LMFDB - Embedded newform 23.2.c.a.6.1

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			6.1
Root			$-0.415415 + 0.909632i$ of defining polynomial
Character	$\chi$	$=$	23.6
Dual form			23.2.c.a.4.1

$q$-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 $\left(\mathbb{Z}/23\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{9}{11}\right)$

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	−0.826163	−	0.563430i	$-0.809481\pi$
$2$	0.198939	−	0.435615i	0.140671	−	0.308026i	0.966834	+	0.255404i	$0.0822085\pi$
$3$	−2.11435	−	0.620830i	−1.22072	−	0.358437i	−0.392981	−	0.919546i	$-0.628556\pi$
$3$	−2.11435	−	0.620830i	−1.22072	−	0.358437i	−0.827741	+	0.561110i	$0.810374\pi$
$4$	1.15954	+	1.33818i	0.579769	+	0.669089i
$5$	−2.18251	+	1.40261i	−0.976047	+	0.627267i	−0.928394	−	0.371597i	$-0.878810\pi$
$5$	−2.18251	+	1.40261i	−0.976047	+	0.627267i	−0.0476526	+	0.998864i	$0.515174\pi$
$6$	−0.691070	+	0.797537i	−0.282128	+	0.325593i
$7$	0.483568	−	3.36329i	0.182772	−	1.27120i	−0.667400	−	0.744699i	$-0.732593\pi$
$7$	0.483568	−	3.36329i	0.182772	−	1.27120i	0.850172	−	0.526505i	$-0.176498\pi$
$8$	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	0.923414	−	0.383805i	$-0.125386\pi$
$11$	0.0950085	+	0.208040i	0.0286461	+	0.0627263i	−0.894768	+	0.446531i	$0.852659\pi$
$12$	−1.62089	−	3.54926i	−0.467911	−	1.02458i
$13$	0.435418	+	3.02840i	0.120763	+	0.839926i	0.956695	+	0.291093i	$0.0940188\pi$
$13$	0.435418	+	3.02840i	0.120763	+	0.839926i	−0.835932	+	0.548833i	$0.815072\pi$
$14$	−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	−0.581820	−	0.813318i	$-0.697659\pi$
$17$	1.26176	−	1.45615i	0.306021	−	0.353167i	0.887841	+	0.460150i	$0.152205\pi$
$18$	0.747694	−	0.480513i	0.176233	−	0.113258i
$19$	−1.26668	−	1.46183i	−0.290596	−	0.335366i	0.591614	−	0.806221i	$-0.298491\pi$
$19$	−1.26668	−	1.46183i	−0.290596	−	0.335366i	−0.882210	+	0.470855i	$0.843945\pi$
$20$	−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	−0.210491	−	0.977596i	$-0.567506\pi$
$29$	4.23872	−	4.89174i	0.787110	−	0.908374i	0.997601	+	0.0692221i	$0.0220517\pi$
$30$	0.389630	−	2.70993i	0.0711363	−	0.494764i
$31$	−1.44518	+	0.424344i	−0.259563	+	0.0762145i	−0.408925	−	0.912568i	$-0.634096\pi$
$31$	−1.44518	+	0.424344i	−0.259563	+	0.0762145i	0.149362	+	0.988783i	$0.452278\pi$
$32$	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	−0.0168987	−	0.999857i	$-0.505379\pi$
$37$	−5.67778	−	3.64889i	−0.933421	−	0.599873i	−0.916522	+	0.399984i	$0.869016\pi$
$38$	−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	0.110005	−	0.993931i	$-0.464913\pi$
$41$	6.78612	−	4.36118i	1.05981	−	0.681101i	0.949809	+	0.312830i	$0.101277\pi$
$42$	2.34817	+	2.70993i	0.362331	+	0.418152i
$43$	−2.55172	−	0.749253i	−0.389134	−	0.114260i	0.0813124	−	0.996689i	$-0.474089\pi$
$43$	−2.55172	−	0.749253i	−0.389134	−	0.114260i	−0.470446	+	0.882429i	$0.655907\pi$
$44$	−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	0.715795	+	0.698311i	$0.246065\pi$
$53$	−1.22118	+	8.49350i	−0.167742	+	1.16667i	−0.883537	+	0.468361i	$0.844845\pi$
$54$	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	0.989241	−	0.146292i	$-0.0467340\pi$
$59$	−0.00878786	−	0.0611209i	−0.00114408	−	0.00795726i	−0.990385	+	0.138335i	$0.955825\pi$
$60$	8.51584	+	5.47280i	1.09939	+	0.706535i
$61$	0.0426294	−	0.0125171i	0.00545814	−	0.00160265i	−0.279002	−	0.960290i	$-0.590004\pi$
$61$	0.0426294	−	0.0125171i	0.00545814	−	0.00160265i	0.284460	+	0.958688i	$0.408186\pi$
$62$	−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	−0.278521	−	0.960430i	$-0.589844\pi$
$67$	5.15445	−	11.2867i	0.629716	−	1.37889i	0.908237	−	0.418456i	$-0.137429\pi$
$68$	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	0.585047	+	0.811000i	$0.301076\pi$
$71$	−3.46306	+	7.58305i	−0.410990	+	0.899943i	−0.996037	+	0.0889431i	$0.971651\pi$
$72$	3.21556	+	0.944173i	0.378957	+	0.111272i
$73$	0.437593	+	0.505009i	0.0512164	+	0.0591069i	0.780780	−	0.624806i	$-0.214822\pi$
$73$	0.437593	+	0.505009i	0.0512164	+	0.0591069i	−0.729563	+	0.683913i	$0.760277\pi$
$74$	−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	0.827655	+	0.561237i	$0.189675\pi$
$79$	1.70338	+	11.8472i	0.191645	+	1.33292i	−0.636010	+	0.771681i	$0.719416\pi$
$80$	−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	0.523889	−	0.851786i	$-0.324481\pi$
$83$	−0.303301	−	0.194920i	−0.0332916	−	0.0213952i	−0.557181	+	0.830391i	$0.688117\pi$
$84$	−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	0.966157	−	0.257953i	$-0.0830481\pi$
$89$	15.4668	+	4.54147i	1.63948	+	0.481395i	0.673323	+	0.739348i	$0.264866\pi$
$90$	−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	−0.557552	−	0.830142i	$-0.688259\pi$
$97$	−0.335292	+	0.215479i	−0.0340438	+	0.0218786i	0.523508	+	0.852021i	$0.324623\pi$
$98$	−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	−0.948246	−	0.317536i	$-0.897145\pi$
$101$	−16.3914	−	10.5341i	−1.63100	−	1.04818i	−0.682756	−	0.730646i	$-0.739219\pi$
$102$	0.289368	+	2.01260i	0.0286517	+	0.199277i
$103$	2.71041	+	5.93497i	0.267065	+	0.584790i	0.994889	−	0.100973i	$-0.0321957\pi$
$103$	2.71041	+	5.93497i	0.267065	+	0.584790i	−0.727824	+	0.685763i	$0.759468\pi$
$104$	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	−0.221210	−	0.975226i	$-0.571001\pi$
$107$	1.24071	−	0.364304i	0.119944	−	0.0352186i	0.341154	+	0.940008i	$0.389182\pi$
$108$	−0.635298	+	4.41860i	−0.0611316	+	0.425180i
$109$	−4.63775	+	5.35225i	−0.444216	+	0.512653i	−0.933061	−	0.359718i	$-0.882873\pi$
$109$	−4.63775	+	5.35225i	−0.444216	+	0.512653i	0.488845	+	0.872371i	$0.337418\pi$
$110$	−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	−0.881375	−	0.472418i	$-0.843381\pi$
$113$	0.561616	−	1.22977i	0.0528324	−	0.115687i	0.934207	+	0.356731i	$0.116109\pi$
$114$	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	0.999808	+	0.0196010i	$0.00623958\pi$
$127$	4.05571	+	8.88077i	0.359886	+	0.788041i	−0.639921	+	0.768440i	$0.721033\pi$
$128$	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	−0.934442	−	0.356116i	$-0.884101\pi$
$131$	0.715092	−	4.97357i	0.0624779	−	0.434543i	0.996920	−	0.0784276i	$-0.0249899\pi$
$132$	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	0.742909	−	0.669393i	$-0.233446\pi$
$149$	−3.04537	−	6.66843i	−0.249487	−	0.546299i	−0.992395	+	0.123094i	$0.960718\pi$
$150$	0.758693	+	1.66131i	0.0619471	+	0.135645i
$151$	−2.43438	−	16.9315i	−0.198107	−	1.37786i	−0.809772	−	0.586745i	$-0.800409\pi$
$151$	−2.43438	−	16.9315i	−0.198107	−	1.37786i	0.611665	−	0.791117i	$-0.290500\pi$
$152$	−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	0.996176	+	0.0873711i	$0.0278466\pi$
$157$	11.7893	+	13.6056i	0.940887	+	1.08584i	−0.0552888	+	0.998470i	$0.517608\pi$
$158$	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	−0.496080	−	0.868277i	$-0.665228\pi$
$163$	6.19185	−	13.5583i	0.484983	−	1.06196i	0.981063	−	0.193688i	$-0.0620448\pi$
$164$	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	−0.915548	−	0.402209i	$-0.868243\pi$
$167$	−5.00291	+	5.77367i	−0.387137	+	0.446780i	0.528411	+	0.848989i	$0.322788\pi$
$168$	−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	0.980282	−	0.197603i	$-0.0633157\pi$
$173$	2.48585	+	5.44324i	0.188995	+	0.413842i	−0.791287	+	0.611445i	$0.790588\pi$
$174$	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	−0.422831	−	0.906209i	$-0.638963\pi$
$179$	3.02147	−	1.94178i	0.225836	−	0.145136i	0.648666	+	0.761073i	$0.275327\pi$
$180$	−5.58307	−	6.44321i	−0.416138	−	0.480248i
$181$	−18.3033	−	5.37433i	−1.36047	−	0.399470i	−0.481542	−	0.876423i	$-0.659923\pi$
$181$	−18.3033	−	5.37433i	−1.36047	−	0.399470i	−0.878929	+	0.476952i	$0.841741\pi$
$182$	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	−0.804397	−	0.594092i	$-0.797511\pi$
$191$	1.86285	−	12.9564i	0.134791	−	0.937494i	0.939188	−	0.343402i	$-0.111579\pi$
$192$	6.36379	−	1.86858i	0.459267	−	0.134853i
$193$	7.89406	+	5.07320i	0.568227	+	0.365177i	0.792988	−	0.609237i	$-0.208524\pi$
$193$	7.89406	+	5.07320i	0.568227	+	0.365177i	−0.224762	+	0.974414i	$0.572160\pi$
$194$	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	0.972443	+	0.233142i	$0.0749007\pi$
$197$	1.47479	+	10.2574i	0.105074	+	0.730809i	−0.867368	+	0.497667i	$0.834190\pi$
$198$	0.171003	+	0.109897i	0.0121527	+	0.00781004i
$199$	−9.84113	+	2.88962i	−0.697619	+	0.204839i	−0.611266	−	0.791425i	$-0.709339\pi$
$199$	−9.84113	+	2.88962i	−0.697619	+	0.204839i	−0.0863529	+	0.996265i	$0.527521\pi$
$200$	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	0.910909	−	0.412607i	$-0.135382\pi$
$211$	5.41619	+	6.25061i	0.372866	+	0.430310i	−0.538043	+	0.842917i	$0.680836\pi$
$212$	−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	−0.871480	−	0.490431i	$-0.836840\pi$
$223$	1.53616	−	10.6843i	0.102869	−	0.715471i	0.974349	−	0.225040i	$-0.0722514\pi$
$224$	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	0.918860	−	0.394584i	$-0.129111\pi$
$227$	22.2762	+	6.54089i	1.47853	+	0.434134i	0.559666	+	0.828718i	$0.310930\pi$
$228$	−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	−0.607260	−	0.794504i	$-0.707731\pi$
$233$	−23.6240	−	6.93663i	−1.54766	−	0.454434i	−0.940400	+	0.340070i	$0.889549\pi$
$234$	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	0.547016	−	0.837122i	$-0.315764\pi$
$239$	0.197590	+	0.126983i	0.0127810	+	0.00821388i	−0.534235	+	0.845336i	$0.679400\pi$
$240$	2.17768	+	15.1461i	0.140569	+	0.977676i
$241$	2.18829	+	4.79168i	0.140960	+	0.308659i	0.966925	−	0.255063i	$-0.0820961\pi$
$241$	2.18829	+	4.79168i	0.140960	+	0.308659i	−0.825964	+	0.563722i	$0.809369\pi$
$242$	−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	−0.0286319	+	0.999590i	$0.509115\pi$
$251$	−12.1250	+	26.5500i	−0.765322	+	1.67582i	−0.736690	+	0.676231i	$0.763612\pi$
$252$	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	0.476225	−	0.879324i	$-0.342005\pi$
$257$	−7.40518	−	8.54603i	−0.461922	−	0.533087i	−0.938147	+	0.346237i	$0.887459\pi$
$258$	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	0.768637	+	0.639685i	$0.220935\pi$
$263$	3.42761	+	23.8395i	0.211355	+	1.47001i	−0.557282	+	0.830324i	$0.688156\pi$
$264$	−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	0.941328	+	0.337492i	$0.109579\pi$
$269$	−0.934084	+	6.49670i	−0.0569521	+	0.396111i	−0.998280	+	0.0586185i	$0.981330\pi$
$270$	−2.05119	+	2.36720i	−0.124832	+	0.144063i
$271$	16.8532	−	10.8309i	1.02376	−	0.657931i	0.0828417	−	0.996563i	$-0.473600\pi$
$271$	16.8532	−	10.8309i	1.02376	−	0.657931i	0.940919	+	0.338632i	$0.109964\pi$
$272$	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	−0.651506	+	0.758644i	$0.725862\pi$
$281$	−27.0260	+	17.3686i	−1.61224	+	1.03612i	−0.960732	+	0.277479i	$0.910501\pi$
$282$	0.994371	−	1.14757i	0.0592139	−	0.0683365i
$283$	0.859497	−	5.97793i	0.0510918	−	0.355351i	−0.948198	−	0.317679i	$-0.897097\pi$
$283$	0.859497	−	5.97793i	0.0510918	−	0.355351i	0.999290	−	0.0376723i	$-0.0119943\pi$
$284$	−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	0.167203	−	0.985922i	$-0.446526\pi$
$293$	19.1592	−	22.1109i	1.11929	−	1.29173i	0.952092	−	0.305813i	$-0.0989281\pi$
$294$	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	−0.0385023	−	0.999259i	$-0.512259\pi$
$307$	8.22363	−	2.41468i	0.469347	−	0.137813i	0.507850	+	0.861446i	$0.330441\pi$
$308$	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	0.912102	−	0.409963i	$-0.134458\pi$
$311$	0.0876947	+	0.192025i	0.00497271	+	0.0108887i	−0.907129	+	0.420852i	$0.861731\pi$
$312$	−1.73259	−	12.0505i	−0.0980888	−	0.682222i
$313$	24.7874	+	15.9299i	1.40107	+	0.900412i	0.999879	−	0.0155835i	$-0.00496059\pi$
$313$	24.7874	+	15.9299i	1.40107	+	0.900412i	0.401189	+	0.915995i	$0.368597\pi$
$314$	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	0.255706	−	0.966755i	$-0.417692\pi$
$317$	22.1011	−	14.2035i	1.24132	−	0.797749i	0.985615	+	0.169006i	$0.0540557\pi$
$318$	−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	0.947998	−	0.318277i	$-0.103104\pi$
$331$	19.1448	+	12.3036i	1.05229	+	0.676269i	0.104297	+	0.994546i	$0.466741\pi$
$332$	−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	−0.297316	−	0.954779i	$-0.596091\pi$
$337$	−0.573517	+	0.168400i	−0.0312414	+	0.00917332i	0.266074	+	0.963952i	$0.414273\pi$
$338$	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	−0.903061	−	0.429511i	$-0.858686\pi$
$347$	0.240693	−	0.527045i	0.0129211	−	0.0282933i	0.915983	+	0.401218i	$0.131413\pi$
$348$	−24.2326	−	7.11532i	−1.29900	−	0.381421i
$349$	−14.2226	−	16.4138i	−0.761320	−	0.878610i	0.234294	−	0.972166i	$-0.424722\pi$
$349$	−14.2226	−	16.4138i	−0.761320	−	0.878610i	−0.995614	+	0.0935554i	$0.970177\pi$
$350$	−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	−0.298744	−	0.954333i	$-0.596568\pi$
$353$	−0.640923	+	0.188192i	−0.0341129	+	0.0100164i	0.264632	+	0.964350i	$0.414750\pi$
$354$	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	0.131819	−	0.991274i	$-0.457918\pi$
$359$	−13.5495	−	8.70775i	−0.715116	−	0.459577i	−0.846935	+	0.531697i	$0.821555\pi$
$360$	−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	−0.127728	−	0.991809i	$-0.540768\pi$
$373$	13.9324	−	8.95383i	0.721394	−	0.463612i	0.849122	+	0.528198i	$0.177132\pi$
$374$	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	0.992603	−	0.121404i	$-0.0387397\pi$
$379$	4.88324	+	10.6928i	0.250835	+	0.549252i	−0.741768	+	0.670657i	$0.766012\pi$
$380$	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	−0.544782	−	0.838578i	$-0.683388\pi$
$383$	−10.7581	+	3.15886i	−0.549712	+	0.161410i	−0.00493016	+	0.999988i	$0.501569\pi$
$384$	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	−0.947827	−	0.318787i	$-0.896725\pi$
$389$	−1.70031	+	3.72317i	−0.0862093	+	0.188772i	0.861617	+	0.507559i	$0.169452\pi$
$390$	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	−0.798647	−	0.601799i	$-0.794451\pi$
$397$	−1.77958	+	2.05374i	−0.0893144	+	0.103074i	0.709333	+	0.704873i	$0.248996\pi$
$398$	−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	−0.946168	−	0.323675i	$-0.895082\pi$
$401$	−2.59356	−	18.0386i	−0.129516	−	0.900805i	0.816652	−	0.577130i	$-0.195828\pi$
$402$	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	−0.783753	−	0.621073i	$-0.786697\pi$
$409$	−11.0096	+	7.07541i	−0.544387	+	0.349856i	0.239365	+	0.970930i	$0.423061\pi$
$410$	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	−0.498353	−	0.866974i	$-0.666062\pi$
$419$	1.70412	−	1.09517i	0.0832517	−	0.0535026i	0.581604	+	0.813472i	$0.302425\pi$
$420$	22.5246	−	25.9948i	1.09909	−	1.26842i
$421$	2.05091	−	14.2644i	0.0999551	−	0.695203i	−0.876802	−	0.480852i	$-0.840327\pi$
$421$	2.05091	−	14.2644i	0.0999551	−	0.695203i	0.976757	−	0.214351i	$-0.0687636\pi$
$422$	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	−0.505833	−	0.862632i	$-0.668815\pi$
$431$	8.71955	−	10.0629i	0.420006	−	0.484713i	0.925839	+	0.377919i	$0.123360\pi$
$432$	−5.67672	+	3.64821i	−0.273121	+	0.175524i
$433$	−23.1416	−	26.7069i	−1.11212	−	1.28345i	−0.955240	−	0.295831i	$-0.904404\pi$
$433$	−23.1416	−	26.7069i	−1.11212	−	1.28345i	−0.156875	−	0.987618i	$-0.550142\pi$
$434$	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	−0.993384	−	0.114840i	$-0.963364\pi$
$439$	−5.36516	+	11.7481i	−0.256065	+	0.560705i	0.737319	+	0.675545i	$0.236092\pi$
$440$	−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	−0.633801	−	0.773496i	$-0.718506\pi$
$443$	4.67301	−	5.39295i	0.222022	−	0.256227i	0.855822	+	0.517270i	$0.173052\pi$
$444$	−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	0.877215	−	0.480098i	$-0.159399\pi$
$449$	−1.27291	−	2.78729i	−0.0600725	−	0.131540i	−0.937287	+	0.348558i	$0.886672\pi$
$450$	−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	−0.121038	−	0.992648i	$-0.538622\pi$
$457$	−16.2369	−	4.76757i	−0.759528	−	0.223018i	−0.638490	+	0.769630i	$0.720441\pi$
$458$	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	0.0170489	−	0.999855i	$-0.494573\pi$
$463$	−10.9561	−	3.21699i	−0.509171	−	0.149506i	−0.526220	+	0.850349i	$0.676391\pi$
$464$	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	0.658808	+	0.752311i	$0.271061\pi$
$467$	−4.00360	+	27.8456i	−0.185264	+	1.28854i	−0.844072	+	0.536230i	$0.819848\pi$
$468$	−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	0.990509	−	0.137450i	$-0.0438907\pi$
$479$	15.6156	+	18.0213i	0.713493	+	0.823415i	−0.277015	+	0.960866i	$0.589345\pi$
$480$	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	0.440837	−	0.897587i	$-0.354682\pi$
$487$	−11.2625	−	12.9976i	−0.510351	−	0.588977i	−0.951189	+	0.308610i	$0.900136\pi$
$488$	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	0.559896	−	0.828563i	$-0.310841\pi$
$491$	32.7695	−	9.62199i	1.47887	−	0.434234i	0.918969	+	0.394329i	$0.129023\pi$
$492$	−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	0.624448	+	0.781067i	$0.285324\pi$
$499$	−4.35055	+	30.2587i	−0.194757	+	1.35457i	−0.819205	+	0.573501i	$0.805585\pi$
$500$	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	0.672273	−	0.740303i	$-0.265318\pi$
$503$	18.7851	+	5.51581i	0.837588	+	0.245938i	0.165314	+	0.986241i	$0.447136\pi$
$504$	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	0.343360	−	0.939204i	$-0.388435\pi$
$509$	2.80753	+	0.824367i	0.124442	+	0.0365394i	−0.218919	+	0.975743i	$0.570253\pi$
$510$	−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	−0.908542	−	0.417794i	$-0.862803\pi$
$521$	−33.0279	+	9.69787i	−1.44698	+	0.424871i	−0.538437	+	0.842666i	$0.680985\pi$
$522$	0.818715	−	5.69429i	0.0358342	−	0.249232i
$523$	−2.73748	+	3.15922i	−0.119702	+	0.138143i	−0.812437	−	0.583048i	$-0.801860\pi$
$523$	−2.73748	+	3.15922i	−0.119702	+	0.138143i	0.692736	+	0.721191i	$0.256405\pi$
$524$	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	0.964327	−	0.264713i	$-0.0852772\pi$
$541$	3.08816	+	6.76213i	0.132771	+	0.290727i	−0.831557	+	0.555440i	$0.812550\pi$
$542$	−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	−0.274567	−	0.961568i	$-0.588534\pi$
$547$	11.3677	−	7.30557i	0.486047	−	0.312363i	0.760614	+	0.649205i	$0.224898\pi$
$548$	−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	−0.0785115	−	0.996913i	$-0.525017\pi$
$557$	18.7791	−	12.0686i	0.795698	−	0.511364i	0.874209	+	0.485549i	$0.161380\pi$
$558$	−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	0.736148	−	0.676820i	$-0.236643\pi$
$563$	−6.10827	−	13.3753i	−0.257433	−	0.563700i	−0.993581	+	0.113121i	$0.963915\pi$
$564$	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	0.0408837	+	0.999164i	$0.486983\pi$
$569$	−22.7547	+	26.2604i	−0.953929	+	1.10089i	−0.994812	+	0.101728i	$0.967563\pi$
$570$	−4.45499	+	2.86305i	−0.186599	+	0.119920i
$571$	14.5902	+	16.8380i	0.610583	+	0.704650i	0.973890	−	0.227019i	$-0.0728980\pi$
$571$	14.5902	+	16.8380i	0.610583	+	0.704650i	−0.363307	+	0.931669i	$0.618353\pi$
$572$	−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	−0.926916	−	0.375269i	$-0.877550\pi$
$577$	−0.872088	+	1.90961i	−0.0363055	+	0.0794980i	0.890610	+	0.454767i	$0.150278\pi$
$578$	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	0.710701	−	0.703494i	$-0.248378\pi$
$587$	−6.93830	−	15.1928i	−0.286374	−	0.627072i	−0.997076	+	0.0764218i	$0.975650\pi$
$588$	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	−0.958049	−	0.286604i	$-0.907474\pi$
$593$	−26.6731	+	17.1418i	−1.09533	+	0.703928i	−0.137284	+	0.990532i	$0.543837\pi$
$594$	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	0.657513	−	0.753443i	$-0.271609\pi$
$601$	19.6933	+	5.78247i	0.803305	+	0.235872i	0.145793	+	0.989315i	$0.453427\pi$
$602$	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	0.445103	−	0.895479i	$-0.353167\pi$
$607$	−4.54687	−	2.92209i	−0.184552	−	0.118604i	−0.629654	+	0.776875i	$0.716803\pi$
$608$	−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	−0.478321	−	0.878185i	$-0.658754\pi$
$613$	−10.0503	+	2.95103i	−0.405928	+	0.119191i	0.0723934	+	0.997376i	$0.476936\pi$
$614$	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	0.442128	−	0.896952i	$-0.354224\pi$
$617$	−12.6337	−	14.5801i	−0.508615	−	0.586973i	−0.950744	+	0.309978i	$0.899678\pi$
$618$	−6.60644	−	1.93983i	−0.265750	−	0.0780312i
$619$	−0.114642	+	0.251031i	−0.00460786	+	0.0100898i	−0.911922	−	0.410364i	$-0.865402\pi$
$619$	−0.114642	+	0.251031i	−0.00460786	+	0.0100898i	0.907314	+	0.420454i	$0.138129\pi$
$620$	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	0.757558	+	0.652768i	$0.226392\pi$
$631$	5.39050	+	37.4917i	0.214592	+	1.49252i	−0.542966	+	0.839755i	$0.682699\pi$
$632$	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	−0.154708	−	0.987960i	$-0.549444\pi$
$641$	−20.7351	−	6.08838i	−0.818988	−	0.240477i	−0.664280	+	0.747483i	$0.731262\pi$
$642$	−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	0.455736	−	0.890115i	$-0.349376\pi$
$647$	9.10342	+	2.67301i	0.357892	+	0.105087i	−0.0978433	+	0.995202i	$0.531194\pi$
$648$	−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	0.859903	−	0.510457i	$-0.170524\pi$
$653$	19.2367	+	12.3627i	0.752792	+	0.483790i	−0.107111	+	0.994247i	$0.534160\pi$
$654$	−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	0.229897	−	0.973215i	$-0.426161\pi$
$659$	24.3735	−	7.15671i	0.949458	−	0.278786i	0.719561	+	0.694429i	$0.244343\pi$
$660$	−0.329481	+	2.29159i	−0.0128250	+	0.0892002i
$661$	−10.1049	+	11.6616i	−0.393034	+	0.453585i	−0.917435	−	0.397886i	$-0.869744\pi$
$661$	−10.1049	+	11.6616i	−0.393034	+	0.453585i	0.524401	+	0.851471i	$0.324289\pi$
$662$	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	−0.369854	−	0.929090i	$-0.620592\pi$
$673$	15.6280	−	18.0356i	0.602414	−	0.695223i	0.972269	+	0.233867i	$0.0751379\pi$
$674$	−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	−0.998092	−	0.0617470i	$-0.980333\pi$
$677$	−1.50458	−	10.4646i	−0.0578259	−	0.402188i	0.940266	−	0.340441i	$-0.110576\pi$
$678$	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	−1.00000		0.000484978i	$-0.999846\pi$
$683$	−1.05505	+	7.33804i	−0.0403704	+	0.280782i	0.959629	+	0.281267i	$0.0907547\pi$
$684$	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	0.947062	−	0.321050i	$-0.104036\pi$
$701$	2.23024	+	4.88354i	0.0842350	+	0.184449i	−0.862827	+	0.505499i	$0.831308\pi$
$702$	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	0.655144	−	0.755504i	$-0.272608\pi$
$709$	−4.95017	−	5.71280i	−0.185907	−	0.214549i	−0.841051	+	0.540956i	$0.818063\pi$
$710$	−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	−0.174302	−	0.984692i	$-0.555767\pi$
$719$	22.1263	−	25.5352i	0.825173	−	0.952301i	0.999475	+	0.0323913i	$0.0103123\pi$
$720$	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	0.678613	−	0.734496i	$-0.262581\pi$
$727$	7.88389	+	5.06667i	0.292397	+	0.187912i	−0.386215	+	0.922409i	$0.626218\pi$
$728$	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	−0.0959708	−	0.995384i	$-0.530596\pi$
$733$	−19.3539	−	5.68281i	−0.714852	−	0.209899i	−0.618881	+	0.785485i	$0.712414\pi$
$734$	−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	−0.361691	−	0.932298i	$-0.617801\pi$
$739$	−31.8060	−	9.33909i	−1.17000	−	0.343544i	−0.808312	+	0.588754i	$0.799619\pi$
$740$	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	0.925888	+	0.377799i	$0.123319\pi$
$743$	−1.87899	+	13.0686i	−0.0689333	+	0.479442i	−0.994821	+	0.101643i	$0.967590\pi$
$744$	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	0.184552	−	0.982823i	$-0.440917\pi$
$751$	23.8736	−	7.00993i	0.871161	−	0.255796i	0.686609	+	0.727027i	$0.259098\pi$
$752$	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	0.612280	+	0.790641i	$0.290253\pi$
$757$	−10.6259	+	23.2675i	−0.386205	+	0.845671i	−0.998485	+	0.0550300i	$0.982475\pi$
$758$	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	−0.483587	−	0.875296i	$-0.660666\pi$
$761$	13.6441	−	29.8765i	0.494600	−	1.08302i	0.978187	−	0.207726i	$-0.0666064\pi$
$762$	−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	−0.897929	−	0.440139i	$-0.854929\pi$
$769$	−4.44731	−	30.9317i	−0.160374	−	1.11543i	0.737555	−	0.675287i	$-0.235980\pi$
$770$	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	0.433248	−	0.901275i	$-0.357368\pi$
$773$	−5.74416	−	3.69155i	−0.206603	−	0.132776i	−0.639851	+	0.768499i	$0.721004\pi$
$774$	−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	−0.909811	−	0.415023i	$-0.863773\pi$
$787$	−25.5355	+	16.4106i	−0.910241	+	0.584976i	−0.000430422		1.00000i	$0.500137\pi$
$788$	−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	0.0717927	−	0.997420i	$-0.477128\pi$
$797$	18.9554	−	5.56580i	0.671434	−	0.197151i	0.599642	+	0.800269i	$0.295310\pi$
$798$	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	0.971338	−	0.237702i	$-0.0763941\pi$
$809$	17.0037	+	19.6234i	0.597820	+	0.689921i	−0.373518	+	0.927623i	$0.621849\pi$
$810$	11.6259	−	7.47152i	0.408493	−	0.262523i
$811$	−34.7301	+	40.0807i	−1.21954	+	1.40742i	−0.334182	+	0.942509i	$0.608460\pi$
$811$	−34.7301	+	40.0807i	−1.21954	+	1.40742i	−0.885356	+	0.464913i	$0.846085\pi$
$812$	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	0.555734	+	0.831360i	$0.312437\pi$
$821$	−6.06615	+	42.1910i	−0.211710	+	1.47248i	−0.767444	+	0.641116i	$0.778472\pi$
$822$	8.02898	−	9.26593i	0.280043	−	0.323186i
$823$	−25.5894	+	16.4453i	−0.891991	+	0.573248i	−0.904405	−	0.426675i	$-0.859685\pi$
$823$	−25.5894	+	16.4453i	−0.891991	+	0.573248i	0.0124137	+	0.999923i	$0.496049\pi$
$824$	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	−0.981126	−	0.193371i	$-0.938058\pi$
$839$	−14.0415	−	30.7465i	−0.484765	−	1.06149i	0.496361	−	0.868116i	$-0.334669\pi$
$840$	−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	0.582234	+	0.813021i	$0.302179\pi$
$853$	−12.0764	+	26.4437i	−0.413488	+	0.905413i	−0.995723	+	0.0923924i	$0.970549\pi$
$854$	−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	−0.525795	−	0.850611i	$-0.676232\pi$
$857$	11.4459	−	13.2093i	0.390986	−	0.451222i	0.916782	+	0.399389i	$0.130778\pi$
$858$	0.105089	−	0.730913i	0.00358769	−	0.0249530i
$859$	42.5405	−	12.4910i	1.45146	−	0.426188i	0.541439	−	0.840740i	$-0.317880\pi$
$859$	42.5405	−	12.4910i	1.45146	−	0.426188i	0.910026	+	0.414552i	$0.136062\pi$
$860$	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	0.815298	−	0.579042i	$-0.196573\pi$
$863$	−4.58924	−	10.0490i	−0.156219	−	0.342073i	−0.971517	+	0.236969i	$0.923846\pi$
$864$	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	0.584425	−	0.811447i	$-0.301320\pi$
$877$	18.8753	+	5.54229i	0.637374	+	0.187150i	0.0529483	+	0.998597i	$0.483138\pi$
$878$	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	−0.875889	−	0.482513i	$-0.839724\pi$
$881$	2.98181	−	20.7390i	0.100460	−	0.698714i	0.976349	−	0.216201i	$-0.0693667\pi$
$882$	−3.87639	+	1.13821i	−0.130525	+	0.0383255i
$883$	−34.5844	−	22.2260i	−1.16386	−	0.747966i	−0.191507	−	0.981491i	$-0.561337\pi$
$883$	−34.5844	−	22.2260i	−1.16386	−	0.747966i	−0.972351	+	0.233525i	$0.924974\pi$
$884$	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	−0.830868	−	0.556470i	$-0.812155\pi$
$887$	−5.67154	−	39.4464i	−0.190432	−	1.32448i	0.640436	−	0.768012i	$-0.278754\pi$
$888$	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	−0.857089	−	0.515169i	$-0.827729\pi$
$907$	−5.41668	−	37.6738i	−0.179858	−	1.25094i	0.677231	−	0.735771i	$-0.263180\pi$
$908$	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	−0.400051	−	0.916493i	$-0.631008\pi$
$911$	−42.2532	−	27.1545i	−1.39991	−	0.899667i	−0.999858	+	0.0168256i	$0.994644\pi$
$912$	−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	0.489956	−	0.871747i	$-0.337013\pi$
$929$	−3.03206	−	1.94859i	−0.0994786	−	0.0639310i	−0.589434	+	0.807816i	$0.700649\pi$
$930$	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	−0.269714	−	0.962940i	$-0.586929\pi$
$937$	22.0949	−	25.4989i	0.721809	−	0.833012i	0.991523	+	0.129928i	$0.0414747\pi$
$938$	−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	−0.553967	−	0.832539i	$-0.686886\pi$
$941$	13.4358	−	29.4203i	0.437995	−	0.959076i	0.991962	−	0.126537i	$-0.0403862\pi$
$942$	−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	0.161368	−	0.986894i	$-0.448409\pi$
$947$	−25.8018	−	29.7769i	−0.838446	−	0.967619i	−0.999814	+	0.0192756i	$0.993864\pi$
$948$	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	0.926858	+	0.375411i	$0.122499\pi$
$953$	4.42408	+	30.7701i	0.143310	+	0.996742i	−0.783548	+	0.621331i	$0.786592\pi$
$954$	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	−0.696506	−	0.717551i	$-0.745263\pi$
$971$	−10.3808	+	6.67136i	−0.333137	+	0.214094i	0.363369	+	0.931645i	$0.381627\pi$
$972$	−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	0.928504	+	0.371321i	$0.121095\pi$
$977$	18.7882	+	41.1405i	0.601089	+	1.31620i	−0.327415	+	0.944881i	$0.606178\pi$
$978$	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	−0.573561	−	0.819163i	$-0.694438\pi$
$983$	9.99811	−	11.5384i	0.318890	−	0.368019i	0.892451	+	0.451144i	$0.148984\pi$
$984$	−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	−0.733405	−	0.679792i	$-0.762070\pi$
$991$	8.20454	−	17.9654i	0.260626	−	0.570691i	0.994031	+	0.109101i	$0.0347973\pi$
$992$	−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	−0.462493	−	0.886623i	$-0.653045\pi$
$997$	−11.7531	+	3.45101i	−0.372223	+	0.109295i	0.0902704	+	0.995917i	$0.471227\pi$
$998$	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.6.1	yes	10
3.2	odd	2		207.2.i.c.190.1		10
4.3	odd	2		368.2.m.c.305.1		10
5.2	odd	4		575.2.p.b.374.2		20
5.3	odd	4		575.2.p.b.374.1		20
5.4	even	2		575.2.k.b.351.1		10
23.2	even	11		529.2.a.i.1.3		5
23.3	even	11		529.2.c.i.399.1		10
23.4	even	11	inner	23.2.c.a.4.1	✓	10
23.5	odd	22		529.2.c.e.334.1		10
23.6	even	11		529.2.c.g.170.1		10
23.7	odd	22		529.2.c.f.501.1		10
23.8	even	11		529.2.c.b.177.1		10
23.9	even	11		529.2.c.i.118.1		10
23.10	odd	22		529.2.c.e.255.1		10
23.11	odd	22		529.2.c.c.266.1		10
23.12	even	11		529.2.c.b.266.1		10
23.13	even	11		529.2.c.d.255.1		10
23.14	odd	22		529.2.c.h.118.1		10
23.15	odd	22		529.2.c.c.177.1		10
23.16	even	11		529.2.c.g.501.1		10
23.17	odd	22		529.2.c.f.170.1		10
23.18	even	11		529.2.c.d.334.1		10
23.19	odd	22		529.2.c.a.487.1		10
23.20	odd	22		529.2.c.h.399.1		10
23.21	odd	22		529.2.a.j.1.3		5
23.22	odd	2		529.2.c.a.466.1		10
69.2	odd	22		4761.2.a.bo.1.3		5
69.44	even	22		4761.2.a.bn.1.3		5
69.50	odd	22		207.2.i.c.73.1		10
92.27	odd	22		368.2.m.c.257.1		10
92.67	even	22		8464.2.a.bt.1.1		5
92.71	odd	22		8464.2.a.bs.1.1		5
115.4	even	22		575.2.k.b.326.1		10
115.27	odd	44		575.2.p.b.349.1		20
115.73	odd	44		575.2.p.b.349.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.2.c.a.4.1	✓	10	23.4	even	11	inner
23.2.c.a.6.1	yes	10	1.1	even	1	trivial
207.2.i.c.73.1		10	69.50	odd	22
207.2.i.c.190.1		10	3.2	odd	2
368.2.m.c.257.1		10	92.27	odd	22
368.2.m.c.305.1		10	4.3	odd	2
529.2.a.i.1.3		5	23.2	even	11
529.2.a.j.1.3		5	23.21	odd	22
529.2.c.a.466.1		10	23.22	odd	2
529.2.c.a.487.1		10	23.19	odd	22
529.2.c.b.177.1		10	23.8	even	11
529.2.c.b.266.1		10	23.12	even	11
529.2.c.c.177.1		10	23.15	odd	22
529.2.c.c.266.1		10	23.11	odd	22
529.2.c.d.255.1		10	23.13	even	11
529.2.c.d.334.1		10	23.18	even	11
529.2.c.e.255.1		10	23.10	odd	22
529.2.c.e.334.1		10	23.5	odd	22
529.2.c.f.170.1		10	23.17	odd	22
529.2.c.f.501.1		10	23.7	odd	22
529.2.c.g.170.1		10	23.6	even	11
529.2.c.g.501.1		10	23.16	even	11
529.2.c.h.118.1		10	23.14	odd	22
529.2.c.h.399.1		10	23.20	odd	22
529.2.c.i.118.1		10	23.9	even	11
529.2.c.i.399.1		10	23.3	even	11
575.2.k.b.326.1		10	115.4	even	22
575.2.k.b.351.1		10	5.4	even	2
575.2.p.b.349.1		20	115.27	odd	44
575.2.p.b.349.2		20	115.73	odd	44
575.2.p.b.374.1		20	5.3	odd	4
575.2.p.b.374.2		20	5.2	odd	4
4761.2.a.bn.1.3		5	69.44	even	22
4761.2.a.bo.1.3		5	69.2	odd	22
8464.2.a.bs.1.1		5	92.71	odd	22
8464.2.a.bt.1.1		5	92.67	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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