0.311600\pi$
$312$	10.1862	+	7.40073i	0.576681	+	0.418984i
$313$	7.51592	+	3.34630i	0.424825	+	0.189144i	0.608002	−	0.793936i	$-0.291971\pi$
$313$	7.51592	+	3.34630i	0.424825	+	0.189144i	−0.183177	+	0.983080i	$0.558638\pi$
$314$	−2.94348	−	9.05910i	−0.166110	−	0.511235i
$315$	−1.57966	+	2.73605i	−0.0890036	+	0.154159i
$316$	1.55913	+	2.70050i	0.0877081	+	0.151915i
$317$	−1.05597	+	1.17277i	−0.0593089	+	0.0658692i	−0.772069	−	0.635539i	$-0.780778\pi$
$317$	−1.05597	+	1.17277i	−0.0593089	+	0.0658692i	0.712760	+	0.701408i	$0.247445\pi$
$318$	−4.76915	+	14.6779i	−0.267441	+	0.823097i
$319$	4.43680	+	4.92757i	0.248413	+	0.275891i
$320$	−6.72168	+	2.99269i	−0.375753	+	0.167296i
$321$	−15.8220	−	3.36307i	−0.883097	−	0.187708i
$322$	−1.98912	+	18.9252i	−0.110850	+	1.05466i
$323$	−1.29458	−	12.3171i	−0.0720326	−	0.685344i
$324$	0.670229	−	0.142462i	0.0372349	−	0.00791453i
$325$	−14.0864	+	10.2344i	−0.781375	+	0.567702i
$326$	21.7688	−	15.8160i	1.20566	−	0.875967i
$327$	−3.21457	+	0.683278i	−0.177766	+	0.0377853i
$328$	−1.21636	−	11.5729i	−0.0671621	−	0.639004i
$329$	−2.18144	+	20.7550i	−0.120266	+	1.14426i
$330$	−5.02898	−	1.06894i	−0.276836	−	0.0588433i
$331$	25.9630	−	11.5595i	1.42706	−	0.635366i	0.459536	−	0.888159i	$-0.348016\pi$
$331$	25.9630	−	11.5595i	1.42706	−	0.635366i	0.967520	+	0.252793i	$0.0813491\pi$
$332$	3.89674	+	4.32777i	0.213861	+	0.237517i
$333$	0.747418	−	2.30032i	0.0409582	−	0.126057i
$334$	−18.4410	+	20.4808i	−1.00905	+	1.12066i
$335$	−3.54586	−	6.14160i	−0.193731	−	0.335552i
$336$	−3.96097	+	6.86059i	−0.216088	+	0.374276i
$337$	1.38552	+	4.26419i	0.0754741	+	0.232285i	0.981675	−	0.190561i	$-0.0610308\pi$
$337$	1.38552	+	4.26419i	0.0754741	+	0.232285i	−0.906201	+	0.422847i	$0.861031\pi$
$338$	−3.89926	−	1.73606i	−0.212092	−	0.0944292i
$339$	−6.76944	−	4.91828i	−0.367665	−	0.267124i
$340$	−1.24732			−0.0676455
$341$	1.06923	−	28.9599i	0.0579023	−	1.56826i
$342$	6.72047			0.363401
$343$	−1.63234	−	1.18596i	−0.0881379	−	0.0640359i
$344$	21.9094	+	9.75471i	1.18128	+	0.525939i
$345$	−1.20464	−	3.70749i	−0.0648554	−	0.199604i
$346$	11.5344	−	19.9782i	0.620093	−	1.07403i
$347$	−8.58966	−	14.8777i	−0.461117	−	0.798678i	0.537900	−	0.843009i	$-0.319218\pi$
$347$	−8.58966	−	14.8777i	−0.461117	−	0.798678i	−0.999017	+	0.0443306i	$0.985884\pi$
$348$	−0.584087	+	0.648694i	−0.0313103	+	0.0347736i
$349$	−2.14285	+	6.59501i	−0.114704	+	0.353023i	−0.991885	−	0.127137i	$-0.959421\pi$
$349$	−2.14285	+	6.59501i	−0.114704	+	0.353023i	0.877181	+	0.480160i	$0.159421\pi$
$350$	−11.9810	−	13.3063i	−0.640412	−	0.711249i
$351$	−3.73576	+	1.66327i	−0.199400	+	0.0887787i
$352$	18.7410	+	3.98352i	0.998898	+	0.212322i
$353$	1.70316	−	16.2045i	0.0906500	−	0.862477i	−0.850837	−	0.525429i	$-0.823905\pi$
$353$	1.70316	−	16.2045i	0.0906500	−	0.862477i	0.941487	−	0.337048i	$-0.109429\pi$
$354$	−1.00477	−	9.55979i	−0.0534031	−	0.508097i
$355$	−0.236564	+	0.0502833i	−0.0125555	+	0.00266876i
$356$	−1.93561	+	1.40630i	−0.102587	+	0.0745340i
$357$	−6.26963	+	4.55515i	−0.331824	+	0.241084i
$358$	−6.65734	+	1.41506i	−0.351851	+	0.0747883i
$359$	−0.943676	−	8.97848i	−0.0498053	−	0.473866i	−0.990789	−	0.135414i	$-0.956763\pi$
$359$	−0.943676	−	8.97848i	−0.0498053	−	0.473866i	0.940984	−	0.338452i	$-0.109903\pi$
$360$	0.277252	−	2.63788i	0.0146125	−	0.139028i
$361$	−15.0156	−	3.19166i	−0.790294	−	0.167982i
$362$	−4.69050	+	2.08835i	−0.246527	+	0.109761i
$363$	10.7669	+	11.9578i	0.565116	+	0.627624i
$364$	−3.17548	+	9.77311i	−0.166440	+	0.512250i
$365$	−1.48885	+	1.65353i	−0.0779299	+	0.0865499i
$366$	−1.15432	−	1.99935i	−0.0603375	−	0.104508i
$367$	6.02734	−	10.4397i	0.314625	−	0.544946i	−0.664733	−	0.747081i	$-0.731455\pi$
$367$	6.02734	−	10.4397i	0.314625	−	0.544946i	0.979358	+	0.202135i	$0.0647880\pi$
$368$	−3.02061	−	9.29647i	−0.157460	−	0.484612i
$369$	3.45263	+	1.53721i	0.179737	+	0.0800240i
$370$	−1.93287	−	1.40431i	−0.100485	−	0.0730067i
$371$	−49.3614			−2.56272
$372$	3.80627	−	0.258520i	0.197346	−	0.0134036i
$373$	12.6279			0.653849			0.326925	−	0.945050i	$-0.393988\pi$
$373$	12.6279			0.653849			0.326925	+	0.945050i	$0.393988\pi$
$374$	−10.2029	−	7.41285i	−0.527580	−	0.383309i
$375$	7.28578	+	3.24384i	0.376236	+	0.167511i
$376$	−5.41425	−	16.6633i	−0.279219	−	0.859347i
$377$	2.60475	−	4.51157i	0.134152	−	0.232358i
$378$	−2.10261	−	3.64182i	−0.108146	−	0.187315i
$379$	−5.10221	+	5.66658i	−0.262083	+	0.291073i	−0.859796	−	0.510637i	$-0.829409\pi$
$379$	−5.10221	+	5.66658i	−0.262083	+	0.291073i	0.597713	+	0.801710i	$0.296076\pi$
$380$	−1.06907	+	3.29025i	−0.0548420	+	0.168786i
$381$	9.78378	+	10.8660i	0.501238	+	0.556681i
$382$	−24.9406	+	11.1043i	−1.27607	+	0.568143i
$383$	29.2621	+	6.21985i	1.49522	+	0.317819i	0.881682	−	0.471844i	$-0.156411\pi$
$383$	29.2621	+	6.21985i	1.49522	+	0.317819i	0.613541	+	0.789663i	$0.289745\pi$
$384$	0.254154	−	2.41812i	0.0129698	−	0.123399i
$385$	−1.71885	−	16.3538i	−0.0876009	−	0.833466i
$386$	−17.4538	+	3.70993i	−0.888377	+	0.188830i
$387$	−6.30162	+	4.57840i	−0.320329	+	0.232733i
$388$	−9.85143	+	7.15748i	−0.500131	+	0.363366i
$389$	−20.3434	+	4.32411i	−1.03145	+	0.219241i	−0.692390	−	0.721524i	$-0.743442\pi$
$389$	−20.3434	+	4.32411i	−1.03145	+	0.219241i	−0.339059	+	0.940765i	$0.610109\pi$
$390$	0.422228	+	4.01723i	0.0213804	+	0.203421i
$391$	0.999538	−	9.50997i	0.0505488	−	0.480940i
$392$	−19.4249	−	4.12890i	−0.981107	−	0.208541i
$393$	2.45598	−	1.09347i	0.123888	−	0.0551584i
$394$	−8.39086	−	9.31899i	−0.422725	−	0.469484i
$395$	−1.21146	+	3.72851i	−0.0609554	+	0.187601i
$396$	−2.38639	+	2.65035i	−0.119921	+	0.133185i
$397$	3.92342	+	6.79556i	0.196911	+	0.341059i	0.947525	−	0.319681i	$-0.103576\pi$
$397$	3.92342	+	6.79556i	0.196911	+	0.341059i	−0.750614	+	0.660740i	$0.770242\pi$
$398$	−2.64182	+	4.57576i	−0.132422	+	0.229362i
$399$	6.64218	+	20.4425i	0.332525	+	1.02341i
$400$	8.40228	+	3.74094i	0.420114	+	0.187047i
$401$	15.7442	+	11.4388i	0.786229	+	0.571229i	0.906842	−	0.421471i	$-0.138486\pi$
$401$	15.7442	+	11.4388i	0.786229	+	0.571229i	−0.120613	+	0.992700i	$0.538486\pi$
$402$	9.43944			0.470797
$403$	−21.8988	+	6.23205i	−1.09085	+	0.310440i
$404$	−1.20582			−0.0599920
$405$	0.696934	+	0.506352i	0.0346309	+	0.0251609i
$406$	4.89402	+	2.17896i	0.242886	+	0.108140i
$407$	3.89023	+	11.9729i	0.192831	+	0.593474i
$408$	3.25314	−	5.63460i	0.161054	−	0.278954i
$409$	−3.67496	−	6.36521i	−0.181715	−	0.314739i	0.760750	−	0.649045i	$-0.224831\pi$
$409$	−3.67496	−	6.36521i	−0.181715	−	0.314739i	−0.942465	+	0.334306i	$0.891498\pi$
$410$	2.49801	−	2.77432i	0.123368	−	0.137014i
$411$	1.65901	−	5.10590i	0.0818327	−	0.251855i
$412$	−4.80435	−	5.33577i	−0.236693	−	0.262874i
$413$	28.0862	−	12.5048i	1.38203	−	0.615320i
$414$	5.07543	+	1.07882i	0.249444	+	0.0530209i
$415$	−0.765315	+	7.28149i	−0.0375679	+	0.357434i
$416$	−1.57348	−	14.9706i	−0.0771460	−	0.733995i
$417$	−1.73960	+	0.369763i	−0.0851886	+	0.0181074i
$418$	−28.2988	+	20.5603i	−1.38414	+	1.00564i
$419$	10.6792	−	7.75892i	0.521715	−	0.379048i	−0.295535	−	0.955332i	$-0.595498\pi$
$419$	10.6792	−	7.75892i	0.521715	−	0.379048i	0.817250	+	0.576284i	$0.195498\pi$
$420$	2.11746	−	0.450081i	0.103322	−	0.0219617i
$421$	1.35716	+	12.9125i	0.0661438	+	0.629316i	0.976504	+	0.215499i	$0.0691379\pi$
$421$	1.35716	+	12.9125i	0.0661438	+	0.629316i	−0.910360	+	0.413817i	$0.864195\pi$
$422$	−1.92059	+	18.2732i	−0.0934929	+	0.889525i
$423$	5.56614	+	1.18312i	0.270635	+	0.0575252i
$424$	37.8587	−	16.8558i	1.83858	−	0.818589i
$425$	6.02048	+	6.68642i	0.292036	+	0.324339i
$426$	0.0994770	−	0.306159i	0.00481968	−	0.0148334i
$427$	4.94081	−	5.48732i	0.239102	−	0.265550i
$428$	5.54173	+	9.59855i	0.267870	+	0.463964i
$429$	10.6422	−	18.4328i	0.513809	−	0.889944i
$430$	2.37761	+	7.31753i	0.114659	+	0.352883i
$431$	−1.87956	−	0.836836i	−0.0905354	−	0.0403090i	0.360969	−	0.932578i	$-0.382446\pi$
$431$	−1.87956	−	0.836836i	−0.0905354	−	0.0403090i	−0.451505	+	0.892269i	$0.649113\pi$
$432$	1.74755	+	1.26967i	0.0840792	+	0.0610871i
$433$	−5.50477			−0.264542			−0.132271	−	0.991214i	$-0.542227\pi$
$433$	−5.50477			−0.264542			−0.132271	+	0.991214i	$0.542227\pi$
$434$	−8.72751	−	21.7262i	−0.418934	−	1.04289i
$435$	−1.09744			−0.0526183
$436$	1.82177	+	1.32360i	0.0872472	+	0.0633888i
$437$	−24.2292	−	10.7875i	−1.15904	−	0.516038i
$438$	−0.915203	−	2.81671i	−0.0437301	−	0.134587i
$439$	2.77239	−	4.80193i	0.132319	−	0.229183i	−0.792251	−	0.610195i	$-0.791091\pi$
$439$	2.77239	−	4.80193i	0.132319	−	0.229183i	0.924570	+	0.381012i	$0.124424\pi$
$440$	6.90275	+	11.9559i	0.329076	+	0.569976i
$441$	4.31578	−	4.79316i	0.205513	−	0.228246i
$442$	−3.06187	+	9.42347i	−0.145638	+	0.448229i
$443$	−13.0344	−	14.4762i	−0.619282	−	0.687783i	0.349148	−	0.937068i	$-0.386471\pi$
$443$	−13.0344	−	14.4762i	−0.619282	−	0.687783i	−0.968430	+	0.249285i	$0.919804\pi$
$444$	−1.51401	+	0.674082i	−0.0718519	+	0.0319905i
$445$	−2.94226	−	0.625396i	−0.139476	−	0.0296466i
$446$	0.168296	−	1.60123i	0.00796907	−	0.0758206i
$447$	0.446437	+	4.24756i	0.0211157	+	0.200903i
$448$	30.6391	−	6.51255i	1.44756	−	0.307689i
$449$	−12.2822	+	8.92352i	−0.579631	+	0.421127i	−0.838591	−	0.544761i	$-0.816620\pi$
$449$	−12.2822	+	8.92352i	−0.579631	+	0.421127i	0.258960	+	0.965888i	$0.416620\pi$
$450$	−3.94986	+	2.86974i	−0.186198	+	0.135281i
$451$	−19.2414	+	4.08988i	−0.906040	+	0.192585i
$452$	0.599305	+	5.70201i	0.0281889	+	0.268200i
$453$	−2.41510	+	22.9781i	−0.113471	+	1.07961i
$454$	31.6046	+	6.71778i	1.48328	+	0.315281i
$455$	−11.8024	+	5.25479i	−0.553307	+	0.246348i
$456$	−12.0750	−	13.4107i	−0.565464	−	0.628011i
$457$	3.10706	−	9.56254i	0.145342	−	0.447317i	−0.851713	−	0.524009i	$-0.824436\pi$
$457$	3.10706	−	9.56254i	0.145342	−	0.447317i	0.997055	+	0.0766921i	$0.0244359\pi$
$458$	17.8931	−	19.8723i	0.836090	−	0.928572i
$459$	1.05656	+	1.83002i	0.0493162	+	0.0854181i
$460$	−1.33556	+	2.31325i	−0.0622706	+	0.107856i
$461$	5.47115	+	16.8385i	0.254817	+	0.784246i	0.993866	+	0.110594i	$0.0352752\pi$
$461$	5.47115	+	16.8385i	0.254817	+	0.784246i	−0.739049	+	0.673652i	$0.764725\pi$
$462$	19.9954	+	8.90252i	0.930269	+	0.414183i
$463$	25.0478	+	18.1983i	1.16407	+	0.845746i	0.990287	−	0.139038i	$-0.0444010\pi$
$463$	25.0478	+	18.1983i	1.16407	+	0.845746i	0.173783	+	0.984784i	$0.444401\pi$
$464$	−2.75182			−0.127750
$465$	3.44357	+	3.33874i	0.159692	+	0.154831i
$466$	1.54185			0.0714247
$467$	21.9955	+	15.9807i	1.01783	+	0.739499i	0.965837	−	0.259149i	$-0.0834420\pi$
$467$	21.9955	+	15.9807i	1.01783	+	0.739499i	0.0519951	+	0.998647i	$0.483442\pi$
$468$	2.55975	+	1.13968i	0.118325	+	0.0526815i
$469$	9.32949	+	28.7132i	0.430796	+	1.32585i
$470$	2.81050	−	4.86792i	0.129639	−	0.224541i
$471$	−4.15355	−	7.19416i	−0.191385	−	0.331489i
$472$	−17.2712	+	19.1816i	−0.794970	+	0.882903i
$473$	12.5282	−	38.5578i	0.576047	−	1.77289i
$474$	−3.49168	−	3.87791i	−0.160378	−	0.178118i
$475$	22.7979	−	10.1503i	1.04604	−	0.465726i
$476$	5.19406	+	1.10403i	0.238069	+	0.0506032i
$477$	−1.40690	+	13.3858i	−0.0644176	+	0.612892i
$478$	−0.895256	−	8.51779i	−0.0409481	−	0.389595i
$479$	4.31583	−	0.917358i	0.197195	−	0.0419151i	−0.108255	−	0.994123i	$-0.534526\pi$
$479$	4.31583	−	0.917358i	0.197195	−	0.0419151i	0.305450	+	0.952208i	$0.401193\pi$
$480$	−2.56548	+	1.86393i	−0.117098	+	0.0850763i
$481$	8.00180	−	5.81365i	0.364851	−	0.265080i
$482$	11.4092	−	2.42511i	0.519676	−	0.110461i
$483$	1.73473	+	16.5049i	0.0789330	+	0.750997i
$484$	1.15248	−	10.9651i	0.0523854	−	0.498414i
$485$	−14.9748	−	3.18300i	−0.679971	−	0.144532i
$486$	−1.04751	+	0.466383i	−0.0475162	+	0.0211556i
$487$	4.30267	+	4.77860i	0.194973	+	0.216539i	0.832702	−	0.553722i	$-0.186793\pi$
$487$	4.30267	+	4.77860i	0.194973	+	0.216539i	−0.637729	+	0.770261i	$0.720126\pi$
$488$	−1.91566	+	5.89578i	−0.0867176	+	0.266889i
$489$	15.7021	−	17.4390i	0.710076	−	0.788619i
$490$	−3.18553	−	5.51751i	−0.143908	−	0.249256i
$491$	13.2329	−	22.9201i	0.597193	−	1.03437i	−0.396040	−	0.918233i	$-0.629616\pi$
$491$	13.2329	−	22.9201i	0.597193	−	1.03437i	0.993233	−	0.116136i	$-0.0370507\pi$
$492$	−0.800241	−	2.46289i	−0.0360777	−	0.111036i
$493$	−2.45925	−	1.09493i	−0.110759	−	0.0493132i
$494$	22.2334	+	16.1535i	1.00033	+	0.726781i
$495$	−4.48379			−0.201532
$496$	8.63471	+	8.37185i	0.387710	+	0.375907i
$497$	1.02960			0.0461839
$498$	−7.88422	−	5.72822i	−0.353300	−	0.256688i
$499$	−27.2372	−	12.1268i	−1.21930	−	0.542869i	−0.306736	−	0.951795i	$-0.599237\pi$
$499$	−27.2372	−	12.1268i	−1.21930	−	0.542869i	−0.912568	+	0.408926i	$0.865904\pi$
$500$	−1.68868	−	5.19722i	−0.0755200	−	0.232427i
$501$	−12.0175	+	20.8149i	−0.536902	+	0.929942i
$502$	−16.9415	−	29.3436i	−0.756138	−	1.30967i
$503$	−8.37955	+	9.30643i	−0.373626	+	0.414953i	−0.900408	−	0.435047i	$-0.856732\pi$
$503$	−8.37955	+	9.30643i	−0.373626	+	0.414953i	0.526782	+	0.850000i	$0.323398\pi$
$504$	−3.48937	+	10.7392i	−0.155429	+	0.478361i
$505$	−1.01440	−	1.12661i	−0.0451403	−	0.0501334i
$506$	−24.6723	+	10.9848i	−1.09682	+	0.488335i
$507$	−3.64105	−	0.773929i	−0.161705	−	0.0343714i
$508$	1.04725	−	9.96389i	0.0464641	−	0.442076i
$509$	−1.88439	−	17.9288i	−0.0835241	−	0.794679i	−0.953461	−	0.301516i	$-0.902507\pi$
$509$	−1.88439	−	17.9288i	−0.0835241	−	0.794679i	0.869937	−	0.493163i	$-0.164159\pi$
$510$	2.04171	−	0.433979i	0.0904084	−	0.0192169i
$511$	7.66340	−	5.56779i	0.339009	−	0.246304i
$512$	−17.1942	+	12.4924i	−0.759886	+	0.552089i
$513$	5.73290	−	1.21857i	0.253114	−	0.0538010i
$514$	2.92917	+	27.8692i	0.129200	+	1.22926i
$515$	0.943569	−	8.97746i	0.0415786	−	0.395594i
$516$	5.22057	+	1.10967i	0.229823	+	0.0488503i
$517$	−27.0577	+	12.0469i	−1.19000	+	0.529821i
$518$	6.80581	+	7.55862i	0.299030	+	0.332107i
$519$	6.21696	−	19.1338i	0.272894	−	0.839882i
$520$	7.25773	−	8.06052i	0.318272	−	0.353477i
$521$	−1.68449	−	2.91763i	−0.0737990	−	0.127824i	0.826764	−	0.562548i	$-0.190179\pi$
$521$	−1.68449	−	2.91763i	−0.0737990	−	0.127824i	−0.900563	+	0.434725i	$0.856846\pi$
$522$	0.730377	−	1.26505i	0.0319677	−	0.0553697i
$523$	4.41932	+	13.6013i	0.193243	+	0.594741i	0.999993	+	0.00384769i	$0.00122476\pi$
$523$	4.41932	+	13.6013i	0.193243	+	0.594741i	−0.806749	+	0.590894i	$0.798775\pi$
$524$	−1.68284	−	0.749249i	−0.0735153	−	0.0327311i
$525$	−12.6331	−	9.17850i	−0.551354	−	0.400582i
$526$	−0.116364			−0.00507373
$527$	4.38559	+	10.9175i	0.191039	+	0.475572i
$528$	−11.2430			−0.489291
$529$	2.04069	+	1.48265i	0.0887258	+	0.0644631i
$530$	12.1457	+	5.40762i	0.527576	+	0.234892i
$531$	−2.59052	−	7.97280i	−0.112419	−	0.345990i
$532$	7.36406	−	12.7549i	0.319272	−	0.552996i
$533$	7.72750	+	13.3844i	0.334715	+	0.579744i
$534$	2.67906	−	2.97540i	0.115934	−	0.128758i
$535$	−4.30599	+	13.2525i	−0.186164	+	0.572954i
$536$	−16.9603	−	18.8364i	−0.732575	−	0.813607i
$537$	−5.42247	+	2.41424i	−0.233997	+	0.104182i
$538$	−3.82395	−	0.812805i	−0.164862	−	0.0350425i
$539$	−3.50909	+	33.3868i	−0.151147	+	1.43807i
$540$	−0.0617003	−	0.587039i	−0.00265516	−	0.0252622i
$541$	4.26987	−	0.907589i	0.183576	−	0.0390203i	−0.115206	−	0.993342i	$-0.536753\pi$
$541$	4.26987	−	0.907589i	0.183576	−	0.0390203i	0.298782	+	0.954321i	$0.403420\pi$
$542$	12.5963	−	9.15171i	0.541055	−	0.393100i
$543$	−3.62258	+	2.63196i	−0.155460	+	0.112948i
$544$	−7.60863	+	1.61726i	−0.326217	+	0.0693396i
$545$	0.295929	+	2.81557i	0.0126762	+	0.120606i
$546$	1.79751	−	17.1022i	0.0769264	−	0.731906i
$547$	8.48369	+	1.80326i	0.362737	+	0.0771020i	0.385675	−	0.922635i	$-0.373969\pi$
$547$	8.48369	+	1.80326i	0.362737	+	0.0771020i	−0.0229381	+	0.999737i	$0.507302\pi$
$548$	−3.36058	+	1.49623i	−0.143557	+	0.0639157i
$549$	−1.34722	−	1.49624i	−0.0574981	−	0.0638581i
$550$	7.85268	−	24.1681i	0.334839	−	1.03053i
$551$	−4.99607	+	5.54870i	−0.212840	+	0.236382i
$552$	−6.96652	−	12.0664i	−0.296515	−	0.513578i
$553$	8.34493	−	14.4538i	0.354863	−	0.614640i
$554$	−0.0671394	−	0.206634i	−0.00285248	−	0.00877903i
$555$	−1.90347	−	0.847478i	−0.0807977	−	0.0359734i
$556$	0.985874	+	0.716279i	0.0418104	+	0.0303770i
$557$	−3.13969			−0.133033			−0.0665164	−	0.997785i	$-0.521188\pi$
$557$	−3.13969			−0.133033			−0.0665164	+	0.997785i	$0.521188\pi$
$558$	−6.14045	+	1.74748i	−0.259946	+	0.0739765i
$559$	−31.8525			−1.34722
$560$	5.52107	+	4.01129i	0.233308	+	0.169508i
$561$	−10.0477	−	4.47353i	−0.424215	−	0.188873i
$562$	6.54442	+	20.1416i	0.276060	+	0.849624i
$563$	−0.503261	+	0.871673i	−0.0212099	+	0.0367366i	−0.876436	−	0.481519i	$-0.840085\pi$
$563$	−0.503261	+	0.871673i	−0.0212099	+	0.0367366i	0.855226	+	0.518256i	$0.173418\pi$
$564$	−1.94957	−	3.37675i	−0.0820916	−	0.142187i
$565$	−4.82325	+	5.35676i	−0.202916	+	0.225361i
$566$	−2.01845	+	6.21216i	−0.0848419	+	0.261117i
$567$	−2.45397	−	2.72541i	−0.103057	−	0.114456i
$568$	−0.789673	+	0.351585i	−0.0331339	+	0.0147522i
$569$	−41.3189	−	8.78260i	−1.73218	−	0.368186i	−0.769461	−	0.638694i	$-0.779475\pi$
$569$	−41.3189	−	8.78260i	−1.73218	−	0.368186i	−0.962718	+	0.270508i	$0.912808\pi$
$570$	0.605157	−	5.75769i	0.0253472	−	0.241163i
$571$	0.0232654	+	0.221356i	0.000973627	+	0.00926344i	0.994998	−	0.0998956i	$-0.0318509\pi$
$571$	0.0232654	+	0.221356i	0.000973627	+	0.00926344i	−0.994024	+	0.109159i	$0.965184\pi$
$572$	−14.2654	+	3.03220i	−0.596466	+	0.126783i
$573$	−19.2621	+	13.9947i	−0.804687	+	0.584639i
$574$	−12.8578	+	9.34172i	−0.536673	+	0.389916i
$575$	18.8468	−	4.00601i	0.785967	−	0.167062i
$576$	−0.892788	−	8.49431i	−0.0371995	−	0.353930i
$577$	−1.32599	+	12.6160i	−0.0552018	+	0.525210i	0.931624	+	0.363424i	$0.118392\pi$
$577$	−1.32599	+	12.6160i	−0.0552018	+	0.525210i	−0.986826	+	0.161786i	$0.948274\pi$
$578$	−14.0588	−	2.98829i	−0.584768	−	0.124296i
$579$	−14.2163	+	6.32951i	−0.590810	+	0.263046i
$580$	0.503166	+	0.558823i	0.0208928	+	0.0232038i
$581$	9.63191	−	29.6440i	0.399599	−	1.22984i
$582$	13.6353	−	15.1435i	0.565200	−	0.627718i
$583$	−35.0276	−	60.6696i	−1.45070	−	2.51268i
$584$	−3.97633	+	6.88720i	−0.164542	+	0.284994i
$585$	1.08859	+	3.35035i	0.0450078	+	0.138520i
$586$	−16.2423	−	7.23152i	−0.670962	−	0.298732i
$587$	28.1533	+	20.4546i	1.16201	+	0.844250i	0.990031	−	0.140851i	$-0.0449838\pi$
$587$	28.1533	+	20.4546i	1.16201	+	0.844250i	0.171979	+	0.985101i	$0.444984\pi$
$588$	−4.41944			−0.182255
$589$	32.5575	−	2.21129i	1.34151	−	0.0911145i
$590$	−8.28072			−0.340912
$591$	−8.84756	−	6.42813i	−0.363940	−	0.264418i
$592$	−4.77292	−	2.12504i	−0.196166	−	0.0873386i
$593$	8.88251	+	27.3375i	0.364761	+	1.12262i	0.950131	+	0.311852i	$0.100949\pi$
$593$	8.88251	+	27.3375i	0.364761	+	1.12262i	−0.585370	+	0.810766i	$0.699051\pi$
$594$	2.98408	−	5.16858i	0.122438	−	0.212070i
$595$	3.33801	+	5.78161i	0.136845	+	0.237023i
$596$	1.95819	−	2.17479i	0.0802106	−	0.0890829i
$597$	−1.42392	+	4.38238i	−0.0582772	+	0.179359i
$598$	14.1981	+	15.7685i	0.580601	+	0.644823i
$599$	−40.3461	+	17.9633i	−1.64850	+	0.733959i	−0.999637	−	0.0269472i	$-0.991421\pi$
$599$	−40.3461	+	17.9633i	−1.64850	+	0.733959i	−0.648862	+	0.760906i	$0.724755\pi$
$600$	12.8235	+	2.72571i	0.523516	+	0.111277i
$601$	1.60462	−	15.2669i	0.0654538	−	0.622752i	−0.911794	−	0.410649i	$-0.865302\pi$
$601$	1.60462	−	15.2669i	0.0654538	−	0.622752i	0.977247	−	0.212103i	$-0.0680312\pi$
$602$	−3.42387	−	32.5759i	−0.139546	−	1.32770i
$603$	8.05233	−	1.71157i	0.327916	−	0.0697007i
$604$	12.8079	−	9.30546i	0.521145	−	0.378634i
$605$	11.2143	−	8.14765i	0.455925	−	0.331249i
$606$	1.97378	−	0.419540i	0.0801794	−	0.0170427i
$607$	1.76455	+	16.7886i	0.0716210	+	0.681429i	0.970149	+	0.242511i	$0.0779712\pi$
$607$	1.76455	+	16.7886i	0.0716210	+	0.681429i	−0.898528	+	0.438917i	$0.855362\pi$
$608$	−2.25518	+	21.4566i	−0.0914596	+	0.870180i
$609$	4.56994	+	0.971371i	0.185183	+	0.0393619i
$610$	−1.81686	+	0.808920i	−0.0735627	+	0.0327522i
$611$	15.5708	+	17.2931i	0.629925	+	0.699603i
$612$	0.447432	−	1.37705i	0.0180864	−	0.0556641i
$613$	20.5721	−	22.8476i	0.830898	−	0.922805i	−0.167107	−	0.985939i	$-0.553443\pi$
$613$	20.5721	−	22.8476i	0.830898	−	0.922805i	0.998005	+	0.0631334i	$0.0201094\pi$
$614$	7.89154	+	13.6686i	0.318477	+	0.551618i
$615$	1.62789	−	2.81958i	0.0656427	−	0.113697i
$616$	−18.1618	−	55.8963i	−0.731760	−	2.25212i
$617$	−8.03857	−	3.57900i	−0.323621	−	0.144085i	0.238495	−	0.971144i	$-0.423346\pi$
$617$	−8.03857	−	3.57900i	−0.323621	−	0.144085i	−0.562116	+	0.827058i	$0.690013\pi$
$618$	9.72057	+	7.06241i	0.391019	+	0.284092i
$619$	−40.8628			−1.64241			−0.821206	−	0.570631i	$-0.806699\pi$
$619$	−40.8628			−1.64241			−0.821206	+	0.570631i	$0.806699\pi$
$620$	0.121259	−	3.28426i	0.00486988	−	0.131899i
$621$	4.52521			0.181591
$622$	18.2545	+	13.2626i	0.731938	+	0.531784i
$623$	11.6985	+	5.20851i	0.468691	+	0.208675i
$624$	2.72963	+	8.40095i	0.109273	+	0.336307i
$625$	−7.20954	+	12.4873i	−0.288382	+	0.499491i
$626$	4.71684	+	8.16981i	0.188523	+	0.326531i
$627$	−20.4123	+	22.6702i	−0.815189	+	0.905360i
$628$	−1.75894	+	5.41345i	−0.0701892	+	0.216020i
$629$	−3.41993	−	3.79822i	−0.136362	−	0.151445i
$630$	−3.30942	+	1.47345i	−0.131851	+	0.0587037i
$631$	−38.1551	−	8.11012i	−1.51893	−	0.322859i	−0.628440	−	0.777858i	$-0.716306\pi$
$631$	−38.1551	−	8.11012i	−1.51893	−	0.322859i	−0.890492	+	0.455000i	$0.849639\pi$
$632$	−1.46466	+	13.9353i	−0.0582609	+	0.554315i
$633$	1.67496	+	15.9362i	0.0665738	+	0.633408i
$634$	−1.77000	+	0.376225i	−0.0702956	+	0.0149418i
$635$	10.1903	−	7.40370i	0.404390	−	0.293807i
$636$	7.46114	−	5.42084i	0.295853	−	0.214950i
$637$	25.7990	−	5.48374i	1.02219	−	0.217274i
$638$	0.794737	+	7.56141i	0.0314639	+	0.299359i
$639$	0.0293458	−	0.279206i	0.00116090	−	0.0110452i
$640$	−2.04881	−	0.435488i	−0.0809863	−	0.0172142i
$641$	24.2438	−	10.7940i	0.957572	−	0.426338i	0.132385	−	0.991198i	$-0.457736\pi$
$641$	24.2438	−	10.7940i	0.957572	−	0.426338i	0.825187	+	0.564860i	$0.191070\pi$
$642$	−12.4107	−	13.7835i	−0.489812	−	0.543991i
$643$	−4.97773	+	15.3199i	−0.196303	+	0.604157i	0.803656	+	0.595094i	$0.202885\pi$
$643$	−4.97773	+	15.3199i	−0.196303	+	0.604157i	−0.999959	+	0.00906369i	$0.997115\pi$
$644$	7.60899	−	8.45064i	0.299836	−	0.333002i
$645$	3.35505	+	5.81111i	0.132105	+	0.228812i
$646$	7.10060	−	12.2986i	0.279369	−	0.483882i
$647$	−2.03052	−	6.24931i	−0.0798281	−	0.245686i	0.903176	−	0.429271i	$-0.141230\pi$
$647$	−2.03052	−	6.24931i	−0.0798281	−	0.245686i	−0.983004	+	0.183586i	$0.941230\pi$
$648$	2.81279	+	1.25233i	0.110497	+	0.0491963i
$649$	35.2999	+	25.6469i	1.38564	+	1.00673i
$650$	−19.9652			−0.783099
$651$	−11.3844	−	16.9511i	−0.446192	−	0.664365i
$652$	−16.0793			−0.629714
$653$	34.0114	+	24.7107i	1.33097	+	0.967005i	0.999725	+	0.0234593i	$0.00746801\pi$
$653$	34.0114	+	24.7107i	1.33097	+	0.967005i	0.331243	+	0.943545i	$0.392532\pi$
$654$	−3.44253	−	1.53271i	−0.134614	−	0.0599339i
$655$	−0.715667	−	2.20260i	−0.0279634	−	0.0860625i
$656$	4.08190	−	7.07006i	0.159372	−	0.276040i
$657$	−1.29144	−	2.23685i	−0.0503840	−	0.0872677i
$658$	−16.0121	+	17.7832i	−0.624217	+	0.693263i
$659$	13.7108	−	42.1975i	0.534097	−	1.64378i	−0.211495	−	0.977379i	$-0.567833\pi$
$659$	13.7108	−	42.1975i	0.534097	−	1.64378i	0.745592	−	0.666403i	$-0.232167\pi$
$660$	2.05577	+	2.28317i	0.0800209	+	0.0888722i
$661$	−20.8414	+	9.27919i	−0.810636	+	0.360919i	−0.769830	−	0.638249i	$-0.779659\pi$
$661$	−20.8414	+	9.27919i	−0.810636	+	0.360919i	−0.0408060	+	0.999167i	$0.512993\pi$
$662$	31.8756	+	6.77538i	1.23888	+	0.263332i
$663$	−0.903253	+	8.59388i	−0.0350794	+	0.333759i
$664$	2.73535	+	26.0251i	0.106152	+	1.00997i
$665$	18.1120	−	3.84983i	0.702354	−	0.149290i
$666$	2.24372	−	1.63016i	0.0869423	−	0.0631673i
$667$	−4.66385	+	3.38848i	−0.180585	+	0.131203i
$668$	16.1089	−	3.42406i	0.623274	−	0.132481i
$669$	−0.146773	−	1.39645i	−0.00567456	−	0.0539899i
$670$	0.849993	−	8.08714i	0.0328381	−	0.312433i
$671$	10.2505	+	2.17881i	0.395716	+	0.0841119i
$672$	12.3329	−	5.49096i	0.475752	−	0.211818i
$673$	−2.54477	−	2.82626i	−0.0980938	−	0.108944i	0.692099	−	0.721803i	$-0.256686\pi$
$673$	−2.54477	−	2.82626i	−0.0980938	−	0.108944i	−0.790193	+	0.612859i	$0.790020\pi$
$674$	−1.58870	+	4.88952i	−0.0611945	+	0.188337i
$675$	−2.84908	+	3.16423i	−0.109661	+	0.121791i
$676$	1.27530	+	2.20888i	0.0490498	+	0.0849568i
$677$	−1.30392	+	2.25845i	−0.0501136	+	0.0867993i	−0.889994	−	0.455972i	$-0.849292\pi$
$677$	−1.30392	+	2.25845i	−0.0501136	+	0.0867993i	0.839880	+	0.542771i	$0.182625\pi$
$678$	−2.96488	−	9.12495i	−0.113865	−	0.350442i
$679$	59.5404	+	26.5091i	2.28495	+	1.01733i
$680$	−4.53444	−	3.29447i	−0.173888	−	0.126337i
$681$	28.1784			1.07980
$682$	20.5103	−	26.1442i	0.785380	−	1.00111i
$683$	6.30337			0.241192			0.120596	−	0.992702i	$-0.461519\pi$
$683$	6.30337			0.241192			0.120596	+	0.992702i	$0.461519\pi$
$684$	−3.24897	−	2.36052i	−0.124228	−	0.0902567i
$685$	−4.22503	−	1.88111i	−0.161430	−	0.0718733i
$686$	−0.714931	−	2.20033i	−0.0272962	−	0.0840090i
$687$	11.6604	−	20.1965i	0.444874	−	0.770544i
$688$	8.41273	+	14.5713i	0.320733	+	0.555525i
$689$	−36.8289	+	40.9027i	−1.40307	+	1.55827i
$690$	1.38129	−	4.25118i	0.0525848	−	0.161840i
$691$	−19.3820	−	21.5259i	−0.737325	−	0.818882i	0.251517	−	0.967853i	$-0.419071\pi$
$691$	−19.3820	−	21.5259i	−0.737325	−	0.818882i	−0.988842	+	0.148971i	$0.952404\pi$
$692$	−12.5934	+	5.60696i	−0.478731	+	0.213145i
$693$	18.6713	+	3.96871i	0.709264	+	0.150759i
$694$	2.05906	−	19.5907i	0.0781610	−	0.743652i
$695$	0.160145	+	1.52368i	0.00607465	+	0.0577965i
$696$	−3.83671	+	0.815517i	−0.145430	+	0.0309121i
$697$	6.46105	−	4.69423i	0.244730	−	0.177807i
$698$	−6.43274	+	4.67366i	−0.243483	+	0.176901i
$699$	1.31527	−	0.279570i	0.0497482	−	0.0105743i
$700$	1.11842	+	10.6411i	0.0422724	+	0.402195i
$701$	4.24004	−	40.3413i	0.160144	−	1.52367i	−0.559209	−	0.829027i	$-0.688895\pi$
$701$	4.24004	−	40.3413i	0.160144	−	1.52367i	0.719353	−	0.694644i	$-0.244438\pi$
$702$	−4.58652	−	0.974894i	−0.173107	−	0.0367950i
$703$	−12.9503	+	5.76586i	−0.488431	+	0.217464i
$704$	29.7465	+	33.0368i	1.12111	+	1.24512i
$705$	1.51484	−	4.66219i	0.0570521	−	0.175588i
$706$	12.5015	−	13.8843i	0.470499	−	0.522542i
$707$	3.22696	+	5.58926i	0.121362	+	0.210206i
$708$	−2.87206	+	4.97455i	−0.107938	+	0.186955i
$709$	2.74233	+	8.44004i	0.102991	+	0.316972i	0.989254	−	0.146210i	$-0.0467075\pi$
$709$	2.74233	+	8.44004i	0.102991	+	0.316972i	−0.886263	+	0.463182i	$0.846708\pi$
$710$	−0.253340	−	0.112794i	−0.00950770	−	0.00423310i
$711$	−3.68173	−	2.67493i	−0.138076	−	0.100318i
$712$	−10.7510			−0.402911
$713$	24.9431	+	3.55635i	0.934125	+	0.133186i
$714$	−8.88615			−0.332556
$715$	−14.8338	−	10.7774i	−0.554753	−	0.403051i
$716$	3.71549	+	1.65424i	0.138854	+	0.0618219i
$717$	−2.30816	−	7.10378i	−0.0861997	−	0.265296i
$718$	5.17593	−	8.96497i	0.193164	−	0.334570i
$719$	1.84890	+	3.20239i	0.0689524	+	0.119429i	0.898440	−	0.439095i	$-0.144701\pi$
$719$	1.84890	+	3.20239i	0.0689524	+	0.119429i	−0.829488	+	0.558525i	$0.811368\pi$
$720$	1.24514	−	1.38287i	0.0464036	−	0.0515364i
$721$	−11.8753	+	36.5485i	−0.442260	+	1.36114i
$722$	−11.7782	−	13.0810i	−0.438338	−	0.486824i
$723$	9.29293	−	4.13748i	0.345608	−	0.153875i
$724$	3.00112	+	0.637907i	0.111536	+	0.0237076i
$725$	0.566992	−	5.39456i	0.0210575	−	0.200349i
$726$	1.92861	+	18.3495i	0.0715773	+	0.681013i
$727$	−3.97503	+	0.844919i	−0.147426	+	0.0313363i	−0.281033	−	0.959698i	$-0.590677\pi$
$727$	−3.97503	+	0.844919i	−0.147426	+	0.0313363i	0.133608	+	0.991034i	$0.457344\pi$
$728$	−37.3570	+	27.1414i	−1.38454	+	1.00593i
$729$	−0.809017	+	0.587785i	−0.0299636	+	0.0217698i
$730$	−2.49559	+	0.530455i	−0.0923660	+	0.0196330i
$731$	1.72050	+	16.3695i	0.0636350	+	0.605447i
$732$	−0.144205	+	1.37202i	−0.00532999	+	0.0507115i
$733$	4.58179	+	0.973889i	0.169232	+	0.0359714i	0.291748	−	0.956495i	$-0.405763\pi$
$733$	4.58179	+	0.973889i	0.169232	+	0.0359714i	−0.122516	+	0.992467i	$0.539096\pi$
$734$	12.6274	−	5.62210i	0.466087	−	0.207515i
$735$	−3.71787	−	4.12911i	−0.137136	−	0.152304i
$736$	−5.14752	+	15.8424i	−0.189740	+	0.583960i
$737$	−28.6708	+	31.8421i	−1.05610	+	1.17292i
$738$	2.16680	+	3.75301i	0.0797611	+	0.138150i
$739$	−9.39531	+	16.2732i	−0.345612	+	0.598618i	−0.985465	−	0.169880i	$-0.945662\pi$
$739$	−9.39531	+	16.2732i	−0.345612	+	0.598618i	0.639853	+	0.768498i	$0.278995\pi$
$740$	0.441180	+	1.35781i	0.0162181	+	0.0499142i
$741$	21.8952	+	9.74838i	0.804341	+	0.358116i
$742$	−45.7904	−	33.2687i	−1.68102	−	1.22133i
$743$	−30.5570			−1.12103			−0.560515	−	0.828145i	$-0.689397\pi$
$743$	−30.5570			−1.12103			−0.560515	+	0.828145i	$0.689397\pi$
$744$	14.5199	+	9.11344i	0.532326	+	0.334115i
$745$	3.67925			0.134797
$746$	11.7144	+	8.51099i	0.428894	+	0.311609i
$747$	−7.76429	−	3.45689i	−0.284081	−	0.126481i
$748$	2.32883	+	7.16741i	0.0851505	+	0.262066i
$749$	29.6609	−	51.3743i	1.08379	−	1.87717i
$750$	4.57242	+	7.91966i	0.166961	+	0.289185i
$751$	18.0281	−	20.0222i	0.657854	−	0.730621i	−0.318230	−	0.948013i	$-0.603089\pi$
$751$	18.0281	−	20.0222i	0.657854	−	0.730621i	0.976084	+	0.217393i	$0.0697552\pi$
$752$	3.79843	−	11.6904i	0.138515	−	0.426304i
$753$	−19.7726	−	21.9597i	−0.720555	−	0.800257i
$754$	5.45703	−	2.42963i	0.198733	−	0.0884818i
$755$	19.4688	+	4.13822i	0.708542	+	0.150605i
$756$	−0.262671	+	2.49915i	−0.00955324	+	0.0908930i
$757$	−1.95295	−	18.5811i	−0.0709811	−	0.675340i	−0.970933	−	0.239351i	$-0.923065\pi$
$757$	−1.95295	−	18.5811i	−0.0709811	−	0.675340i	0.899952	−	0.435989i	$-0.143601\pi$
$758$	−8.55227	+	1.81784i	−0.310633	+	0.0660270i
$759$	−19.0550	+	13.8442i	−0.691652	+	0.502514i
$760$	−12.5767	+	9.13754i	−0.456206	+	0.331453i
$761$	−36.2478	+	7.70470i	−1.31398	+	0.279295i	−0.811022	−	0.585015i	$-0.801088\pi$
$761$	−36.2478	+	7.70470i	−1.31398	+	0.279295i	−0.502958	+	0.864311i	$0.667755\pi$
$762$	1.75251	+	16.6740i	0.0634866	+	0.604035i
$763$	1.25983	−	11.9865i	0.0456088	−	0.433939i
$764$	15.9577	+	3.39191i	0.577328	+	0.122715i
$765$	1.66299	−	0.740411i	0.0601256	−	0.0267696i
$766$	22.9531	+	25.4920i	0.829329	+	0.921063i
$767$	10.5934	−	32.6032i	0.382506	−	1.17723i
$768$	−9.56468	+	10.6227i	−0.345136	+	0.383312i
$769$	−2.30168	−	3.98663i	−0.0830008	−	0.143762i	0.821537	−	0.570156i	$-0.193117\pi$
$769$	−2.30168	−	3.98663i	−0.0830008	−	0.143762i	−0.904538	+	0.426394i	$0.859784\pi$
$770$	9.42765	−	16.3292i	0.339749	−	0.588463i
$771$	7.55201	+	23.2427i	0.271979	+	0.837065i
$772$	9.74105	+	4.33700i	0.350588	+	0.156092i
$773$	−35.0803	−	25.4873i	−1.26175	−	0.916716i	−0.262908	−	0.964821i	$-0.584682\pi$
$773$	−35.0803	−	25.4873i	−1.26175	−	0.916716i	−0.998842	+	0.0481052i	$0.984682\pi$
$774$	−8.93149			−0.321036
$775$	−18.1910	+	15.2022i	−0.653439	+	0.546079i
$776$	−54.7179			−1.96426
$777$	7.17624	+	5.21385i	0.257446	+	0.187046i
$778$	−21.7860	−	9.69976i	−0.781067	−	0.347753i
$779$	−6.84498	−	21.0667i	−0.245247	−	0.754792i
$780$	1.20690	−	2.09042i	0.0432140	−	0.0748489i
$781$	0.730621	+	1.26547i	0.0261437	+	0.0452822i
$782$	7.33677	−	8.14831i	0.262363	−	0.291383i
$783$	0.393668	−	1.21159i	0.0140685	−	0.0432985i
$784$	−9.32249	−	10.3537i	−0.332946	−	0.369774i
$785$	−6.53753	+	2.91069i	−0.233334	+	0.103887i
$786$	3.01528	+	0.640918i	0.107552	+	0.0228608i
$787$	−1.73459	+	16.5035i	−0.0618313	+	0.588285i	0.919113	+	0.393995i	$0.128907\pi$
$787$	−1.73459	+	16.5035i	−0.0618313	+	0.588285i	−0.980944	+	0.194291i	$0.937759\pi$
$788$	0.783284	+	7.45245i	0.0279033	+	0.265483i
$789$	−0.0992647	+	0.0210994i	−0.00353392	+	0.000751157i
$790$	−3.63677	+	2.64227i	−0.129390	+	0.0940076i
$791$	24.8262	−	18.0373i	0.882719	−	0.641333i
$792$	−15.6755	+	3.33194i	−0.557006	+	0.118395i
$793$	−0.860622	−	8.18827i	−0.0305616	−	0.290774i
$794$	−0.940500	+	8.94826i	−0.0333771	+	0.317562i
$795$	11.3414	+	2.41069i	0.402239	+	0.0854985i
$796$	2.88438	−	1.28421i	0.102234	−	0.0455176i
$797$	−21.7903	−	24.2006i	−0.771853	−	0.857229i	0.221160	−	0.975238i	$-0.429016\pi$
$797$	−21.7903	−	24.2006i	−0.771853	−	0.857229i	−0.993013	+	0.118008i	$0.962349\pi$
$798$	−7.61623	+	23.4404i	−0.269612	+	0.829780i
$799$	8.04611	−	8.93611i	0.284651	−	0.316137i
$800$	−7.83684	−	13.5738i	−0.277074	−	0.479906i
$801$	1.74587	−	3.02394i	0.0616873	−	0.106846i
$802$	6.89565	+	21.2226i	0.243494	+	0.749397i
$803$	12.2814	+	5.46802i	0.433401	+	0.192962i
$804$	−4.56345	−	3.31554i	−0.160940	−	0.116930i
$805$	14.2966			0.503888
$806$	−24.5148	−	8.97817i	−0.863497	−	0.316243i
$807$	−3.40940			−0.120017
$808$	−4.38358	−	3.18486i	−0.154214	−	0.112043i
$809$	3.36371	+	1.49762i	0.118262	+	0.0526536i	0.465015	−	0.885303i	$-0.346049\pi$
$809$	3.36371	+	1.49762i	0.118262	+	0.0526536i	−0.346753	+	0.937957i	$0.612716\pi$
$810$	0.305243	+	0.939442i	0.0107252	+	0.0330086i
$811$	1.89156	−	3.27628i	0.0664218	−	0.115046i	−0.830902	−	0.556419i	$-0.812175\pi$
$811$	1.89156	−	3.27628i	0.0664218	−	0.115046i	0.897324	+	0.441373i	$0.145508\pi$
$812$	−1.60064	−	2.77240i	−0.0561716	−	0.0972921i
$813$	9.08584	−	10.0908i	0.318654	−	0.353901i
$814$	−4.46071	+	13.7287i	−0.156348	+	0.481190i
$815$	−13.5267	−	15.0230i	−0.473821	−	0.526232i
$816$	4.16993	−	1.85657i	0.145977	−	0.0649930i
$817$	44.6549	+	9.49169i	1.56228	+	0.332072i
$818$	0.880940	−	8.38158i	0.0308013	−	0.293055i
$819$	−1.56763	−	14.9150i	−0.0547773	−	0.521171i
$820$	−2.18211	+	0.463822i	−0.0762027	+	0.0161974i
$821$	−37.6148	+	27.3288i	−1.31277	+	0.953781i	−0.312775	+	0.949827i	$0.601259\pi$
$821$	−37.6148	+	27.3288i	−1.31277	+	0.953781i	−0.999992	+	0.00395394i	$0.998741\pi$
$822$	4.98027	−	3.61838i	0.173707	−	0.126205i
$823$	31.0074	−	6.59083i	1.08085	−	0.229742i	0.367128	−	0.930171i	$-0.380341\pi$
$823$	31.0074	−	6.59083i	1.08085	−	0.229742i	0.713722	+	0.700429i	$0.247008\pi$
$824$	−3.37245	−	32.0867i	−0.117485	−	1.11779i
$825$	2.31654	−	22.0404i	0.0806517	−	0.767350i
$826$	34.4823	+	7.32945i	1.19979	+	0.255024i
$827$	−10.6322	+	4.73375i	−0.369717	+	0.164608i	−0.583181	−	0.812342i	$-0.698192\pi$
$827$	−10.6322	+	4.73375i	−0.369717	+	0.164608i	0.213464	+	0.976951i	$0.431525\pi$
$828$	−2.07476	−	2.30426i	−0.0721030	−	0.0800785i
$829$	11.4661	−	35.2891i	0.398235	−	1.22564i	−0.528179	−	0.849133i	$-0.677125\pi$
$829$	11.4661	−	35.2891i	0.398235	−	1.22564i	0.926414	−	0.376507i	$-0.122875\pi$
$830$	−5.61754	+	6.23891i	−0.194988	+	0.216556i
$831$	−0.0947405	−	0.164095i	−0.00328651	−	0.00569240i
$832$	17.4636	−	30.2478i	0.605440	−	1.04865i
$833$	−4.21169	−	12.9623i	−0.145926	−	0.449115i
$834$	−1.86297	−	0.829446i	−0.0645092	−	0.0287213i
$835$	16.7508	+	12.1702i	0.579686	+	0.421166i
$836$	20.9026			0.722931
$837$	−4.92126	+	2.60408i	−0.170104	+	0.0900102i
$838$	15.1360			0.522866
$839$	−40.9016	−	29.7167i	−1.41208	−	1.02594i	−0.993016	−	0.117979i	$-0.962358\pi$
$839$	−40.9016	−	29.7167i	−1.41208	−	1.02594i	−0.419064	−	0.907957i	$-0.637642\pi$
$840$	8.88647	+	3.95651i	0.306612	+	0.136513i
$841$	−8.45999	−	26.0372i	−0.291724	−	0.897833i
$842$	−7.44380	+	12.8930i	−0.256530	+	0.444324i
$843$	9.23484	+	15.9952i	0.318065	+	0.550904i
$844$	7.34684	−	8.15949i	0.252889	−	0.280861i
$845$	−0.990920	+	3.04974i	−0.0340887	+	0.104914i
$846$	4.36606	+	4.84900i	0.150108	+	0.166712i
$847$	−53.9099	+	24.0022i	−1.85237	+	0.824726i
$848$	28.4385	+	6.04478i	0.976580	+	0.207579i
$849$	−0.595445	+	5.66528i	−0.0204356	+	0.194432i
$850$	1.07841	+	10.2604i	0.0369892	+	0.351929i
$851$	−10.7059	+	2.27562i	−0.366995	+	0.0780071i
$852$	−0.155628	+	0.113070i	−0.00533172	+	0.00387372i
$853$	−20.0988	+	14.6027i	−0.688171	+	0.499986i	−0.876058	−	0.482205i	$-0.839836\pi$
$853$	−20.0988	+	14.6027i	−0.688171	+	0.499986i	0.187887	+	0.982191i	$0.439836\pi$
$854$	8.28173	−	1.76034i	0.283395	−	0.0602374i
$855$	−0.527763	−	5.02133i	−0.0180491	−	0.171726i
$856$	−5.20592	+	49.5310i	−0.177935	+	1.69294i
$857$	18.0255	+	3.83144i	0.615740	+	0.130879i	0.505214	−	0.862994i	$-0.331413\pi$
$857$	18.0255	+	3.83144i	0.615740	+	0.130879i	0.110525	+	0.993873i	$0.464747\pi$
$858$	22.2957	−	9.92667i	0.761161	−	0.338891i
$859$	23.8590	+	26.4981i	0.814058	+	0.904103i	0.996871	−	0.0790443i	$-0.0251869\pi$
$859$	23.8590	+	26.4981i	0.814058	+	0.904103i	−0.182813	+	0.983148i	$0.558520\pi$
$860$	1.42079	−	4.37274i	0.0484485	−	0.149109i
$861$	−9.27447	+	10.3003i	−0.316073	+	0.351035i
$862$	−1.17958	−	2.04309i	−0.0401766	−	0.0695879i
$863$	−19.9060	+	34.4781i	−0.677607	+	1.17365i	0.298093	+	0.954537i	$0.403649\pi$
$863$	−19.9060	+	34.4781i	−0.677607	+	1.17365i	−0.975700	+	0.219112i	$0.929684\pi$
$864$	−1.13752	−	3.50093i	−0.0386992	−	0.119104i
$865$	−15.8329	−	7.04925i	−0.538334	−	0.239682i
$866$	−5.10653	−	3.71011i	−0.173527	−	0.126075i
$867$	−12.5347			−0.425701
$868$	−3.41192	+	13.5689i	−0.115808	+	0.460559i
$869$	23.6868			0.803519
$870$	−1.01805	−	0.739656i	−0.0345151	−	0.0250767i
$871$	30.7536	+	13.6924i	1.04205	+	0.463949i
$872$	3.12685	+	9.62346i	0.105889	+	0.325891i
$873$	8.88573	−	15.3905i	0.300736	−	0.520891i
$874$	−15.2058	−	26.3372i	−0.514343	−	0.890868i
$875$	−19.5711	+	21.7359i	−0.661624	+	0.734808i
$876$	−0.546898	+	1.68318i	−0.0184780	+	0.0568694i
$877$	−5.18145	−	5.75458i	−0.174965	−	0.194318i	0.649284	−	0.760546i	$-0.275069\pi$
$877$	−5.18145	−	5.75458i	−0.174965	−	0.194318i	−0.824249	+	0.566228i	$0.808402\pi$
$878$	5.80824	−	2.58599i	0.196019	−	0.0872731i
$879$	−15.1667	−	3.22378i	−0.511561	−	0.108736i
$880$	−1.01240	+	9.63236i	−0.0341281	+	0.324707i
$881$	−2.08978	−	19.8829i	−0.0704065	−	0.669873i	−0.971628	−	0.236514i	$-0.923995\pi$
$881$	−2.08978	−	19.8829i	−0.0704065	−	0.669873i	0.901221	−	0.433359i	$-0.142672\pi$
$882$	7.23407	−	1.53765i	0.243584	−	0.0517753i
$883$	28.1772	−	20.4720i	0.948239	−	0.688936i	−0.00215067	−	0.999998i	$-0.500685\pi$
$883$	28.1772	−	20.4720i	0.948239	−	0.688936i	0.950390	+	0.311062i	$0.100685\pi$
$884$	4.79017	−	3.48026i	0.161111	−	0.117054i
$885$	−7.06387	+	1.50147i	−0.237449	+	0.0504714i
$886$	−2.33477	−	22.2138i	−0.0784381	−	0.746288i
$887$	1.07689	−	10.2459i	0.0361583	−	0.344023i	−0.961454	−	0.274965i	$-0.911334\pi$
$887$	1.07689	−	10.2459i	0.0361583	−	0.344023i	0.997613	−	0.0690585i	$-0.0219995\pi$
$888$	−7.28437	−	1.54834i	−0.244447	−	0.0519589i
$889$	−48.9874	+	21.8106i	−1.64298	+	0.731504i
$890$	−2.30790	−	2.56318i	−0.0773609	−	0.0859180i
$891$	1.60840	−	4.95014i	0.0538834	−	0.165836i
$892$	−0.643785	+	0.714995i	−0.0215555	+	0.0239398i
$893$	−16.6759	−	28.8835i	−0.558038	−	0.966550i
$894$	−2.44864	+	4.24117i	−0.0818947	+	0.141846i
$895$	1.58010	+	4.86304i	0.0528168	+	0.162553i
$896$	8.14613	+	3.62689i	0.272143	+	0.121166i
$897$	14.9708	+	10.8769i	0.499862	+	0.363171i
$898$	−17.4079			−0.580910
$899$	3.12209	−	6.36890i	0.104127	−	0.212415i
$900$	2.91752			0.0972505
$901$	23.0098	+	16.7176i	0.766566	+	0.556943i
$902$	−20.6059	−	9.17433i	−0.686101	−	0.305472i
$903$	−8.82745	−	27.1681i	−0.293759	−	0.904098i
$904$	−12.8816	+	22.3117i	−0.428437	+	0.742075i
$905$	1.92870	+	3.34060i	0.0641121	+	0.111045i
$906$	−17.7272	+	19.6881i	−0.588948	+	0.654093i
$907$	8.66223	−	26.6596i	0.287624	−	0.885217i	−0.697975	−	0.716122i	$-0.745915\pi$
$907$	8.66223	−	26.6596i	0.287624	−	0.885217i	0.985600	−	0.169095i	$-0.0540845\pi$
$908$	−12.9195	−	14.3486i	−0.428750	−	0.476175i
$909$	1.60766	−	0.715778i	0.0533229	−	0.0237409i
$910$	−14.4902	−	3.08000i	−0.480347	−	0.102101i
$911$	2.45175	−	23.3268i	0.0812299	−	0.772851i	−0.875763	−	0.482741i	$-0.839641\pi$
$911$	2.45175	−	23.3268i	0.0812299	−	0.772851i	0.956993	−	0.290110i	$-0.0936920\pi$
$912$	−1.32336	−	12.5909i	−0.0438207	−	0.416926i
$913$	43.2701	−	9.19734i	1.43203	−	0.304387i
$914$	9.32726	−	6.77665i	0.308518	−	0.224152i
$915$	−1.40320	+	1.01949i	−0.0463884	+	0.0337032i
$916$	−15.6303	+	3.32233i	−0.516441	+	0.109773i
$917$	1.03059	+	9.80544i	0.0340332	+	0.323804i
$918$	−0.253273	+	2.40974i	−0.00835927	+	0.0795331i
$919$	−18.7012	−	3.97507i	−0.616896	−	0.131125i	−0.111144	−	0.993804i	$-0.535452\pi$
$919$	−18.7012	−	3.97507i	−0.616896	−	0.131125i	−0.505752	+	0.862679i	$0.668785\pi$
$920$	−10.9650	+	4.88195i	−0.361506	+	0.160953i
$921$	9.21029	+	10.2291i	0.303489	+	0.337059i
$922$	−6.27347	+	19.3078i	−0.206606	+	0.635867i
$923$	0.768194	−	0.853166i	0.0252854	−	0.0280823i
$924$	−6.53971	−	11.3271i	−0.215141	−	0.372635i
$925$	5.14927	−	8.91879i	0.169307	−	0.293248i
$926$	10.9704	+	33.7635i	0.360511	+	1.10954i
$927$	9.57271	+	4.26205i	0.314409	+	0.139984i
$928$	3.79386	+	2.75640i	0.124540	+	0.0904834i
$929$	−1.80477			−0.0592126			−0.0296063	−	0.999562i	$-0.509425\pi$
$929$	−1.80477			−0.0592126			−0.0296063	+	0.999562i	$0.509425\pi$
$930$	0.944202	+	5.41811i	0.0309616	+	0.177667i
$931$	−37.8023			−1.23892
$932$	−0.745398	−	0.541563i	−0.0244163	−	0.0177395i
$933$	17.9768	+	8.00378i	0.588534	+	0.262032i
$934$	9.63361	+	29.6492i	0.315221	+	0.970151i
$935$	−4.73741	+	8.20544i	−0.154930	+	0.268347i
$936$	6.29543	+	10.9040i	0.205773	+	0.356409i
$937$	38.5120	−	42.7719i	1.25813	−	1.39730i	0.375782	−	0.926708i	$-0.377374\pi$
$937$	38.5120	−	42.7719i	1.25813	−	1.39730i	0.882352	−	0.470590i	$-0.155959\pi$
$938$	−10.6976	+	32.9239i	−0.349290	+	1.07500i
$939$	5.50507	+	6.11400i	0.179651	+	0.199523i
$940$	−3.06854	+	1.36620i	−0.100085	+	0.0445607i
$941$	14.6459	+	3.11308i	0.477443	+	0.101484i	0.440346	−	0.897828i	$-0.354856\pi$
$941$	14.6459	+	3.11308i	0.477443	+	0.101484i	0.0370966	+	0.999312i	$0.488189\pi$
$942$	0.995665	−	9.47312i	0.0324405	−	0.308651i
$943$	−1.78770	−	17.0088i	−0.0582154	−	0.553882i
$944$	−17.7126	+	3.76492i	−0.576495	+	0.122538i
$945$	−2.55594	+	1.85700i	−0.0831447	+	0.0604081i
$946$	37.6091	−	27.3246i	1.22278	−	0.888400i
$947$	−6.46984	+	1.37521i	−0.210242	+	0.0446883i	−0.311828	−	0.950138i	$-0.600941\pi$
$947$	−6.46984	+	1.37521i	−0.210242	+	0.0446883i	0.101587	+	0.994827i	$0.467608\pi$
$948$	0.325947	+	3.10118i	0.0105863	+	0.100722i
$949$	1.10405	−	10.5043i	0.0358390	−	0.340986i
$950$	27.9897	+	5.94939i	0.908106	+	0.193024i
$951$	−1.44168	+	0.641877i	−0.0467497	+	0.0208143i
$952$	15.9662	+	17.7323i	0.517467	+	0.574706i
$953$	−11.3866	+	35.0444i	−0.368848	+	1.13520i	0.578687	+	0.815549i	$0.303565\pi$
$953$	−11.3866	+	35.0444i	−0.368848	+	1.13520i	−0.947536	+	0.319649i	$0.896435\pi$
$954$	−10.3269	+	11.4692i	−0.334345	+	0.371328i
$955$	10.2554	+	17.7628i	0.331855	+	0.574790i
$956$	−2.55901	+	4.43233i	−0.0827643	+	0.143352i
$957$	2.04900	+	6.30617i	0.0662347	+	0.203849i
$958$	4.62189	+	2.05780i	0.149326	+	0.0664844i
$959$	15.9288	+	11.5729i	0.514366	+	0.373709i
$960$	−7.35780			−0.237472
$961$	−29.1726	+	10.4861i	−0.941052	+	0.338263i
$962$	11.3412			0.365656
$963$	−13.0862	−	9.50769i	−0.421697	−	0.306381i
$964$	−6.36754	−	2.83501i	−0.205085	−	0.0913095i
$965$	4.14261	+	12.7496i	0.133355	+	0.410425i
$966$	−9.51474	+	16.4800i	−0.306132	+	0.530236i
$967$	7.20720	+	12.4832i	0.231768	+	0.401434i	0.958328	−	0.285669i	$-0.0922156\pi$
$967$	7.20720	+	12.4832i	0.231768	+	0.401434i	−0.726560	+	0.687103i	$0.758882\pi$
$968$	33.1510	−	36.8179i	1.06551	−	1.18337i
$969$	3.82717	−	11.7788i	0.122946	−	0.378390i
$970$	−11.7462	−	13.0455i	−0.377148	−	0.418865i
$971$	1.52494	−	0.678947i	0.0489376	−	0.0217884i	−0.382122	−	0.924112i	$-0.624807\pi$
$971$	1.52494	−	0.678947i	0.0489376	−	0.0217884i	0.431060	+	0.902323i	$0.358140\pi$
$972$	0.670229	+	0.142462i	0.0214976	+	0.00456946i
$973$	0.681770	−	6.48661i	0.0218566	−	0.207951i
$974$	0.770710	+	7.33282i	0.0246951	+	0.234959i
$975$	−17.0313	+	3.62012i	−0.545438	+	0.115937i
$976$	−3.51851	+	2.55635i	−0.112625	+	0.0818267i
$977$	1.64889	−	1.19799i	0.0527526	−	0.0383270i	−0.561096	−	0.827750i	$-0.689620\pi$
$977$	1.64889	−	1.19799i	0.0527526	−	0.0383270i	0.613849	+	0.789423i	$0.289620\pi$
$978$	26.3198	−	5.59444i	0.841613	−	0.178890i
$979$	1.89971	+	18.0746i	0.0607151	+	0.577666i
$980$	−0.397957	+	3.78631i	−0.0127123	+	0.120949i
$981$	−3.21457	−	0.683278i	−0.102633	−	0.0218154i
$982$	27.7233	−	12.3432i	0.884686	−	0.393888i
$983$	−3.94476	−	4.38110i	−0.125818	−	0.139735i	0.676944	−	0.736035i	$-0.263304\pi$
$983$	−3.94476	−	4.38110i	−0.125818	−	0.139735i	−0.802762	+	0.596299i	$0.796637\pi$
$984$	3.59591	−	11.0671i	0.114633	−	0.352805i
$985$	−6.30393	+	7.00122i	−0.200860	+	0.223077i
$986$	−1.54338	−	2.67321i	−0.0491512	−	0.0851324i
$987$	−10.4347	+	18.0733i	−0.332139	+	0.575281i
$988$	−5.07481	−	15.6187i	−0.161451	−	0.496896i
$989$	32.2006	+	14.3366i	1.02392	+	0.455878i
$990$	−4.15942	−	3.02200i	−0.132195	−	0.0960453i
$991$	−13.3164			−0.423010			−0.211505	−	0.977377i	$-0.567837\pi$
$991$	−13.3164			−0.423010			−0.211505	+	0.977377i	$0.567837\pi$
$992$	−3.51866	−	20.1911i	−0.111718	−	0.641069i
$993$	28.4201			0.901883
$994$	0.955116	+	0.693933i	0.0302945	+	0.0220102i
$995$	3.62633	+	1.61455i	0.114963	+	0.0511846i
$996$	1.79959	+	5.53856i	0.0570221	+	0.175496i
$997$	−28.6142	+	49.5612i	−0.906220	+	1.56962i	−0.0869480	+	0.996213i	$0.527711\pi$
$997$	−28.6142	+	49.5612i	−0.906220	+	1.56962i	−0.819272	+	0.573406i	$0.805622\pi$
$998$	−17.0935	−	29.6069i	−0.541086	−	0.937188i
$999$	1.61842	−	1.79744i	0.0512046	−	0.0568685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	93.2.m.b.19.3	✓	24
3.2	odd	2		279.2.y.d.19.1		24
31.7	even	15		2883.2.a.t.1.3		12
31.18	even	15	inner	93.2.m.b.49.3	yes	24
31.24	odd	30		2883.2.a.s.1.3		12
93.38	odd	30		8649.2.a.bk.1.10		12
93.80	odd	30		279.2.y.d.235.1		24
93.86	even	30		8649.2.a.bl.1.10		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
93.2.m.b.19.3	✓	24	1.1	even	1	trivial
93.2.m.b.49.3	yes	24	31.18	even	15	inner
279.2.y.d.19.1		24	3.2	odd	2
279.2.y.d.235.1		24	93.80	odd	30
2883.2.a.s.1.3		12	31.24	odd	30
2883.2.a.t.1.3		12	31.7	even	15
8649.2.a.bk.1.10		12	93.38	odd	30
8649.2.a.bl.1.10		12	93.86	even	30

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:	\( N \)	\(=\)	\( 93 = 3 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	93.m (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.927656 + 0.673982i) q^{2} +(0.913545 + 0.406737i) q^{3} +(-0.211739 - 0.651666i) q^{4} +(0.430729 - 0.746045i) q^{5} +(0.573323 + 0.993025i) q^{6} +(-2.45397 + 2.72541i) q^{7} +(0.951456 - 2.92828i) q^{8} +(0.669131 + 0.743145i) q^{9} +O(q^{10})\)	\(q+(0.927656 + 0.673982i) q^{2} +(0.913545 + 0.406737i) q^{3} +(-0.211739 - 0.651666i) q^{4} +(0.430729 - 0.746045i) q^{5} +(0.573323 + 0.993025i) q^{6} +(-2.45397 + 2.72541i) q^{7} +(0.951456 - 2.92828i) q^{8} +(0.669131 + 0.743145i) q^{9} +(0.902389 - 0.401770i) q^{10} +(-5.09115 - 1.08216i) q^{11} +(0.0716231 - 0.681448i) q^{12} +(0.427448 + 4.06690i) q^{13} +(-4.11332 + 0.874313i) q^{14} +(0.696934 - 0.506352i) q^{15} +(1.74755 - 1.26967i) q^{16} +(2.06695 - 0.439344i) q^{17} +(0.119857 + 1.14036i) q^{18} +(0.612639 - 5.82887i) q^{19} +(-0.577374 - 0.122725i) q^{20} +(-3.35034 + 1.49167i) q^{21} +(-3.99348 - 4.43521i) q^{22} +(1.39837 - 4.30373i) q^{23} +(2.06024 - 2.28813i) q^{24} +(2.12894 + 3.68744i) q^{25} +(-2.34449 + 4.06078i) q^{26} +(0.309017 + 0.951057i) q^{27} +(2.29566 + 1.02209i) q^{28} +(-1.03064 - 0.748801i) q^{29} +0.987788 q^{30} +(0.955875 + 5.48510i) q^{31} -3.68109 q^{32} +(-4.21084 - 3.05936i) q^{33} +(2.21353 + 0.985527i) q^{34} +(0.976281 + 3.00469i) q^{35} +(0.342601 - 0.593402i) q^{36} +(-1.20935 - 2.09465i) q^{37} +(4.49687 - 4.99428i) q^{38} +(-1.26366 + 3.88916i) q^{39} +(-1.77481 - 1.97112i) q^{40} +(3.45263 - 1.53721i) q^{41} +(-4.11332 - 0.874313i) q^{42} +(-0.814196 + 7.74656i) q^{43} +(0.372790 + 3.54686i) q^{44} +(0.842633 - 0.179107i) q^{45} +(4.19784 - 3.04991i) q^{46} +(4.60370 - 3.34478i) q^{47} +(2.11289 - 0.449109i) q^{48} +(-0.674191 - 6.41450i) q^{49} +(-0.510339 + 4.85555i) q^{50} +(2.06695 + 0.439344i) q^{51} +(2.55975 - 1.13968i) q^{52} +(9.00616 + 10.0024i) q^{53} +(-0.354333 + 1.09053i) q^{54} +(-3.00024 + 3.33211i) q^{55} +(5.64592 + 9.77903i) q^{56} +(2.93049 - 5.07575i) q^{57} +(-0.451398 - 1.38926i) q^{58} +(-7.65834 - 3.40971i) q^{59} +(-0.477541 - 0.346954i) q^{60} -2.01339 q^{61} +(-2.81013 + 5.73253i) q^{62} -3.66740 q^{63} +(-6.90989 - 5.02033i) q^{64} +(3.21820 + 1.43284i) q^{65} +(-1.84427 - 5.67606i) q^{66} +(4.11611 - 7.12931i) q^{67} +(-0.723960 - 1.25393i) q^{68} +(3.02796 - 3.36289i) q^{69} +(-1.11945 + 3.44531i) q^{70} +(-0.187855 - 0.208634i) q^{71} +(2.81279 - 1.25233i) q^{72} +(-2.52645 - 0.537013i) q^{73} +(0.289898 - 2.75819i) q^{74} +(0.445071 + 4.23456i) q^{75} +(-3.92819 + 0.834964i) q^{76} +(15.4429 - 11.2199i) q^{77} +(-3.79347 + 2.75612i) q^{78} +(-4.45142 + 0.946179i) q^{79} +(-0.194510 - 1.85064i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(4.23891 + 0.901007i) q^{82} +(-7.76429 + 3.45689i) q^{83} +(1.68147 + 1.86746i) q^{84} +(0.562525 - 1.73128i) q^{85} +(-5.97634 + 6.63739i) q^{86} +(-0.636968 - 1.10326i) q^{87} +(-8.01287 + 13.8787i) q^{88} +(-1.07901 - 3.32084i) q^{89} +(0.902389 + 0.401770i) q^{90} +(-12.1329 - 8.81508i) q^{91} -3.10069 q^{92} +(-1.35775 + 5.39968i) q^{93} +6.52498 q^{94} +(-4.08471 - 2.96772i) q^{95} +(-3.36284 - 1.49723i) q^{96} +(-5.49168 - 16.9017i) q^{97} +(3.69784 - 6.40485i) q^{98} +(-2.60244 - 4.50757i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9	\( 24 q + 3 q^{3} - 4 q^{4} - 6 q^{5} - 5 q^{6} - q^{7} - 22 q^{8} + 3 q^{9} + 24 q^{10} - 22 q^{11} + 12 q^{12} - 8 q^{13} + 10 q^{14} - 8 q^{15} - 2 q^{16} - 17 q^{17} + 5 q^{19} - 22 q^{20} - 11 q^{21} - 37 q^{22} + 26 q^{23} + 26 q^{24} - 8 q^{25} + 4 q^{26} - 6 q^{27} - 36 q^{28} + 2 q^{29} + 42 q^{30} + 36 q^{32} + 14 q^{33} + 40 q^{34} + 9 q^{35} - 13 q^{36} - 13 q^{37} - q^{38} - 19 q^{39} - 27 q^{40} + 36 q^{41} + 10 q^{42} - 11 q^{43} - 38 q^{44} - q^{45} - 23 q^{46} - 13 q^{47} - 14 q^{48} - 22 q^{49} + 71 q^{50} - 17 q^{51} + 9 q^{52} - 20 q^{53} - 5 q^{54} + 26 q^{55} + 28 q^{56} - 15 q^{57} + 40 q^{58} - 16 q^{59} - 61 q^{60} + 70 q^{61} - 2 q^{62} + 12 q^{63} + 34 q^{64} + 94 q^{65} - 16 q^{66} + 4 q^{67} + 51 q^{68} - 13 q^{69} - 43 q^{70} - 5 q^{71} + q^{72} - 12 q^{73} + 74 q^{74} - 8 q^{75} + 71 q^{76} + 25 q^{77} + 17 q^{78} - 29 q^{79} - 113 q^{80} + 3 q^{81} - 60 q^{82} - 11 q^{83} - 41 q^{84} + 16 q^{85} - 144 q^{86} + 14 q^{87} + 26 q^{88} - 27 q^{89} + 24 q^{90} - 81 q^{91} + 28 q^{92} - 36 q^{93} - 80 q^{94} - 56 q^{95} - 43 q^{96} - 21 q^{97} - 14 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q + 3 * q^3 - 4 * q^4 - 6 * q^5 - 5 * q^6 - q^7 - 22 * q^8 + 3 * q^9 + 24 * q^10 - 22 * q^11 + 12 * q^12 - 8 * q^13 + 10 * q^14 - 8 * q^15 - 2 * q^16 - 17 * q^17 + 5 * q^19 - 22 * q^20 - 11 * q^21 - 37 * q^22 + 26 * q^23 + 26 * q^24 - 8 * q^25 + 4 * q^26 - 6 * q^27 - 36 * q^28 + 2 * q^29 + 42 * q^30 + 36 * q^32 + 14 * q^33 + 40 * q^34 + 9 * q^35 - 13 * q^36 - 13 * q^37 - q^38 - 19 * q^39 - 27 * q^40 + 36 * q^41 + 10 * q^42 - 11 * q^43 - 38 * q^44 - q^45 - 23 * q^46 - 13 * q^47 - 14 * q^48 - 22 * q^49 + 71 * q^50 - 17 * q^51 + 9 * q^52 - 20 * q^53 - 5 * q^54 + 26 * q^55 + 28 * q^56 - 15 * q^57 + 40 * q^58 - 16 * q^59 - 61 * q^60 + 70 * q^61 - 2 * q^62 + 12 * q^63 + 34 * q^64 + 94 * q^65 - 16 * q^66 + 4 * q^67 + 51 * q^68 - 13 * q^69 - 43 * q^70 - 5 * q^71 + q^72 - 12 * q^73 + 74 * q^74 - 8 * q^75 + 71 * q^76 + 25 * q^77 + 17 * q^78 - 29 * q^79 - 113 * q^80 + 3 * q^81 - 60 * q^82 - 11 * q^83 - 41 * q^84 + 16 * q^85 - 144 * q^86 + 14 * q^87 + 26 * q^88 - 27 * q^89 + 24 * q^90 - 81 * q^91 + 28 * q^92 - 36 * q^93 - 80 * q^94 - 56 * q^95 - 43 * q^96 - 21 * q^97 - 14 * q^98 - 2 * q^99

Introduction

L-functions

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