LMFDB - Embedded newform 138.2.e.d.127.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [138,2,Mod(13,138)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(138, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("138.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 138 = 2 \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	138.e (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:	$1.10193554789$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			127.1
Root			$-0.841254 + 0.540641i$ of defining polynomial
Character	$\chi$	$=$	138.127
Dual form			138.2.e.d.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.841254 + 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(1.78074 - 0.522874i) q^{5} +(0.415415 + 0.909632i) q^{6} +(-2.54487 - 2.93694i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(-0.841254 + 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(1.78074 - 0.522874i) q^{5} +(0.415415 + 0.909632i) q^{6} +(-2.54487 - 2.93694i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-1.21537 + 1.40261i) q^{10} +(1.81329 + 1.16533i) q^{11} +(-0.841254 - 0.540641i) q^{12} +(4.55742 - 5.25954i) q^{13} +(3.72871 + 1.09485i) q^{14} +(-0.264125 - 1.83703i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(2.36483 + 5.17825i) q^{17} +(0.959493 - 0.281733i) q^{18} +(-0.810827 + 1.77546i) q^{19} +(0.264125 - 1.83703i) q^{20} +(-3.26921 + 2.10100i) q^{21} -2.15546 q^{22} +(-4.40644 - 1.89296i) q^{23} +1.00000 q^{24} +(-1.30862 + 0.840996i) q^{25} +(-0.990421 + 6.88853i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(-3.72871 + 1.09485i) q^{28} +(-0.0455430 - 0.0997253i) q^{29} +(1.21537 + 1.40261i) q^{30} +(1.21361 + 8.44082i) q^{31} +(0.959493 + 0.281733i) q^{32} +(1.41153 - 1.62899i) q^{33} +(-4.78899 - 3.07770i) q^{34} +(-6.06741 - 3.89929i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(1.65904 + 0.487137i) q^{37} +(-0.277777 - 1.93198i) q^{38} +(-4.55742 - 5.25954i) q^{39} +(0.770978 + 1.68821i) q^{40} +(-7.89200 + 2.31730i) q^{41} +(1.61435 - 3.53494i) q^{42} +(0.147532 - 1.02611i) q^{43} +(1.81329 - 1.16533i) q^{44} -1.85592 q^{45} +(4.73034 - 0.789845i) q^{46} +3.27175 q^{47} +(-0.841254 + 0.540641i) q^{48} +(-1.15303 + 8.01948i) q^{49} +(0.646201 - 1.41498i) q^{50} +(5.46209 - 1.60381i) q^{51} +(-2.89102 - 6.33046i) q^{52} +(7.20264 + 8.31229i) q^{53} +(-0.142315 - 0.989821i) q^{54} +(3.83833 + 1.12704i) q^{55} +(2.54487 - 2.93694i) q^{56} +(1.64200 + 1.05525i) q^{57} +(0.0922288 + 0.0592718i) q^{58} +(1.62990 - 1.88101i) q^{59} +(-1.78074 - 0.522874i) q^{60} +(0.899677 + 6.25739i) q^{61} +(-5.58440 - 6.44475i) q^{62} +(1.61435 + 3.53494i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(5.36552 - 11.7488i) q^{65} +(-0.306755 + 2.13353i) q^{66} +(-3.07739 + 1.97772i) q^{67} +5.69269 q^{68} +(-2.50079 + 4.09219i) q^{69} +7.21234 q^{70} +(-0.478315 + 0.307394i) q^{71} +(0.142315 - 0.989821i) q^{72} +(5.79550 - 12.6904i) q^{73} +(-1.65904 + 0.487137i) q^{74} +(0.646201 + 1.41498i) q^{75} +(1.27819 + 1.47511i) q^{76} +(-1.19209 - 8.29114i) q^{77} +(6.67746 + 1.96068i) q^{78} +(9.59166 - 11.0694i) q^{79} +(-1.56130 - 1.00339i) q^{80} +(0.841254 + 0.540641i) q^{81} +(5.38635 - 6.21618i) q^{82} +(-9.91575 - 2.91153i) q^{83} +(0.553053 + 3.84657i) q^{84} +(6.91872 + 7.98463i) q^{85} +(0.430643 + 0.942977i) q^{86} +(-0.105192 + 0.0308871i) q^{87} +(-0.895412 + 1.96068i) q^{88} +(-0.730279 + 5.07920i) q^{89} +(1.56130 - 1.00339i) q^{90} -27.0449 q^{91} +(-3.55240 + 3.22188i) q^{92} +8.52762 q^{93} +(-2.75237 + 1.76884i) q^{94} +(-0.515533 + 3.58561i) q^{95} +(0.415415 - 0.909632i) q^{96} +(6.38188 - 1.87389i) q^{97} +(-3.36567 - 7.36979i) q^{98} +(-1.41153 - 1.62899i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + q^{8} - q^{9}+O(q^{10}) $ 10 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 + 2 * q^7 + q^8 - q^9	\( 10 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + q^{8} - q^{9} - 13 q^{10} - 5 q^{11} + q^{12} + 13 q^{13} + 9 q^{14} + 9 q^{15} - q^{16} + q^{18} - 9 q^{20} - 13 q^{21} - 6 q^{22} - 32 q^{23} + 10 q^{24} + q^{25} - 13 q^{26} + q^{27} - 9 q^{28} + 27 q^{29} + 13 q^{30} - 8 q^{31} + q^{32} - 6 q^{33} - 11 q^{34} - 26 q^{35} - q^{36} - 11 q^{37} + 11 q^{38} - 13 q^{39} + 9 q^{40} - 10 q^{41} + 2 q^{42} + 34 q^{43} - 5 q^{44} + 2 q^{45} - q^{46} + 8 q^{47} + q^{48} + 25 q^{49} + 21 q^{50} - 11 q^{51} + 2 q^{52} + 9 q^{53} - q^{54} - 23 q^{55} - 2 q^{56} - 11 q^{57} - 5 q^{58} - 21 q^{59} - 2 q^{60} - 4 q^{61} + 8 q^{62} + 2 q^{63} - q^{64} + 29 q^{65} + 6 q^{66} - 32 q^{67} + 22 q^{68} - q^{69} - 18 q^{70} + 22 q^{71} + q^{72} + 43 q^{73} + 11 q^{74} + 21 q^{75} + 10 q^{77} + 2 q^{78} - 16 q^{79} + 2 q^{80} - q^{81} + 32 q^{82} - 3 q^{83} + 9 q^{84} + 33 q^{85} + 32 q^{86} + 6 q^{87} - 6 q^{88} - 11 q^{89} - 2 q^{90} - 70 q^{91} - 21 q^{92} + 8 q^{93} + 3 q^{94} - q^{96} + 39 q^{97} - 14 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 + 2 * q^7 + q^8 - q^9 - 13 * q^10 - 5 * q^11 + q^12 + 13 * q^13 + 9 * q^14 + 9 * q^15 - q^16 + q^18 - 9 * q^20 - 13 * q^21 - 6 * q^22 - 32 * q^23 + 10 * q^24 + q^25 - 13 * q^26 + q^27 - 9 * q^28 + 27 * q^29 + 13 * q^30 - 8 * q^31 + q^32 - 6 * q^33 - 11 * q^34 - 26 * q^35 - q^36 - 11 * q^37 + 11 * q^38 - 13 * q^39 + 9 * q^40 - 10 * q^41 + 2 * q^42 + 34 * q^43 - 5 * q^44 + 2 * q^45 - q^46 + 8 * q^47 + q^48 + 25 * q^49 + 21 * q^50 - 11 * q^51 + 2 * q^52 + 9 * q^53 - q^54 - 23 * q^55 - 2 * q^56 - 11 * q^57 - 5 * q^58 - 21 * q^59 - 2 * q^60 - 4 * q^61 + 8 * q^62 + 2 * q^63 - q^64 + 29 * q^65 + 6 * q^66 - 32 * q^67 + 22 * q^68 - q^69 - 18 * q^70 + 22 * q^71 + q^72 + 43 * q^73 + 11 * q^74 + 21 * q^75 + 10 * q^77 + 2 * q^78 - 16 * q^79 + 2 * q^80 - q^81 + 32 * q^82 - 3 * q^83 + 9 * q^84 + 33 * q^85 + 32 * q^86 + 6 * q^87 - 6 * q^88 - 11 * q^89 - 2 * q^90 - 70 * q^91 - 21 * q^92 + 8 * q^93 + 3 * q^94 - q^96 + 39 * q^97 - 14 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/138\mathbb{Z}\right)^\times$.

$n$	$47$	$97$
$\chi(n)$	$1$	$e\left(\frac{10}{11}\right)$

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 $

$2$	−0.841254	+	0.540641i	−0.594856	+	0.382291i
$2$	−0.841254	+	0.540641i	−0.594856	+	0.382291i
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$3$	0.142315	−	0.989821i	0.0821655	−	0.571474i
$4$	0.415415	−	0.909632i	0.207708	−	0.454816i
$5$	1.78074	−	0.522874i	0.796373	−	0.233836i	0.141860	−	0.989887i	$-0.454692\pi$
$5$	1.78074	−	0.522874i	0.796373	−	0.233836i	0.654513	+	0.756051i	$0.272874\pi$
$6$	0.415415	+	0.909632i	0.169592	+	0.371356i
$7$	−2.54487	−	2.93694i	−0.961870	−	1.11006i	−0.993868	−	0.110569i	$-0.964733\pi$
$7$	−2.54487	−	2.93694i	−0.961870	−	1.11006i	0.0319983	−	0.999488i	$-0.489813\pi$
$8$	0.142315	+	0.989821i	0.0503159	+	0.349955i
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$	−1.21537	+	1.40261i	−0.384334	+	0.443545i
$11$	1.81329	+	1.16533i	0.546728	+	0.351361i	0.784665	−	0.619920i	$-0.212835\pi$
$11$	1.81329	+	1.16533i	0.546728	+	0.351361i	−0.237937	+	0.971281i	$0.576471\pi$
$12$	−0.841254	−	0.540641i	−0.242849	−	0.156070i
$13$	4.55742	−	5.25954i	1.26400	−	1.45873i	0.434056	−	0.900886i	$-0.357082\pi$
$13$	4.55742	−	5.25954i	1.26400	−	1.45873i	0.829944	−	0.557847i	$-0.188373\pi$
$14$	3.72871	+	1.09485i	0.996539	+	0.292610i
$15$	−0.264125	−	1.83703i	−0.0681968	−	0.474319i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	2.36483	+	5.17825i	0.573555	+	1.25591i	0.944883	+	0.327408i	$0.106175\pi$
$17$	2.36483	+	5.17825i	0.573555	+	1.25591i	−0.371328	+	0.928502i	$0.621098\pi$
$18$	0.959493	−	0.281733i	0.226155	−	0.0664050i
$19$	−0.810827	+	1.77546i	−0.186017	+	0.407319i	−0.979548	−	0.201209i	$-0.935513\pi$
$19$	−0.810827	+	1.77546i	−0.186017	+	0.407319i	0.793532	+	0.608529i	$0.208240\pi$
$20$	0.264125	−	1.83703i	0.0590602	−	0.410773i
$21$	−3.26921	+	2.10100i	−0.713401	+	0.458475i
$22$	−2.15546			−0.459547
$23$	−4.40644	−	1.89296i	−0.918806	−	0.394709i
$23$	−4.40644	−	1.89296i	−0.918806	−	0.394709i
$24$	1.00000			0.204124
$25$	−1.30862	+	0.840996i	−0.261723	+	0.168199i
$26$	−0.990421	+	6.88853i	−0.194238	+	1.35095i
$27$	−0.415415	+	0.909632i	−0.0799467	+	0.175059i
$28$	−3.72871	+	1.09485i	−0.704659	+	0.206907i
$29$	−0.0455430	−	0.0997253i	−0.00845712	−	0.0185185i	0.905356	−	0.424653i	$-0.139604\pi$
$29$	−0.0455430	−	0.0997253i	−0.00845712	−	0.0185185i	−0.913813	+	0.406134i	$0.866877\pi$
$30$	1.21537	+	1.40261i	0.221895	+	0.256081i
$31$	1.21361	+	8.44082i	0.217970	+	1.51602i	0.745515	+	0.666489i	$0.232204\pi$
$31$	1.21361	+	8.44082i	0.217970	+	1.51602i	−0.527545	+	0.849527i	$0.676887\pi$
$32$	0.959493	+	0.281733i	0.169616	+	0.0498038i
$33$	1.41153	−	1.62899i	0.245716	−	0.283571i
$34$	−4.78899	−	3.07770i	−0.821305	−	0.527821i
$35$	−6.06741	−	3.89929i	−1.02558	−	0.659100i
$36$	−0.654861	+	0.755750i	−0.109143	+	0.125958i
$37$	1.65904	+	0.487137i	0.272744	+	0.0800848i	0.415244	−	0.909710i	$-0.363696\pi$
$37$	1.65904	+	0.487137i	0.272744	+	0.0800848i	−0.142501	+	0.989795i	$0.545514\pi$
$38$	−0.277777	−	1.93198i	−0.0450614	−	0.313409i
$39$	−4.55742	−	5.25954i	−0.729770	−	0.842200i
$40$	0.770978	+	1.68821i	0.121902	+	0.266929i
$41$	−7.89200	+	2.31730i	−1.23252	+	0.361902i	−0.832202	−	0.554473i	$-0.812920\pi$
$41$	−7.89200	+	2.31730i	−1.23252	+	0.361902i	−0.400322	+	0.916375i	$0.631102\pi$
$42$	1.61435	−	3.53494i	0.249100	−	0.545453i
$43$	0.147532	−	1.02611i	0.0224984	−	0.156480i	−0.975475	−	0.220109i	$-0.929359\pi$
$43$	0.147532	−	1.02611i	0.0224984	−	0.156480i	0.997974	+	0.0636297i	$0.0202677\pi$
$44$	1.81329	−	1.16533i	0.273364	−	0.175680i
$45$	−1.85592			−0.276664
$46$	4.73034	−	0.789845i	0.697451	−	0.116456i
$47$	3.27175			0.477234			0.238617	−	0.971114i	$-0.423306\pi$
$47$	3.27175			0.477234			0.238617	+	0.971114i	$0.423306\pi$
$48$	−0.841254	+	0.540641i	−0.121424	+	0.0780348i
$49$	−1.15303	+	8.01948i	−0.164718	+	1.14564i
$50$	0.646201	−	1.41498i	0.0913866	−	0.200109i
$51$	5.46209	−	1.60381i	0.764846	−	0.224579i
$52$	−2.89102	−	6.33046i	−0.400913	−	0.877877i
$53$	7.20264	+	8.31229i	0.989359	+	1.14178i	0.989898	+	0.141781i	$0.0452830\pi$
$53$	7.20264	+	8.31229i	0.989359	+	1.14178i	−0.000538809		1.00000i	$0.500172\pi$
$54$	−0.142315	−	0.989821i	−0.0193666	−	0.134698i
$55$	3.83833	+	1.12704i	0.517560	+	0.151969i
$56$	2.54487	−	2.93694i	0.340072	−	0.392465i
$57$	1.64200	+	1.05525i	0.217488	+	0.139771i
$58$	0.0922288	+	0.0592718i	0.0121102	+	0.00778277i
$59$	1.62990	−	1.88101i	0.212195	−	0.244886i	−0.639667	−	0.768652i	$-0.720928\pi$
$59$	1.62990	−	1.88101i	0.212195	−	0.244886i	0.851862	+	0.523766i	$0.175473\pi$
$60$	−1.78074	−	0.522874i	−0.229893	−	0.0675027i
$61$	0.899677	+	6.25739i	0.115192	+	0.801177i	0.962734	+	0.270449i	$0.0871722\pi$
$61$	0.899677	+	6.25739i	0.115192	+	0.801177i	−0.847542	+	0.530728i	$0.821919\pi$
$62$	−5.58440	−	6.44475i	−0.709220	−	0.818484i
$63$	1.61435	+	3.53494i	0.203389	+	0.445361i
$64$	−0.959493	+	0.281733i	−0.119937	+	0.0352166i
$65$	5.36552	−	11.7488i	0.665510	−	1.45726i
$66$	−0.306755	+	2.13353i	−0.0377589	+	0.262619i
$67$	−3.07739	+	1.97772i	−0.375963	+	0.241617i	−0.714952	−	0.699174i	$-0.753551\pi$
$67$	−3.07739	+	1.97772i	−0.375963	+	0.241617i	0.338989	+	0.940790i	$0.389915\pi$
$68$	5.69269			0.690340
$69$	−2.50079	+	4.09219i	−0.301060	+	0.492642i
$70$	7.21234			0.862039
$71$	−0.478315	+	0.307394i	−0.0567656	+	0.0364810i	−0.568716	−	0.822534i	$-0.692560\pi$
$71$	−0.478315	+	0.307394i	−0.0567656	+	0.0364810i	0.511950	+	0.859015i	$0.328923\pi$
$72$	0.142315	−	0.989821i	0.0167720	−	0.116652i
$73$	5.79550	−	12.6904i	0.678312	−	1.48530i	−0.186110	−	0.982529i	$-0.559588\pi$
$73$	5.79550	−	12.6904i	0.678312	−	1.48530i	0.864422	−	0.502767i	$-0.167685\pi$
$74$	−1.65904	+	0.487137i	−0.192859	+	0.0566285i
$75$	0.646201	+	1.41498i	0.0746168	+	0.163388i
$76$	1.27819	+	1.47511i	0.146618	+	0.169207i
$77$	−1.19209	−	8.29114i	−0.135851	−	0.944863i
$78$	6.67746	+	1.96068i	0.756074	+	0.222003i
$79$	9.59166	−	11.0694i	1.07915	−	1.24540i	0.111319	−	0.993785i	$-0.464492\pi$
$79$	9.59166	−	11.0694i	1.07915	−	1.24540i	0.967827	−	0.251617i	$-0.0809622\pi$
$80$	−1.56130	−	1.00339i	−0.174559	−	0.112182i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	5.38635	−	6.21618i	0.594823	−	0.686462i
$83$	−9.91575	−	2.91153i	−1.08839	−	0.319582i	−0.312163	−	0.950029i	$-0.601053\pi$
$83$	−9.91575	−	2.91153i	−1.08839	−	0.319582i	−0.776232	+	0.630447i	$0.782872\pi$
$84$	0.553053	+	3.84657i	0.0603430	+	0.419695i
$85$	6.91872	+	7.98463i	0.750441	+	0.866055i
$86$	0.430643	+	0.942977i	0.0464374	+	0.101684i
$87$	−0.105192	+	0.0308871i	−0.0112777	+	0.00331144i
$88$	−0.895412	+	1.96068i	−0.0954513	+	0.209009i
$89$	−0.730279	+	5.07920i	−0.0774094	+	0.538394i	0.913807	+	0.406148i	$0.133128\pi$
$89$	−0.730279	+	5.07920i	−0.0774094	+	0.538394i	−0.991217	+	0.132247i	$0.957781\pi$
$90$	1.56130	−	1.00339i	0.164576	−	0.105766i
$91$	−27.0449			−2.83508
$92$	−3.55240	+	3.22188i	−0.370363	+	0.335904i
$93$	8.52762			0.884273
$94$	−2.75237	+	1.76884i	−0.283885	+	0.182442i
$95$	−0.515533	+	3.58561i	−0.0528925	+	0.367876i
$96$	0.415415	−	0.909632i	0.0423981	−	0.0928389i
$97$	6.38188	−	1.87389i	0.647982	−	0.190265i	0.0588058	−	0.998269i	$-0.481271\pi$
$97$	6.38188	−	1.87389i	0.647982	−	0.190265i	0.589176	+	0.808005i	$0.299453\pi$
$98$	−3.36567	−	7.36979i	−0.339984	−	0.744461i
$99$	−1.41153	−	1.62899i	−0.141864	−	0.163720i
$100$	0.221378	+	1.53972i	0.0221378	+	0.153972i
$101$	−8.33312	−	2.44683i	−0.829177	−	0.243468i	−0.160514	−	0.987034i	$-0.551315\pi$
$101$	−8.33312	−	2.44683i	−0.829177	−	0.243468i	−0.668663	+	0.743565i	$0.733133\pi$
$102$	−3.72792	+	4.30224i	−0.369119	+	0.425986i
$103$	7.87385	+	5.06021i	0.775833	+	0.498598i	0.867648	−	0.497178i	$-0.165631\pi$
$103$	7.87385	+	5.06021i	0.775833	+	0.498598i	−0.0918152	+	0.995776i	$0.529267\pi$
$104$	5.85459	+	3.76252i	0.574090	+	0.368945i
$105$	−4.72308	+	5.45072i	−0.460925	+	0.531936i
$106$	−10.5532	−	3.09870i	−1.02502	−	0.300973i
$107$	−0.332225	−	2.31068i	−0.0321174	−	0.223382i	0.967441	−	0.253097i	$-0.0814491\pi$
$107$	−0.332225	−	2.31068i	−0.0321174	−	0.223382i	−0.999558	+	0.0297151i	$0.990540\pi$
$108$	0.654861	+	0.755750i	0.0630140	+	0.0727220i
$109$	3.35656	+	7.34985i	0.321500	+	0.703988i	0.999518	−	0.0310584i	$-0.00988778\pi$
$109$	3.35656	+	7.34985i	0.321500	+	0.703988i	−0.678017	+	0.735046i	$0.737161\pi$
$110$	−3.83833	+	1.12704i	−0.365970	+	0.107459i
$111$	0.718284	−	1.57282i	0.0681765	−	0.149286i
$112$	−0.553053	+	3.84657i	−0.0522586	+	0.363466i
$113$	−7.30000	+	4.69142i	−0.686726	+	0.441332i	−0.836921	−	0.547324i	$-0.815646\pi$
$113$	−7.30000	+	4.69142i	−0.686726	+	0.441332i	0.150194	+	0.988656i	$0.452010\pi$
$114$	−1.95185			−0.182807
$115$	−8.83652	−	1.06686i	−0.824010	−	0.0994853i
$116$	−0.109633			−0.0101791
$117$	−5.85459	+	3.76252i	−0.541257	+	0.347845i
$118$	−0.354212	+	2.46360i	−0.0326078	+	0.226792i
$119$	9.19001	−	20.1233i	0.842447	−	1.84470i
$120$	1.78074	−	0.522874i	0.162559	−	0.0477316i
$121$	−2.63954	−	5.77978i	−0.239958	−	0.525434i
$122$	−4.13986	−	4.77765i	−0.374805	−	0.432548i
$123$	1.17057	+	8.14146i	0.105546	+	0.734091i
$124$	8.18219	+	2.40251i	0.734783	+	0.215752i
$125$	−7.96743	+	9.19490i	−0.712628	+	0.822417i
$126$	−3.26921	−	2.10100i	−0.291245	−	0.187172i
$127$	−9.37135	−	6.02260i	−0.831573	−	0.534419i	0.0542046	−	0.998530i	$-0.482738\pi$
$127$	−9.37135	−	6.02260i	−0.831573	−	0.534419i	−0.885777	+	0.464111i	$0.846374\pi$
$128$	0.654861	−	0.755750i	0.0578821	−	0.0667995i
$129$	−0.994666	−	0.292060i	−0.0875754	−	0.0257145i
$130$	1.83814	+	12.7846i	0.161216	+	1.12128i
$131$	8.82678	+	10.1867i	0.771200	+	0.890012i	0.996441	−	0.0842910i	$-0.0268625\pi$
$131$	8.82678	+	10.1867i	0.771200	+	0.890012i	−0.225241	+	0.974303i	$0.572317\pi$
$132$	−0.895412	−	1.96068i	−0.0779357	−	0.170655i
$133$	7.27787	−	2.13698i	0.631072	−	0.185299i
$134$	1.51963	−	3.32753i	0.131276	−	0.287454i
$135$	−0.264125	+	1.83703i	−0.0227323	+	0.158106i
$136$	−4.78899	+	3.07770i	−0.410653	+	0.263910i
$137$	6.04662			0.516598			0.258299	−	0.966065i	$-0.416838\pi$
$137$	6.04662			0.516598			0.258299	+	0.966065i	$0.416838\pi$
$138$	−0.108607	−	4.79460i	−0.00924525	−	0.408144i
$139$	−1.93190			−0.163862			−0.0819308	−	0.996638i	$-0.526109\pi$
$139$	−1.93190			−0.163862			−0.0819308	+	0.996638i	$0.526109\pi$
$140$	−6.06741	+	3.89929i	−0.512789	+	0.329550i
$141$	0.465618	−	3.23845i	0.0392121	−	0.272726i
$142$	0.236194	−	0.517193i	0.0198210	−	0.0434019i
$143$	14.3930	−	4.22618i	1.20361	−	0.353411i
$144$	0.415415	+	0.909632i	0.0346179	+	0.0758027i
$145$	−0.133244	−	0.153772i	−0.0110653	−	0.0127701i
$146$	1.98545	+	13.8091i	0.164317	+	1.14285i
$147$	7.77376	+	2.28258i	0.641169	+	0.188264i
$148$	1.13230	−	1.30675i	0.0930748	−	0.107414i
$149$	−10.7428	−	6.90400i	−0.880087	−	0.565598i	0.0207353	−	0.999785i	$-0.493399\pi$
$149$	−10.7428	−	6.90400i	−0.880087	−	0.565598i	−0.900823	+	0.434187i	$0.857036\pi$
$150$	−1.30862	−	0.840996i	−0.106848	−	0.0686670i
$151$	−3.46657	+	4.00064i	−0.282106	+	0.325567i	−0.879063	−	0.476706i	$-0.841831\pi$
$151$	−3.46657	+	4.00064i	−0.282106	+	0.325567i	0.596957	+	0.802273i	$0.296376\pi$
$152$	−1.87279	−	0.549899i	−0.151903	−	0.0446027i
$153$	−0.810154	−	5.63474i	−0.0654970	−	0.455542i
$154$	5.48538	+	6.33046i	0.442024	+	0.510123i
$155$	6.57461	+	14.3964i	0.528085	+	1.15635i
$156$	−6.67746	+	1.96068i	−0.534625	+	0.156980i
$157$	−2.53347	+	5.54753i	−0.202193	+	0.442741i	−0.983381	−	0.181555i	$-0.941887\pi$
$157$	−2.53347	+	5.54753i	−0.202193	+	0.442741i	0.781188	+	0.624296i	$0.214614\pi$
$158$	−2.08447	+	14.4978i	−0.165831	+	1.15338i
$159$	9.25273	−	5.94637i	0.733789	−	0.471578i
$160$	1.85592			0.146724
$161$	5.65432	+	17.7588i	0.445623	+	1.39959i
$162$	−1.00000			−0.0785674
$163$	1.84938	−	1.18853i	0.144855	−	0.0930926i	−0.466206	−	0.884676i	$-0.654379\pi$
$163$	1.84938	−	1.18853i	0.144855	−	0.0930926i	0.611061	+	0.791584i	$0.290743\pi$
$164$	−1.17057	+	8.14146i	−0.0914058	+	0.635741i
$165$	1.66182	−	3.63887i	0.129372	−	0.283286i
$166$	9.91575	−	2.91153i	0.769611	−	0.225978i
$167$	−7.68773	−	16.8338i	−0.594894	−	1.30264i	−0.932439	−	0.361328i	$-0.882324\pi$
$167$	−7.68773	−	16.8338i	−0.594894	−	1.30264i	0.337545	−	0.941310i	$-0.390404\pi$
$168$	−2.54487	−	2.93694i	−0.196341	−	0.226589i
$169$	−5.04261	−	35.0721i	−0.387893	−	2.69785i
$170$	−10.1372	−	2.97655i	−0.777489	−	0.228291i
$171$	1.27819	−	1.47511i	0.0977456	−	0.112804i
$172$	−0.872092	−	0.560459i	−0.0664964	−	0.0427346i
$173$	−19.2766	−	12.3883i	−1.46557	−	0.941866i	−0.998332	−	0.0577352i	$-0.981612\pi$
$173$	−19.2766	−	12.3883i	−1.46557	−	0.941866i	−0.467240	−	0.884131i	$-0.654752\pi$
$174$	0.0717940	−	0.0828547i	0.00544269	−	0.00628120i
$175$	5.80021	+	1.70309i	0.438454	+	0.128742i
$176$	−0.306755	−	2.13353i	−0.0231225	−	0.160821i
$177$	−1.62990	−	1.88101i	−0.122511	−	0.141385i
$178$	−2.13167	−	4.66772i	−0.159776	−	0.349860i
$179$	0.953987	−	0.280116i	0.0713043	−	0.0209368i	−0.245886	−	0.969299i	$-0.579079\pi$
$179$	0.953987	−	0.280116i	0.0713043	−	0.0209368i	0.317190	+	0.948362i	$0.397261\pi$
$180$	−0.770978	+	1.68821i	−0.0574653	+	0.125831i
$181$	1.19175	−	8.28881i	0.0885821	−	0.616102i	−0.896374	−	0.443298i	$-0.853808\pi$
$181$	1.19175	−	8.28881i	0.0885821	−	0.616102i	0.984956	−	0.172804i	$-0.0552827\pi$
$182$	22.7517	−	14.6216i	1.68647	−	1.08383i
$183$	6.32174			0.467316
$184$	1.24659	−	4.63098i	0.0918997	−	0.341401i
$185$	3.20903			0.235932
$186$	−7.17389	+	4.61038i	−0.526015	+	0.338049i
$187$	−1.74626	+	12.1455i	−0.127699	+	0.888166i
$188$	1.35913	−	2.97609i	0.0991250	−	0.217054i
$189$	3.72871	−	1.09485i	0.271224	−	0.0796384i
$190$	−1.50483	−	3.29512i	−0.109172	−	0.239053i
$191$	15.6550	+	18.0669i	1.13276	+	1.30727i	0.945743	+	0.324917i	$0.105336\pi$
$191$	15.6550	+	18.0669i	1.13276	+	1.30727i	0.187016	+	0.982357i	$0.440118\pi$
$192$	0.142315	+	0.989821i	0.0102707	+	0.0714342i
$193$	−14.9056	−	4.37669i	−1.07293	−	0.315041i	−0.302883	−	0.953028i	$-0.597949\pi$
$193$	−14.9056	−	4.37669i	−1.07293	−	0.315041i	−0.770047	+	0.637987i	$0.779767\pi$
$194$	−4.35568	+	5.02672i	−0.312719	+	0.360897i
$195$	−10.8657	−	6.98294i	−0.778106	−	0.500059i
$196$	6.81579	+	4.38024i	0.486842	+	0.312875i
$197$	11.3013	−	13.0424i	0.805186	−	0.929235i	−0.193467	−	0.981107i	$-0.561973\pi$
$197$	11.3013	−	13.0424i	0.805186	−	0.929235i	0.998654	+	0.0518720i	$0.0165188\pi$
$198$	2.06815	+	0.607265i	0.146977	+	0.0431564i
$199$	3.15100	+	21.9157i	0.223369	+	1.55356i	0.725164	+	0.688576i	$0.241764\pi$
$199$	3.15100	+	21.9157i	0.223369	+	1.55356i	−0.501796	+	0.864986i	$0.667327\pi$
$200$	−1.01867	−	1.17561i	−0.0720309	−	0.0831281i
$201$	1.51963	+	3.32753i	0.107186	+	0.234706i
$202$	8.33312	−	2.44683i	0.586316	−	0.172158i
$203$	−0.176986	+	0.387545i	−0.0124220	+	0.0272003i
$204$	0.810154	−	5.63474i	0.0567221	−	0.394511i
$205$	−12.8420	+	8.25304i	−0.896923	+	0.576417i
$206$	−9.35966			−0.652118
$207$	3.69464	+	3.05772i	0.256795	+	0.212526i
$208$	−6.95937			−0.482545
$209$	−3.53927	+	2.27455i	−0.244817	+	0.157334i
$210$	1.02642	−	7.13893i	0.0708299	−	0.492633i
$211$	−9.02879	+	19.7703i	−0.621568	+	1.36104i	0.292806	+	0.956172i	$0.405411\pi$
$211$	−9.02879	+	19.7703i	−0.621568	+	1.36104i	−0.914374	+	0.404872i	$0.867316\pi$
$212$	10.5532	−	3.09870i	0.724798	−	0.212820i
$213$	0.236194	+	0.517193i	0.0161838	+	0.0354375i
$214$	1.52873	+	1.76425i	0.104502	+	0.120602i
$215$	−0.273807	−	1.90437i	−0.0186735	−	0.129877i
$216$	−0.959493	−	0.281733i	−0.0652852	−	0.0191695i
$217$	21.7017	−	25.0451i	1.47321	−	1.70017i
$218$	−6.79735	−	4.36839i	−0.460374	−	0.295865i
$219$	−11.7364	−	7.54254i	−0.793074	−	0.509678i
$220$	2.61969	−	3.02328i	0.176619	−	0.203830i
$221$	38.0127	+	11.1615i	2.55701	+	0.750806i
$222$	0.246073	+	1.71148i	0.0165153	+	0.114867i
$223$	−11.9479	−	13.7886i	−0.800089	−	0.923352i	0.198297	−	0.980142i	$-0.436459\pi$
$223$	−11.9479	−	13.7886i	−0.800089	−	0.923352i	−0.998386	+	0.0567898i	$0.981914\pi$
$224$	−1.61435	−	3.53494i	−0.107864	−	0.236188i
$225$	1.49254	−	0.438250i	0.0995029	−	0.0292167i
$226$	3.60477	−	7.89336i	0.239786	−	0.525058i
$227$	−0.612472	+	4.25983i	−0.0406512	+	0.282735i	0.959349	+	0.282223i	$0.0910720\pi$
$227$	−0.612472	+	4.25983i	−0.0406512	+	0.282735i	−1.00000		0.000511662i	$0.999837\pi$
$228$	1.64200	−	1.05525i	0.108744	−	0.0698856i
$229$	−9.84706			−0.650712			−0.325356	−	0.945592i	$-0.605484\pi$
$229$	−9.84706			−0.650712			−0.325356	+	0.945592i	$0.605484\pi$
$230$	8.01054	−	3.87988i	0.528199	−	0.255832i
$231$	−8.37640			−0.551127
$232$	0.0922288	−	0.0592718i	0.00605511	−	0.00389139i
$233$	0.315630	−	2.19525i	0.0206776	−	0.143816i	−0.976867	−	0.213847i	$-0.931401\pi$
$233$	0.315630	−	2.19525i	0.0206776	−	0.143816i	0.997545	+	0.0700309i	$0.0223098\pi$
$234$	2.89102	−	6.33046i	0.188992	−	0.413835i
$235$	5.82615	−	1.71071i	0.380056	−	0.111594i
$236$	−1.03394	−	2.26401i	−0.0673037	−	0.147375i
$237$	−9.59166	−	11.0694i	−0.623045	−	0.719033i
$238$	3.14836	+	21.8973i	0.204078	+	1.41939i
$239$	11.5400	+	3.38846i	0.746462	+	0.219181i	0.632775	−	0.774336i	$-0.281916\pi$
$239$	11.5400	+	3.38846i	0.746462	+	0.219181i	0.113687	+	0.993517i	$0.463734\pi$
$240$	−1.21537	+	1.40261i	−0.0784518	+	0.0905382i
$241$	−14.5401	−	9.34433i	−0.936608	−	0.601921i	−0.0191767	−	0.999816i	$-0.506105\pi$
$241$	−14.5401	−	9.34433i	−0.936608	−	0.601921i	−0.917431	+	0.397895i	$0.869741\pi$
$242$	5.34530	+	3.43522i	0.343609	+	0.220824i
$243$	0.654861	−	0.755750i	0.0420093	−	0.0484814i
$244$	6.06566	+	1.78104i	0.388314	+	0.114019i
$245$	2.13993	+	14.8835i	0.136715	+	0.950874i
$246$	−5.38635	−	6.21618i	−0.343421	−	0.396329i
$247$	5.64284	+	12.3561i	0.359046	+	0.786200i
$248$	−8.18219	+	2.40251i	−0.519570	+	0.152559i
$249$	−4.29305	+	9.40047i	−0.272061	+	0.595730i
$250$	1.73149	−	12.0428i	0.109509	−	0.761651i
$251$	2.24670	−	1.44387i	0.141810	−	0.0911360i	−0.467812	−	0.883828i	$-0.654958\pi$
$251$	2.24670	−	1.44387i	0.141810	−	0.0911360i	0.609622	+	0.792692i	$0.291321\pi$
$252$	3.88612			0.244803
$253$	−5.78424	−	8.56745i	−0.363652	−	0.538631i
$254$	11.1397			0.698970
$255$	8.88799	−	5.71197i	0.556588	−	0.357697i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	−12.1446	+	26.5930i	−0.757561	+	1.65883i	−0.00527932	+	0.999986i	$0.501680\pi$
$257$	−12.1446	+	26.5930i	−0.757561	+	1.65883i	−0.752282	+	0.658841i	$0.771047\pi$
$258$	0.994666	−	0.292060i	0.0619252	−	0.0181829i
$259$	−2.79134	−	6.11218i	−0.173445	−	0.379792i
$260$	−8.45821	−	9.76129i	−0.524556	−	0.605370i
$261$	0.0156023	+	0.108517i	0.000965760	+	0.00671701i
$262$	−12.9329	−	3.79744i	−0.798996	−	0.234606i
$263$	−7.66080	+	8.84103i	−0.472385	+	0.545161i	−0.941074	−	0.338202i	$-0.890181\pi$
$263$	−7.66080	+	8.84103i	−0.472385	+	0.545161i	0.468688	+	0.883364i	$0.344727\pi$
$264$	1.81329	+	1.16533i	0.111600	+	0.0717212i
$265$	17.1723	+	11.0360i	1.05489	+	0.677936i
$266$	−4.96720	+	5.73246i	−0.304559	+	0.351479i
$267$	4.92357	+	1.44569i	0.301318	+	0.0884749i
$268$	0.520602	+	3.62087i	0.0318008	+	0.221180i
$269$	−15.5355	−	17.9289i	−0.947215	−	1.09314i	−0.995543	−	0.0943124i	$-0.969935\pi$
$269$	−15.5355	−	17.9289i	−0.947215	−	1.09314i	0.0483281	−	0.998832i	$-0.484611\pi$
$270$	−0.770978	−	1.68821i	−0.0469202	−	0.102741i
$271$	15.9753	−	4.69076i	0.970428	−	0.284943i	0.242160	−	0.970236i	$-0.422144\pi$
$271$	15.9753	−	4.69076i	0.970428	−	0.284943i	0.728268	+	0.685293i	$0.240326\pi$
$272$	2.36483	−	5.17825i	0.143389	−	0.313977i
$273$	−3.84890	+	26.7697i	−0.232946	+	1.62017i
$274$	−5.08674	+	3.26905i	−0.307301	+	0.197491i
$275$	−3.35294			−0.202190
$276$	2.68352	+	3.97476i	0.161529	+	0.239252i
$277$	8.80188			0.528854			0.264427	−	0.964406i	$-0.414817\pi$
$277$	8.80188			0.528854			0.264427	+	0.964406i	$0.414817\pi$
$278$	1.62522	−	1.04446i	0.0974741	−	0.0626428i
$279$	1.21361	−	8.44082i	0.0726567	−	0.505339i
$280$	2.99611	−	6.56058i	0.179052	−	0.392069i
$281$	−0.904628	+	0.265623i	−0.0539656	+	0.0158457i	−0.308604	−	0.951191i	$-0.599862\pi$
$281$	−0.904628	+	0.265623i	−0.0539656	+	0.0158457i	0.254638	+	0.967036i	$0.418044\pi$
$282$	1.35913	+	2.97609i	0.0809352	+	0.177223i
$283$	7.65735	+	8.83706i	0.455182	+	0.525309i	0.936231	−	0.351386i	$-0.114289\pi$
$283$	7.65735	+	8.83706i	0.455182	+	0.525309i	−0.481048	+	0.876694i	$0.659744\pi$
$284$	0.0809166	+	0.562787i	0.00480151	+	0.0333953i
$285$	3.47574	+	1.02057i	0.205885	+	0.0604534i
$286$	−9.82335	+	11.3367i	−0.580867	+	0.670356i
$287$	26.8899	+	17.2811i	1.58726	+	1.02007i
$288$	−0.841254	−	0.540641i	−0.0495713	−	0.0318576i
$289$	−10.0892	+	11.6436i	−0.593484	+	0.684917i
$290$	0.195227	+	0.0573240i	0.0114642	+	0.00336618i
$291$	−0.946579	−	6.58360i	−0.0554894	−	0.385938i
$292$	−9.13604	−	10.5435i	−0.534646	−	0.617014i
$293$	−12.2058	−	26.7270i	−0.713072	−	1.56141i	−0.823366	−	0.567511i	$-0.807907\pi$
$293$	−12.2058	−	26.7270i	−0.713072	−	1.56141i	0.110294	−	0.993899i	$-0.464821\pi$
$294$	−7.77376	+	2.28258i	−0.453375	+	0.133123i
$295$	1.91891	−	4.20183i	0.111723	−	0.244640i
$296$	−0.246073	+	1.71148i	−0.0143027	+	0.0994775i
$297$	−1.81329	+	1.16533i	−0.105218	+	0.0676194i
$298$	12.7700			0.739748
$299$	−30.0381	+	14.5488i	−1.73715	+	0.841381i
$300$	1.55555			0.0898100
$301$	−3.38906	+	2.17801i	−0.195342	+	0.125539i
$302$	0.753358	−	5.23972i	0.0433509	−	0.301512i
$303$	−3.60785	+	7.90008i	−0.207265	+	0.453848i
$304$	1.87279	−	0.549899i	0.107412	−	0.0315389i
$305$	4.87392	+	10.6724i	0.279080	+	0.611100i
$306$	3.72792	+	4.30224i	0.213111	+	0.245943i
$307$	−0.325579	−	2.26445i	−0.0185818	−	0.129239i	0.978419	−	0.206631i	$-0.0662499\pi$
$307$	−0.325579	−	2.26445i	−0.0185818	−	0.129239i	−0.997001	+	0.0773917i	$0.975341\pi$
$308$	−8.03710	−	2.35990i	−0.457956	−	0.134468i
$309$	6.12927	−	7.07356i	0.348682	−	0.402401i
$310$	−13.3142	−	8.55650i	−0.756195	−	0.485977i
$311$	−9.37165	−	6.02279i	−0.531417	−	0.341521i	0.247256	−	0.968950i	$-0.420471\pi$
$311$	−9.37165	−	6.02279i	−0.531417	−	0.341521i	−0.778674	+	0.627429i	$0.784107\pi$
$312$	4.55742	−	5.25954i	0.258013	−	0.297763i
$313$	−16.8630	−	4.95142i	−0.953152	−	0.279871i	−0.232053	−	0.972703i	$-0.574544\pi$
$313$	−16.8630	−	4.95142i	−0.953152	−	0.279871i	−0.721099	+	0.692832i	$0.756363\pi$
$314$	−0.867929	−	6.03658i	−0.0489801	−	0.340664i
$315$	4.72308	+	5.45072i	0.266115	+	0.307113i
$316$	−6.08453	−	13.3233i	−0.342282	−	0.749492i
$317$	−7.29900	+	2.14318i	−0.409953	+	0.120373i	−0.480205	−	0.877156i	$-0.659438\pi$
$317$	−7.29900	+	2.14318i	−0.409953	+	0.120373i	0.0702524	+	0.997529i	$0.477620\pi$
$318$	−4.56904	+	10.0048i	−0.256219	+	0.561042i
$319$	0.0336303	−	0.233904i	0.00188293	−	0.0130961i
$320$	−1.56130	+	1.00339i	−0.0872794	+	0.0560910i
$321$	−2.33444			−0.130296
$322$	−14.3578	−	11.8827i	−0.800130	−	0.662195i
$323$	−11.1113			−0.618247
$324$	0.841254	−	0.540641i	0.0467363	−	0.0300356i
$325$	−1.54065	+	10.7155i	−0.0854601	+	0.594388i
$326$	−0.913235	+	1.99971i	−0.0505794	+	0.110753i
$327$	7.75272	−	2.27641i	0.428727	−	0.125886i
$328$	−3.41686	−	7.48189i	−0.188665	−	0.413118i
$329$	−8.32617	−	9.60892i	−0.459037	−	0.529757i
$330$	0.569313	+	3.95966i	0.0313396	+	0.217972i
$331$	−18.0608	−	5.30313i	−0.992711	−	0.291486i	−0.255249	−	0.966875i	$-0.582158\pi$
$331$	−18.0608	−	5.30313i	−0.992711	−	0.291486i	−0.737462	+	0.675389i	$0.763976\pi$
$332$	−6.76757	+	7.81019i	−0.371419	+	0.428640i
$333$	−1.45459	−	0.934809i	−0.0797111	−	0.0512272i
$334$	15.5684	+	10.0052i	0.851863	+	0.547459i
$335$	−4.44595	+	5.13090i	−0.242908	+	0.280331i
$336$	3.72871	+	1.09485i	0.203418	+	0.0597288i
$337$	1.88842	+	13.1343i	0.102869	+	0.715469i	0.974350	+	0.225039i	$0.0722510\pi$
$337$	1.88842	+	13.1343i	0.102869	+	0.715469i	−0.871481	+	0.490430i	$0.836840\pi$
$338$	23.2035	+	26.7783i	1.26211	+	1.45655i
$339$	3.60477	+	7.89336i	0.195784	+	0.428708i
$340$	10.1372	−	2.97655i	0.549768	−	0.161426i
$341$	−7.63574	+	16.7199i	−0.413498	+	0.905435i
$342$	−0.277777	+	1.93198i	−0.0150205	+	0.104470i
$343$	3.60251	−	2.31519i	0.194517	−	0.125009i
$344$	1.03666			0.0558928
$345$	−2.31357	+	8.59475i	−0.124558	+	0.462726i
$346$	22.9141			1.23187
$347$	−0.676473	+	0.434743i	−0.0363150	+	0.0233382i	−0.558672	−	0.829388i	$-0.688689\pi$
$347$	−0.676473	+	0.434743i	−0.0363150	+	0.0233382i	0.522357	+	0.852727i	$0.325053\pi$
$348$	−0.0156023	+	0.108517i	−0.000836373	+	0.00581710i
$349$	4.66638	−	10.2179i	0.249786	−	0.546954i	−0.742656	−	0.669673i	$-0.766434\pi$
$349$	4.66638	−	10.2179i	0.249786	−	0.546954i	0.992441	+	0.122719i	$0.0391614\pi$
$350$	−5.80021	+	1.70309i	−0.310034	+	0.0910342i
$351$	2.89102	+	6.33046i	0.154311	+	0.337895i
$352$	1.41153	+	1.62899i	0.0752348	+	0.0868255i
$353$	−0.254081	−	1.76717i	−0.0135233	−	0.0940569i	0.981942	−	0.189183i	$-0.0605838\pi$
$353$	−0.254081	−	1.76717i	−0.0135233	−	0.0940569i	−0.995465	+	0.0951256i	$0.969675\pi$
$354$	2.38811	+	0.701213i	0.126927	+	0.0372690i
$355$	−0.691028	+	0.797489i	−0.0366760	+	0.0423263i
$356$	4.31684	+	2.77426i	0.228792	+	0.147036i
$357$	−18.6106	−	11.9603i	−0.984978	−	0.633007i
$358$	−0.651103	+	0.751413i	−0.0344118	+	0.0397134i
$359$	23.2504	+	6.82692i	1.22711	+	0.360311i	0.830157	−	0.557529i	$-0.188250\pi$
$359$	23.2504	+	6.82692i	1.22711	+	0.360311i	0.396950	+	0.917840i	$0.370069\pi$
$360$	−0.264125	−	1.83703i	−0.0139206	−	0.0968200i
$361$	9.94752	+	11.4801i	0.523554	+	0.604213i
$362$	3.47870	+	7.61730i	0.182837	+	0.400356i
$363$	−6.09659	+	1.79012i	−0.319988	+	0.0939570i
$364$	−11.2349	+	24.6009i	−0.588868	+	1.28944i
$365$	3.68484	−	25.6286i	0.192873	−	1.34146i
$366$	−5.31818	+	3.41779i	−0.277986	+	0.178651i
$367$	−1.63035			−0.0851034			−0.0425517	−	0.999094i	$-0.513549\pi$
$367$	−1.63035			−0.0851034			−0.0425517	+	0.999094i	$0.513549\pi$
$368$	1.45500	+	4.56979i	0.0758473	+	0.238217i
$369$	8.22518			0.428186
$370$	−2.69961	+	1.73493i	−0.140346	+	0.0901948i
$371$	6.08289	−	42.3074i	0.315808	−	2.19649i
$372$	3.54250	−	7.75700i	0.183670	−	0.402182i
$373$	2.17490	−	0.638609i	0.112612	−	0.0330659i	−0.224941	−	0.974372i	$-0.572219\pi$
$373$	2.17490	−	0.638609i	0.112612	−	0.0330659i	0.337553	+	0.941306i	$0.390401\pi$
$374$	−5.09730	−	11.1615i	−0.263575	−	0.577149i
$375$	7.96743	+	9.19490i	0.411436	+	0.474823i
$376$	0.465618	+	3.23845i	0.0240124	+	0.167010i
$377$	−0.732067	−	0.214954i	−0.0377034	−	0.0110707i
$378$	−2.54487	+	2.93694i	−0.130894	+	0.151060i
$379$	5.98176	+	3.84425i	0.307262	+	0.197466i	0.685180	−	0.728374i	$-0.259723\pi$
$379$	5.98176	+	3.84425i	0.307262	+	0.197466i	−0.377918	+	0.925839i	$0.623360\pi$
$380$	3.04742	+	1.95846i	0.156330	+	0.100467i
$381$	−7.29498	+	8.41886i	−0.373733	+	0.431311i
$382$	−22.9375	−	6.73507i	−1.17359	−	0.344596i
$383$	−5.33120	−	37.0793i	−0.272412	−	1.89466i	−0.423100	−	0.906083i	$-0.639058\pi$
$383$	−5.33120	−	37.0793i	−0.272412	−	1.89466i	0.150689	−	0.988581i	$-0.451851\pi$
$384$	−0.654861	−	0.755750i	−0.0334182	−	0.0385667i
$385$	−6.45802	−	14.1411i	−0.329131	−	0.720697i
$386$	14.9056	−	4.37669i	0.758677	−	0.222768i
$387$	−0.430643	+	0.942977i	−0.0218908	+	0.0479342i
$388$	0.946579	−	6.58360i	0.0480553	−	0.334232i
$389$	0.904743	−	0.581443i	0.0458723	−	0.0294803i	−0.517504	−	0.855681i	$-0.673139\pi$
$389$	0.904743	−	0.581443i	0.0458723	−	0.0294803i	0.563376	+	0.826201i	$0.309502\pi$
$390$	12.9160			0.654029
$391$	−0.618266	−	27.2942i	−0.0312671	−	1.38032i
$392$	−8.10195			−0.409210
$393$	11.3391	−	7.28723i	0.571984	−	0.367592i
$394$	−2.45601	+	17.0820i	−0.123732	+	0.860576i
$395$	11.2924	−	24.7269i	0.568183	−	1.24415i
$396$	−2.06815	+	0.607265i	−0.103929	+	0.0305162i
$397$	4.96350	+	10.8686i	0.249111	+	0.545477i	0.992337	−	0.123564i	$-0.0394323\pi$
$397$	4.96350	+	10.8686i	0.249111	+	0.545477i	−0.743226	+	0.669041i	$0.766705\pi$
$398$	−14.4993	−	16.7331i	−0.726785	−	0.838754i
$399$	−1.07948	−	7.50792i	−0.0540414	−	0.375866i
$400$	1.49254	+	0.438250i	0.0746272	+	0.0219125i
$401$	19.5043	−	22.5092i	0.974001	−	1.12406i	−0.0182538	−	0.999833i	$-0.505811\pi$
$401$	19.5043	−	22.5092i	0.974001	−	1.12406i	0.992254	−	0.124223i	$-0.0396439\pi$
$402$	−3.07739	−	1.97772i	−0.153486	−	0.0986396i
$403$	49.9257	+	32.0853i	2.48698	+	1.59828i
$404$	−5.68742	+	6.56363i	−0.282959	+	0.326553i
$405$	1.78074	+	0.522874i	0.0884859	+	0.0259818i
$406$	−0.0606326	−	0.421709i	−0.00300915	−	0.0209291i
$407$	2.44064	+	2.81665i	0.120978	+	0.139616i
$408$	2.36483	+	5.17825i	0.117076	+	0.256362i
$409$	27.2851	−	8.01164i	1.34916	−	0.396150i	0.474233	−	0.880400i	$-0.342726\pi$
$409$	27.2851	−	8.01164i	1.34916	−	0.396150i	0.874930	+	0.484250i	$0.160907\pi$
$410$	6.34143	−	13.8858i	0.313181	−	0.685771i
$411$	0.860524	−	5.98508i	0.0424465	−	0.295222i
$412$	7.87385	−	5.06021i	0.387917	−	0.249299i
$413$	−9.67229			−0.475942
$414$	−4.76126	−	0.574841i	−0.234003	−	0.0282519i
$415$	−19.1798			−0.941498
$416$	5.85459	−	3.76252i	0.287045	−	0.184473i
$417$	−0.274938	+	1.91224i	−0.0134638	+	0.0936426i
$418$	1.74771	−	3.82695i	0.0854833	−	0.187182i
$419$	−31.4611	+	9.23780i	−1.53697	+	0.451296i	−0.937176	−	0.348856i	$-0.886570\pi$
$419$	−31.4611	+	9.23780i	−1.53697	+	0.451296i	−0.599797	+	0.800152i	$0.704752\pi$
$420$	2.99611	+	6.56058i	0.146195	+	0.320123i
$421$	23.2803	+	26.8669i	1.13461	+	1.30941i	0.944821	+	0.327587i	$0.106236\pi$
$421$	23.2803	+	26.8669i	1.13461	+	1.30941i	0.189791	+	0.981825i	$0.439219\pi$
$422$	−3.09313	−	21.5132i	−0.150571	−	1.04724i
$423$	−3.13922	−	0.921758i	−0.152634	−	0.0448174i
$424$	−7.20264	+	8.31229i	−0.349791	+	0.403681i
$425$	−7.44954	−	4.78753i	−0.361356	−	0.232229i
$426$	−0.478315	−	0.307394i	−0.0231744	−	0.0148933i
$427$	16.0880	−	18.5665i	0.778553	−	0.898498i
$428$	−2.23988	−	0.657687i	−0.108269	−	0.0317905i
$429$	−2.13482	−	14.8480i	−0.103070	−	0.716867i
$430$	1.25992	+	1.45403i	0.0607589	+	0.0701195i
$431$	−11.5054	−	25.1933i	−0.554196	−	1.21352i	−0.954794	−	0.297267i	$-0.903925\pi$
$431$	−11.5054	−	25.1933i	−0.554196	−	1.21352i	0.400598	−	0.916254i	$-0.368802\pi$
$432$	0.959493	−	0.281733i	0.0461636	−	0.0135549i
$433$	−9.87651	+	21.6265i	−0.474635	+	1.03931i	0.509269	+	0.860607i	$0.329916\pi$
$433$	−9.87651	+	21.6265i	−0.474635	+	1.03931i	−0.983904	+	0.178698i	$0.942811\pi$
$434$	−4.71623	+	32.8021i	−0.226386	+	1.57455i
$435$	−0.171169	+	0.110004i	−0.00820694	+	0.00527428i
$436$	8.08002			0.386963
$437$	6.93374	−	6.28862i	0.331686	−	0.300825i
$438$	13.9511			0.666610
$439$	28.3616	−	18.2269i	1.35363	−	0.869922i	0.355719	−	0.934593i	$-0.384236\pi$
$439$	28.3616	−	18.2269i	1.35363	−	0.869922i	0.997907	+	0.0646707i	$0.0205997\pi$
$440$	−0.569313	+	3.95966i	−0.0271409	+	0.188769i
$441$	3.36567	−	7.36979i	0.160270	−	0.350943i
$442$	−38.0127	+	11.1615i	−1.80808	+	0.530900i
$443$	4.97713	+	10.8984i	0.236471	+	0.517798i	0.990245	−	0.139335i	$-0.0444963\pi$
$443$	4.97713	+	10.8984i	0.236471	+	0.517798i	−0.753775	+	0.657133i	$0.771769\pi$
$444$	−1.13230	−	1.30675i	−0.0537368	−	0.0620155i
$445$	1.35534	+	9.42660i	0.0642493	+	0.446864i
$446$	17.5059	+	5.14019i	0.828927	+	0.243395i
$447$	−8.36259	+	9.65095i	−0.395537	+	0.456474i
$448$	3.26921	+	2.10100i	0.154456	+	0.0992628i
$449$	−0.606817	−	0.389978i	−0.0286375	−	0.0184042i	0.526244	−	0.850334i	$-0.323600\pi$
$449$	−0.606817	−	0.389978i	−0.0286375	−	0.0184042i	−0.554881	+	0.831930i	$0.687236\pi$
$450$	−1.01867	+	1.17561i	−0.0480206	+	0.0554188i
$451$	−17.0109	−	4.99486i	−0.801014	−	0.235199i
$452$	1.23494	+	8.58920i	0.0580867	+	0.404002i
$453$	3.46657	+	4.00064i	0.162874	+	0.187966i
$454$	−1.78780	−	3.91473i	−0.0839054	−	0.183727i
$455$	−48.1601	+	14.1411i	−2.25778	+	0.662944i
$456$	−0.810827	+	1.77546i	−0.0379705	+	0.0831437i
$457$	−0.596629	+	4.14965i	−0.0279091	+	0.194112i	−0.999006	−	0.0445729i	$-0.985807\pi$
$457$	−0.596629	+	4.14965i	−0.0279091	+	0.194112i	0.971097	+	0.238685i	$0.0767164\pi$
$458$	8.28387	−	5.32372i	0.387080	−	0.248761i
$459$	−5.69269			−0.265712
$460$	−4.64127	+	7.59479i	−0.216400	+	0.354109i
$461$	18.6186			0.867156			0.433578	−	0.901116i	$-0.357251\pi$
$461$	18.6186			0.867156			0.433578	+	0.901116i	$0.357251\pi$
$462$	7.04668	−	4.52862i	0.327841	−	0.210691i
$463$	1.57410	−	10.9481i	0.0731545	−	0.508801i	−0.919993	−	0.391935i	$-0.871806\pi$
$463$	1.57410	−	10.9481i	0.0731545	−	0.508801i	0.993148	−	0.116866i	$-0.0372849\pi$
$464$	−0.0455430	+	0.0997253i	−0.00211428	+	0.00462963i
$465$	15.1855	−	4.45887i	0.704211	−	0.206775i
$466$	0.921318	+	2.01741i	0.0426793	+	0.0934545i
$467$	15.5954	+	17.9980i	0.721669	+	0.832850i	0.991507	−	0.130056i	$-0.0415156\pi$
$467$	15.5954	+	17.9980i	0.721669	+	0.832850i	−0.269838	+	0.962906i	$0.586970\pi$
$468$	0.990421	+	6.88853i	0.0457822	+	0.318422i
$469$	13.6400	+	4.00506i	0.629836	+	0.184937i
$470$	−3.97639	+	4.58899i	−0.183417	+	0.211675i
$471$	5.13051	+	3.29718i	0.236402	+	0.151926i
$472$	2.09382	+	1.34562i	0.0963759	+	0.0619371i
$473$	1.46327	−	1.68871i	0.0672813	−	0.0776468i
$474$	14.0536	+	4.12650i	0.645502	+	0.189536i
$475$	−0.432097	−	3.00530i	−0.0198260	−	0.137893i
$476$	−14.4871	−	16.7191i	−0.664017	−	0.766316i
$477$	−4.56904	−	10.0048i	−0.209202	−	0.458089i
$478$	−11.5400	+	3.38846i	−0.527829	+	0.154984i
$479$	9.71459	−	21.2720i	0.443871	−	0.971942i	−0.547001	−	0.837132i	$-0.684230\pi$
$479$	9.71459	−	21.2720i	0.443871	−	0.971942i	0.990872	−	0.134810i	$-0.0430423\pi$
$480$	0.264125	−	1.83703i	0.0120556	−	0.0838486i
$481$	10.1230	−	6.50568i	0.461570	−	0.296633i
$482$	17.2838			0.787256
$483$	18.3827	−	3.06943i	0.836442	−	0.139664i
$484$	−6.35397			−0.288817
$485$	10.3847	−	6.67383i	0.471544	−	0.303043i
$486$	−0.142315	+	0.989821i	−0.00645553	+	0.0448992i
$487$	−5.87931	+	12.8739i	−0.266417	+	0.583372i	−0.994806	−	0.101792i	$-0.967542\pi$
$487$	−5.87931	+	12.8739i	−0.266417	+	0.583372i	0.728389	+	0.685164i	$0.240270\pi$
$488$	−6.06566	+	1.78104i	−0.274580	+	0.0806239i
$489$	−0.913235	−	1.99971i	−0.0412979	−	0.0904298i
$490$	−9.84687	−	11.3639i	−0.444836	−	0.513368i
$491$	0.835757	+	5.81282i	0.0377172	+	0.262329i	0.999951	−	0.00989541i	$-0.00314986\pi$
$491$	0.835757	+	5.81282i	0.0377172	+	0.262329i	−0.962234	+	0.272224i	$0.912241\pi$
$492$	7.89200	+	2.31730i	0.355799	+	0.104472i
$493$	0.408701	−	0.471666i	0.0184070	−	0.0212428i
$494$	−11.4273	−	7.34387i	−0.514138	−	0.330416i
$495$	−3.36533	−	2.16277i	−0.151260	−	0.0972091i
$496$	5.58440	−	6.44475i	0.250747	−	0.289378i
$497$	2.12005	+	0.622502i	0.0950971	+	0.0279230i
$498$	−1.47073	−	10.2292i	−0.0659051	−	0.458380i
$499$	−0.558955	−	0.645068i	−0.0250223	−	0.0288772i	0.743101	−	0.669180i	$-0.233354\pi$
$499$	−0.558955	−	0.645068i	−0.0250223	−	0.0288772i	−0.768123	+	0.640303i	$0.778809\pi$
$500$	5.05419	+	11.0671i	0.226030	+	0.494937i
$501$	−17.7565	+	5.21378i	−0.793303	+	0.232935i
$502$	−1.10943	+	2.42931i	−0.0495163	+	0.108426i
$503$	−4.10013	+	28.5170i	−0.182816	+	1.27151i	0.667250	+	0.744834i	$0.267471\pi$
$503$	−4.10013	+	28.5170i	−0.182816	+	1.27151i	−0.850065	+	0.526677i	$0.823438\pi$
$504$	−3.26921	+	2.10100i	−0.145622	+	0.0935858i
$505$	−16.1185			−0.717266
$506$	9.49793	+	4.08020i	0.422234	+	0.181387i
$507$	−35.4328			−1.57362
$508$	−9.37135	+	6.02260i	−0.415786	+	0.267210i
$509$	2.40455	−	16.7240i	0.106580	−	0.741277i	−0.864519	−	0.502600i	$-0.832377\pi$
$509$	2.40455	−	16.7240i	0.106580	−	0.741277i	0.971099	−	0.238678i	$-0.0767139\pi$
$510$	−4.38893	+	9.61043i	−0.194345	+	0.425557i
$511$	−52.0196	+	15.2743i	−2.30121	+	0.675697i
$512$	−0.415415	−	0.909632i	−0.0183589	−	0.0402004i
$513$	−1.27819	−	1.47511i	−0.0564334	−	0.0651277i
$514$	−4.16056	−	28.9374i	−0.183515	−	1.27637i
$515$	16.6672	+	4.89392i	0.734443	+	0.215652i
$516$	−0.678866	+	0.783454i	−0.0298854	+	0.0344896i
$517$	5.93264	+	3.81267i	0.260917	+	0.167681i
$518$	5.65272	+	3.63278i	0.248366	+	0.159615i
$519$	−15.0056	+	17.3173i	−0.658671	+	0.760147i
$520$	12.3928	+	3.63887i	0.543462	+	0.159575i
$521$	−0.639077	−	4.44488i	−0.0279985	−	0.194734i	0.971022	−	0.238992i	$-0.0768168\pi$
$521$	−0.639077	−	4.44488i	−0.0279985	−	0.194734i	−0.999020	+	0.0442577i	$0.985908\pi$
$522$	−0.0717940	−	0.0828547i	−0.00314234	−	0.00362645i
$523$	4.80446	+	10.5203i	0.210084	+	0.460020i	0.985114	−	0.171905i	$-0.0549922\pi$
$523$	4.80446	+	10.5203i	0.210084	+	0.460020i	−0.775029	+	0.631925i	$0.782265\pi$
$524$	12.9329	−	3.79744i	0.564976	−	0.165892i
$525$	2.51121	−	5.49879i	0.109598	−	0.239987i
$526$	1.66485	−	11.5793i	0.0725909	−	0.504881i
$527$	−40.8387	+	26.2454i	−1.77896	+	1.14327i
$528$	−2.15546			−0.0938046
$529$	15.8334	+	16.6824i	0.688410	+	0.725322i
$530$	−20.4128			−0.886676
$531$	−2.09382	+	1.34562i	−0.0908641	+	0.0583948i
$532$	1.07948	−	7.50792i	0.0468012	−	0.325510i
$533$	−23.7792	+	52.0692i	−1.02999	+	2.25537i
$534$	−4.92357	+	1.44569i	−0.213064	+	0.0625612i
$535$	−1.79980	−	3.94101i	−0.0778122	−	0.170385i
$536$	−2.39555	−	2.76461i	−0.103472	−	0.119413i
$537$	−0.141498	−	0.984141i	−0.00610610	−	0.0424688i
$538$	22.7624	+	6.68363i	0.981355	+	0.288152i
$539$	−11.4361	+	13.1980i	−0.492589	+	0.568478i
$540$	1.56130	+	1.00339i	0.0671877	+	0.0431789i
$541$	−24.8837	−	15.9918i	−1.06983	−	0.687539i	−0.117645	−	0.993056i	$-0.537534\pi$
$541$	−24.8837	−	15.9918i	−1.06983	−	0.687539i	−0.952187	+	0.305517i	$0.901171\pi$
$542$	−10.9032	+	12.5830i	−0.468334	+	0.540486i
$543$	−8.03484	−	2.35924i	−0.344808	−	0.101245i
$544$	0.810154	+	5.63474i	0.0347350	+	0.241588i
$545$	9.82022	+	11.3331i	0.420652	+	0.485458i
$546$	−11.2349	−	24.6009i	−0.480808	−	1.05282i
$547$	19.1886	−	5.63427i	0.820444	−	0.240904i	0.155537	−	0.987830i	$-0.450289\pi$
$547$	19.1886	−	5.63427i	0.820444	−	0.240904i	0.664907	+	0.746926i	$0.268471\pi$
$548$	2.51186	−	5.50020i	0.107301	−	0.234957i
$549$	0.899677	−	6.25739i	0.0383973	−	0.267059i
$550$	2.82067	−	1.81274i	0.120274	−	0.0772954i
$551$	0.213986			0.00911612
$552$	−4.40644	−	1.89296i	−0.187551	−	0.0805696i
$553$	−56.9196			−2.42047
$554$	−7.40462	+	4.75866i	−0.314592	+	0.202176i
$555$	0.456692	−	3.17637i	0.0193855	−	0.134829i
$556$	−0.802540	+	1.75732i	−0.0340353	+	0.0745269i
$557$	14.2834	−	4.19399i	0.605208	−	0.177705i	0.0352494	−	0.999379i	$-0.488777\pi$
$557$	14.2834	−	4.19399i	0.605208	−	0.177705i	0.569959	+	0.821673i	$0.306959\pi$
$558$	3.54250	+	7.75700i	0.149966	+	0.328380i
$559$	−4.72448	−	5.45234i	−0.199824	−	0.230609i
$560$	1.02642	+	7.13893i	0.0433743	+	0.301675i
$561$	11.7733	+	3.45697i	0.497071	+	0.145953i
$562$	0.617415	−	0.712535i	0.0260441	−	0.0300565i
$563$	−3.69059	−	2.37180i	−0.155540	−	0.0999595i	0.460556	−	0.887631i	$-0.347650\pi$
$563$	−3.69059	−	2.37180i	−0.155540	−	0.0999595i	−0.616096	+	0.787671i	$0.711287\pi$
$564$	−2.75237	−	1.76884i	−0.115896	−	0.0744816i
$565$	−10.5464	+	12.1712i	−0.443691	+	0.512046i
$566$	−11.2194	−	3.29433i	−0.471589	−	0.138471i
$567$	−0.553053	−	3.84657i	−0.0232260	−	0.161541i
$568$	−0.372337	−	0.429700i	−0.0156229	−	0.0180298i
$569$	1.65647	+	3.62716i	0.0694427	+	0.152058i	0.941170	−	0.337932i	$-0.109727\pi$
$569$	1.65647	+	3.62716i	0.0694427	+	0.152058i	−0.871728	+	0.489991i	$0.837000\pi$
$570$	−3.47574	+	1.02057i	−0.145583	+	0.0427470i
$571$	12.2072	−	26.7300i	0.510855	−	1.11862i	−0.461932	−	0.886915i	$-0.652844\pi$
$571$	12.2072	−	26.7300i	0.510855	−	1.11862i	0.972787	−	0.231701i	$-0.0744292\pi$
$572$	2.13482	−	14.8480i	0.0892612	−	0.620825i
$573$	20.1109	−	12.9245i	0.840146	−	0.539929i
$574$	−31.9641			−1.33415
$575$	7.35831	−	1.22865i	0.306863	−	0.0512381i
$576$	1.00000			0.0416667
$577$	10.1425	−	6.51818i	0.422237	−	0.271355i	−0.312221	−	0.950010i	$-0.601073\pi$
$577$	10.1425	−	6.51818i	0.422237	−	0.271355i	0.734458	+	0.678654i	$0.237436\pi$
$578$	2.19260	−	15.2499i	0.0912000	−	0.634310i
$579$	−6.45343	+	14.1310i	−0.268195	+	0.587266i
$580$	−0.195227	+	0.0573240i	−0.00810638	+	0.00238025i
$581$	16.6833	+	36.5314i	0.692141	+	1.51558i
$582$	4.35568	+	5.02672i	0.180549	+	0.208364i
$583$	3.37391	+	23.4661i	0.139733	+	0.971866i
$584$	13.3860	+	3.93048i	0.553916	+	0.162645i
$585$	−8.45821	+	9.76129i	−0.349704	+	0.403580i
$586$	24.7179	+	15.8852i	1.02109	+	0.656213i
$587$	10.9528	+	7.03894i	0.452071	+	0.290528i	0.746795	−	0.665054i	$-0.231592\pi$
$587$	10.9528	+	7.03894i	0.452071	+	0.290528i	−0.294724	+	0.955582i	$0.595228\pi$
$588$	5.30565	−	6.12304i	0.218801	−	0.252510i
$589$	−15.9704	−	4.68933i	−0.658049	−	0.193221i
$590$	0.657389	+	4.57224i	0.0270643	+	0.188236i
$591$	−11.3013	−	13.0424i	−0.464875	−	0.536494i
$592$	−0.718284	−	1.57282i	−0.0295213	−	0.0646426i
$593$	−2.83339	+	0.831957i	−0.116353	+	0.0341644i	−0.339391	−	0.940645i	$-0.610221\pi$
$593$	−2.83339	+	0.831957i	−0.116353	+	0.0341644i	0.223038	+	0.974810i	$0.428403\pi$
$594$	0.895412	−	1.96068i	0.0367392	−	0.0804477i
$595$	5.84310	−	40.6397i	0.239544	−	1.66606i
$596$	−10.7428	+	6.90400i	−0.440044	+	0.282799i
$597$	22.1411			0.906173
$598$	17.4039	−	28.4791i	0.711699	−	1.16460i
$599$	24.7280			1.01036			0.505179	−	0.863015i	$-0.331426\pi$
$599$	24.7280			1.01036			0.505179	+	0.863015i	$0.331426\pi$
$600$	−1.30862	+	0.840996i	−0.0534240	+	0.0343335i
$601$	2.95561	−	20.5567i	0.120562	−	0.838525i	−0.836360	−	0.548180i	$-0.815321\pi$
$601$	2.95561	−	20.5567i	0.120562	−	0.838525i	0.956922	−	0.290345i	$-0.0937700\pi$
$602$	1.67353	−	3.66452i	0.0682081	−	0.149355i
$603$	3.50992	−	1.03061i	0.142935	−	0.0419695i
$604$	2.19904	+	4.81523i	0.0894777	+	0.195929i
$605$	−7.72243	−	8.91216i	−0.313961	−	0.362331i
$606$	−1.23599	−	8.59652i	−0.0502088	−	0.349210i
$607$	−29.3134	−	8.60719i	−1.18979	−	0.349355i	−0.373851	−	0.927489i	$-0.621963\pi$
$607$	−29.3134	−	8.60719i	−1.18979	−	0.349355i	−0.815942	+	0.578134i	$0.803781\pi$
$608$	−1.27819	+	1.47511i	−0.0518374	+	0.0598236i
$609$	0.358412	+	0.230338i	0.0145236	+	0.00933375i
$610$	−9.87013	−	6.34315i	−0.399630	−	0.256827i
$611$	14.9107	−	17.2079i	0.603223	−	0.696157i
$612$	−5.46209	−	1.60381i	−0.220792	−	0.0648304i
$613$	3.16868	+	22.0386i	0.127982	+	0.890133i	0.948108	+	0.317949i	$0.102994\pi$
$613$	3.16868	+	22.0386i	0.127982	+	0.890133i	−0.820126	+	0.572183i	$0.806097\pi$
$614$	1.49815	+	1.72896i	0.0604604	+	0.0697751i
$615$	6.34143	+	13.8858i	0.255711	+	0.559929i
$616$	8.03710	−	2.35990i	0.323824	−	0.0950833i
$617$	−6.02311	+	13.1888i	−0.242481	+	0.530960i	−0.991270	−	0.131849i	$-0.957909\pi$
$617$	−6.02311	+	13.1888i	−0.242481	+	0.530960i	0.748789	+	0.662809i	$0.230636\pi$
$618$	−1.33202	+	9.26439i	−0.0535816	+	0.372668i
$619$	−13.4184	+	8.62351i	−0.539333	+	0.346608i	−0.781778	−	0.623557i	$-0.785687\pi$
$619$	−13.4184	+	8.62351i	−0.539333	+	0.346608i	0.242445	+	0.970165i	$0.422051\pi$
$620$	15.8266			0.635611
$621$	3.55240	−	3.22188i	0.142553	−	0.129289i
$622$	11.1401			0.446677
$623$	16.7758	−	10.7811i	0.672106	−	0.431937i
$624$	−0.990421	+	6.88853i	−0.0396486	+	0.275762i
$625$	−6.14917	+	13.4648i	−0.245967	+	0.538592i
$626$	16.8630	−	4.95142i	0.673980	−	0.197898i
$627$	1.74771	+	3.82695i	0.0697968	+	0.152834i
$628$	3.99377	+	4.60905i	0.159369	+	0.183921i
$629$	1.40082	+	9.74289i	0.0558542	+	0.388475i
$630$	−6.92019	−	2.03195i	−0.275707	−	0.0809549i
$631$	19.1810	−	22.1361i	0.763584	−	0.881222i	−0.232227	−	0.972662i	$-0.574601\pi$
$631$	19.1810	−	22.1361i	0.763584	−	0.881222i	0.995811	+	0.0914391i	$0.0291467\pi$
$632$	12.3217	+	7.91870i	0.490132	+	0.314989i
$633$	18.2841	+	11.7505i	0.726729	+	0.467040i
$634$	4.98162	−	5.74909i	0.197845	−	0.228326i
$635$	−19.8370	−	5.82468i	−0.787208	−	0.231145i
$636$	−1.56528	−	10.8868i	−0.0620675	−	0.431689i
$637$	36.9239	+	42.6125i	1.46298	+	1.68837i
$638$	0.0981663	+	0.214954i	0.00388644	+	0.00851012i
$639$	0.545543	−	0.160186i	0.0215813	−	0.00633686i
$640$	0.770978	−	1.68821i	0.0304756	−	0.0667322i
$641$	1.97160	−	13.7128i	0.0778735	−	0.541622i	−0.913118	−	0.407696i	$-0.866332\pi$
$641$	1.97160	−	13.7128i	0.0778735	−	0.541622i	0.990991	−	0.133926i	$-0.0427586\pi$
$642$	1.96386	−	1.26209i	0.0775072	−	0.0498108i
$643$	21.6577			0.854097			0.427048	−	0.904229i	$-0.359553\pi$
$643$	21.6577			0.854097			0.427048	+	0.904229i	$0.359553\pi$
$644$	18.5028	+	2.23390i	0.729113	+	0.0880281i
$645$	−1.92396			−0.0757557
$646$	9.34739	−	6.00720i	0.367768	−	0.236350i
$647$	−1.88070	+	13.0806i	−0.0739381	+	0.514251i	0.918872	+	0.394555i	$0.129101\pi$
$647$	−1.88070	+	13.0806i	−0.0739381	+	0.514251i	−0.992811	+	0.119696i	$0.961808\pi$
$648$	−0.415415	+	0.909632i	−0.0163190	+	0.0357337i
$649$	5.14749	−	1.51144i	0.202057	−	0.0593292i
$650$	−4.49715	−	9.84738i	−0.176393	−	0.386246i
$651$	−21.7017	−	25.0451i	−0.850556	−	0.981594i
$652$	−0.312860	−	2.17599i	−0.0122526	−	0.0852184i
$653$	−1.32064	−	0.387774i	−0.0516806	−	0.0151748i	0.255790	−	0.966732i	$-0.417664\pi$
$653$	−1.32064	−	0.387774i	−0.0516806	−	0.0151748i	−0.307471	+	0.951558i	$0.599483\pi$
$654$	−5.29129	+	6.10647i	−0.206906	+	0.238782i
$655$	21.0446	+	13.5245i	0.822280	+	0.528447i
$656$	6.91946	+	4.44687i	0.270160	+	0.173621i
$657$	−9.13604	+	10.5435i	−0.356431	+	0.411343i
$658$	12.1994	+	3.58207i	0.475582	+	0.139643i
$659$	−0.897828	−	6.24453i	−0.0349744	−	0.243253i	0.964833	−	0.262863i	$-0.0846666\pi$
$659$	−0.897828	−	6.24453i	−0.0349744	−	0.243253i	−0.999808	+	0.0196101i	$0.993758\pi$
$660$	−2.61969	−	3.02328i	−0.101971	−	0.117681i
$661$	1.03841	+	2.27381i	0.0403897	+	0.0884410i	0.928751	−	0.370703i	$-0.120883\pi$
$661$	1.03841	+	2.27381i	0.0403897	+	0.0884410i	−0.888362	+	0.459144i	$0.848156\pi$
$662$	18.0608	−	5.30313i	0.701953	−	0.206112i
$663$	16.4577	−	36.0373i	0.639164	−	1.39957i
$664$	1.47073	−	10.2292i	0.0570755	−	0.396969i
$665$	11.8427	−	7.61082i	0.459239	−	0.295135i
$666$	1.72908			0.0670003
$667$	0.0119069	+	0.525644i	0.000461036	+	0.0203530i
$668$	−18.5061			−0.716024
$669$	−15.3486	+	9.86395i	−0.593411	+	0.381362i
$670$	0.966197	−	6.72004i	0.0373274	−	0.259618i
$671$	−5.66056	+	12.3949i	−0.218524	+	0.478500i
$672$	−3.72871	+	1.09485i	−0.143838	+	0.0422347i
$673$	−1.76124	−	3.85657i	−0.0678907	−	0.148660i	0.872645	−	0.488356i	$-0.162403\pi$
$673$	−1.76124	−	3.85657i	−0.0678907	−	0.148660i	−0.940535	+	0.339696i	$0.889676\pi$
$674$	−8.68956	−	10.0283i	−0.334709	−	0.386275i
$675$	−0.221378	−	1.53972i	−0.00852086	−	0.0592639i
$676$	−33.9975	−	9.98256i	−1.30760	−	0.383945i
$677$	−24.8481	+	28.6762i	−0.954990	+	1.10212i	0.0397010	+	0.999212i	$0.487359\pi$
$677$	−24.8481	+	28.6762i	−0.954990	+	1.10212i	−0.994691	+	0.102906i	$0.967186\pi$
$678$	−7.30000	−	4.69142i	−0.280355	−	0.180173i
$679$	−21.7445	−	13.9744i	−0.834479	−	0.536287i
$680$	−6.91872	+	7.98463i	−0.265321	+	0.306197i
$681$	4.12931	+	1.21248i	0.158236	+	0.0464622i
$682$	−2.61589	−	18.1939i	−0.100167	−	0.696680i
$683$	−30.9769	−	35.7493i	−1.18530	−	1.36791i	−0.914153	−	0.405370i	$-0.867143\pi$
$683$	−30.9769	−	35.7493i	−1.18530	−	1.36791i	−0.271147	−	0.962538i	$-0.587403\pi$
$684$	−0.810827	−	1.77546i	−0.0310028	−	0.0678866i
$685$	10.7675	−	3.16162i	0.411405	−	0.120799i
$686$	−1.77894	+	3.89533i	−0.0679201	+	0.148724i
$687$	−1.40138	+	9.74683i	−0.0534661	+	0.371865i
$688$	−0.872092	+	0.560459i	−0.0332482	+	0.0213673i
$689$	76.5443			2.91610
$690$	−2.70037	−	8.48117i	−0.102801	−	0.322873i
$691$	−31.2607			−1.18921			−0.594607	−	0.804017i	$-0.702692\pi$
$691$	−31.2607			−1.18921			−0.594607	+	0.804017i	$0.702692\pi$
$692$	−19.2766	+	12.3883i	−0.732786	+	0.470933i
$693$	−1.19209	+	8.29114i	−0.0452836	+	0.314954i
$694$	0.334046	−	0.731458i	0.0126802	−	0.0277658i
$695$	−3.44022	+	1.01014i	−0.130495	+	0.0383168i
$696$	−0.0455430	−	0.0997253i	−0.00172630	−	0.00378008i
$697$	−30.6628	−	35.3867i	−1.16144	−	1.34037i
$698$	1.59863	+	11.1187i	0.0605091	+	0.420850i
$699$	−2.12799	−	0.624834i	−0.0804879	−	0.0236334i
$700$	3.95868	−	4.56856i	0.149624	−	0.172675i
$701$	29.2493	+	18.7974i	1.10473	+	0.709967i	0.960138	−	0.279525i	$-0.0901770\pi$
$701$	29.2493	+	18.7974i	1.10473	+	0.709967i	0.144591	+	0.989491i	$0.453813\pi$
$702$	−5.85459	−	3.76252i	−0.220967	−	0.142007i
$703$	−2.21009	+	2.55058i	−0.0833550	+	0.0961968i
$704$	−2.06815	−	0.607265i	−0.0779465	−	0.0228871i
$705$	−0.864151	−	6.01031i	−0.0325458	−	0.226361i
$706$	1.16915	+	1.34927i	0.0440015	+	0.0507805i
$707$	14.0205	+	30.7007i	0.527297	+	1.15462i
$708$	−2.38811	+	0.701213i	−0.0897507	+	0.0263532i
$709$	−4.46658	+	9.78045i	−0.167746	+	0.367312i	−0.974772	−	0.223204i	$-0.928348\pi$
$709$	−4.46658	+	9.78045i	−0.167746	+	0.367312i	0.807026	+	0.590516i	$0.201076\pi$
$710$	0.150175	−	1.04449i	0.00563596	−	0.0391990i
$711$	−12.3217	+	7.91870i	−0.462101	+	0.296974i
$712$	−5.13143			−0.192309
$713$	10.6304	−	39.4913i	0.398113	−	1.47896i
$714$	22.1225			0.827913
$715$	23.4206	−	15.0515i	0.875879	−	0.562893i
$716$	0.141498	−	0.984141i	0.00528803	−	0.0367791i
$717$	4.99628	−	10.9403i	0.186590	−	0.408574i
$718$	−23.2504	+	6.82692i	−0.867696	+	0.254779i
$719$	13.8708	+	30.3727i	0.517292	+	1.13271i	0.970455	+	0.241284i	$0.0775685\pi$
$719$	13.8708	+	30.3727i	0.517292	+	1.13271i	−0.453162	+	0.891428i	$0.649704\pi$
$720$	1.21537	+	1.40261i	0.0452942	+	0.0522723i
$721$	−5.17639	−	36.0026i	−0.192779	−	1.34081i
$722$	−14.5750	−	4.27960i	−0.542424	−	0.159270i
$723$	−11.3185	+	13.0622i	−0.420939	+	0.485789i
$724$	−7.04469	−	4.52735i	−0.261814	−	0.168258i
$725$	0.143467	+	0.0922005i	0.00532822	+	0.00342424i
$726$	4.16097	−	4.80201i	0.154428	−	0.178219i
$727$	9.75305	+	2.86375i	0.361721	+	0.106211i	0.457543	−	0.889188i	$-0.348730\pi$
$727$	9.75305	+	2.86375i	0.361721	+	0.106211i	−0.0958219	+	0.995398i	$0.530548\pi$
$728$	−3.84890	−	26.7697i	−0.142650	−	0.992150i
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$	10.7560	+	23.5524i	0.398097	+	0.871712i
$731$	5.66232	−	1.66261i	0.209428	−	0.0614937i
$732$	2.62614	−	5.75045i	0.0970651	−	0.212543i
$733$	6.31365	−	43.9124i	0.233200	−	1.62194i	−0.450915	−	0.892567i	$-0.648902\pi$
$733$	6.31365	−	43.9124i	0.233200	−	1.62194i	0.684115	−	0.729374i	$-0.260189\pi$
$734$	1.37153	−	0.881432i	0.0506243	−	0.0325342i
$735$	15.0366			0.554633
$736$	−3.69464	−	3.05772i	−0.136186	−	0.112709i
$737$	−7.88491			−0.290444
$738$	−6.91946	+	4.44687i	−0.254709	+	0.163691i
$739$	−1.82504	+	12.6935i	−0.0671353	+	0.466937i	0.928326	+	0.371768i	$0.121248\pi$
$739$	−1.82504	+	12.6935i	−0.0671353	+	0.466937i	−0.995461	+	0.0951689i	$0.969661\pi$
$740$	1.33308	−	2.91904i	0.0490050	−	0.107306i
$741$	13.0334	−	3.82695i	0.478794	−	0.140587i
$742$	17.7559	+	38.8799i	0.651838	+	1.42733i
$743$	−18.0493	−	20.8300i	−0.662165	−	0.764180i	0.320964	−	0.947091i	$-0.395993\pi$
$743$	−18.0493	−	20.8300i	−0.662165	−	0.764180i	−0.983129	+	0.182912i	$0.941448\pi$
$744$	1.21361	+	8.44082i	0.0444930	+	0.309456i
$745$	−22.7402	−	6.67711i	−0.833135	−	0.244631i
$746$	−1.48439	+	1.71307i	−0.0543472	+	0.0627200i
$747$	8.69382	+	5.58718i	0.318090	+	0.204424i
$748$	10.3225	+	6.63387i	0.377428	+	0.242558i
$749$	−5.94084	+	6.85610i	−0.217074	+	0.250516i
$750$	−11.6738	−	3.42773i	−0.426266	−	0.125163i
$751$	−2.52158	−	17.5380i	−0.0920137	−	0.639969i	−0.982680	−	0.185311i	$-0.940671\pi$
$751$	−2.52158	−	17.5380i	−0.0920137	−	0.639969i	0.890666	−	0.454658i	$-0.150238\pi$
$752$	−2.14254	−	2.47262i	−0.0781304	−	0.0901673i
$753$	−1.10943	−	2.42931i	−0.0404299	−	0.0885291i
$754$	0.732067	−	0.214954i	0.0266603	−	0.00782817i
$755$	−4.08125	+	8.93669i	−0.148532	+	0.325239i
$756$	0.553053	−	3.84657i	0.0201143	−	0.139898i
$757$	−6.95768	+	4.47143i	−0.252881	+	0.162517i	−0.660940	−	0.750439i	$-0.729842\pi$
$757$	−6.95768	+	4.47143i	−0.252881	+	0.162517i	0.408059	+	0.912956i	$0.366206\pi$
$758$	−7.11053			−0.258266
$759$	−9.30343	+	4.50609i	−0.337693	+	0.163561i
$760$	−3.62248			−0.131401
$761$	−13.5041	+	8.67855i	−0.489523	+	0.314597i	−0.762013	−	0.647561i	$-0.775789\pi$
$761$	−13.5041	+	8.67855i	−0.489523	+	0.314597i	0.272491	+	0.962158i	$0.412153\pi$
$762$	1.58535	−	11.0264i	0.0574312	−	0.399443i
$763$	13.0440	−	28.5624i	0.472225	−	1.03403i
$764$	22.9375	−	6.73507i	0.829851	−	0.243666i
$765$	−4.38893	−	9.61043i	−0.158682	−	0.347466i
$766$	24.5315	+	28.3108i	0.886358	+	1.02291i
$767$	−2.46509	−	17.1451i	−0.0890092	−	0.619073i
$768$	0.959493	+	0.281733i	0.0346227	+	0.0101661i
$769$	−17.0848	+	19.7170i	−0.616095	+	0.711012i	−0.974961	−	0.222377i	$-0.928618\pi$
$769$	−17.0848	+	19.7170i	−0.616095	+	0.711012i	0.358865	+	0.933389i	$0.383164\pi$
$770$	13.0781	+	8.40477i	0.471301	+	0.302887i
$771$	24.5940	+	15.8056i	0.885731	+	0.569225i
$772$	−10.1732	+	11.7405i	−0.366141	+	0.422550i
$773$	−27.4217	−	8.05173i	−0.986289	−	0.289601i	−0.251471	−	0.967865i	$-0.580914\pi$
$773$	−27.4217	−	8.05173i	−0.986289	−	0.289601i	−0.734818	+	0.678264i	$0.762732\pi$
$774$	−0.147532	−	1.02611i	−0.00530292	−	0.0368826i
$775$	−8.68684	−	10.0252i	−0.312041	−	0.360114i
$776$	2.76305	+	6.05024i	0.0991877	+	0.217191i
$777$	−6.44722	+	1.89307i	−0.231293	+	0.0679136i
$778$	−0.446767	+	0.978282i	−0.0160174	+	0.0350731i
$779$	2.28477	−	15.8909i	0.0818603	−	0.569351i
$780$	−10.8657	+	6.98294i	−0.389053	+	0.250029i
$781$	−1.22554			−0.0438533
$782$	15.2765	+	22.6270i	0.546285	+	0.809142i
$783$	0.109633			0.00391795
$784$	6.81579	−	4.38024i	0.243421	−	0.156437i
$785$	−1.61081	+	11.2034i	−0.0574922	+	0.399867i
$786$	−5.59933	+	12.2608i	−0.199721	+	0.437329i
$787$	−49.8749	+	14.6446i	−1.77785	+	0.522023i	−0.994972	−	0.100156i	$-0.968066\pi$
$787$	−49.8749	+	14.6446i	−1.77785	+	0.522023i	−0.782875	+	0.622179i	$0.786248\pi$
$788$	−7.16907	−	15.6981i	−0.255388	−	0.559221i
$789$	7.66080	+	8.84103i	0.272732	+	0.314749i
$790$	3.86861	+	26.9068i	0.137639	+	0.957300i
$791$	32.3560	+	9.50057i	1.15045	+	0.337801i
$792$	1.41153	−	1.62899i	0.0501565	−	0.0578837i
$793$	37.0112	+	23.7856i	1.31431	+	0.844653i
$794$	−10.0516	−	6.45974i	−0.356716	−	0.229248i
$795$	13.3675	−	15.4270i	0.474098	−	0.547138i
$796$	21.2442	+	6.23786i	0.752980	+	0.221095i
$797$	−6.09049	−	42.3603i	−0.215736	−	1.50048i	−0.753536	−	0.657406i	$-0.771654\pi$
$797$	−6.09049	−	42.3603i	−0.215736	−	1.50048i	0.537800	−	0.843072i	$-0.319256\pi$
$798$	4.96720	+	5.73246i	0.175837	+	0.202927i
$799$	7.73712	+	16.9419i	0.273720	+	0.599362i
$800$	−1.49254	+	0.438250i	−0.0527694	+	0.0154945i
$801$	2.13167	−	4.66772i	0.0753190	−	0.164926i
$802$	−4.23870	+	29.4808i	−0.149674	+	1.04100i
$803$	25.2974	−	16.2577i	0.892728	−	0.573721i
$804$	3.65810			0.129011
$805$	19.3545	+	28.6673i	0.682156	+	1.01039i
$806$	−59.3468			−2.09040
$807$	−19.9573	+	12.8258i	−0.702531	+	0.451489i
$808$	1.23599	−	8.59652i	0.0434821	−	0.302425i
$809$	−3.41357	+	7.47467i	−0.120015	+	0.262795i	−0.960099	−	0.279660i	$-0.909778\pi$
$809$	−3.41357	+	7.47467i	−0.120015	+	0.262795i	0.840084	+	0.542456i	$0.182505\pi$
$810$	−1.78074	+	0.522874i	−0.0625690	+	0.0183719i
$811$	10.7657	+	23.5736i	0.378035	+	0.827782i	0.999033	+	0.0439694i	$0.0140004\pi$
$811$	10.7657	+	23.5736i	0.378035	+	0.827782i	−0.620998	+	0.783813i	$0.713272\pi$
$812$	0.279000	+	0.321984i	0.00979100	+	0.0112994i
$813$	−2.36950	−	16.4802i	−0.0831019	−	0.577987i
$814$	−3.57599	−	1.05001i	−0.125338	−	0.0368027i
$815$	2.67183	−	3.08346i	0.0935901	−	0.108009i
$816$	−4.78899	−	3.07770i	−0.167648	−	0.107741i
$817$	1.70219	+	1.09393i	0.0595522	+	0.0382718i
$818$	−18.6223	+	21.4913i	−0.651113	+	0.751425i
$819$	25.9494	+	7.61944i	0.906747	+	0.266245i
$820$	2.17248	+	15.1099i	0.0758662	+	0.527661i
$821$	12.1733	+	14.0488i	0.424852	+	0.490305i	0.927309	−	0.374297i	$-0.122116\pi$
$821$	12.1733	+	14.0488i	0.424852	+	0.490305i	−0.502457	+	0.864602i	$0.667571\pi$
$822$	2.51186	+	5.50020i	0.0876111	+	0.191842i
$823$	10.2202	−	3.00091i	0.356253	−	0.104605i	−0.0987088	−	0.995116i	$-0.531471\pi$
$823$	10.2202	−	3.00091i	0.356253	−	0.104605i	0.454961	+	0.890511i	$0.349653\pi$
$824$	−3.88814	+	8.51385i	−0.135450	+	0.296594i
$825$	−0.477173	+	3.31881i	−0.0166130	+	0.115546i
$826$	8.13685	−	5.22923i	0.283117	−	0.181948i
$827$	−26.5475			−0.923148			−0.461574	−	0.887102i	$-0.652715\pi$
$827$	−26.5475			−0.923148			−0.461574	+	0.887102i	$0.652715\pi$
$828$	4.31621	−	2.09054i	0.149999	−	0.0726514i
$829$	5.30529			0.184260			0.0921301	−	0.995747i	$-0.470632\pi$
$829$	5.30529			0.184260			0.0921301	+	0.995747i	$0.470632\pi$
$830$	16.1350	−	10.3694i	0.560056	−	0.359926i
$831$	1.25264	−	8.71229i	0.0434536	−	0.302226i
$832$	−2.89102	+	6.33046i	−0.100228	+	0.219469i
$833$	−44.2536	+	12.9940i	−1.53330	+	0.450216i
$834$	−0.802540	−	1.75732i	−0.0277897	−	0.0608509i
$835$	−22.4918	−	25.9569i	−0.778361	−	0.898277i
$836$	0.598739	+	4.16432i	0.0207078	+	0.144026i
$837$	−8.18219	−	2.40251i	−0.282818	−	0.0830428i
$838$	21.4724	−	24.7805i	0.741752	−	0.856027i
$839$	−46.4479	−	29.8502i	−1.60356	−	1.03054i	−0.965447	−	0.260601i	$-0.916079\pi$
$839$	−46.4479	−	29.8502i	−1.60356	−	1.03054i	−0.638112	−	0.769944i	$-0.720284\pi$
$840$	−6.06741	−	3.89929i	−0.209345	−	0.134538i
$841$	18.9831	−	21.9077i	0.654589	−	0.755436i
$842$	−34.1100	−	10.0156i	−1.17551	−	0.345160i
$843$	0.134177	+	0.933222i	0.00462130	+	0.0321419i
$844$	14.2330	+	16.4258i	0.489920	+	0.565398i
$845$	−27.3179	−	59.8178i	−0.939763	−	2.05779i
$846$	3.13922	−	0.921758i	0.107929	−	0.0316907i
$847$	−10.2576	+	22.4609i	−0.352454	+	0.771766i
$848$	1.56528	−	10.8868i	0.0537521	−	0.373854i
$849$	9.83686	−	6.32177i	0.337600	−	0.216963i
$850$	8.85528			0.303734
$851$	−6.38831	−	5.28702i	−0.218989	−	0.181237i
$852$	0.568574			0.0194790
$853$	−35.3409	+	22.7122i	−1.21005	+	0.777651i	−0.980667	−	0.195686i	$-0.937307\pi$
$853$	−35.3409	+	22.7122i	−1.21005	+	0.777651i	−0.229382	+	0.973337i	$0.573670\pi$
$854$	−3.49626	+	24.3170i	−0.119639	+	0.832110i
$855$	1.50483	−	3.29512i	0.0514642	−	0.112691i
$856$	2.23988	−	0.657687i	0.0765574	−	0.0224793i
$857$	16.7460	+	36.6686i	0.572032	+	1.25258i	0.945708	+	0.325016i	$0.105370\pi$
$857$	16.7460	+	36.6686i	0.572032	+	1.25258i	−0.373676	+	0.927559i	$0.621903\pi$
$858$	9.82335	+	11.3367i	0.335364	+	0.387030i
$859$	0.822115	+	5.71794i	0.0280502	+	0.195093i	0.999028	−	0.0440753i	$-0.0140342\pi$
$859$	0.822115	+	5.71794i	0.0280502	+	0.195093i	−0.970978	+	0.239169i	$0.923125\pi$
$860$	−1.84602	−	0.542041i	−0.0629488	−	0.0184834i
$861$	20.9320	−	24.1568i	0.713361	−	0.823262i
$862$	23.2995	+	14.9737i	0.793585	+	0.510006i
$863$	12.7377	+	8.18600i	0.433595	+	0.278655i	0.739177	−	0.673511i	$-0.235215\pi$
$863$	12.7377	+	8.18600i	0.433595	+	0.278655i	−0.305582	+	0.952166i	$0.598851\pi$
$864$	−0.654861	+	0.755750i	−0.0222788	+	0.0257111i
$865$	−40.8042	−	11.9812i	−1.38738	−	0.407373i
$866$	−3.38354	−	23.5331i	−0.114977	−	0.799686i
$867$	10.0892	+	11.6436i	0.342648	+	0.395437i
$868$	−13.7666	−	30.1446i	−0.467269	−	1.02318i
$869$	30.2920	−	8.89453i	1.02759	−	0.301726i
$870$	0.0845242	−	0.185082i	0.00286564	−	0.00627488i
$871$	−3.62306	+	25.1989i	−0.122763	+	0.853833i
$872$	−6.79735	+	4.36839i	−0.230187	+	0.147932i
$873$	−6.65130			−0.225112
$874$	−2.43315	+	9.03898i	−0.0823026	+	0.305748i
$875$	47.2809			1.59839
$876$	−11.7364	+	7.54254i	−0.396537	+	0.254839i
$877$	−4.64024	+	32.2736i	−0.156690	+	1.08980i	0.747990	+	0.663710i	$0.231019\pi$
$877$	−4.64024	+	32.2736i	−0.156690	+	1.08980i	−0.904680	+	0.426091i	$0.859890\pi$
$878$	−14.0051	+	30.6669i	−0.472649	+	1.03496i
$879$	−28.1921	+	8.27793i	−0.950894	+	0.279208i
$880$	−1.66182	−	3.63887i	−0.0560198	−	0.122666i
$881$	−2.92223	−	3.37243i	−0.0984524	−	0.113620i	0.704385	−	0.709818i	$-0.251223\pi$
$881$	−2.92223	−	3.37243i	−0.0984524	−	0.113620i	−0.802838	+	0.596198i	$0.796677\pi$
$882$	1.15303	+	8.01948i	0.0388245	+	0.270030i
$883$	25.8754	+	7.59771i	0.870778	+	0.255683i	0.686446	−	0.727181i	$-0.259170\pi$
$883$	25.8754	+	7.59771i	0.870778	+	0.255683i	0.184332	+	0.982864i	$0.440988\pi$
$884$	25.9439	−	29.9409i	0.872589	−	1.00702i
$885$	−3.88597	−	2.49736i	−0.130625	−	0.0839479i
$886$	−10.0791	−	6.47747i	−0.338615	−	0.217615i
$887$	−22.4135	+	25.8665i	−0.752570	+	0.868513i	−0.994815	−	0.101703i	$-0.967571\pi$
$887$	−22.4135	+	25.8665i	−0.752570	+	0.868513i	0.242244	+	0.970215i	$0.422116\pi$
$888$	1.65904	+	0.487137i	0.0556736	+	0.0163472i
$889$	6.16087	+	42.8498i	0.206629	+	1.43714i
$890$	−6.23659	−	7.19741i	−0.209051	−	0.241258i
$891$	0.895412	+	1.96068i	0.0299974	+	0.0656852i
$892$	−17.5059	+	5.14019i	−0.586140	+	0.172106i
$893$	−2.65282	+	5.80887i	−0.0887734	+	0.194387i
$894$	1.81737	−	12.6401i	0.0607818	−	0.422747i
$895$	1.55234	−	0.997629i	0.0518890	−	0.0333471i
$896$	−3.88612			−0.129826
$897$	10.1259	+	31.8028i	0.338094	+	1.06187i
$898$	0.721325			0.0240709
$899$	0.786492	−	0.505448i	0.0262310	−	0.0168576i
$900$	0.221378	−	1.53972i	0.00737928	−	0.0513240i
$901$	−26.0101	+	56.9542i	−0.866523	+	1.89742i
$902$	17.0109	−	4.99486i	0.566402	−	0.166311i
$903$	1.67353	+	3.66452i	0.0556917	+	0.121948i
$904$	−5.68257	−	6.55804i	−0.189000	−	0.218117i
$905$	−2.21180	−	15.3834i	−0.0735226	−	0.511361i
$906$	−5.07917	−	1.49138i	−0.168744	−	0.0495478i
$907$	23.2630	−	26.8469i	0.772434	−	0.891436i	−0.224105	−	0.974565i	$-0.571946\pi$
$907$	23.2630	−	26.8469i	0.772434	−	0.891436i	0.996539	+	0.0831290i	$0.0264914\pi$
$908$	3.62045	+	2.32672i	0.120149	+	0.0772150i
$909$	7.30622	+	4.69542i	0.242332	+	0.155737i
$910$	32.8696	−	37.9336i	1.08962	−	1.25749i
$911$	−16.1581	−	4.74446i	−0.535343	−	0.157191i	0.00287613	−	0.999996i	$-0.499084\pi$
$911$	−16.1581	−	4.74446i	−0.535343	−	0.157191i	−0.538219	+	0.842805i	$0.680903\pi$
$912$	−0.277777	−	1.93198i	−0.00919812	−	0.0639743i
$913$	−14.5873	−	16.8346i	−0.482768	−	0.557144i
$914$	−1.74155	−	3.81347i	−0.0576054	−	0.126138i
$915$	11.2574	−	3.30547i	0.372158	−	0.109275i
$916$	−4.09062	+	8.95720i	−0.135158	+	0.295954i
$917$	7.45453	−	51.8474i	0.246170	−	1.71215i
$918$	4.78899	−	3.07770i	0.158060	−	0.101579i
$919$	3.06801			0.101204			0.0506021	−	0.998719i	$-0.483886\pi$
$919$	3.06801			0.101204			0.0506021	+	0.998719i	$0.483886\pi$
$920$	−0.201566	−	8.89841i	−0.00664545	−	0.293372i
$921$	−2.28774			−0.0753836
$922$	−15.6630	+	10.0660i	−0.515833	+	0.331506i
$923$	−0.563128	+	3.91664i	−0.0185356	+	0.128918i
$924$	−3.47968	+	7.61944i	−0.114473	+	0.250661i
$925$	−2.58072	+	0.757768i	−0.0848536	+	0.0249153i
$926$	4.59477	+	10.0611i	0.150993	+	0.330630i
$927$	−6.12927	−	7.07356i	−0.201312	−	0.232326i
$928$	−0.0156023	−	0.108517i	−0.000512172	−	0.00356223i
$929$	−17.2466	−	5.06406i	−0.565842	−	0.166146i	−0.0137147	−	0.999906i	$-0.504366\pi$
$929$	−17.2466	−	5.06406i	−0.565842	−	0.166146i	−0.552128	+	0.833760i	$0.686184\pi$
$930$	−10.3642	+	11.9609i	−0.339856	+	0.392215i
$931$	−13.3034	−	8.54958i	−0.436001	−	0.280201i
$932$	−1.86575	−	1.19905i	−0.0611148	−	0.0392761i
$933$	−7.29521	+	8.41913i	−0.238835	+	0.275630i
$934$	−22.8502	−	6.70941i	−0.747680	−	0.219539i
$935$	3.24092	+	22.5411i	0.105989	+	0.737172i
$936$	−4.55742	−	5.25954i	−0.148964	−	0.171913i
$937$	−19.8049	−	43.3666i	−0.646997	−	1.41673i	−0.894158	−	0.447752i	$-0.852225\pi$
$937$	−19.8049	−	43.3666i	−0.646997	−	1.41673i	0.247161	−	0.968974i	$-0.420502\pi$
$938$	−13.6400	+	4.00506i	−0.445361	+	0.130770i
$939$	−7.30087	+	15.9867i	−0.238255	+	0.521706i
$940$	0.864151	−	6.01031i	0.0281855	−	0.196035i
$941$	43.2692	−	27.8074i	1.41054	−	0.906497i	0.410551	−	0.911838i	$-0.365337\pi$
$941$	43.2692	−	27.8074i	1.41054	−	0.906497i	0.999986	+	0.00534126i	$0.00170018\pi$
$942$	−6.09865			−0.198705
$943$	39.1622	+	4.72817i	1.27530	+	0.153971i
$944$	−2.48893			−0.0810078
$945$	6.06741	−	3.89929i	0.197373	−	0.126844i
$946$	−0.318000	+	2.21174i	−0.0103391	+	0.0719097i
$947$	17.1709	−	37.5990i	0.557979	−	1.22180i	−0.394976	−	0.918691i	$-0.629247\pi$
$947$	17.1709	−	37.5990i	0.557979	−	1.22180i	0.952955	−	0.303112i	$-0.0980255\pi$
$948$	−14.0536	+	4.12650i	−0.456439	+	0.134023i
$949$	−40.3330	−	88.3170i	−1.30927	−	2.86689i
$950$	1.98829	+	2.29461i	0.0645087	+	0.0744471i
$951$	1.08261	+	7.52971i	0.0351060	+	0.244168i
$952$	21.2264	+	6.23262i	0.687950	+	0.202000i
$953$	0.619591	−	0.715046i	0.0200705	−	0.0231626i	−0.745626	−	0.666365i	$-0.767849\pi$
$953$	0.619591	−	0.715046i	0.0200705	−	0.0231626i	0.765696	+	0.643203i	$0.222395\pi$
$954$	9.25273	+	5.94637i	0.299568	+	0.192521i
$955$	37.3243	+	23.9869i	1.20779	+	0.776197i
$956$	7.87615	−	9.08956i	0.254733	−	0.293977i
$957$	−0.226737	−	0.0665760i	−0.00732936	−	0.00215210i
$958$	3.32807	+	23.1472i	0.107525	+	0.747853i
$959$	−15.3879	−	17.7585i	−0.496900	−	0.573453i
$960$	0.770978	+	1.68821i	0.0248832	+	0.0544866i
$961$	−40.0304	+	11.7540i	−1.29130	+	0.379160i
$962$	−4.99880	+	10.9458i	−0.161168	+	0.352908i
$963$	−0.332225	+	2.31068i	−0.0107058	+	0.0744606i
$964$	−14.5401	+	9.34433i	−0.468304	+	0.300961i
$965$	−28.8316			−0.928121
$966$	−13.8050	+	12.5206i	−0.444170	+	0.402844i
$967$	51.3969			1.65281			0.826407	−	0.563074i	$-0.190381\pi$
$967$	51.3969			1.65281			0.826407	+	0.563074i	$0.190381\pi$
$968$	5.34530	−	3.43522i	0.171804	−	0.110412i
$969$	−1.58130	+	10.9982i	−0.0507986	+	0.353312i
$970$	−5.12801	+	11.2288i	−0.164650	+	0.360534i
$971$	−8.42596	+	2.47408i	−0.270402	+	0.0793971i	−0.414122	−	0.910221i	$-0.635911\pi$
$971$	−8.42596	+	2.47408i	−0.270402	+	0.0793971i	0.143721	+	0.989618i	$0.454093\pi$
$972$	−0.415415	−	0.909632i	−0.0133244	−	0.0291765i
$973$	4.91643	+	5.67386i	0.157614	+	0.181896i
$974$	−2.01416	−	14.0088i	−0.0645379	−	0.448871i
$975$	10.3872	+	3.04994i	0.332655	+	0.0976764i
$976$	4.13986	−	4.77765i	0.132514	−	0.152929i
$977$	13.6562	+	8.77632i	0.436901	+	0.280779i	0.740546	−	0.672006i	$-0.234567\pi$
$977$	13.6562	+	8.77632i	0.436901	+	0.280779i	−0.303644	+	0.952785i	$0.598203\pi$
$978$	1.84938	+	1.18853i	0.0591368	+	0.0380049i
$979$	−7.24317	+	8.35906i	−0.231493	+	0.267157i
$980$	14.4275	+	4.23630i	0.460870	+	0.135323i
$981$	−1.14991	−	7.99778i	−0.0367137	−	0.255349i
$982$	−3.84573	−	4.43821i	−0.122722	−	0.141629i
$983$	−2.53187	−	5.54403i	−0.0807542	−	0.176827i	0.864948	−	0.501862i	$-0.167351\pi$
$983$	−2.53187	−	5.54403i	−0.0807542	−	0.176827i	−0.945702	+	0.325035i	$0.894624\pi$
$984$	−7.89200	+	2.31730i	−0.251588	+	0.0738729i
$985$	13.3052	−	29.1344i	0.423940	−	0.928299i
$986$	−0.0888192	+	0.617751i	−0.00282858	+	0.0196732i
$987$	−10.6960	+	6.87393i	−0.340459	+	0.218800i
$988$	13.5836			0.432153
$989$	−2.59246	+	4.24220i	−0.0824356	+	0.134894i
$990$	4.00037			0.127140
$991$	21.0256	−	13.5123i	0.667899	−	0.429233i	−0.162269	−	0.986747i	$-0.551881\pi$
$991$	21.0256	−	13.5123i	0.667899	−	0.429233i	0.830168	+	0.557514i	$0.188245\pi$
$992$	−1.21361	+	8.44082i	−0.0385321	+	0.267996i
$993$	−7.81947	+	17.1222i	−0.248143	+	0.543358i
$994$	−2.12005	+	0.622502i	−0.0672438	+	0.0197446i
$995$	17.0703	+	37.3787i	0.541164	+	1.18498i
$996$	6.76757	+	7.81019i	0.214439	+	0.247475i
$997$	4.86655	+	33.8476i	0.154125	+	1.07196i	0.909210	+	0.416337i	$0.136686\pi$
$997$	4.86655	+	33.8476i	0.154125	+	1.07196i	−0.755085	+	0.655627i	$0.772405\pi$
$998$	0.818973	+	0.240472i	0.0259241	+	0.00761201i
$999$	−1.13230	+	1.30675i	−0.0358245	+	0.0413437i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	138.2.e.d.127.1	yes	10
3.2	odd	2		414.2.i.a.127.1		10
23.2	even	11	inner	138.2.e.d.25.1	✓	10
23.5	odd	22		3174.2.a.w.1.4		5
23.18	even	11		3174.2.a.x.1.2		5
69.2	odd	22		414.2.i.a.163.1		10
69.5	even	22		9522.2.a.by.1.2		5
69.41	odd	22		9522.2.a.bx.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
138.2.e.d.25.1	✓	10	23.2	even	11	inner
138.2.e.d.127.1	yes	10	1.1	even	1	trivial
414.2.i.a.127.1		10	3.2	odd	2
414.2.i.a.163.1		10	69.2	odd	22
3174.2.a.w.1.4		5	23.5	odd	22
3174.2.a.x.1.2		5	23.18	even	11
9522.2.a.bx.1.4		5	69.41	odd	22
9522.2.a.by.1.2		5	69.5	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:	\( N \)	\(=\)	\( 138 = 2 \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	138.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.841254 + 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(1.78074 - 0.522874i) q^{5} +(0.415415 + 0.909632i) q^{6} +(-2.54487 - 2.93694i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(-0.841254 + 0.540641i) q^{2} +(0.142315 - 0.989821i) q^{3} +(0.415415 - 0.909632i) q^{4} +(1.78074 - 0.522874i) q^{5} +(0.415415 + 0.909632i) q^{6} +(-2.54487 - 2.93694i) q^{7} +(0.142315 + 0.989821i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(-1.21537 + 1.40261i) q^{10} +(1.81329 + 1.16533i) q^{11} +(-0.841254 - 0.540641i) q^{12} +(4.55742 - 5.25954i) q^{13} +(3.72871 + 1.09485i) q^{14} +(-0.264125 - 1.83703i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(2.36483 + 5.17825i) q^{17} +(0.959493 - 0.281733i) q^{18} +(-0.810827 + 1.77546i) q^{19} +(0.264125 - 1.83703i) q^{20} +(-3.26921 + 2.10100i) q^{21} -2.15546 q^{22} +(-4.40644 - 1.89296i) q^{23} +1.00000 q^{24} +(-1.30862 + 0.840996i) q^{25} +(-0.990421 + 6.88853i) q^{26} +(-0.415415 + 0.909632i) q^{27} +(-3.72871 + 1.09485i) q^{28} +(-0.0455430 - 0.0997253i) q^{29} +(1.21537 + 1.40261i) q^{30} +(1.21361 + 8.44082i) q^{31} +(0.959493 + 0.281733i) q^{32} +(1.41153 - 1.62899i) q^{33} +(-4.78899 - 3.07770i) q^{34} +(-6.06741 - 3.89929i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(1.65904 + 0.487137i) q^{37} +(-0.277777 - 1.93198i) q^{38} +(-4.55742 - 5.25954i) q^{39} +(0.770978 + 1.68821i) q^{40} +(-7.89200 + 2.31730i) q^{41} +(1.61435 - 3.53494i) q^{42} +(0.147532 - 1.02611i) q^{43} +(1.81329 - 1.16533i) q^{44} -1.85592 q^{45} +(4.73034 - 0.789845i) q^{46} +3.27175 q^{47} +(-0.841254 + 0.540641i) q^{48} +(-1.15303 + 8.01948i) q^{49} +(0.646201 - 1.41498i) q^{50} +(5.46209 - 1.60381i) q^{51} +(-2.89102 - 6.33046i) q^{52} +(7.20264 + 8.31229i) q^{53} +(-0.142315 - 0.989821i) q^{54} +(3.83833 + 1.12704i) q^{55} +(2.54487 - 2.93694i) q^{56} +(1.64200 + 1.05525i) q^{57} +(0.0922288 + 0.0592718i) q^{58} +(1.62990 - 1.88101i) q^{59} +(-1.78074 - 0.522874i) q^{60} +(0.899677 + 6.25739i) q^{61} +(-5.58440 - 6.44475i) q^{62} +(1.61435 + 3.53494i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(5.36552 - 11.7488i) q^{65} +(-0.306755 + 2.13353i) q^{66} +(-3.07739 + 1.97772i) q^{67} +5.69269 q^{68} +(-2.50079 + 4.09219i) q^{69} +7.21234 q^{70} +(-0.478315 + 0.307394i) q^{71} +(0.142315 - 0.989821i) q^{72} +(5.79550 - 12.6904i) q^{73} +(-1.65904 + 0.487137i) q^{74} +(0.646201 + 1.41498i) q^{75} +(1.27819 + 1.47511i) q^{76} +(-1.19209 - 8.29114i) q^{77} +(6.67746 + 1.96068i) q^{78} +(9.59166 - 11.0694i) q^{79} +(-1.56130 - 1.00339i) q^{80} +(0.841254 + 0.540641i) q^{81} +(5.38635 - 6.21618i) q^{82} +(-9.91575 - 2.91153i) q^{83} +(0.553053 + 3.84657i) q^{84} +(6.91872 + 7.98463i) q^{85} +(0.430643 + 0.942977i) q^{86} +(-0.105192 + 0.0308871i) q^{87} +(-0.895412 + 1.96068i) q^{88} +(-0.730279 + 5.07920i) q^{89} +(1.56130 - 1.00339i) q^{90} -27.0449 q^{91} +(-3.55240 + 3.22188i) q^{92} +8.52762 q^{93} +(-2.75237 + 1.76884i) q^{94} +(-0.515533 + 3.58561i) q^{95} +(0.415415 - 0.909632i) q^{96} +(6.38188 - 1.87389i) q^{97} +(-3.36567 - 7.36979i) q^{98} +(-1.41153 - 1.62899i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + q^{8} - q^{9}+O(q^{10}) \) 10 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 + 2 * q^7 + q^8 - q^9	\( 10 q + q^{2} + q^{3} - q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + q^{8} - q^{9} - 13 q^{10} - 5 q^{11} + q^{12} + 13 q^{13} + 9 q^{14} + 9 q^{15} - q^{16} + q^{18} - 9 q^{20} - 13 q^{21} - 6 q^{22} - 32 q^{23} + 10 q^{24} + q^{25} - 13 q^{26} + q^{27} - 9 q^{28} + 27 q^{29} + 13 q^{30} - 8 q^{31} + q^{32} - 6 q^{33} - 11 q^{34} - 26 q^{35} - q^{36} - 11 q^{37} + 11 q^{38} - 13 q^{39} + 9 q^{40} - 10 q^{41} + 2 q^{42} + 34 q^{43} - 5 q^{44} + 2 q^{45} - q^{46} + 8 q^{47} + q^{48} + 25 q^{49} + 21 q^{50} - 11 q^{51} + 2 q^{52} + 9 q^{53} - q^{54} - 23 q^{55} - 2 q^{56} - 11 q^{57} - 5 q^{58} - 21 q^{59} - 2 q^{60} - 4 q^{61} + 8 q^{62} + 2 q^{63} - q^{64} + 29 q^{65} + 6 q^{66} - 32 q^{67} + 22 q^{68} - q^{69} - 18 q^{70} + 22 q^{71} + q^{72} + 43 q^{73} + 11 q^{74} + 21 q^{75} + 10 q^{77} + 2 q^{78} - 16 q^{79} + 2 q^{80} - q^{81} + 32 q^{82} - 3 q^{83} + 9 q^{84} + 33 q^{85} + 32 q^{86} + 6 q^{87} - 6 q^{88} - 11 q^{89} - 2 q^{90} - 70 q^{91} - 21 q^{92} + 8 q^{93} + 3 q^{94} - q^{96} + 39 q^{97} - 14 q^{98} + 6 q^{99}+O(q^{100}) \) 10 * q + q^2 + q^3 - q^4 + 2 * q^5 - q^6 + 2 * q^7 + q^8 - q^9 - 13 * q^10 - 5 * q^11 + q^12 + 13 * q^13 + 9 * q^14 + 9 * q^15 - q^16 + q^18 - 9 * q^20 - 13 * q^21 - 6 * q^22 - 32 * q^23 + 10 * q^24 + q^25 - 13 * q^26 + q^27 - 9 * q^28 + 27 * q^29 + 13 * q^30 - 8 * q^31 + q^32 - 6 * q^33 - 11 * q^34 - 26 * q^35 - q^36 - 11 * q^37 + 11 * q^38 - 13 * q^39 + 9 * q^40 - 10 * q^41 + 2 * q^42 + 34 * q^43 - 5 * q^44 + 2 * q^45 - q^46 + 8 * q^47 + q^48 + 25 * q^49 + 21 * q^50 - 11 * q^51 + 2 * q^52 + 9 * q^53 - q^54 - 23 * q^55 - 2 * q^56 - 11 * q^57 - 5 * q^58 - 21 * q^59 - 2 * q^60 - 4 * q^61 + 8 * q^62 + 2 * q^63 - q^64 + 29 * q^65 + 6 * q^66 - 32 * q^67 + 22 * q^68 - q^69 - 18 * q^70 + 22 * q^71 + q^72 + 43 * q^73 + 11 * q^74 + 21 * q^75 + 10 * q^77 + 2 * q^78 - 16 * q^79 + 2 * q^80 - q^81 + 32 * q^82 - 3 * q^83 + 9 * q^84 + 33 * q^85 + 32 * q^86 + 6 * q^87 - 6 * q^88 - 11 * q^89 - 2 * q^90 - 70 * q^91 - 21 * q^92 + 8 * q^93 + 3 * q^94 - q^96 + 39 * q^97 - 14 * q^98 + 6 * q^99

Introduction

L-functions

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