LMFDB - Embedded newform 23.2.c.a.4.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,2,Mod(2,23)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(23, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("23.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	23.c (of order $11$, degree $10$, 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:	$0.183655924649$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1 $ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			4.1
Root			$-0.415415 - 0.909632i$ of defining polynomial
Character	$\chi$	$=$	23.4
Dual form			23.2.c.a.6.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.198939 + 0.435615i) q^{2} +(-2.11435 + 0.620830i) q^{3} +(1.15954 - 1.33818i) q^{4} +(-2.18251 - 1.40261i) q^{5} +(-0.691070 - 0.797537i) q^{6} +(0.483568 + 3.36329i) q^{7} +(1.73259 + 0.508735i) q^{8} +(1.56130 - 1.00339i) q^{9} +O(q^{10})$	\(q+(0.198939 + 0.435615i) q^{2} +(-2.11435 + 0.620830i) q^{3} +(1.15954 - 1.33818i) q^{4} +(-2.18251 - 1.40261i) q^{5} +(-0.691070 - 0.797537i) q^{6} +(0.483568 + 3.36329i) q^{7} +(1.73259 + 0.508735i) q^{8} +(1.56130 - 1.00339i) q^{9} +(0.176814 - 1.22977i) q^{10} +(0.0950085 - 0.208040i) q^{11} +(-1.62089 + 3.54926i) q^{12} +(0.435418 - 3.02840i) q^{13} +(-1.36890 + 0.879739i) q^{14} +(5.48538 + 1.61065i) q^{15} +(-0.380916 - 2.64933i) q^{16} +(1.26176 + 1.45615i) q^{17} +(0.747694 + 0.480513i) q^{18} +(-1.26668 + 1.46183i) q^{19} +(-4.40764 + 1.29420i) q^{20} +(-3.11047 - 6.81097i) q^{21} +0.109526 q^{22} +(-4.62936 - 1.25259i) q^{23} -3.97915 q^{24} +(0.718941 + 1.57426i) q^{25} +(1.40584 - 0.412791i) q^{26} +(1.65098 - 1.90533i) q^{27} +(5.06140 + 3.25276i) q^{28} +(4.23872 + 4.89174i) q^{29} +(0.389630 + 2.70993i) q^{30} +(-1.44518 - 0.424344i) q^{31} +(4.11648 - 2.64550i) q^{32} +(-0.0717243 + 0.498853i) q^{33} +(-0.383307 + 0.839324i) q^{34} +(3.66200 - 8.01867i) q^{35} +(0.467677 - 3.25276i) q^{36} +(-5.67778 + 3.64889i) q^{37} +(-0.888785 - 0.260971i) q^{38} +(0.959493 + 6.67342i) q^{39} +(-3.06784 - 3.54047i) q^{40} +(6.78612 + 4.36118i) q^{41} +(2.34817 - 2.70993i) q^{42} +(-2.55172 + 0.749253i) q^{43} +(-0.168228 - 0.368368i) q^{44} -4.81491 q^{45} +(-0.375312 - 2.26581i) q^{46} -1.43889 q^{47} +(2.45018 + 5.36514i) q^{48} +(-4.36144 + 1.28064i) q^{49} +(-0.542747 + 0.626363i) q^{50} +(-3.57182 - 2.29547i) q^{51} +(-3.54765 - 4.09421i) q^{52} +(-1.22118 - 8.49350i) q^{53} +(1.15843 + 0.340146i) q^{54} +(-0.499156 + 0.320788i) q^{55} +(-0.873198 + 6.07322i) q^{56} +(1.77066 - 3.87721i) q^{57} +(-1.28767 + 2.81961i) q^{58} +(-0.00878786 + 0.0611209i) q^{59} +(8.51584 - 5.47280i) q^{60} +(0.0426294 + 0.0125171i) q^{61} +(-0.102652 - 0.713962i) q^{62} +(4.12968 + 4.76590i) q^{63} +(-2.53201 - 1.62722i) q^{64} +(-5.19797 + 5.99877i) q^{65} +(-0.231577 + 0.0679971i) q^{66} +(5.15445 + 11.2867i) q^{67} +3.41164 q^{68} +(10.5658 - 0.225629i) q^{69} +4.22157 q^{70} +(-3.46306 - 7.58305i) q^{71} +(3.21556 - 0.944173i) q^{72} +(0.437593 - 0.505009i) q^{73} +(-2.71904 - 1.74742i) q^{74} +(-2.49745 - 2.88221i) q^{75} +(0.487421 + 3.39009i) q^{76} +(0.745641 + 0.218940i) q^{77} +(-2.71616 + 1.74557i) q^{78} +(1.70338 - 11.8472i) q^{79} +(-2.88463 + 6.31646i) q^{80} +(-4.62079 + 10.1181i) q^{81} +(-0.549771 + 3.82374i) q^{82} +(-0.303301 + 0.194920i) q^{83} +(-12.7210 - 3.73522i) q^{84} +(-0.711387 - 4.94781i) q^{85} +(-0.834022 - 0.962513i) q^{86} +(-11.9991 - 7.71135i) q^{87} +(0.270448 - 0.312114i) q^{88} +(15.4668 - 4.54147i) q^{89} +(-0.957872 - 2.09745i) q^{90} +10.3959 q^{91} +(-7.04411 + 4.74249i) q^{92} +3.31908 q^{93} +(-0.286250 - 0.626800i) q^{94} +(4.81491 - 1.41379i) q^{95} +(-7.06128 + 8.14915i) q^{96} +(-0.335292 - 0.215479i) q^{97} +(-1.42552 - 1.64514i) q^{98} +(-0.0604074 - 0.420143i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 7 q^{2} - 7 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 5 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) $ 10 * q - 7 * q^2 - 7 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 - 5 * q^7 + 4 * q^8 - 2 * q^9	\( 10 q - 7 q^{2} - 7 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 5 q^{7} + 4 q^{8} - 2 q^{9} + q^{10} + 7 q^{11} + 12 q^{12} - 3 q^{13} + 9 q^{14} + 12 q^{15} + q^{16} - 10 q^{17} - 14 q^{18} + 2 q^{19} - 9 q^{20} - 2 q^{21} - 6 q^{22} - 12 q^{23} - 38 q^{24} - 4 q^{25} + 12 q^{26} - 4 q^{27} + 7 q^{28} + 14 q^{29} + 7 q^{30} + 10 q^{31} + 21 q^{32} + 16 q^{33} + 29 q^{34} + 7 q^{35} + 27 q^{36} - 19 q^{37} - 8 q^{38} + q^{39} + q^{40} + 7 q^{41} - 25 q^{42} - 11 q^{43} - 34 q^{44} - 6 q^{45} - 29 q^{46} - 18 q^{47} + 18 q^{48} - 18 q^{49} + 16 q^{50} + 7 q^{51} - 20 q^{52} + 29 q^{53} - 6 q^{54} - q^{55} - 2 q^{56} - 8 q^{57} - 23 q^{58} - 21 q^{59} + 25 q^{60} + 3 q^{61} + 4 q^{62} + 34 q^{63} + 24 q^{64} + 2 q^{65} + 2 q^{66} + 45 q^{67} - 30 q^{68} + 26 q^{69} + 38 q^{70} - 14 q^{71} + 19 q^{72} + 19 q^{73} + 10 q^{74} - 28 q^{75} - 16 q^{76} + 2 q^{77} - 4 q^{78} - 15 q^{79} - 52 q^{80} - 44 q^{81} + 16 q^{82} + 18 q^{83} - 17 q^{84} - 19 q^{85} - 11 q^{86} - 23 q^{87} + 27 q^{88} + 25 q^{89} - 20 q^{90} - 4 q^{91} + 52 q^{92} + 4 q^{93} + 17 q^{94} + 6 q^{95} - 51 q^{96} - 34 q^{97} + 17 q^{98} - 30 q^{99}+O(q^{100}) \) 10 * q - 7 * q^2 - 7 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 - 5 * q^7 + 4 * q^8 - 2 * q^9 + q^10 + 7 * q^11 + 12 * q^12 - 3 * q^13 + 9 * q^14 + 12 * q^15 + q^16 - 10 * q^17 - 14 * q^18 + 2 * q^19 - 9 * q^20 - 2 * q^21 - 6 * q^22 - 12 * q^23 - 38 * q^24 - 4 * q^25 + 12 * q^26 - 4 * q^27 + 7 * q^28 + 14 * q^29 + 7 * q^30 + 10 * q^31 + 21 * q^32 + 16 * q^33 + 29 * q^34 + 7 * q^35 + 27 * q^36 - 19 * q^37 - 8 * q^38 + q^39 + q^40 + 7 * q^41 - 25 * q^42 - 11 * q^43 - 34 * q^44 - 6 * q^45 - 29 * q^46 - 18 * q^47 + 18 * q^48 - 18 * q^49 + 16 * q^50 + 7 * q^51 - 20 * q^52 + 29 * q^53 - 6 * q^54 - q^55 - 2 * q^56 - 8 * q^57 - 23 * q^58 - 21 * q^59 + 25 * q^60 + 3 * q^61 + 4 * q^62 + 34 * q^63 + 24 * q^64 + 2 * q^65 + 2 * q^66 + 45 * q^67 - 30 * q^68 + 26 * q^69 + 38 * q^70 - 14 * q^71 + 19 * q^72 + 19 * q^73 + 10 * q^74 - 28 * q^75 - 16 * q^76 + 2 * q^77 - 4 * q^78 - 15 * q^79 - 52 * q^80 - 44 * q^81 + 16 * q^82 + 18 * q^83 - 17 * q^84 - 19 * q^85 - 11 * q^86 - 23 * q^87 + 27 * q^88 + 25 * q^89 - 20 * q^90 - 4 * q^91 + 52 * q^92 + 4 * q^93 + 17 * q^94 + 6 * q^95 - 51 * q^96 - 34 * q^97 + 17 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/23\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{2}{11}\right)$

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 $

$2$	0.198939	+	0.435615i	0.140671	+	0.308026i	0.966834	−	0.255404i	$-0.0822085\pi$
$2$	0.198939	+	0.435615i	0.140671	+	0.308026i	−0.826163	+	0.563430i	$0.809481\pi$
$3$	−2.11435	+	0.620830i	−1.22072	+	0.358437i	−0.827741	−	0.561110i	$-0.810374\pi$
$3$	−2.11435	+	0.620830i	−1.22072	+	0.358437i	−0.392981	+	0.919546i	$0.628556\pi$
$4$	1.15954	−	1.33818i	0.579769	−	0.669089i
$5$	−2.18251	−	1.40261i	−0.976047	−	0.627267i	−0.0476526	−	0.998864i	$-0.515174\pi$
$5$	−2.18251	−	1.40261i	−0.976047	−	0.627267i	−0.928394	+	0.371597i	$0.878810\pi$
$6$	−0.691070	−	0.797537i	−0.282128	−	0.325593i
$7$	0.483568	+	3.36329i	0.182772	+	1.27120i	0.850172	+	0.526505i	$0.176498\pi$
$7$	0.483568	+	3.36329i	0.182772	+	1.27120i	−0.667400	+	0.744699i	$0.732593\pi$
$8$	1.73259	+	0.508735i	0.612564	+	0.179865i
$9$	1.56130	−	1.00339i	0.520434	−	0.334462i
$10$	0.176814	−	1.22977i	0.0559134	−	0.388886i
$11$	0.0950085	−	0.208040i	0.0286461	−	0.0627263i	−0.894768	−	0.446531i	$-0.852659\pi$
$11$	0.0950085	−	0.208040i	0.0286461	−	0.0627263i	0.923414	+	0.383805i	$0.125386\pi$
$12$	−1.62089	+	3.54926i	−0.467911	+	1.02458i
$13$	0.435418	−	3.02840i	0.120763	−	0.839926i	−0.835932	−	0.548833i	$-0.815072\pi$
$13$	0.435418	−	3.02840i	0.120763	−	0.839926i	0.956695	−	0.291093i	$-0.0940188\pi$
$14$	−1.36890	+	0.879739i	−0.365854	+	0.235120i
$15$	5.48538	+	1.61065i	1.41632	+	0.415868i
$16$	−0.380916	−	2.64933i	−0.0952290	−	0.662332i
$17$	1.26176	+	1.45615i	0.306021	+	0.353167i	0.887841	−	0.460150i	$-0.152205\pi$
$17$	1.26176	+	1.45615i	0.306021	+	0.353167i	−0.581820	+	0.813318i	$0.697659\pi$
$18$	0.747694	+	0.480513i	0.176233	+	0.113258i
$19$	−1.26668	+	1.46183i	−0.290596	+	0.335366i	−0.882210	−	0.470855i	$-0.843945\pi$
$19$	−1.26668	+	1.46183i	−0.290596	+	0.335366i	0.591614	+	0.806221i	$0.298491\pi$
$20$	−4.40764	+	1.29420i	−0.985579	+	0.289392i
$21$	−3.11047	−	6.81097i	−0.678760	−	1.48628i
$22$	0.109526			0.0233510
$23$	−4.62936	−	1.25259i	−0.965289	−	0.261183i
$23$	−4.62936	−	1.25259i	−0.965289	−	0.261183i
$24$	−3.97915			−0.812241
$25$	0.718941	+	1.57426i	0.143788	+	0.314852i
$26$	1.40584	−	0.412791i	0.275707	−	0.0809549i
$27$	1.65098	−	1.90533i	0.317730	−	0.366680i
$28$	5.06140	+	3.25276i	0.956514	+	0.614714i
$29$	4.23872	+	4.89174i	0.787110	+	0.908374i	0.997601	−	0.0692221i	$-0.0220517\pi$
$29$	4.23872	+	4.89174i	0.787110	+	0.908374i	−0.210491	+	0.977596i	$0.567506\pi$
$30$	0.389630	+	2.70993i	0.0711363	+	0.494764i
$31$	−1.44518	−	0.424344i	−0.259563	−	0.0762145i	0.149362	−	0.988783i	$-0.452278\pi$
$31$	−1.44518	−	0.424344i	−0.259563	−	0.0762145i	−0.408925	+	0.912568i	$0.634096\pi$
$32$	4.11648	−	2.64550i	0.727697	−	0.467662i
$33$	−0.0717243	+	0.498853i	−0.0124856	+	0.0868392i
$34$	−0.383307	+	0.839324i	−0.0657365	+	0.143943i
$35$	3.66200	−	8.01867i	0.618991	−	1.35540i
$36$	0.467677	−	3.25276i	0.0779461	−	0.542127i
$37$	−5.67778	+	3.64889i	−0.933421	+	0.599873i	−0.916522	−	0.399984i	$-0.869016\pi$
$37$	−5.67778	+	3.64889i	−0.933421	+	0.599873i	−0.0168987	+	0.999857i	$0.505379\pi$
$38$	−0.888785	−	0.260971i	−0.144180	−	0.0423351i
$39$	0.959493	+	6.67342i	0.153642	+	1.06860i
$40$	−3.06784	−	3.54047i	−0.485068	−	0.559798i
$41$	6.78612	+	4.36118i	1.05981	+	0.681101i	0.949809	−	0.312830i	$-0.101277\pi$
$41$	6.78612	+	4.36118i	1.05981	+	0.681101i	0.110005	+	0.993931i	$0.464913\pi$
$42$	2.34817	−	2.70993i	0.362331	−	0.418152i
$43$	−2.55172	+	0.749253i	−0.389134	+	0.114260i	−0.470446	−	0.882429i	$-0.655907\pi$
$43$	−2.55172	+	0.749253i	−0.389134	+	0.114260i	0.0813124	+	0.996689i	$0.474089\pi$
$44$	−0.168228	−	0.368368i	−0.0253613	−	0.0555336i
$45$	−4.81491			−0.717765
$46$	−0.375312	−	2.26581i	−0.0553368	−	0.334075i
$47$	−1.43889			−0.209883			−0.104942	−	0.994478i	$-0.533466\pi$
$47$	−1.43889			−0.209883			−0.104942	+	0.994478i	$0.533466\pi$
$48$	2.45018	+	5.36514i	0.353652	+	0.774391i
$49$	−4.36144	+	1.28064i	−0.623063	+	0.182948i
$50$	−0.542747	+	0.626363i	−0.0767560	+	0.0885811i
$51$	−3.57182	−	2.29547i	−0.500155	−	0.321430i
$52$	−3.54765	−	4.09421i	−0.491970	−	0.567764i
$53$	−1.22118	−	8.49350i	−0.167742	−	1.16667i	−0.883537	−	0.468361i	$-0.844845\pi$
$53$	−1.22118	−	8.49350i	−0.167742	−	1.16667i	0.715795	−	0.698311i	$-0.246065\pi$
$54$	1.15843	+	0.340146i	0.157643	+	0.0462880i
$55$	−0.499156	+	0.320788i	−0.0673061	+	0.0432550i
$56$	−0.873198	+	6.07322i	−0.116686	+	0.811569i
$57$	1.77066	−	3.87721i	0.234530	−	0.513549i
$58$	−1.28767	+	2.81961i	−0.169079	+	0.370232i
$59$	−0.00878786	+	0.0611209i	−0.00114408	+	0.00795726i	−0.990385	−	0.138335i	$-0.955825\pi$
$59$	−0.00878786	+	0.0611209i	−0.00114408	+	0.00795726i	0.989241	+	0.146292i	$0.0467340\pi$
$60$	8.51584	−	5.47280i	1.09939	−	0.706535i
$61$	0.0426294	+	0.0125171i	0.00545814	+	0.00160265i	0.284460	−	0.958688i	$-0.408186\pi$
$61$	0.0426294	+	0.0125171i	0.00545814	+	0.00160265i	−0.279002	+	0.960290i	$0.590004\pi$
$62$	−0.102652	−	0.713962i	−0.0130369	−	0.0906733i
$63$	4.12968	+	4.76590i	0.520291	+	0.600447i
$64$	−2.53201	−	1.62722i	−0.316501	−	0.203403i
$65$	−5.19797	+	5.99877i	−0.644728	+	0.744056i
$66$	−0.231577	+	0.0679971i	−0.0285051	+	0.00836986i
$67$	5.15445	+	11.2867i	0.629716	+	1.37889i	0.908237	+	0.418456i	$0.137429\pi$
$67$	5.15445	+	11.2867i	0.629716	+	1.37889i	−0.278521	+	0.960430i	$0.589844\pi$
$68$	3.41164			0.413722
$69$	10.5658	−	0.225629i	1.27197	−	0.0271626i
$70$	4.22157			0.504574
$71$	−3.46306	−	7.58305i	−0.410990	−	0.899943i	−0.996037	−	0.0889431i	$-0.971651\pi$
$71$	−3.46306	−	7.58305i	−0.410990	−	0.899943i	0.585047	−	0.811000i	$-0.301076\pi$
$72$	3.21556	−	0.944173i	0.378957	−	0.111272i
$73$	0.437593	−	0.505009i	0.0512164	−	0.0591069i	−0.729563	−	0.683913i	$-0.760277\pi$
$73$	0.437593	−	0.505009i	0.0512164	−	0.0591069i	0.780780	+	0.624806i	$0.214822\pi$
$74$	−2.71904	−	1.74742i	−0.316082	−	0.203133i
$75$	−2.49745	−	2.88221i	−0.288380	−	0.332808i
$76$	0.487421	+	3.39009i	0.0559110	+	0.388869i
$77$	0.745641	+	0.218940i	0.0849737	+	0.0249505i
$78$	−2.71616	+	1.74557i	−0.307545	+	0.197647i
$79$	1.70338	−	11.8472i	0.191645	−	1.33292i	−0.636010	−	0.771681i	$-0.719416\pi$
$79$	1.70338	−	11.8472i	0.191645	−	1.33292i	0.827655	−	0.561237i	$-0.189675\pi$
$80$	−2.88463	+	6.31646i	−0.322511	+	0.706202i
$81$	−4.62079	+	10.1181i	−0.513422	+	1.12424i
$82$	−0.549771	+	3.82374i	−0.0607121	+	0.422262i
$83$	−0.303301	+	0.194920i	−0.0332916	+	0.0213952i	−0.557181	−	0.830391i	$-0.688117\pi$
$83$	−0.303301	+	0.194920i	−0.0332916	+	0.0213952i	0.523889	+	0.851786i	$0.324481\pi$
$84$	−12.7210	−	3.73522i	−1.38797	−	0.407546i
$85$	−0.711387	−	4.94781i	−0.0771608	−	0.536665i
$86$	−0.834022	−	0.962513i	−0.0899349	−	0.103790i
$87$	−11.9991	−	7.71135i	−1.28644	−	0.826743i
$88$	0.270448	−	0.312114i	0.0288299	−	0.0332714i
$89$	15.4668	−	4.54147i	1.63948	−	0.481395i	0.673323	−	0.739348i	$-0.264866\pi$
$89$	15.4668	−	4.54147i	1.63948	−	0.481395i	0.966157	+	0.257953i	$0.0830481\pi$
$90$	−0.957872	−	2.09745i	−0.100969	−	0.221090i
$91$	10.3959			1.08979
$92$	−7.04411	+	4.74249i	−0.734399	+	0.494438i
$93$	3.31908			0.344172
$94$	−0.286250	−	0.626800i	−0.0295245	−	0.0646495i
$95$	4.81491	−	1.41379i	0.494000	−	0.145051i
$96$	−7.06128	+	8.14915i	−0.720689	+	0.831719i
$97$	−0.335292	−	0.215479i	−0.0340438	−	0.0218786i	0.523508	−	0.852021i	$-0.324623\pi$
$97$	−0.335292	−	0.215479i	−0.0340438	−	0.0218786i	−0.557552	+	0.830142i	$0.688259\pi$
$98$	−1.42552	−	1.64514i	−0.144000	−	0.166184i
$99$	−0.0604074	−	0.420143i	−0.00607117	−	0.0422259i
$100$	2.94028	+	0.863345i	0.294028	+	0.0863345i
$101$	−16.3914	+	10.5341i	−1.63100	+	1.04818i	−0.682756	+	0.730646i	$0.739219\pi$
$101$	−16.3914	+	10.5341i	−1.63100	+	1.04818i	−0.948246	+	0.317536i	$0.897145\pi$
$102$	0.289368	−	2.01260i	0.0286517	−	0.199277i
$103$	2.71041	−	5.93497i	0.267065	−	0.584790i	−0.727824	−	0.685763i	$-0.759468\pi$
$103$	2.71041	−	5.93497i	0.267065	−	0.584790i	0.994889	+	0.100973i	$0.0321957\pi$
$104$	2.29505	−	5.02547i	0.225048	−	0.492787i
$105$	−2.76454	+	19.2278i	−0.269791	+	1.87644i
$106$	3.45696	−	2.22165i	0.335769	−	0.215786i
$107$	1.24071	+	0.364304i	0.119944	+	0.0352186i	0.341154	−	0.940008i	$-0.389182\pi$
$107$	1.24071	+	0.364304i	0.119944	+	0.0352186i	−0.221210	+	0.975226i	$0.571001\pi$
$108$	−0.635298	−	4.41860i	−0.0611316	−	0.425180i
$109$	−4.63775	−	5.35225i	−0.444216	−	0.512653i	0.488845	−	0.872371i	$-0.337418\pi$
$109$	−4.63775	−	5.35225i	−0.444216	−	0.512653i	−0.933061	+	0.359718i	$0.882873\pi$
$110$	−0.239041	−	0.153623i	−0.0227917	−	0.0146473i
$111$	9.73949	−	11.2400i	0.924431	−	1.06685i
$112$	8.72627	−	2.56226i	0.824555	−	0.242111i
$113$	0.561616	+	1.22977i	0.0528324	+	0.115687i	0.934207	−	0.356731i	$-0.116109\pi$
$113$	0.561616	+	1.22977i	0.0528324	+	0.115687i	−0.881375	+	0.472418i	$0.843381\pi$
$114$	2.04122			0.191178
$115$	8.34672	+	9.22699i	0.778336	+	0.860421i
$116$	11.4610			1.06412
$117$	−2.35884	−	5.16513i	−0.218074	−	0.477516i
$118$	−0.0283734	+	0.00833119i	−0.00261199	+	0.000766948i
$119$	−4.28730	+	4.94781i	−0.393016	+	0.453565i
$120$	8.68453	+	5.58121i	0.792785	+	0.509492i
$121$	7.16921	+	8.27371i	0.651747	+	0.752156i
$122$	0.00302799	+	0.0210602i	0.000274142	+	0.00190670i
$123$	−17.0558	−	5.00804i	−1.53787	−	0.451560i
$124$	−2.24359	+	1.44187i	−0.201481	+	0.129484i
$125$	−1.20709	+	8.39549i	−0.107965	+	0.750915i
$126$	−1.25455	+	2.74707i	−0.111764	+	0.244729i
$127$	4.05571	−	8.88077i	0.359886	−	0.788041i	−0.639921	−	0.768440i	$-0.721033\pi$
$127$	4.05571	−	8.88077i	0.359886	−	0.788041i	0.999808	−	0.0196010i	$-0.00623958\pi$
$128$	1.59790	−	11.1136i	0.141235	−	0.982314i
$129$	4.93008	−	3.16837i	0.434070	−	0.278960i
$130$	−3.64723	−	1.07092i	−0.319883	−	0.0939262i
$131$	0.715092	+	4.97357i	0.0624779	+	0.434543i	0.996920	+	0.0784276i	$0.0249899\pi$
$131$	0.715092	+	4.97357i	0.0624779	+	0.434543i	−0.934442	+	0.356116i	$0.884101\pi$
$132$	0.584388	+	0.674419i	0.0508644	+	0.0587007i
$133$	−5.52908	−	3.55332i	−0.479432	−	0.308112i
$134$	−3.89122	+	4.49071i	−0.336150	+	0.387938i
$135$	−6.27570	+	1.84271i	−0.540126	+	0.158595i
$136$	1.44532	+	3.16481i	0.123935	+	0.271380i
$137$	−11.6182			−0.992608			−0.496304	−	0.868149i	$-0.665310\pi$
$137$	−11.6182			−0.992608			−0.496304	+	0.868149i	$0.665310\pi$
$138$	2.20023	+	4.55772i	0.187296	+	0.387979i
$139$	−17.3118			−1.46837			−0.734183	−	0.678952i	$-0.762435\pi$
$139$	−17.3118			−1.46837			−0.734183	+	0.678952i	$0.762435\pi$
$140$	−6.48417	−	14.1984i	−0.548013	−	1.19998i
$141$	3.04231	−	0.893304i	0.256209	−	0.0752298i
$142$	2.61435	−	3.01713i	0.219392	−	0.253192i
$143$	−0.588658	−	0.378307i	−0.0492260	−	0.0316357i
$144$	−3.25303	−	3.75419i	−0.271086	−	0.312850i
$145$	−2.38982	−	16.6215i	−0.198463	−	1.38034i
$146$	0.307044	+	0.0901562i	0.0254111	+	0.00746138i
$147$	8.42658	−	5.41543i	0.695012	−	0.446657i
$148$	−1.70074	+	11.8289i	−0.139800	+	0.972329i
$149$	−3.04537	+	6.66843i	−0.249487	+	0.546299i	−0.992395	−	0.123094i	$-0.960718\pi$
$149$	−3.04537	+	6.66843i	−0.249487	+	0.546299i	0.742909	+	0.669393i	$0.233446\pi$
$150$	0.758693	−	1.66131i	0.0619471	−	0.135645i
$151$	−2.43438	+	16.9315i	−0.198107	+	1.37786i	0.611665	+	0.791117i	$0.290500\pi$
$151$	−2.43438	+	16.9315i	−0.198107	+	1.37786i	−0.809772	+	0.586745i	$0.800409\pi$
$152$	−2.93832	+	1.88835i	−0.238329	+	0.153165i
$153$	3.43106	+	1.00745i	0.277385	+	0.0814476i
$154$	0.0529633	+	0.368368i	0.00426791	+	0.0296839i
$155$	2.55893	+	2.95317i	0.205538	+	0.237204i
$156$	10.0428	+	6.45411i	0.804067	+	0.516742i
$157$	11.7893	−	13.6056i	0.940887	−	1.08584i	−0.0552888	−	0.998470i	$-0.517608\pi$
$157$	11.7893	−	13.6056i	0.940887	−	1.08584i	0.996176	−	0.0873711i	$-0.0278466\pi$
$158$	5.49970	−	1.61486i	0.437533	−	0.128471i
$159$	7.85503	+	17.2001i	0.622944	+	1.36406i
$160$	−12.6948			−1.00362
$161$	1.97421	−	16.1756i	0.155590	−	1.27482i
$162$	−5.32686			−0.418518
$163$	6.19185	+	13.5583i	0.484983	+	1.06196i	0.981063	+	0.193688i	$0.0620448\pi$
$163$	6.19185	+	13.5583i	0.484983	+	1.06196i	−0.496080	+	0.868277i	$0.665228\pi$
$164$	13.7048	−	4.02409i	1.07016	−	0.314229i
$165$	0.856237	−	0.988150i	0.0666579	−	0.0769274i
$166$	−0.145248	−	0.0933454i	−0.0112735	−	0.00724501i
$167$	−5.00291	−	5.77367i	−0.387137	−	0.446780i	0.528411	−	0.848989i	$-0.322788\pi$
$167$	−5.00291	−	5.77367i	−0.387137	−	0.446780i	−0.915548	+	0.402209i	$0.868243\pi$
$168$	−1.92419	−	13.3831i	−0.148455	−	1.03252i
$169$	3.49182	+	1.02529i	0.268601	+	0.0788684i
$170$	2.01382	−	1.29420i	0.154453	−	0.0992607i
$171$	−0.510890	+	3.55332i	−0.0390688	+	0.271729i
$172$	−1.95618	+	4.28344i	−0.149158	+	0.326610i
$173$	2.48585	−	5.44324i	0.188995	−	0.413842i	−0.791287	−	0.611445i	$-0.790588\pi$
$173$	2.48585	−	5.44324i	0.188995	−	0.413842i	0.980282	+	0.197603i	$0.0633157\pi$
$174$	0.972095	−	6.76107i	0.0736943	−	0.512555i
$175$	−4.94704	+	3.17927i	−0.373961	+	0.240330i
$176$	−0.587356	−	0.172463i	−0.0442736	−	0.0129999i
$177$	−0.0193651	−	0.134687i	−0.00145557	−	0.0101237i
$178$	5.05528	+	5.83411i	0.378909	+	0.437285i
$179$	3.02147	+	1.94178i	0.225836	+	0.145136i	0.648666	−	0.761073i	$-0.275327\pi$
$179$	3.02147	+	1.94178i	0.225836	+	0.145136i	−0.422831	+	0.906209i	$0.638963\pi$
$180$	−5.58307	+	6.44321i	−0.416138	+	0.480248i
$181$	−18.3033	+	5.37433i	−1.36047	+	0.399470i	−0.878929	−	0.476952i	$-0.841741\pi$
$181$	−18.3033	+	5.37433i	−1.36047	+	0.399470i	−0.481542	+	0.876423i	$0.659923\pi$
$182$	2.06815	+	4.52862i	0.153302	+	0.335684i
$183$	−0.0979047			−0.00723732
$184$	−7.38357	−	4.52535i	−0.544324	−	0.333613i
$185$	17.5098			1.28734
$186$	0.660293	+	1.44584i	0.0484150	+	0.106014i
$187$	0.422814	−	0.124149i	0.0309192	−	0.00907870i
$188$	−1.66844	+	1.92549i	−0.121684	+	0.140430i
$189$	7.20653	+	4.63136i	0.524198	+	0.336882i
$190$	1.57374	+	1.81619i	0.114171	+	0.131760i
$191$	1.86285	+	12.9564i	0.134791	+	0.937494i	0.939188	+	0.343402i	$0.111579\pi$
$191$	1.86285	+	12.9564i	0.134791	+	0.937494i	−0.804397	+	0.594092i	$0.797511\pi$
$192$	6.36379	+	1.86858i	0.459267	+	0.134853i
$193$	7.89406	−	5.07320i	0.568227	−	0.365177i	−0.224762	−	0.974414i	$-0.572160\pi$
$193$	7.89406	−	5.07320i	0.568227	−	0.365177i	0.792988	+	0.609237i	$0.208524\pi$
$194$	0.0271634	−	0.188925i	0.00195022	−	0.0135641i
$195$	7.26612	−	15.9106i	0.520338	−	1.13938i
$196$	−3.34354	+	7.32133i	−0.238824	+	0.522952i
$197$	1.47479	−	10.2574i	0.105074	−	0.730809i	−0.867368	−	0.497667i	$-0.834190\pi$
$197$	1.47479	−	10.2574i	0.105074	−	0.730809i	0.972443	−	0.233142i	$-0.0749007\pi$
$198$	0.171003	−	0.109897i	0.0121527	−	0.00781004i
$199$	−9.84113	−	2.88962i	−0.697619	−	0.204839i	−0.0863529	−	0.996265i	$-0.527521\pi$
$199$	−9.84113	−	2.88962i	−0.697619	−	0.204839i	−0.611266	+	0.791425i	$0.709339\pi$
$200$	0.444750	+	3.09331i	0.0314486	+	0.218730i
$201$	−17.9054	−	20.6640i	−1.26295	−	1.45752i
$202$	−7.84969	−	5.04469i	−0.552302	−	0.354943i
$203$	−14.4026	+	16.6215i	−1.01087	+	1.16660i
$204$	−7.21341	+	2.11805i	−0.505040	+	0.148293i
$205$	−8.69372	−	19.0366i	−0.607196	−	1.32957i
$206$	3.12457			0.217699
$207$	−8.48466	+	2.68937i	−0.589725	+	0.186924i
$208$	−8.18908			−0.567810
$209$	0.183772	+	0.402405i	0.0127118	+	0.0278350i
$210$	−8.92588	+	2.62088i	−0.615944	+	0.180858i
$211$	5.41619	−	6.25061i	0.372866	−	0.430310i	−0.538043	−	0.842917i	$-0.680836\pi$
$211$	5.41619	−	6.25061i	0.372866	−	0.430310i	0.910909	+	0.412607i	$0.135382\pi$
$212$	−12.7818	−	8.21438i	−0.877859	−	0.564166i
$213$	12.0299	+	13.8833i	0.824277	+	0.951267i
$214$	0.0881282	+	0.612945i	0.00602432	+	0.0419000i
$215$	6.62006	+	1.94383i	0.451484	+	0.132568i
$216$	3.82977	−	2.46125i	0.260583	−	0.167467i
$217$	0.728348	−	5.06577i	0.0494435	−	0.343887i
$218$	1.40889	−	3.08504i	0.0954222	−	0.208946i
$219$	−0.611702	+	1.33944i	−0.0413350	+	0.0905110i
$220$	−0.149519	+	1.03992i	−0.0100805	+	0.0701117i
$221$	4.95918	−	3.18707i	0.333590	−	0.214386i
$222$	6.83386	+	2.00660i	0.458659	+	0.134674i
$223$	1.53616	+	10.6843i	0.102869	+	0.715471i	0.974349	+	0.225040i	$0.0722514\pi$
$223$	1.53616	+	10.6843i	0.102869	+	0.715471i	−0.871480	+	0.490431i	$0.836840\pi$
$224$	10.8882	+	12.5656i	0.727497	+	0.839577i
$225$	2.70208	+	1.73652i	0.180138	+	0.115768i
$226$	−0.423978	+	0.489296i	−0.0282026	+	0.0325475i
$227$	22.2762	−	6.54089i	1.47853	−	0.434134i	0.559666	−	0.828718i	$-0.310930\pi$
$227$	22.2762	−	6.54089i	1.47853	−	0.434134i	0.918860	+	0.394584i	$0.129111\pi$
$228$	−3.13525	−	6.86523i	−0.207637	−	0.454661i
$229$	14.1883			0.937587			0.468794	−	0.883308i	$-0.344689\pi$
$229$	14.1883			0.937587			0.468794	+	0.883308i	$0.344689\pi$
$230$	−2.35893	+	5.47156i	−0.155543	+	0.360784i
$231$	−1.71247			−0.112672
$232$	4.85537	+	10.6318i	0.318771	+	0.698011i
$233$	−23.6240	+	6.93663i	−1.54766	+	0.454434i	−0.940400	−	0.340070i	$-0.889549\pi$
$233$	−23.6240	+	6.93663i	−1.54766	+	0.454434i	−0.607260	+	0.794504i	$0.707731\pi$
$234$	1.78074	−	2.05509i	0.116411	−	0.134345i
$235$	3.14038	+	2.01820i	0.204856	+	0.131653i
$236$	0.0716008	+	0.0826317i	0.00466081	+	0.00537887i
$237$	3.75358	+	26.1068i	0.243822	+	1.69582i
$238$	−3.00825	−	0.883301i	−0.194996	−	0.0572559i
$239$	0.197590	−	0.126983i	0.0127810	−	0.00821388i	−0.534235	−	0.845336i	$-0.679400\pi$
$239$	0.197590	−	0.126983i	0.0127810	−	0.00821388i	0.547016	+	0.837122i	$0.315764\pi$
$240$	2.17768	−	15.1461i	0.140569	−	0.977676i
$241$	2.18829	−	4.79168i	0.140960	−	0.308659i	−0.825964	−	0.563722i	$-0.809369\pi$
$241$	2.18829	−	4.79168i	0.140960	−	0.308659i	0.966925	+	0.255063i	$0.0820961\pi$
$242$	−2.17792	+	4.76898i	−0.140002	+	0.306562i
$243$	2.41198	−	16.7757i	0.154729	−	1.07616i
$244$	0.0661806	−	0.0425317i	0.00423678	−	0.00272281i
$245$	11.3151	+	3.32242i	0.722896	+	0.212261i
$246$	−1.21148	−	8.42606i	−0.0772414	−	0.537226i
$247$	3.87545	+	4.47251i	0.246589	+	0.284579i
$248$	−2.28804	−	1.47043i	−0.145290	−	0.0933725i
$249$	0.520274	−	0.600428i	0.0329710	−	0.0380506i
$250$	−3.89734	+	1.14436i	−0.246489	+	0.0723758i
$251$	−12.1250	−	26.5500i	−0.765322	−	1.67582i	−0.736690	−	0.676231i	$-0.763612\pi$
$251$	−12.1250	−	26.5500i	−0.765322	−	1.67582i	−0.0286319	−	0.999590i	$-0.509115\pi$
$252$	11.1661			0.703401
$253$	−0.700417	+	0.844084i	−0.0440349	+	0.0530671i
$254$	4.67544			0.293363
$255$	4.57587	+	10.0198i	0.286552	+	0.627462i
$256$	−0.616632	+	0.181059i	−0.0385395	+	0.0113162i
$257$	−7.40518	+	8.54603i	−0.461922	+	0.533087i	−0.938147	−	0.346237i	$-0.887459\pi$
$257$	−7.40518	+	8.54603i	−0.461922	+	0.533087i	0.476225	+	0.879324i	$0.342005\pi$
$258$	2.36097	+	1.51731i	0.146988	+	0.0944634i
$259$	−15.0179	−	17.3315i	−0.933164	−	1.07693i
$260$	2.00019	+	13.9116i	0.124046	+	0.862761i
$261$	11.5262	+	3.38441i	0.713455	+	0.209489i
$262$	−2.02430	+	1.30094i	−0.125062	+	0.0803724i
$263$	3.42761	−	23.8395i	0.211355	−	1.47001i	−0.557282	−	0.830324i	$-0.688156\pi$
$263$	3.42761	−	23.8395i	0.211355	−	1.47001i	0.768637	−	0.639685i	$-0.220935\pi$
$264$	−0.378053	+	0.827821i	−0.0232676	+	0.0509489i
$265$	−9.24785	+	20.2500i	−0.568091	+	1.24395i
$266$	0.447933	−	3.11544i	0.0274645	−	0.191020i
$267$	−29.8829	+	19.2045i	−1.82880	+	1.17530i
$268$	21.0803	+	6.18975i	1.28769	+	0.378099i
$269$	−0.934084	−	6.49670i	−0.0569521	−	0.396111i	−0.998280	−	0.0586185i	$-0.981330\pi$
$269$	−0.934084	−	6.49670i	−0.0569521	−	0.396111i	0.941328	−	0.337492i	$-0.109579\pi$
$270$	−2.05119	−	2.36720i	−0.124832	−	0.144063i
$271$	16.8532	+	10.8309i	1.02376	+	0.657931i	0.940919	−	0.338632i	$-0.109964\pi$
$271$	16.8532	+	10.8309i	1.02376	+	0.657931i	0.0828417	+	0.996563i	$0.473600\pi$
$272$	3.37719	−	3.89748i	0.204772	−	0.236320i
$273$	−21.9807	+	6.45411i	−1.33033	+	0.390621i
$274$	−2.31131	−	5.06105i	−0.139631	−	0.305750i
$275$	0.395814			0.0238685
$276$	11.9495	−	14.4005i	0.719273	−	0.866808i
$277$	−7.60036			−0.456661			−0.228331	−	0.973584i	$-0.573327\pi$
$277$	−7.60036			−0.456661			−0.228331	+	0.973584i	$0.573327\pi$
$278$	−3.44398	−	7.54127i	−0.206556	−	0.452295i
$279$	−2.68215	+	0.787550i	−0.160576	+	0.0471494i
$280$	10.4241	−	12.0301i	0.622961	−	0.718936i
$281$	−27.0260	−	17.3686i	−1.61224	−	1.03612i	−0.960732	−	0.277479i	$-0.910501\pi$
$281$	−27.0260	−	17.3686i	−1.61224	−	1.03612i	−0.651506	−	0.758644i	$-0.725862\pi$
$282$	0.994371	+	1.14757i	0.0592139	+	0.0683365i
$283$	0.859497	+	5.97793i	0.0510918	+	0.355351i	0.999290	+	0.0376723i	$0.0119943\pi$
$283$	0.859497	+	5.97793i	0.0510918	+	0.355351i	−0.948198	+	0.317679i	$0.897097\pi$
$284$	−14.1630	−	4.15864i	−0.840421	−	0.246770i
$285$	−9.30271	+	5.97849i	−0.551045	+	0.354135i
$286$	0.0476896	−	0.331688i	0.00281994	−	0.0196131i
$287$	−11.3864	+	24.9326i	−0.672115	+	1.47173i
$288$	3.77260	−	8.26084i	0.222302	−	0.486775i
$289$	1.89102	−	13.1524i	0.111237	−	0.773668i
$290$	6.76516	−	4.34771i	0.397264	−	0.255306i
$291$	0.842702	+	0.247440i	0.0494001	+	0.0145052i
$292$	−0.168387	−	1.17116i	−0.00985408	−	0.0685367i
$293$	19.1592	+	22.1109i	1.11929	+	1.29173i	0.952092	+	0.305813i	$0.0989281\pi$
$293$	19.1592	+	22.1109i	1.11929	+	1.29173i	0.167203	+	0.985922i	$0.446526\pi$
$294$	4.03542	+	2.59340i	0.235350	+	0.151250i
$295$	0.104908	−	0.121071i	0.00610801	−	0.00704902i
$296$	−11.6936	+	3.43355i	−0.679676	+	0.199571i
$297$	−0.239527	−	0.524490i	−0.0138988	−	0.0304340i
$298$	−3.51071			−0.203370
$299$	−5.80905	+	13.4741i	−0.335946	+	0.779230i
$300$	−6.75279			−0.389872
$301$	−3.75389	−	8.21987i	−0.216371	−	0.473785i
$302$	−7.85989	+	2.30787i	−0.452286	+	0.132803i
$303$	28.1173	−	32.4491i	1.61530	−	1.86415i
$304$	4.35536	+	2.79902i	0.249797	+	0.160535i
$305$	−0.0754823	−	0.0871112i	−0.00432211	−	0.00498798i
$306$	0.243710	+	1.69504i	0.0139320	+	0.0968991i
$307$	8.22363	+	2.41468i	0.469347	+	0.137813i	0.507850	−	0.861446i	$-0.330441\pi$
$307$	8.22363	+	2.41468i	0.469347	+	0.137813i	−0.0385023	+	0.999259i	$0.512259\pi$
$308$	1.15758	−	0.743931i	0.0659592	−	0.0423894i
$309$	−2.04616	+	14.2313i	−0.116402	+	0.809592i
$310$	−0.777373	+	1.70221i	−0.0441518	+	0.0966790i
$311$	0.0876947	−	0.192025i	0.00497271	−	0.0108887i	−0.907129	−	0.420852i	$-0.861731\pi$
$311$	0.0876947	−	0.192025i	0.00497271	−	0.0108887i	0.912102	+	0.409963i	$0.134458\pi$
$312$	−1.73259	+	12.0505i	−0.0980888	+	0.682222i
$313$	24.7874	−	15.9299i	1.40107	−	0.900412i	0.401189	−	0.915995i	$-0.368597\pi$
$313$	24.7874	−	15.9299i	1.40107	−	0.900412i	0.999879	+	0.0155835i	$0.00496059\pi$
$314$	8.27213	+	2.42892i	0.466823	+	0.137072i
$315$	−2.32834	−	16.1940i	−0.131187	−	0.912426i
$316$	−13.8786	−	16.0167i	−0.780731	−	0.901012i
$317$	22.1011	+	14.2035i	1.24132	+	0.797749i	0.985615	−	0.169006i	$-0.0540557\pi$
$317$	22.1011	+	14.2035i	1.24132	+	0.797749i	0.255706	+	0.966755i	$0.417692\pi$
$318$	−5.92996	+	6.84354i	−0.332536	+	0.383767i
$319$	1.42039	−	0.417064i	0.0795266	−	0.0233511i
$320$	3.24376	+	7.10285i	0.181332	+	0.397061i
$321$	−2.84947			−0.159042
$322$	7.43909	−	2.35796i	0.414564	−	0.131404i
$323$	−3.72688			−0.207369
$324$	8.18187	+	17.9158i	0.454548	+	0.995322i
$325$	5.08053	−	1.49178i	0.281817	−	0.0827489i
$326$	−4.67438	+	5.39452i	−0.258890	+	0.298775i
$327$	13.1287	+	8.43730i	0.726018	+	0.466583i
$328$	9.53891	+	11.0085i	0.526698	+	0.607842i
$329$	−0.695800	−	4.83939i	−0.0383607	−	0.266804i
$330$	0.600791	+	0.176408i	0.0330725	+	0.00971096i
$331$	19.1448	−	12.3036i	1.05229	−	0.676269i	0.104297	−	0.994546i	$-0.466741\pi$
$331$	19.1448	−	12.3036i	1.05229	−	0.676269i	0.947998	+	0.318277i	$0.103104\pi$
$332$	−0.0908517	+	0.631888i	−0.00498614	+	0.0346793i
$333$	−5.20347	+	11.3940i	−0.285149	+	0.624388i
$334$	1.51982	−	3.32795i	0.0831611	−	0.182097i
$335$	4.58120	−	31.8629i	0.250298	−	1.74086i
$336$	−16.8597	+	10.8351i	−0.919772	+	0.591101i
$337$	−0.573517	−	0.168400i	−0.0312414	−	0.00917332i	0.266074	−	0.963952i	$-0.414273\pi$
$337$	−0.573517	−	0.168400i	−0.0312414	−	0.00917332i	−0.297316	+	0.954779i	$0.596091\pi$
$338$	0.248026	+	1.72506i	0.0134908	+	0.0938307i
$339$	−1.95093	−	2.25149i	−0.105960	−	0.122284i
$340$	−7.44592	−	4.78520i	−0.403812	−	0.259514i
$341$	−0.225585	+	0.260339i	−0.0122161	+	0.0140982i
$342$	−1.64952	+	0.484341i	−0.0891956	+	0.0261902i
$343$	3.46450	+	7.58619i	0.187065	+	0.409616i
$344$	−4.80227			−0.258921
$345$	−23.3763	−	14.3272i	−1.25854	−	0.771352i
$346$	2.86569			0.154060
$347$	0.240693	+	0.527045i	0.0129211	+	0.0282933i	0.915983	−	0.401218i	$-0.131413\pi$
$347$	0.240693	+	0.527045i	0.0129211	+	0.0282933i	−0.903061	+	0.429511i	$0.858686\pi$
$348$	−24.2326	+	7.11532i	−1.29900	+	0.381421i
$349$	−14.2226	+	16.4138i	−0.761320	+	0.878610i	−0.995614	−	0.0935554i	$-0.970177\pi$
$349$	−14.2226	+	16.4138i	−0.761320	+	0.878610i	0.234294	+	0.972166i	$0.424722\pi$
$350$	−2.36910	−	1.52253i	−0.126634	−	0.0813825i
$351$	−5.05122	−	5.82942i	−0.269614	−	0.311151i
$352$	−0.159268	−	1.10773i	−0.00848902	−	0.0590425i
$353$	−0.640923	−	0.188192i	−0.0341129	−	0.0100164i	0.264632	−	0.964350i	$-0.414750\pi$
$353$	−0.640923	−	0.188192i	−0.0341129	−	0.0100164i	−0.298744	+	0.954333i	$0.596568\pi$
$354$	0.0548192	−	0.0352302i	0.00291361	−	0.00187246i
$355$	−3.07792	+	21.4074i	−0.163359	+	1.13619i
$356$	11.8571	−	25.9634i	0.628424	−	1.37606i
$357$	5.99312	−	13.1231i	0.317189	−	0.694548i
$358$	−0.244782	+	1.70250i	−0.0129371	+	0.0899797i
$359$	−13.5495	+	8.70775i	−0.715116	+	0.459577i	−0.846935	−	0.531697i	$-0.821555\pi$
$359$	−13.5495	+	8.70775i	−0.715116	+	0.459577i	0.131819	+	0.991274i	$0.457918\pi$
$360$	−8.34229	−	2.44952i	−0.439677	−	0.129101i
$361$	2.17152	+	15.1033i	0.114291	+	0.794909i
$362$	−5.98237	−	6.90402i	−0.314426	−	0.362867i
$363$	−20.2948	−	13.0427i	−1.06520	−	0.684564i
$364$	12.0545	−	13.9116i	0.631826	−	0.729166i
$365$	−1.66338	+	0.488413i	−0.0870654	+	0.0255647i
$366$	−0.0194770	−	0.0426487i	−0.00101808	−	0.00222929i
$367$	−27.2461			−1.42223			−0.711117	−	0.703074i	$-0.751810\pi$
$367$	−27.2461			−1.42223			−0.711117	+	0.703074i	$0.751810\pi$
$368$	−1.55513	+	12.7418i	−0.0810666	+	0.664215i
$369$	14.9711			0.779366
$370$	3.48337	+	7.62751i	0.181092	+	0.396536i
$371$	27.9756	−	8.21438i	1.45242	−	0.426469i
$372$	3.84859	−	4.44151i	0.199540	−	0.230282i
$373$	13.9324	+	8.95383i	0.721394	+	0.463612i	0.849122	−	0.528198i	$-0.177132\pi$
$373$	13.9324	+	8.95383i	0.721394	+	0.463612i	−0.127728	+	0.991809i	$0.540768\pi$
$374$	0.138195	+	0.159486i	0.00714591	+	0.00824682i
$375$	−2.65996	−	18.5004i	−0.137360	−	0.955358i
$376$	−2.49300	−	0.732012i	−0.128567	−	0.0377506i
$377$	16.6597	−	10.7066i	0.858020	−	0.551416i
$378$	−0.583830	+	4.06063i	−0.0300290	+	0.208856i
$379$	4.88324	−	10.6928i	0.250835	−	0.549252i	−0.741768	−	0.670657i	$-0.766012\pi$
$379$	4.88324	−	10.6928i	0.250835	−	0.549252i	0.992603	+	0.121404i	$0.0387397\pi$
$380$	3.69118	−	8.08255i	0.189353	−	0.414626i
$381$	−3.06176	+	21.2950i	−0.156859	+	1.09098i
$382$	−5.27342	+	3.38902i	−0.269812	+	0.173397i
$383$	−10.7581	−	3.15886i	−0.549712	−	0.161410i	−0.00493016	−	0.999988i	$-0.501569\pi$
$383$	−10.7581	−	3.15886i	−0.549712	−	0.161410i	−0.544782	+	0.838578i	$0.683388\pi$
$384$	3.52115	+	24.4901i	0.179688	+	1.24976i
$385$	−1.32028	−	1.52368i	−0.0672876	−	0.0776541i
$386$	3.78040	+	2.42951i	0.192417	+	0.123659i
$387$	−3.23221	+	3.73017i	−0.164303	+	0.189615i
$388$	−0.677133	+	0.198824i	−0.0343762	+	0.0100938i
$389$	−1.70031	−	3.72317i	−0.0862093	−	0.188772i	0.861617	−	0.507559i	$-0.169452\pi$
$389$	−1.70031	−	3.72317i	−0.0862093	−	0.188772i	−0.947827	+	0.318787i	$0.896725\pi$
$390$	8.37640			0.424156
$391$	−4.01718	−	8.32150i	−0.203158	−	0.420836i
$392$	−8.20811			−0.414572
$393$	−4.59970	−	10.0719i	−0.232024	−	0.508062i
$394$	4.76167	−	1.39815i	0.239889	−	0.0704379i
$395$	−20.3347	+	23.4675i	−1.02315	+	1.18078i
$396$	−0.632270	−	0.406335i	−0.0317728	−	0.0204191i
$397$	−1.77958	−	2.05374i	−0.0893144	−	0.103074i	0.709333	−	0.704873i	$-0.248996\pi$
$397$	−1.77958	−	2.05374i	−0.0893144	−	0.103074i	−0.798647	+	0.601799i	$0.794451\pi$
$398$	−0.699021	−	4.86180i	−0.0350388	−	0.243700i
$399$	13.8964	+	4.08036i	0.695692	+	0.204273i
$400$	3.89688	−	2.50437i	0.194844	−	0.125219i
$401$	−2.59356	+	18.0386i	−0.129516	+	0.900805i	0.816652	+	0.577130i	$0.195828\pi$
$401$	−2.59356	+	18.0386i	−0.129516	+	0.900805i	−0.946168	+	0.323675i	$0.895082\pi$
$402$	5.43945	−	11.9107i	0.271295	−	0.594054i
$403$	−1.91434	+	4.19182i	−0.0953601	+	0.208809i
$404$	−4.90992	+	34.1493i	−0.244278	+	1.69899i
$405$	24.2767	−	15.6017i	1.20632	−	0.775255i
$406$	−10.1058	−	2.96734i	−0.501544	−	0.147267i
$407$	0.219676	+	1.52788i	0.0108889	+	0.0757341i
$408$	−5.02073	−	5.79423i	−0.248563	−	0.286857i
$409$	−11.0096	−	7.07541i	−0.544387	−	0.349856i	0.239365	−	0.970930i	$-0.423061\pi$
$409$	−11.0096	−	7.07541i	−0.544387	−	0.349856i	−0.783753	+	0.621073i	$0.786697\pi$
$410$	6.56311	−	7.57423i	0.324129	−	0.374065i
$411$	24.5649	−	7.21292i	1.21170	−	0.355787i
$412$	−4.79922	−	10.5088i	−0.236441	−	0.517733i
$413$	−0.209817			−0.0103244
$414$	−2.85946	−	3.16103i	−0.140535	−	0.155356i
$415$	0.935353			0.0459147
$416$	−6.21923	−	13.6182i	−0.304923	−	0.667688i
$417$	36.6032	−	10.7477i	1.79247	−	0.526316i
$418$	−0.138734	+	0.160108i	−0.00678572	+	0.00783114i
$419$	1.70412	+	1.09517i	0.0832517	+	0.0535026i	0.581604	−	0.813472i	$-0.302425\pi$
$419$	1.70412	+	1.09517i	0.0832517	+	0.0535026i	−0.498353	+	0.866974i	$0.666062\pi$
$420$	22.5246	+	25.9948i	1.09909	+	1.26842i
$421$	2.05091	+	14.2644i	0.0999551	+	0.695203i	0.976757	+	0.214351i	$0.0687636\pi$
$421$	2.05091	+	14.2644i	0.0999551	+	0.695203i	−0.876802	+	0.480852i	$0.840327\pi$
$422$	3.80035	+	1.11588i	0.184998	+	0.0543203i
$423$	−2.24653	+	1.44376i	−0.109230	+	0.0701980i
$424$	2.20513	−	15.3370i	0.107091	−	0.744832i
$425$	−1.38523	+	3.03322i	−0.0671933	+	0.147133i
$426$	−3.65455	+	8.00234i	−0.177063	+	0.387715i
$427$	−0.0214845	+	0.149428i	−0.00103971	+	0.00723133i
$428$	1.92615	−	1.23786i	0.0931040	−	0.0598343i
$429$	1.47950	+	0.434419i	0.0714307	+	0.0209740i
$430$	0.470227	+	3.27050i	0.0226764	+	0.157718i
$431$	8.71955	+	10.0629i	0.420006	+	0.484713i	0.925839	−	0.377919i	$-0.123360\pi$
$431$	8.71955	+	10.0629i	0.420006	+	0.484713i	−0.505833	+	0.862632i	$0.668815\pi$
$432$	−5.67672	−	3.64821i	−0.273121	−	0.175524i
$433$	−23.1416	+	26.7069i	−1.11212	+	1.28345i	−0.156875	+	0.987618i	$0.550142\pi$
$433$	−23.1416	+	26.7069i	−1.11212	+	1.28345i	−0.955240	+	0.295831i	$0.904404\pi$
$434$	2.35162	−	0.690499i	0.112882	−	0.0331450i
$435$	15.3721	+	33.6601i	0.737034	+	1.61388i
$436$	−12.5399			−0.600553
$437$	7.69499	−	5.18070i	0.368101	−	0.247826i
$438$	−0.705171			−0.0336944
$439$	−5.36516	−	11.7481i	−0.256065	−	0.560705i	0.737319	−	0.675545i	$-0.236092\pi$
$439$	−5.36516	−	11.7481i	−0.256065	−	0.560705i	−0.993384	+	0.114840i	$0.963364\pi$
$440$	−1.02803	+	0.301857i	−0.0490094	+	0.0143905i
$441$	−5.52455	+	6.37567i	−0.263074	+	0.303603i
$442$	2.37491	+	1.52626i	0.112963	+	0.0725968i
$443$	4.67301	+	5.39295i	0.222022	+	0.256227i	0.855822	−	0.517270i	$-0.173052\pi$
$443$	4.67301	+	5.39295i	0.222022	+	0.256227i	−0.633801	+	0.773496i	$0.718506\pi$
$444$	−3.74777	−	26.0663i	−0.177861	−	1.23705i
$445$	−40.1264	−	11.7822i	−1.90217	−	0.558528i
$446$	−4.34862	+	2.79469i	−0.205913	+	0.132332i
$447$	2.29903	−	15.9901i	0.108740	−	0.756305i
$448$	4.24843	−	9.30276i	0.200719	−	0.439514i
$449$	−1.27291	+	2.78729i	−0.0600725	+	0.131540i	−0.937287	−	0.348558i	$-0.886672\pi$
$449$	−1.27291	+	2.78729i	−0.0600725	+	0.131540i	0.877215	+	0.480098i	$0.159399\pi$
$450$	−0.218906	+	1.52253i	−0.0103193	+	0.0717726i
$451$	1.55204	−	0.997433i	0.0730825	−	0.0469673i
$452$	2.29686	+	0.674419i	0.108035	+	0.0317220i
$453$	−5.36443	−	37.3104i	−0.252043	−	1.75300i
$454$	7.28092	+	8.40262i	0.341710	+	0.394355i
$455$	−22.6892	−	14.5815i	−1.06369	−	0.683589i
$456$	5.04031	−	5.81683i	0.236034	−	0.272398i
$457$	−16.2369	+	4.76757i	−0.759528	+	0.223018i	−0.638490	−	0.769630i	$-0.720441\pi$
$457$	−16.2369	+	4.76757i	−0.759528	+	0.223018i	−0.121038	+	0.992648i	$0.538622\pi$
$458$	2.82260	+	6.18062i	0.131891	+	0.288801i
$459$	4.85756			0.226732
$460$	22.0257	−	0.470354i	1.02695	−	0.0219304i
$461$	−3.84880			−0.179257			−0.0896283	−	0.995975i	$-0.528568\pi$
$461$	−3.84880			−0.179257			−0.0896283	+	0.995975i	$0.528568\pi$
$462$	−0.340677	−	0.745979i	−0.0158497	−	0.0347061i
$463$	−10.9561	+	3.21699i	−0.509171	+	0.149506i	−0.526220	−	0.850349i	$-0.676391\pi$
$463$	−10.9561	+	3.21699i	−0.509171	+	0.149506i	0.0170489	+	0.999855i	$0.494573\pi$
$464$	11.3452	−	13.0931i	0.526690	−	0.607832i
$465$	−7.24391	−	4.65538i	−0.335928	−	0.215888i
$466$	−7.72143	−	8.91100i	−0.357688	−	0.412794i
$467$	−4.00360	−	27.8456i	−0.185264	−	1.28854i	−0.844072	−	0.536230i	$-0.819848\pi$
$467$	−4.00360	−	27.8456i	−0.185264	−	1.28854i	0.658808	−	0.752311i	$-0.271061\pi$
$468$	−9.64702	−	2.83262i	−0.445934	−	0.130938i
$469$	−35.4678	+	22.7938i	−1.63775	+	1.05252i
$470$	−0.254415	+	1.76949i	−0.0117353	+	0.0816207i
$471$	−16.4800	+	36.0861i	−0.759357	+	1.66276i
$472$	−0.0463201	+	0.101427i	−0.00213206	+	0.00466856i
$473$	−0.0865609	+	0.602045i	−0.00398008	+	0.0276820i
$474$	−10.6258	+	6.82876i	−0.488057	+	0.313655i
$475$	−3.21197	−	0.943118i	−0.147375	−	0.0432732i
$476$	1.64976	+	11.4743i	0.0756166	+	0.525925i
$477$	−10.4289	−	12.0356i	−0.477507	−	0.551072i
$478$	0.0946242	+	0.0608113i	0.00432801	+	0.00278144i
$479$	15.6156	−	18.0213i	0.713493	−	0.823415i	−0.277015	−	0.960866i	$-0.589345\pi$
$479$	15.6156	−	18.0213i	0.713493	−	0.823415i	0.990509	+	0.137450i	$0.0438907\pi$
$480$	26.8414	−	7.88134i	1.22514	−	0.359733i
$481$	8.57807	+	18.7833i	0.391126	+	0.856447i
$482$	2.52266			0.114904
$483$	5.86813	+	35.4266i	0.267009	+	1.61197i
$484$	19.3847			0.881122
$485$	0.429544	+	0.940570i	0.0195046	+	0.0427091i
$486$	7.78758	−	2.28664i	0.353252	−	0.103724i
$487$	−11.2625	+	12.9976i	−0.510351	+	0.588977i	−0.951189	−	0.308610i	$-0.900136\pi$
$487$	−11.2625	+	12.9976i	−0.510351	+	0.588977i	0.440837	+	0.897587i	$0.354682\pi$
$488$	0.0674915	+	0.0433742i	0.00305520	+	0.00196346i
$489$	−21.5091	−	24.8229i	−0.972676	−	1.12253i
$490$	0.803719	+	5.58999i	0.0363083	+	0.252530i
$491$	32.7695	+	9.62199i	1.47887	+	0.434234i	0.918969	−	0.394329i	$-0.129023\pi$
$491$	32.7695	+	9.62199i	1.47887	+	0.434234i	0.559896	+	0.828563i	$0.310841\pi$
$492$	−26.4785	+	17.0167i	−1.19374	+	0.767172i
$493$	−1.77485	+	12.3444i	−0.0799354	+	0.555963i
$494$	−1.17732	+	2.57796i	−0.0529699	+	0.115988i
$495$	−0.457458	+	1.00169i	−0.0205612	+	0.0450227i
$496$	−0.573734	+	3.99041i	−0.0257614	+	0.179175i
$497$	23.8294	−	15.3142i	1.06889	−	0.686937i
$498$	0.365058	+	0.107191i	0.0163586	+	0.00480333i
$499$	−4.35055	−	30.2587i	−0.194757	−	1.35457i	−0.819205	−	0.573501i	$-0.805585\pi$
$499$	−4.35055	−	30.2587i	−0.194757	−	1.35457i	0.624448	−	0.781067i	$-0.285324\pi$
$500$	9.83499	+	11.3502i	0.439834	+	0.507596i
$501$	14.1624	+	9.10162i	0.632729	+	0.406630i
$502$	9.15345	−	10.5636i	0.408538	−	0.471478i
$503$	18.7851	−	5.51581i	0.837588	−	0.245938i	0.165314	−	0.986241i	$-0.447136\pi$
$503$	18.7851	−	5.51581i	0.837588	−	0.245938i	0.672273	+	0.740303i	$0.265318\pi$
$504$	4.73047	+	10.3583i	0.210712	+	0.461395i
$505$	50.5495			2.24942
$506$	−0.507036	−	0.137191i	−0.0225405	−	0.00609890i
$507$	−8.01947			−0.356157
$508$	−7.18130	−	15.7249i	−0.318619	−	0.697678i
$509$	2.80753	−	0.824367i	0.124442	−	0.0365394i	−0.218919	−	0.975743i	$-0.570253\pi$
$509$	2.80753	−	0.824367i	0.124442	−	0.0365394i	0.343360	+	0.939204i	$0.388435\pi$
$510$	−3.45444	+	3.98664i	−0.152965	+	0.176531i
$511$	1.91010	+	1.22755i	0.0844979	+	0.0543035i
$512$	−14.9070	−	17.2036i	−0.658801	−	0.760297i
$513$	0.694000	+	4.82688i	0.0306409	+	0.213112i
$514$	−5.19596	−	1.52567i	−0.229184	−	0.0672944i
$515$	−14.2400	+	9.15146i	−0.627487	+	0.403262i
$516$	1.47677	−	10.2712i	0.0650113	−	0.452163i
$517$	−0.136706	+	0.299345i	−0.00601234	+	0.0131652i
$518$	4.56224	−	9.98992i	0.200453	−	0.438932i
$519$	−1.87663	+	13.0522i	−0.0823748	+	0.572929i
$520$	−12.0577	+	7.74904i	−0.528767	+	0.339818i
$521$	−33.0279	−	9.69787i	−1.44698	−	0.424871i	−0.538437	−	0.842666i	$-0.680985\pi$
$521$	−33.0279	−	9.69787i	−1.44698	−	0.424871i	−0.908542	+	0.417794i	$0.862803\pi$
$522$	0.818715	+	5.69429i	0.0358342	+	0.249232i
$523$	−2.73748	−	3.15922i	−0.119702	−	0.138143i	0.692736	−	0.721191i	$-0.256405\pi$
$523$	−2.73748	−	3.15922i	−0.119702	−	0.138143i	−0.812437	+	0.583048i	$0.801860\pi$
$524$	7.48470	+	4.81013i	0.326971	+	0.210131i
$525$	8.48601	−	9.79338i	0.370360	−	0.427418i
$526$	11.0667	−	3.24949i	0.482533	−	0.141684i
$527$	−1.20556	−	2.63982i	−0.0525152	−	0.114992i
$528$	1.34895			0.0587054
$529$	19.8620	+	11.5974i	0.863567	+	0.504235i
$530$	−10.6609			−0.463082
$531$	0.0476074	+	0.104246i	0.00206599	+	0.00452388i
$532$	−11.1661	+	3.27868i	−0.484114	+	0.142149i
$533$	16.1622	−	18.6521i	0.700061	−	0.807914i
$534$	−14.3106	−	9.19689i	−0.619282	−	0.397989i
$535$	−2.19687	−	2.53533i	−0.0949792	−	0.109612i
$536$	3.18864	+	22.1775i	0.137728	+	0.957920i
$537$	−7.59398	−	2.22979i	−0.327705	−	0.0962227i
$538$	2.64423	−	1.69935i	0.114001	−	0.0732640i
$539$	−0.147951	+	1.02902i	−0.00637271	+	0.0443232i
$540$	−4.81103	+	10.5347i	−0.207034	+	0.453341i
$541$	3.08816	−	6.76213i	0.132771	−	0.290727i	−0.831557	−	0.555440i	$-0.812550\pi$
$541$	3.08816	−	6.76213i	0.132771	−	0.290727i	0.964327	+	0.264713i	$0.0852772\pi$
$542$	−1.36535	+	9.49621i	−0.0586467	+	0.407897i
$543$	35.3630	−	22.7264i	1.51757	−	0.975285i
$544$	9.04623	+	2.65621i	0.387854	+	0.113884i
$545$	2.61479	+	18.1863i	0.112005	+	0.779015i
$546$	−7.18431	−	8.29114i	−0.307460	−	0.354828i
$547$	11.3677	+	7.30557i	0.486047	+	0.312363i	0.760614	−	0.649205i	$-0.224898\pi$
$547$	11.3677	+	7.30557i	0.486047	+	0.312363i	−0.274567	+	0.961568i	$0.588534\pi$
$548$	−13.4717	+	15.5472i	−0.575483	+	0.664143i
$549$	0.0791169	−	0.0232308i	0.00337663	−	0.000991467i
$550$	0.0787428	+	0.172423i	0.00335760	+	0.00735213i
$551$	−12.5200			−0.533369
$552$	18.4209	+	4.98425i	0.784048	+	0.212144i
$553$	40.6694			1.72944
$554$	−1.51201	−	3.31083i	−0.0642390	−	0.140664i
$555$	−37.0218	+	10.8706i	−1.57149	+	0.461431i
$556$	−20.0737	+	23.1662i	−0.851313	+	0.982467i
$557$	18.7791	+	12.0686i	0.795698	+	0.511364i	0.874209	−	0.485549i	$-0.161380\pi$
$557$	18.7791	+	12.0686i	0.795698	+	0.511364i	−0.0785115	+	0.996913i	$0.525017\pi$
$558$	−0.876651	−	1.01171i	−0.0371116	−	0.0428291i
$559$	1.15797	+	8.05386i	0.0489769	+	0.340642i
$560$	−22.6390	−	6.64741i	−0.956673	−	0.280904i
$561$	−0.816902	+	0.524991i	−0.0344896	+	0.0221651i
$562$	2.18949	−	15.2282i	0.0923580	−	0.642364i
$563$	−6.10827	+	13.3753i	−0.257433	+	0.563700i	−0.993581	−	0.113121i	$-0.963915\pi$
$563$	−6.10827	+	13.3753i	−0.257433	+	0.563700i	0.736148	+	0.676820i	$0.236643\pi$
$564$	2.33228	−	5.10698i	0.0982066	−	0.215043i
$565$	0.499156	−	3.47170i	0.0209996	−	0.146056i
$566$	−2.43309	+	1.56365i	−0.102270	+	0.0657252i
$567$	−36.2647	−	10.6483i	−1.52297	−	0.447185i
$568$	−2.14231	−	14.9001i	−0.0898895	−	0.625195i
$569$	−22.7547	−	26.2604i	−0.953929	−	1.10089i	−0.994812	−	0.101728i	$-0.967563\pi$
$569$	−22.7547	−	26.2604i	−0.953929	−	1.10089i	0.0408837	−	0.999164i	$-0.486983\pi$
$570$	−4.45499	−	2.86305i	−0.186599	−	0.119920i
$571$	14.5902	−	16.8380i	0.610583	−	0.704650i	−0.363307	−	0.931669i	$-0.618353\pi$
$571$	14.5902	−	16.8380i	0.610583	−	0.704650i	0.973890	+	0.227019i	$0.0728980\pi$
$572$	−1.18881	+	0.349067i	−0.0497068	+	0.0145952i
$573$	−11.9825	−	26.2380i	−0.500575	−	1.09611i
$574$	−13.1262			−0.547878
$575$	−1.35634	−	8.18837i	−0.0565631	−	0.341479i
$576$	−5.58596			−0.232748
$577$	−0.872088	−	1.90961i	−0.0363055	−	0.0794980i	0.890610	−	0.454767i	$-0.150278\pi$
$577$	−0.872088	−	1.90961i	−0.0363055	−	0.0794980i	−0.926916	+	0.375269i	$0.877550\pi$
$578$	6.10556	−	1.79275i	0.253958	−	0.0745688i
$579$	−13.5412	+	15.6274i	−0.562754	+	0.649453i
$580$	−25.0137	−	16.0753i	−1.03864	−	0.667491i
$581$	−0.802239	−	0.925833i	−0.0332825	−	0.0384100i
$582$	0.0598576	+	0.416319i	0.00248118	+	0.0172570i
$583$	−1.88301	−	0.552901i	−0.0779862	−	0.0228988i
$584$	1.01509	−	0.652357i	0.0420046	−	0.0269947i
$585$	−2.09650	+	14.5815i	−0.0866795	+	0.602869i
$586$	−5.82034	+	12.7448i	−0.240436	+	0.526482i
$587$	−6.93830	+	15.1928i	−0.286374	+	0.627072i	−0.997076	−	0.0764218i	$-0.975650\pi$
$587$	−6.93830	+	15.1928i	−0.286374	+	0.627072i	0.710701	+	0.703494i	$0.248378\pi$
$588$	2.52412	−	17.5557i	0.104093	−	0.723983i
$589$	2.45090	−	1.57510i	0.100988	−	0.0649008i
$590$	0.0736106	+	0.0216140i	0.00303050	+	0.000889836i
$591$	3.24987	+	22.6034i	0.133682	+	0.929778i
$592$	11.8299	+	13.6524i	0.486204	+	0.561110i
$593$	−26.6731	−	17.1418i	−1.09533	−	0.703928i	−0.137284	−	0.990532i	$-0.543837\pi$
$593$	−26.6731	−	17.1418i	−1.09533	−	0.703928i	−0.958049	+	0.286604i	$0.907474\pi$
$594$	0.180825	−	0.208683i	0.00741933	−	0.00856236i
$595$	16.2969	−	4.78520i	0.668108	−	0.196174i
$596$	5.39233	+	11.8075i	0.220878	+	0.483656i
$597$	22.6016			0.925021
$598$	−7.02518	+	0.150021i	−0.287281	+	0.00613482i
$599$	−2.96111			−0.120988			−0.0604938	−	0.998169i	$-0.519268\pi$
$599$	−2.96111			−0.120988			−0.0604938	+	0.998169i	$0.519268\pi$
$600$	−2.86078	−	6.26423i	−0.116791	−	0.255736i
$601$	19.6933	−	5.78247i	0.803305	−	0.235872i	0.145793	−	0.989315i	$-0.453427\pi$
$601$	19.6933	−	5.78247i	0.803305	−	0.235872i	0.657513	+	0.753443i	$0.271609\pi$
$602$	2.83390	−	3.27050i	0.115501	−	0.133296i
$603$	19.3725	+	12.4500i	0.788911	+	0.507002i
$604$	19.8345	+	22.8903i	0.807056	+	0.931393i
$605$	−4.04205	−	28.1131i	−0.164333	−	1.14296i
$606$	19.7289	+	5.79293i	0.801432	+	0.235322i
$607$	−4.54687	+	2.92209i	−0.184552	+	0.118604i	−0.629654	−	0.776875i	$-0.716803\pi$
$607$	−4.54687	+	2.92209i	−0.184552	+	0.118604i	0.445103	+	0.895479i	$0.353167\pi$
$608$	−1.34700	+	9.36857i	−0.0546280	+	0.379946i
$609$	20.1331	−	44.0854i	0.815836	−	1.78643i
$610$	0.0229306	−	0.0502110i	0.000928433	−	0.00203299i
$611$	−0.626516	+	4.35752i	−0.0253461	+	0.176286i
$612$	5.32659	−	3.42319i	0.215315	−	0.138374i
$613$	−10.0503	−	2.95103i	−0.405928	−	0.119191i	0.0723934	−	0.997376i	$-0.476936\pi$
$613$	−10.0503	−	2.95103i	−0.405928	−	0.119191i	−0.478321	+	0.878185i	$0.658754\pi$
$614$	0.584129	+	4.06271i	0.0235735	+	0.163958i
$615$	30.2001	+	34.8528i	1.21779	+	1.40540i
$616$	1.18051	+	0.758668i	0.0475641	+	0.0305676i
$617$	−12.6337	+	14.5801i	−0.508615	+	0.586973i	−0.950744	−	0.309978i	$-0.899678\pi$
$617$	−12.6337	+	14.5801i	−0.508615	+	0.586973i	0.442128	+	0.896952i	$0.354224\pi$
$618$	−6.60644	+	1.93983i	−0.265750	+	0.0780312i
$619$	−0.114642	−	0.251031i	−0.00460786	−	0.0100898i	0.907314	−	0.420454i	$-0.138129\pi$
$619$	−0.114642	−	0.251031i	−0.00460786	−	0.0100898i	−0.911922	+	0.410364i	$0.865402\pi$
$620$	6.91904			0.277875
$621$	−10.0296	+	6.75246i	−0.402472	+	0.270967i
$622$	0.101095			0.00405353
$623$	22.7536	+	49.8233i	0.911602	+	1.99613i
$624$	17.3146	−	5.08403i	0.693139	−	0.203524i
$625$	20.0768	−	23.1699i	0.803072	−	0.926794i
$626$	11.8705	+	7.62870i	0.474440	+	0.304904i
$627$	−0.638385	−	0.736736i	−0.0254947	−	0.0294224i
$628$	−4.53654	−	31.5523i	−0.181028	−	1.25907i
$629$	−12.4773	−	3.66366i	−0.497502	−	0.146080i
$630$	6.59113	−	4.23586i	0.262597	−	0.168761i
$631$	5.39050	−	37.4917i	0.214592	−	1.49252i	−0.542966	−	0.839755i	$-0.682699\pi$
$631$	5.39050	−	37.4917i	0.214592	−	1.49252i	0.757558	−	0.652768i	$-0.226392\pi$
$632$	8.97836	−	19.6599i	0.357140	−	0.782028i
$633$	−7.57116	+	16.5785i	−0.300927	+	0.658938i
$634$	−1.79050	+	12.4532i	−0.0711098	+	0.494580i
$635$	−21.3079	+	13.6938i	−0.845578	+	0.543420i
$636$	32.1250	+	9.43276i	1.27384	+	0.374033i
$637$	1.97922	+	13.7658i	0.0784196	+	0.545420i
$638$	0.464250	+	0.535773i	0.0183798	+	0.0212115i
$639$	−13.0156	−	8.36463i	−0.514890	−	0.330900i
$640$	−19.0755	+	22.0143i	−0.754026	+	0.870192i
$641$	−20.7351	+	6.08838i	−0.818988	+	0.240477i	−0.664280	−	0.747483i	$-0.731262\pi$
$641$	−20.7351	+	6.08838i	−0.818988	+	0.240477i	−0.154708	+	0.987960i	$0.549444\pi$
$642$	−0.566869	−	1.24127i	−0.0223725	−	0.0489890i
$643$	−26.9690			−1.06355			−0.531777	−	0.846884i	$-0.678476\pi$
$643$	−26.9690			−1.06355			−0.531777	+	0.846884i	$0.678476\pi$
$644$	−19.3567	−	21.3981i	−0.762760	−	0.843203i
$645$	−15.2039			−0.598655
$646$	−0.741420	−	1.62348i	−0.0291708	−	0.0638751i
$647$	9.10342	−	2.67301i	0.357892	−	0.105087i	−0.0978433	−	0.995202i	$-0.531194\pi$
$647$	9.10342	−	2.67301i	0.357892	−	0.105087i	0.455736	+	0.890115i	$0.349376\pi$
$648$	−13.1534	+	15.1798i	−0.516715	+	0.596320i
$649$	0.0118806	+	0.00763523i	0.000466356	+	0.000299709i
$650$	1.66055	+	1.91638i	0.0651323	+	0.0751667i
$651$	1.60500	+	11.1630i	0.0629049	+	0.437513i
$652$	25.3230	+	7.43551i	0.991726	+	0.291197i
$653$	19.2367	−	12.3627i	0.752792	−	0.483790i	−0.107111	−	0.994247i	$-0.534160\pi$
$653$	19.2367	−	12.3627i	0.752792	−	0.483790i	0.859903	+	0.510457i	$0.170524\pi$
$654$	−1.06361	+	7.39756i	−0.0415904	+	0.289267i
$655$	5.41530	−	11.8579i	0.211593	−	0.463325i
$656$	8.96925	−	19.6399i	0.350190	−	0.766810i
$657$	0.176495	−	1.22755i	0.00688571	−	0.0478912i
$658$	1.96969	−	1.26584i	0.0767866	−	0.0493477i
$659$	24.3735	+	7.15671i	0.949458	+	0.278786i	0.719561	−	0.694429i	$-0.244343\pi$
$659$	24.3735	+	7.15671i	0.949458	+	0.278786i	0.229897	+	0.973215i	$0.426161\pi$
$660$	−0.329481	−	2.29159i	−0.0128250	−	0.0892002i
$661$	−10.1049	−	11.6616i	−0.393034	−	0.453585i	0.524401	−	0.851471i	$-0.324289\pi$
$661$	−10.1049	−	11.6616i	−0.393034	−	0.453585i	−0.917435	+	0.397886i	$0.869744\pi$
$662$	9.16829	+	5.89210i	0.356336	+	0.229003i
$663$	−8.50683	+	9.81740i	−0.330378	+	0.381276i
$664$	−0.624660	+	0.183417i	−0.0242415	+	0.00711795i
$665$	7.08331	+	15.5103i	0.274679	+	0.601463i
$666$	−5.99858			−0.232440
$667$	−13.4952	−	27.9550i	−0.522537	−	1.08242i
$668$	−13.5273			−0.523386
$669$	−9.88111	−	21.6366i	−0.382026	−	0.836520i
$670$	14.7913	−	4.34313i	0.571439	−	0.167790i
$671$	0.00665421	−	0.00767937i	0.000256883	−	0.000296459i
$672$	−30.8226	−	19.8085i	−1.18901	−	0.764129i
$673$	15.6280	+	18.0356i	0.602414	+	0.695223i	0.972269	−	0.233867i	$-0.0751379\pi$
$673$	15.6280	+	18.0356i	0.602414	+	0.695223i	−0.369854	+	0.929090i	$0.620592\pi$
$674$	−0.0407372	−	0.283334i	−0.00156914	−	0.0109136i
$675$	4.18644	+	1.22925i	0.161136	+	0.0473138i
$676$	5.42091	−	3.48381i	0.208497	−	0.133993i
$677$	−1.50458	+	10.4646i	−0.0578259	+	0.402188i	0.940266	+	0.340441i	$0.110576\pi$
$677$	−1.50458	+	10.4646i	−0.0578259	+	0.402188i	−0.998092	+	0.0617470i	$0.980333\pi$
$678$	0.592669	−	1.29776i	0.0227613	−	0.0498403i
$679$	0.562583	−	1.23188i	0.0215899	−	0.0472754i
$680$	1.28458	−	8.93444i	0.0492614	−	0.342620i
$681$	−43.0391	+	27.6595i	−1.64926	+	1.05992i
$682$	−0.158285	−	0.0464767i	−0.00606105	−	0.00177969i
$683$	−1.05505	−	7.33804i	−0.0403704	−	0.280782i	0.959629	−	0.281267i	$-0.0907547\pi$
$683$	−1.05505	−	7.33804i	−0.0403704	−	0.280782i	−1.00000		0.000484978i	$0.999846\pi$
$684$	4.16258	+	4.80387i	0.159160	+	0.183681i
$685$	25.3568	+	16.2958i	0.968832	+	0.622631i
$686$	−2.61544	+	3.01838i	−0.0998578	+	0.115242i
$687$	−29.9990	+	8.80851i	−1.14453	+	0.336065i
$688$	2.95701	+	6.47495i	0.112735	+	0.246855i
$689$	−26.2534			−1.00018
$690$	1.59070	−	13.0333i	0.0605569	−	0.496170i
$691$	−29.9490			−1.13932			−0.569658	−	0.821882i	$-0.692924\pi$
$691$	−29.9490			−1.13932			−0.569658	+	0.821882i	$0.692924\pi$
$692$	−4.40160	−	9.63815i	−0.167324	−	0.366388i
$693$	1.38385	−	0.406335i	0.0525682	−	0.0154354i
$694$	−0.181706	+	0.209699i	−0.00689745	+	0.00796008i
$695$	37.7831	+	24.2817i	1.43319	+	0.921058i
$696$	−16.8665	−	19.4650i	−0.639323	−	0.737819i
$697$	2.21193	+	15.3843i	0.0837829	+	0.582723i
$698$	−9.97953	−	2.93025i	−0.377731	−	0.110912i
$699$	45.6430	−	29.3330i	1.72638	−	1.10948i
$700$	−1.48185	+	10.3065i	−0.0560088	+	0.389550i
$701$	2.23024	−	4.88354i	0.0842350	−	0.184449i	−0.862827	−	0.505499i	$-0.831308\pi$
$701$	2.23024	−	4.88354i	0.0842350	−	0.184449i	0.947062	+	0.321050i	$0.104036\pi$
$702$	1.53450	−	3.36008i	0.0579159	−	0.126818i
$703$	1.85789	−	12.9219i	0.0700716	−	0.487358i
$704$	−0.579089	+	0.372158i	−0.0218252	+	0.0140262i
$705$	−7.89283	−	2.31754i	−0.297261	−	0.0872838i
$706$	−0.0455251	−	0.316634i	−0.00171336	−	0.0119167i
$707$	−43.3556	−	50.0350i	−1.63055	−	1.88176i
$708$	−0.202690	−	0.130261i	−0.00761754	−	0.00489550i
$709$	−4.95017	+	5.71280i	−0.185907	+	0.214549i	−0.841051	−	0.540956i	$-0.818063\pi$
$709$	−4.95017	+	5.71280i	−0.185907	+	0.214549i	0.655144	+	0.755504i	$0.272608\pi$
$710$	−9.93770	+	2.91797i	−0.372955	+	0.109510i
$711$	−9.22788	−	20.2062i	−0.346073	−	0.757793i
$712$	29.1081			1.09087
$713$	6.15875	+	3.77467i	0.230647	+	0.141362i
$714$	6.90888			0.258558
$715$	0.754131	+	1.65132i	0.0282029	+	0.0617558i
$716$	6.10196	−	1.79170i	0.228041	−	0.0669589i
$717$	−0.338940	+	0.391158i	−0.0126580	+	0.0146081i
$718$	−6.48875	−	4.17006i	−0.242158	−	0.155625i
$719$	22.1263	+	25.5352i	0.825173	+	0.952301i	0.999475	−	0.0323913i	$-0.0103123\pi$
$719$	22.1263	+	25.5352i	0.825173	+	0.952301i	−0.174302	+	0.984692i	$0.555767\pi$
$720$	1.83408	+	12.7563i	0.0683520	+	0.475399i
$721$	21.2717	+	6.24594i	0.792200	+	0.232611i
$722$	−6.14721	+	3.95057i	−0.228776	+	0.147025i
$723$	−1.65199	+	11.4899i	−0.0614383	+	0.427313i
$724$	−14.0315	+	30.7248i	−0.521478	+	1.14188i
$725$	−4.65349	+	10.1897i	−0.172826	+	0.378437i
$726$	1.64417	−	11.4354i	0.0610207	−	0.424408i
$727$	7.88389	−	5.06667i	0.292397	−	0.187912i	−0.386215	−	0.922409i	$-0.626218\pi$
$727$	7.88389	−	5.06667i	0.292397	−	0.187912i	0.678613	+	0.734496i	$0.262581\pi$
$728$	18.0119	+	5.28878i	0.667566	+	0.196015i
$729$	0.566036	+	3.93687i	0.0209643	+	0.145810i
$730$	−0.543671	−	0.627430i	−0.0201222	−	0.0232222i
$731$	−4.31068	−	2.77030i	−0.159436	−	0.102463i
$732$	−0.113524	+	0.131014i	−0.00419597	+	0.00484241i
$733$	−19.3539	+	5.68281i	−0.714852	+	0.209899i	−0.618881	−	0.785485i	$-0.712414\pi$
$733$	−19.3539	+	5.68281i	−0.714852	+	0.209899i	−0.0959708	+	0.995384i	$0.530596\pi$
$734$	−5.42030	−	11.8688i	−0.200067	−	0.438085i
$735$	−25.9868			−0.958538
$736$	−22.3704	+	7.09072i	−0.824584	+	0.261367i
$737$	2.83779			0.104531
$738$	2.97834	+	6.52165i	0.109634	+	0.240065i
$739$	−31.8060	+	9.33909i	−1.17000	+	0.343544i	−0.808312	−	0.588754i	$-0.799619\pi$
$739$	−31.8060	+	9.33909i	−1.17000	+	0.343544i	−0.361691	+	0.932298i	$0.617801\pi$
$740$	20.3032	−	23.4312i	0.746361	−	0.861347i
$741$	−10.9708	−	7.05047i	−0.403021	−	0.259006i
$742$	9.14373	+	10.5524i	0.335677	+	0.387392i
$743$	−1.87899	−	13.0686i	−0.0689333	−	0.479442i	−0.994821	−	0.101643i	$-0.967590\pi$
$743$	−1.87899	−	13.0686i	−0.0689333	−	0.479442i	0.925888	−	0.377799i	$-0.123319\pi$
$744$	5.75061	+	1.68853i	0.210827	+	0.0619045i
$745$	15.9998	−	10.2824i	0.586186	−	0.376719i
$746$	−1.12872	+	7.85044i	−0.0413255	+	0.287425i
$747$	−0.277964	+	0.608657i	−0.0101702	+	0.0222696i
$748$	0.324135	−	0.709756i	0.0118515	−	0.0259512i
$749$	−0.625296	+	4.34903i	−0.0228478	+	0.158910i
$750$	7.52990	−	4.83917i	0.274953	−	0.176702i
$751$	23.8736	+	7.00993i	0.871161	+	0.255796i	0.686609	−	0.727027i	$-0.259098\pi$
$751$	23.8736	+	7.00993i	0.871161	+	0.255796i	0.184552	+	0.982823i	$0.440917\pi$
$752$	0.548095	+	3.81208i	0.0199870	+	0.139012i
$753$	42.1195	+	48.6085i	1.53492	+	1.77139i
$754$	7.97821	+	5.12728i	0.290549	+	0.186725i
$755$	29.0613	−	33.5385i	1.05765	−	1.22059i
$756$	14.5538	−	4.27339i	0.529317	−	0.155422i
$757$	−10.6259	−	23.2675i	−0.386205	−	0.845671i	−0.998485	−	0.0550300i	$-0.982475\pi$
$757$	−10.6259	−	23.2675i	−0.386205	−	0.845671i	0.612280	−	0.790641i	$-0.290253\pi$
$758$	5.62941			0.204469
$759$	0.956897	−	2.21953i	0.0347332	−	0.0805639i
$760$	9.06153			0.328696
$761$	13.6441	+	29.8765i	0.494600	+	1.08302i	0.978187	+	0.207726i	$0.0666064\pi$
$761$	13.6441	+	29.8765i	0.494600	+	1.08302i	−0.483587	+	0.875296i	$0.660666\pi$
$762$	−9.88553	+	2.90265i	−0.358115	+	0.105152i
$763$	15.7585	−	18.1863i	0.570496	−	0.658388i
$764$	19.4981	+	12.5306i	0.705415	+	0.453343i
$765$	−6.07525	−	7.01122i	−0.219651	−	0.253491i
$766$	−0.764152	−	5.31480i	−0.0276099	−	0.192031i
$767$	0.181272	+	0.0532262i	0.00654535	+	0.00192189i
$768$	1.19137	−	0.765647i	0.0429899	−	0.0276279i
$769$	−4.44731	+	30.9317i	−0.160374	+	1.11543i	0.737555	+	0.675287i	$0.235980\pi$
$769$	−4.44731	+	30.9317i	−0.160374	+	1.11543i	−0.897929	+	0.440139i	$0.854929\pi$
$770$	0.401085	−	0.878253i	0.0144541	−	0.0316500i
$771$	10.3515	−	22.6667i	0.372801	−	0.816321i
$772$	2.36461	−	16.4462i	0.0851041	−	0.591912i
$773$	−5.74416	+	3.69155i	−0.206603	+	0.132776i	−0.639851	−	0.768499i	$-0.721004\pi$
$773$	−5.74416	+	3.69155i	−0.206603	+	0.132776i	0.433248	+	0.901275i	$0.357368\pi$
$774$	−2.26793	−	0.665925i	−0.0815191	−	0.0239362i
$775$	−0.370973	−	2.58018i	−0.0133258	−	0.0926827i
$776$	−0.471303	−	0.543913i	−0.0169188	−	0.0195253i
$777$	42.5130	+	27.3215i	1.52515	+	0.980152i
$778$	1.28361	−	1.48136i	0.0460196	−	0.0531095i
$779$	−14.9711	+	4.39592i	−0.536396	+	0.157500i
$780$	−12.8658	−	28.1723i	−0.460671	−	1.00873i
$781$	−1.90660			−0.0682234
$782$	2.82580	−	3.40541i	0.101050	−	0.121777i
$783$	16.3184			0.583172
$784$	5.05417	+	11.0671i	0.180506	+	0.395253i
$785$	−44.8135	+	13.1584i	−1.59946	+	0.469645i
$786$	3.47243	−	4.00740i	0.123857	−	0.142939i
$787$	−25.5355	−	16.4106i	−0.910241	−	0.584976i	−0.000430422	−	1.00000i	$-0.500137\pi$
$787$	−25.5355	−	16.4106i	−0.910241	−	0.584976i	−0.909811	+	0.415023i	$0.863773\pi$
$788$	−12.0161	−	13.8674i	−0.428057	−	0.494005i
$789$	7.55313	+	52.5332i	0.268899	+	1.87023i
$790$	−14.2682	−	4.18951i	−0.507638	−	0.149056i
$791$	−3.86448	+	2.48355i	−0.137405	+	0.0883050i
$792$	0.109080	−	0.758668i	0.00387599	−	0.0269581i
$793$	0.0564684	−	0.123649i	0.00200525	−	0.00439089i
$794$	0.540614	−	1.18378i	0.0191857	−	0.0420107i
$795$	6.98143	−	48.5569i	0.247606	−	1.72214i
$796$	−15.2780	+	9.81856i	−0.541513	+	0.348010i
$797$	18.9554	+	5.56580i	0.671434	+	0.197151i	0.599642	−	0.800269i	$-0.295310\pi$
$797$	18.9554	+	5.56580i	0.671434	+	0.197151i	0.0717927	+	0.997420i	$0.477128\pi$
$798$	0.987072	+	6.86523i	0.0349420	+	0.243027i
$799$	−1.81553	−	2.09523i	−0.0642287	−	0.0741239i
$800$	7.12421	+	4.57845i	0.251879	+	0.161873i
$801$	19.5915	−	22.6098i	0.692232	−	0.798879i
$802$	−8.37385	+	2.45878i	−0.295691	+	0.0868227i
$803$	−0.0634869	−	0.139017i	−0.00224040	−	0.00490580i
$804$	−48.4141			−1.70743
$805$	−26.9969	+	32.5343i	−0.951514	+	1.14668i
$806$	−2.20686			−0.0777332
$807$	6.00833	+	13.1564i	0.211503	+	0.463128i
$808$	−33.7586	+	9.91243i	−1.18763	+	0.348718i
$809$	17.0037	−	19.6234i	0.597820	−	0.689921i	−0.373518	−	0.927623i	$-0.621849\pi$
$809$	17.0037	−	19.6234i	0.597820	−	0.689921i	0.971338	+	0.237702i	$0.0763941\pi$
$810$	11.6259	+	7.47152i	0.408493	+	0.262523i
$811$	−34.7301	−	40.0807i	−1.21954	−	1.40742i	−0.885356	−	0.464913i	$-0.846085\pi$
$811$	−34.7301	−	40.0807i	−1.21954	−	1.40742i	−0.334182	−	0.942509i	$-0.608460\pi$
$812$	5.54216	+	38.5466i	0.194492	+	1.35272i
$813$	−42.3578	−	12.4374i	−1.48555	−	0.436198i
$814$	−0.621864	+	0.399648i	−0.0217963	+	0.0140077i
$815$	5.50322	−	38.2757i	0.192769	−	1.34074i
$816$	−4.72089	+	10.3373i	−0.165264	+	0.361878i
$817$	2.13694	−	4.67924i	0.0747619	−	0.163706i
$818$	0.891928	−	6.20350i	0.0311855	−	0.216900i
$819$	16.2312	−	10.4311i	0.567163	−	0.364494i
$820$	−35.5550	−	10.4399i	−1.24164	−	0.364577i
$821$	−6.06615	−	42.1910i	−0.211710	−	1.47248i	−0.767444	−	0.641116i	$-0.778472\pi$
$821$	−6.06615	−	42.1910i	−0.211710	−	1.47248i	0.555734	−	0.831360i	$-0.312437\pi$
$822$	8.02898	+	9.26593i	0.280043	+	0.323186i
$823$	−25.5894	−	16.4453i	−0.891991	−	0.573248i	0.0124137	−	0.999923i	$-0.496049\pi$
$823$	−25.5894	−	16.4453i	−0.891991	−	0.573248i	−0.904405	+	0.426675i	$0.859685\pi$
$824$	7.71537	−	8.90401i	0.268778	−	0.310186i
$825$	−0.836891	+	0.245733i	−0.0291368	+	0.00855534i
$826$	−0.0417407	−	0.0913994i	−0.00145235	−	0.00318019i
$827$	41.6718			1.44907			0.724535	−	0.689238i	$-0.242055\pi$
$827$	41.6718			1.44907			0.724535	+	0.689238i	$0.242055\pi$
$828$	−6.23943	+	14.4724i	−0.216835	+	0.502951i
$829$	−7.98458			−0.277316			−0.138658	−	0.990340i	$-0.544279\pi$
$829$	−7.98458			−0.277316			−0.138658	+	0.990340i	$0.544279\pi$
$830$	0.186078	+	0.407454i	0.00645886	+	0.0141429i
$831$	16.0699	−	4.71853i	0.557457	−	0.163684i
$832$	−6.03036	+	6.95940i	−0.209065	+	0.241274i
$833$	−7.36788	−	4.73505i	−0.255282	−	0.164060i
$834$	11.9636	+	13.8068i	0.414267	+	0.478090i
$835$	2.82067	+	19.6182i	0.0976135	+	0.678917i
$836$	0.751581	+	0.220684i	0.0259940	+	0.00763252i
$837$	−3.19448	+	2.05297i	−0.110417	+	0.0709609i
$838$	−0.138058	+	0.960212i	−0.00476912	+	0.0331700i
$839$	−14.0415	+	30.7465i	−0.484765	+	1.06149i	0.496361	+	0.868116i	$0.334669\pi$
$839$	−14.0415	+	30.7465i	−0.484765	+	1.06149i	−0.981126	+	0.193371i	$0.938058\pi$
$840$	−14.5717	+	31.9075i	−0.502770	+	1.10091i
$841$	−1.83527	+	12.7646i	−0.0632853	+	0.440159i
$842$	−5.80577	+	3.73114i	−0.200080	+	0.128584i
$843$	67.9255	+	19.9447i	2.33948	+	0.686933i
$844$	−2.08416	−	14.4956i	−0.0717397	−	0.498961i
$845$	−6.18283	−	7.13537i	−0.212696	−	0.245464i
$846$	−1.07585	−	0.691404i	−0.0369883	−	0.0237710i
$847$	−24.3601	+	28.1131i	−0.837023	+	0.965976i
$848$	−22.0369	+	6.47062i	−0.756751	+	0.222202i
$849$	−5.52856	−	12.1059i	−0.189740	−	0.415472i
$850$	−1.59689			−0.0547729
$851$	30.8551	−	9.78009i	1.05770	−	0.335257i
$852$	32.5275			1.11437
$853$	−12.0764	−	26.4437i	−0.413488	−	0.905413i	−0.995723	−	0.0923924i	$-0.970549\pi$
$853$	−12.0764	−	26.4437i	−0.413488	−	0.905413i	0.582234	−	0.813021i	$-0.302179\pi$
$854$	−0.0693672	+	0.0203680i	−0.00237370	+	0.000696980i
$855$	6.09895	−	7.03857i	0.208580	−	0.240714i
$856$	1.96431	+	1.26238i	0.0671386	+	0.0431474i
$857$	11.4459	+	13.2093i	0.390986	+	0.451222i	0.916782	−	0.399389i	$-0.130778\pi$
$857$	11.4459	+	13.2093i	0.390986	+	0.451222i	−0.525795	+	0.850611i	$0.676232\pi$
$858$	0.105089	+	0.730913i	0.00358769	+	0.0249530i
$859$	42.5405	+	12.4910i	1.45146	+	0.426188i	0.910026	−	0.414552i	$-0.136062\pi$
$859$	42.5405	+	12.4910i	1.45146	+	0.426188i	0.541439	+	0.840740i	$0.317880\pi$
$860$	10.2774	−	6.60488i	0.350456	−	0.225225i
$861$	8.59584	−	59.7854i	0.292946	−	2.03748i
$862$	−2.64889	+	5.80027i	−0.0902216	+	0.197558i
$863$	−4.58924	+	10.0490i	−0.156219	+	0.342073i	−0.971517	−	0.236969i	$-0.923846\pi$
$863$	−4.58924	+	10.0490i	−0.156219	+	0.342073i	0.815298	+	0.579042i	$0.196573\pi$
$864$	1.75566	−	12.2109i	0.0597288	−	0.415423i
$865$	−13.0601	+	8.39324i	−0.444058	+	0.285379i
$866$	−16.2377	−	4.76781i	−0.551778	−	0.162017i
$867$	4.16709	+	28.9827i	0.141522	+	0.984305i
$868$	−5.93436	−	6.84862i	−0.201425	−	0.232457i
$869$	−2.30286	−	1.47996i	−0.0781191	−	0.0502041i
$870$	−11.6048	+	13.3926i	−0.393438	+	0.454052i
$871$	36.4248	−	10.6953i	1.23421	−	0.362396i
$872$	−5.31246	−	11.6327i	−0.179903	−	0.393932i
$873$	−0.739701			−0.0250351
$874$	3.78762	+	2.32141i	0.128118	+	0.0785230i
$875$	−28.8202			−0.974300
$876$	1.08312	+	2.37170i	0.0365951	+	0.0801322i
$877$	18.8753	−	5.54229i	0.637374	−	0.187150i	0.0529483	−	0.998597i	$-0.483138\pi$
$877$	18.8753	−	5.54229i	0.637374	−	0.187150i	0.584425	+	0.811447i	$0.301320\pi$
$878$	4.05030	−	4.67429i	0.136691	−	0.157750i
$879$	−54.2366	−	34.8557i	−1.82935	−	1.17565i
$880$	1.04001	+	1.20023i	0.0350587	+	0.0404599i
$881$	2.98181	+	20.7390i	0.100460	+	0.698714i	0.976349	+	0.216201i	$0.0693667\pi$
$881$	2.98181	+	20.7390i	0.100460	+	0.698714i	−0.875889	+	0.482513i	$0.839724\pi$
$882$	−3.87639	−	1.13821i	−0.130525	−	0.0383255i
$883$	−34.5844	+	22.2260i	−1.16386	+	0.747966i	−0.972351	−	0.233525i	$-0.924974\pi$
$883$	−34.5844	+	22.2260i	−1.16386	+	0.747966i	−0.191507	+	0.981491i	$0.561337\pi$
$884$	1.48549	−	10.3318i	0.0499623	−	0.347496i
$885$	−0.146649	+	0.321117i	−0.00492956	+	0.0107942i
$886$	−1.41960	+	3.10850i	−0.0476926	+	0.104432i
$887$	−5.67154	+	39.4464i	−0.190432	+	1.32448i	0.640436	+	0.768012i	$0.278754\pi$
$887$	−5.67154	+	39.4464i	−0.190432	+	1.32448i	−0.830868	+	0.556470i	$0.812155\pi$
$888$	22.5927	−	14.5195i	0.758163	−	0.487242i
$889$	31.8298	+	9.34609i	1.06754	+	0.313458i
$890$	−2.85020	−	19.8236i	−0.0955390	−	0.664488i
$891$	1.66596	+	1.92262i	0.0558116	+	0.0644101i
$892$	16.0787	+	10.3331i	0.538354	+	0.345979i
$893$	1.82261	−	2.10340i	0.0609913	−	0.0703877i
$894$	7.42289	−	2.17956i	0.248258	−	0.0728952i
$895$	−3.87082	−	8.47591i	−0.129387	−	0.283319i
$896$	38.1510			1.27454
$897$	3.91722	−	32.0955i	0.130792	−	1.07164i
$898$	−1.46742			−0.0489683
$899$	−4.04994	−	8.86814i	−0.135073	−	0.295769i
$900$	5.45693	−	1.60230i	0.181898	−	0.0534100i
$901$	10.8269	−	12.4950i	0.360698	−	0.416267i
$902$	0.743257	+	0.477662i	0.0247478	+	0.0159044i
$903$	13.0402	+	15.0492i	0.433950	+	0.500806i
$904$	0.347426	+	2.41640i	0.0115552	+	0.0803682i
$905$	47.4851	+	13.9429i	1.57846	+	0.463477i
$906$	15.1858	−	9.75931i	0.504514	−	0.324231i
$907$	−5.41668	+	37.6738i	−0.179858	+	1.25094i	0.677231	+	0.735771i	$0.263180\pi$
$907$	−5.41668	+	37.6738i	−0.179858	+	1.25094i	−0.857089	+	0.515169i	$0.827729\pi$
$908$	17.0773	−	37.3940i	0.566729	−	1.24096i
$909$	−15.0221	+	32.8938i	−0.498251	+	1.09102i
$910$	1.83814	−	12.7846i	0.0609339	−	0.423804i
$911$	−42.2532	+	27.1545i	−1.39991	+	0.899667i	−0.999858	−	0.0168256i	$-0.994644\pi$
$911$	−42.2532	+	27.1545i	−1.39991	+	0.899667i	−0.400051	+	0.916493i	$0.631008\pi$
$912$	−10.9465	−	3.21418i	−0.362474	−	0.106432i
$913$	0.0117348	+	0.0816177i	0.000388367	+	0.00270115i
$914$	−5.30696	−	6.12456i	−0.175539	−	0.202582i
$915$	0.213678	+	0.137322i	0.00706396	+	0.00453973i
$916$	16.4518	−	18.9864i	0.543584	−	0.627329i
$917$	−16.3818	+	4.81013i	−0.540974	+	0.158844i
$918$	0.966358	+	2.11603i	0.0318946	+	0.0698393i
$919$	50.0605			1.65134			0.825671	−	0.564152i	$-0.190797\pi$
$919$	50.0605			1.65134			0.825671	+	0.564152i	$0.190797\pi$
$920$	9.76738	+	20.2329i	0.322021	+	0.667059i
$921$	−18.8868			−0.622340
$922$	−0.765676	−	1.67660i	−0.0252162	−	0.0552157i
$923$	−24.4724	+	7.18573i	−0.805518	+	0.236521i
$924$	−1.98568	+	2.29159i	−0.0653240	+	0.0753879i
$925$	−9.82629	−	6.31497i	−0.323086	−	0.207635i
$926$	−3.58095	−	4.13264i	−0.117677	−	0.135807i
$927$	−1.72331	−	11.9859i	−0.0566008	−	0.393667i
$928$	30.3897	+	8.92322i	0.997590	+	0.292919i
$929$	−3.03206	+	1.94859i	−0.0994786	+	0.0639310i	−0.589434	−	0.807816i	$-0.700649\pi$
$929$	−3.03206	+	1.94859i	−0.0994786	+	0.0639310i	0.489956	+	0.871747i	$0.337013\pi$
$930$	0.586858	−	4.08169i	0.0192438	−	0.133844i
$931$	3.65249	−	7.99783i	0.119705	−	0.262118i
$932$	−18.1105	+	39.6564i	−0.593228	+	1.29899i
$933$	−0.0662029	+	0.460451i	−0.00216739	+	0.0150745i
$934$	11.3335	−	7.28360i	0.370843	−	0.238327i
$935$	−1.09693	−	0.322087i	−0.0358734	−	0.0105334i
$936$	−1.45922	−	10.1491i	−0.0476961	−	0.331733i
$937$	22.0949	+	25.4989i	0.721809	+	0.833012i	0.991523	−	0.129928i	$-0.0414747\pi$
$937$	22.0949	+	25.4989i	0.721809	+	0.833012i	−0.269714	+	0.962940i	$0.586929\pi$
$938$	−16.9852	−	10.9158i	−0.554588	−	0.356412i
$939$	−42.5196	+	49.0702i	−1.38757	+	1.60135i
$940$	6.34210	−	1.86221i	0.206856	−	0.0607385i
$941$	13.4358	+	29.4203i	0.437995	+	0.959076i	0.991962	+	0.126537i	$0.0403862\pi$
$941$	13.4358	+	29.4203i	0.437995	+	0.959076i	−0.553967	+	0.832539i	$0.686886\pi$
$942$	−18.9981			−0.618993
$943$	−25.9527	−	28.6897i	−0.845135	−	0.934265i
$944$	0.165277			0.00537930
$945$	−9.23231	−	20.2159i	−0.300327	−	0.657624i
$946$	−0.279480	+	0.0820627i	−0.00908668	+	0.00266809i
$947$	−25.8018	+	29.7769i	−0.838446	+	0.967619i	−0.999814	−	0.0192756i	$-0.993864\pi$
$947$	−25.8018	+	29.7769i	−0.838446	+	0.967619i	0.161368	+	0.986894i	$0.448409\pi$
$948$	39.2879	+	25.2488i	1.27601	+	0.820043i
$949$	−1.33883	−	1.54510i	−0.0434604	−	0.0501559i
$950$	−0.228148	−	1.58680i	−0.00740209	−	0.0514827i
$951$	−55.5475	−	16.3102i	−1.80125	−	0.528895i
$952$	−9.94527	+	6.39143i	−0.322328	+	0.207148i
$953$	4.42408	−	30.7701i	0.143310	−	0.996742i	−0.783548	−	0.621331i	$-0.786592\pi$
$953$	4.42408	−	30.7701i	0.143310	−	0.996742i	0.926858	−	0.375411i	$-0.122499\pi$
$954$	3.16817	−	6.93733i	0.102573	−	0.224604i
$955$	14.1072	−	30.8904i	0.456497	−	0.999589i
$956$	0.0591867	−	0.411653i	0.00191424	−	0.0133138i
$957$	−2.74428	+	1.76364i	−0.0887100	+	0.0570105i
$958$	10.9569	+	3.21724i	0.354001	+	0.103944i
$959$	−5.61819	−	39.0753i	−0.181421	−	1.26181i
$960$	−11.2681	−	13.0041i	−0.363677	−	0.419706i
$961$	−24.1704	−	15.5334i	−0.779689	−	0.501076i
$962$	−6.47580	+	7.47347i	−0.208788	+	0.240954i
$963$	2.30266	−	0.676121i	0.0742020	−	0.0217877i
$964$	−3.87472	−	8.48446i	−0.124796	−	0.273266i
$965$	−24.3446			−0.783679
$966$	−14.2650	+	9.60397i	−0.458968	+	0.309003i
$967$	33.5947			1.08033			0.540167	−	0.841558i	$-0.318361\pi$
$967$	33.5947			1.08033			0.540167	+	0.841558i	$0.318361\pi$
$968$	8.21220	+	17.9822i	0.263950	+	0.577970i
$969$	7.87993	−	2.31376i	0.253140	−	0.0743286i
$970$	−0.324273	+	0.374231i	−0.0104118	+	0.0120158i
$971$	−10.3808	−	6.67136i	−0.333137	−	0.214094i	0.363369	−	0.931645i	$-0.381627\pi$
$971$	−10.3808	−	6.67136i	−0.333137	−	0.214094i	−0.696506	+	0.717551i	$0.745263\pi$
$972$	−19.6521	−	22.6797i	−0.630340	−	0.727452i
$973$	−8.37143	−	58.2246i	−0.268376	−	1.86659i
$974$	−7.90249	−	2.32038i	−0.253212	−	0.0743497i
$975$	−9.81589	+	6.30829i	−0.314360	+	0.202027i
$976$	0.0169238	−	0.117707i	0.000541716	−	0.00376772i
$977$	18.7882	−	41.1405i	0.601089	−	1.31620i	−0.327415	−	0.944881i	$-0.606178\pi$
$977$	18.7882	−	41.1405i	0.601089	−	1.31620i	0.928504	−	0.371321i	$-0.121095\pi$
$978$	6.53421	−	14.3079i	0.208941	−	0.457517i
$979$	0.524674	−	3.64919i	0.0167687	−	0.116629i
$980$	17.5663	−	11.2892i	0.561134	−	0.360619i
$981$	−12.6113	−	3.70301i	−0.402648	−	0.118228i
$982$	2.32764	+	16.1891i	0.0742778	+	0.516614i
$983$	9.99811	+	11.5384i	0.318890	+	0.368019i	0.892451	−	0.451144i	$-0.148984\pi$
$983$	9.99811	+	11.5384i	0.318890	+	0.368019i	−0.573561	+	0.819163i	$0.694438\pi$
$984$	−27.0030	−	17.3538i	−0.860825	−	0.553219i
$985$	−17.6059	+	20.3183i	−0.560970	+	0.647394i
$986$	−5.73049	+	1.68262i	−0.182496	+	0.0535856i
$987$	4.47561	+	9.80022i	0.142460	+	0.311944i
$988$	10.4788			0.333374
$989$	12.7514	−	0.272302i	0.405470	−	0.00865871i
$990$	−0.527358			−0.0167605
$991$	8.20454	+	17.9654i	0.260626	+	0.570691i	0.994031	−	0.109101i	$-0.0347973\pi$
$991$	8.20454	+	17.9654i	0.260626	+	0.570691i	−0.733405	+	0.679792i	$0.762070\pi$
$992$	−7.07167	+	2.07643i	−0.224526	+	0.0659267i
$993$	−32.8405	+	37.8999i	−1.04216	+	1.20272i
$994$	11.4117	+	7.33385i	0.361957	+	0.232616i
$995$	17.4253	+	20.1099i	0.552420	+	0.637526i
$996$	−0.200202	−	1.39244i	−0.00634365	−	0.0441211i
$997$	−11.7531	−	3.45101i	−0.372223	−	0.109295i	0.0902704	−	0.995917i	$-0.471227\pi$
$997$	−11.7531	−	3.45101i	−0.372223	−	0.109295i	−0.462493	+	0.886623i	$0.653045\pi$
$998$	12.3157	−	7.91480i	0.389846	−	0.250539i
$999$	−2.42155	+	16.8422i	−0.0766144	+	0.532865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.2.c.a.4.1	✓	10
3.2	odd	2		207.2.i.c.73.1		10
4.3	odd	2		368.2.m.c.257.1		10
5.2	odd	4		575.2.p.b.349.1		20
5.3	odd	4		575.2.p.b.349.2		20
5.4	even	2		575.2.k.b.326.1		10
23.2	even	11		529.2.c.b.177.1		10
23.3	even	11		529.2.c.b.266.1		10
23.4	even	11		529.2.c.g.501.1		10
23.5	odd	22		529.2.c.h.399.1		10
23.6	even	11	inner	23.2.c.a.6.1	yes	10
23.7	odd	22		529.2.c.e.334.1		10
23.8	even	11		529.2.c.i.118.1		10
23.9	even	11		529.2.c.d.255.1		10
23.10	odd	22		529.2.c.f.170.1		10
23.11	odd	22		529.2.a.j.1.3		5
23.12	even	11		529.2.a.i.1.3		5
23.13	even	11		529.2.c.g.170.1		10
23.14	odd	22		529.2.c.e.255.1		10
23.15	odd	22		529.2.c.h.118.1		10
23.16	even	11		529.2.c.d.334.1		10
23.17	odd	22		529.2.c.a.466.1		10
23.18	even	11		529.2.c.i.399.1		10
23.19	odd	22		529.2.c.f.501.1		10
23.20	odd	22		529.2.c.c.266.1		10
23.21	odd	22		529.2.c.c.177.1		10
23.22	odd	2		529.2.c.a.487.1		10
69.11	even	22		4761.2.a.bn.1.3		5
69.29	odd	22		207.2.i.c.190.1		10
69.35	odd	22		4761.2.a.bo.1.3		5
92.11	even	22		8464.2.a.bt.1.1		5
92.35	odd	22		8464.2.a.bs.1.1		5
92.75	odd	22		368.2.m.c.305.1		10
115.29	even	22		575.2.k.b.351.1		10
115.52	odd	44		575.2.p.b.374.2		20
115.98	odd	44		575.2.p.b.374.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.2.c.a.4.1	✓	10	1.1	even	1	trivial
23.2.c.a.6.1	yes	10	23.6	even	11	inner
207.2.i.c.73.1		10	3.2	odd	2
207.2.i.c.190.1		10	69.29	odd	22
368.2.m.c.257.1		10	4.3	odd	2
368.2.m.c.305.1		10	92.75	odd	22
529.2.a.i.1.3		5	23.12	even	11
529.2.a.j.1.3		5	23.11	odd	22
529.2.c.a.466.1		10	23.17	odd	22
529.2.c.a.487.1		10	23.22	odd	2
529.2.c.b.177.1		10	23.2	even	11
529.2.c.b.266.1		10	23.3	even	11
529.2.c.c.177.1		10	23.21	odd	22
529.2.c.c.266.1		10	23.20	odd	22
529.2.c.d.255.1		10	23.9	even	11
529.2.c.d.334.1		10	23.16	even	11
529.2.c.e.255.1		10	23.14	odd	22
529.2.c.e.334.1		10	23.7	odd	22
529.2.c.f.170.1		10	23.10	odd	22
529.2.c.f.501.1		10	23.19	odd	22
529.2.c.g.170.1		10	23.13	even	11
529.2.c.g.501.1		10	23.4	even	11
529.2.c.h.118.1		10	23.15	odd	22
529.2.c.h.399.1		10	23.5	odd	22
529.2.c.i.118.1		10	23.8	even	11
529.2.c.i.399.1		10	23.18	even	11
575.2.k.b.326.1		10	5.4	even	2
575.2.k.b.351.1		10	115.29	even	22
575.2.p.b.349.1		20	5.2	odd	4
575.2.p.b.349.2		20	5.3	odd	4
575.2.p.b.374.1		20	115.98	odd	44
575.2.p.b.374.2		20	115.52	odd	44
4761.2.a.bn.1.3		5	69.11	even	22
4761.2.a.bo.1.3		5	69.35	odd	22
8464.2.a.bs.1.1		5	92.35	odd	22
8464.2.a.bt.1.1		5	92.11	even	22

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:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	23.c (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.198939 + 0.435615i) q^{2} +(-2.11435 + 0.620830i) q^{3} +(1.15954 - 1.33818i) q^{4} +(-2.18251 - 1.40261i) q^{5} +(-0.691070 - 0.797537i) q^{6} +(0.483568 + 3.36329i) q^{7} +(1.73259 + 0.508735i) q^{8} +(1.56130 - 1.00339i) q^{9} +O(q^{10})\)	\(q+(0.198939 + 0.435615i) q^{2} +(-2.11435 + 0.620830i) q^{3} +(1.15954 - 1.33818i) q^{4} +(-2.18251 - 1.40261i) q^{5} +(-0.691070 - 0.797537i) q^{6} +(0.483568 + 3.36329i) q^{7} +(1.73259 + 0.508735i) q^{8} +(1.56130 - 1.00339i) q^{9} +(0.176814 - 1.22977i) q^{10} +(0.0950085 - 0.208040i) q^{11} +(-1.62089 + 3.54926i) q^{12} +(0.435418 - 3.02840i) q^{13} +(-1.36890 + 0.879739i) q^{14} +(5.48538 + 1.61065i) q^{15} +(-0.380916 - 2.64933i) q^{16} +(1.26176 + 1.45615i) q^{17} +(0.747694 + 0.480513i) q^{18} +(-1.26668 + 1.46183i) q^{19} +(-4.40764 + 1.29420i) q^{20} +(-3.11047 - 6.81097i) q^{21} +0.109526 q^{22} +(-4.62936 - 1.25259i) q^{23} -3.97915 q^{24} +(0.718941 + 1.57426i) q^{25} +(1.40584 - 0.412791i) q^{26} +(1.65098 - 1.90533i) q^{27} +(5.06140 + 3.25276i) q^{28} +(4.23872 + 4.89174i) q^{29} +(0.389630 + 2.70993i) q^{30} +(-1.44518 - 0.424344i) q^{31} +(4.11648 - 2.64550i) q^{32} +(-0.0717243 + 0.498853i) q^{33} +(-0.383307 + 0.839324i) q^{34} +(3.66200 - 8.01867i) q^{35} +(0.467677 - 3.25276i) q^{36} +(-5.67778 + 3.64889i) q^{37} +(-0.888785 - 0.260971i) q^{38} +(0.959493 + 6.67342i) q^{39} +(-3.06784 - 3.54047i) q^{40} +(6.78612 + 4.36118i) q^{41} +(2.34817 - 2.70993i) q^{42} +(-2.55172 + 0.749253i) q^{43} +(-0.168228 - 0.368368i) q^{44} -4.81491 q^{45} +(-0.375312 - 2.26581i) q^{46} -1.43889 q^{47} +(2.45018 + 5.36514i) q^{48} +(-4.36144 + 1.28064i) q^{49} +(-0.542747 + 0.626363i) q^{50} +(-3.57182 - 2.29547i) q^{51} +(-3.54765 - 4.09421i) q^{52} +(-1.22118 - 8.49350i) q^{53} +(1.15843 + 0.340146i) q^{54} +(-0.499156 + 0.320788i) q^{55} +(-0.873198 + 6.07322i) q^{56} +(1.77066 - 3.87721i) q^{57} +(-1.28767 + 2.81961i) q^{58} +(-0.00878786 + 0.0611209i) q^{59} +(8.51584 - 5.47280i) q^{60} +(0.0426294 + 0.0125171i) q^{61} +(-0.102652 - 0.713962i) q^{62} +(4.12968 + 4.76590i) q^{63} +(-2.53201 - 1.62722i) q^{64} +(-5.19797 + 5.99877i) q^{65} +(-0.231577 + 0.0679971i) q^{66} +(5.15445 + 11.2867i) q^{67} +3.41164 q^{68} +(10.5658 - 0.225629i) q^{69} +4.22157 q^{70} +(-3.46306 - 7.58305i) q^{71} +(3.21556 - 0.944173i) q^{72} +(0.437593 - 0.505009i) q^{73} +(-2.71904 - 1.74742i) q^{74} +(-2.49745 - 2.88221i) q^{75} +(0.487421 + 3.39009i) q^{76} +(0.745641 + 0.218940i) q^{77} +(-2.71616 + 1.74557i) q^{78} +(1.70338 - 11.8472i) q^{79} +(-2.88463 + 6.31646i) q^{80} +(-4.62079 + 10.1181i) q^{81} +(-0.549771 + 3.82374i) q^{82} +(-0.303301 + 0.194920i) q^{83} +(-12.7210 - 3.73522i) q^{84} +(-0.711387 - 4.94781i) q^{85} +(-0.834022 - 0.962513i) q^{86} +(-11.9991 - 7.71135i) q^{87} +(0.270448 - 0.312114i) q^{88} +(15.4668 - 4.54147i) q^{89} +(-0.957872 - 2.09745i) q^{90} +10.3959 q^{91} +(-7.04411 + 4.74249i) q^{92} +3.31908 q^{93} +(-0.286250 - 0.626800i) q^{94} +(4.81491 - 1.41379i) q^{95} +(-7.06128 + 8.14915i) q^{96} +(-0.335292 - 0.215479i) q^{97} +(-1.42552 - 1.64514i) q^{98} +(-0.0604074 - 0.420143i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 7 q^{2} - 7 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 5 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 10 * q - 7 * q^2 - 7 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 - 5 * q^7 + 4 * q^8 - 2 * q^9	\( 10 q - 7 q^{2} - 7 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 5 q^{7} + 4 q^{8} - 2 q^{9} + q^{10} + 7 q^{11} + 12 q^{12} - 3 q^{13} + 9 q^{14} + 12 q^{15} + q^{16} - 10 q^{17} - 14 q^{18} + 2 q^{19} - 9 q^{20} - 2 q^{21} - 6 q^{22} - 12 q^{23} - 38 q^{24} - 4 q^{25} + 12 q^{26} - 4 q^{27} + 7 q^{28} + 14 q^{29} + 7 q^{30} + 10 q^{31} + 21 q^{32} + 16 q^{33} + 29 q^{34} + 7 q^{35} + 27 q^{36} - 19 q^{37} - 8 q^{38} + q^{39} + q^{40} + 7 q^{41} - 25 q^{42} - 11 q^{43} - 34 q^{44} - 6 q^{45} - 29 q^{46} - 18 q^{47} + 18 q^{48} - 18 q^{49} + 16 q^{50} + 7 q^{51} - 20 q^{52} + 29 q^{53} - 6 q^{54} - q^{55} - 2 q^{56} - 8 q^{57} - 23 q^{58} - 21 q^{59} + 25 q^{60} + 3 q^{61} + 4 q^{62} + 34 q^{63} + 24 q^{64} + 2 q^{65} + 2 q^{66} + 45 q^{67} - 30 q^{68} + 26 q^{69} + 38 q^{70} - 14 q^{71} + 19 q^{72} + 19 q^{73} + 10 q^{74} - 28 q^{75} - 16 q^{76} + 2 q^{77} - 4 q^{78} - 15 q^{79} - 52 q^{80} - 44 q^{81} + 16 q^{82} + 18 q^{83} - 17 q^{84} - 19 q^{85} - 11 q^{86} - 23 q^{87} + 27 q^{88} + 25 q^{89} - 20 q^{90} - 4 q^{91} + 52 q^{92} + 4 q^{93} + 17 q^{94} + 6 q^{95} - 51 q^{96} - 34 q^{97} + 17 q^{98} - 30 q^{99}+O(q^{100}) \) 10 * q - 7 * q^2 - 7 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 - 5 * q^7 + 4 * q^8 - 2 * q^9 + q^10 + 7 * q^11 + 12 * q^12 - 3 * q^13 + 9 * q^14 + 12 * q^15 + q^16 - 10 * q^17 - 14 * q^18 + 2 * q^19 - 9 * q^20 - 2 * q^21 - 6 * q^22 - 12 * q^23 - 38 * q^24 - 4 * q^25 + 12 * q^26 - 4 * q^27 + 7 * q^28 + 14 * q^29 + 7 * q^30 + 10 * q^31 + 21 * q^32 + 16 * q^33 + 29 * q^34 + 7 * q^35 + 27 * q^36 - 19 * q^37 - 8 * q^38 + q^39 + q^40 + 7 * q^41 - 25 * q^42 - 11 * q^43 - 34 * q^44 - 6 * q^45 - 29 * q^46 - 18 * q^47 + 18 * q^48 - 18 * q^49 + 16 * q^50 + 7 * q^51 - 20 * q^52 + 29 * q^53 - 6 * q^54 - q^55 - 2 * q^56 - 8 * q^57 - 23 * q^58 - 21 * q^59 + 25 * q^60 + 3 * q^61 + 4 * q^62 + 34 * q^63 + 24 * q^64 + 2 * q^65 + 2 * q^66 + 45 * q^67 - 30 * q^68 + 26 * q^69 + 38 * q^70 - 14 * q^71 + 19 * q^72 + 19 * q^73 + 10 * q^74 - 28 * q^75 - 16 * q^76 + 2 * q^77 - 4 * q^78 - 15 * q^79 - 52 * q^80 - 44 * q^81 + 16 * q^82 + 18 * q^83 - 17 * q^84 - 19 * q^85 - 11 * q^86 - 23 * q^87 + 27 * q^88 + 25 * q^89 - 20 * q^90 - 4 * q^91 + 52 * q^92 + 4 * q^93 + 17 * q^94 + 6 * q^95 - 51 * q^96 - 34 * q^97 + 17 * q^98 - 30 * q^99

Introduction

L-functions

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