LMFDB - Embedded newform 230.2.g.b.131.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(31,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("230.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.g (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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 5 x^{19} + 12 x^{18} + 16 x^{17} - 49 x^{16} + 59 x^{15} - 197 x^{14} + 42 x^{13} + 1625 x^{12} + \cdots + 529 $ x^20 - 5x^19 + 12x^18 + 16x^17 - 49x^16 + 59x^15 - 197x^14 + 42x^13 + 1625x^12 - 5910x^11 + 14651x^10 - 22501x^9 + 26003x^8 - 19607x^7 + 13040x^6 + 348x^5 + 7193x^4 + 10771x^3 + 8781x^2 + 3105*x + 529
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			131.1
Root			$-0.319826 - 0.205540i$ of defining polynomial
Character	$\chi$	$=$	230.131
Dual form			230.2.g.b.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 - 0.755750i) q^{2} +(-1.71555 + 1.10252i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.415415 + 0.909632i) q^{5} +(-0.290219 + 2.01852i) q^{6} +(3.10381 - 0.911362i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.481321 - 1.05395i) q^{9} +O(q^{10})$	\(q+(0.654861 - 0.755750i) q^{2} +(-1.71555 + 1.10252i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.415415 + 0.909632i) q^{5} +(-0.290219 + 2.01852i) q^{6} +(3.10381 - 0.911362i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.481321 - 1.05395i) q^{9} +(0.959493 + 0.281733i) q^{10} +(1.85273 + 2.13817i) q^{11} +(1.33544 + 1.54118i) q^{12} +(5.91432 + 1.73660i) q^{13} +(1.34380 - 2.94252i) q^{14} +(-1.71555 - 1.10252i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(-0.475893 + 3.30991i) q^{17} +(-0.481321 - 1.05395i) q^{18} +(-1.06213 - 7.38724i) q^{19} +(0.841254 - 0.540641i) q^{20} +(-4.31995 + 4.98549i) q^{21} +2.82920 q^{22} +(-0.991625 + 4.69219i) q^{23} +2.03928 q^{24} +(-0.654861 + 0.755750i) q^{25} +(5.18549 - 3.33251i) q^{26} +(-0.534395 - 3.71680i) q^{27} +(-1.34380 - 2.94252i) q^{28} +(0.656331 - 4.56488i) q^{29} +(-1.95667 + 0.574531i) q^{30} +(-6.36959 - 4.09348i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(-5.53582 - 1.62546i) q^{33} +(2.18982 + 2.52718i) q^{34} +(2.11838 + 2.44474i) q^{35} +(-1.11172 - 0.326429i) q^{36} +(-4.04484 + 8.85697i) q^{37} +(-6.27845 - 4.03492i) q^{38} +(-12.0609 + 3.54141i) q^{39} +(0.142315 - 0.989821i) q^{40} +(-0.910569 - 1.99387i) q^{41} +(0.938816 + 6.52961i) q^{42} +(0.0224065 - 0.0143998i) q^{43} +(1.85273 - 2.13817i) q^{44} +1.15865 q^{45} +(2.89675 + 3.82215i) q^{46} -7.99727 q^{47} +(1.33544 - 1.54118i) q^{48} +(2.91431 - 1.87291i) q^{49} +(0.142315 + 0.989821i) q^{50} +(-2.83281 - 6.20298i) q^{51} +(0.877230 - 6.10127i) q^{52} +(10.5990 - 3.11216i) q^{53} +(-3.15893 - 2.03012i) q^{54} +(-1.17529 + 2.57353i) q^{55} +(-3.10381 - 0.911362i) q^{56} +(9.96668 + 11.5022i) q^{57} +(-3.02010 - 3.48539i) q^{58} +(0.649652 + 0.190755i) q^{59} +(-0.847146 + 1.85499i) q^{60} +(1.17992 + 0.758288i) q^{61} +(-7.26484 + 2.13315i) q^{62} +(0.533404 - 3.70991i) q^{63} +(0.415415 + 0.909632i) q^{64} +(0.877230 + 6.10127i) q^{65} +(-4.85363 + 3.11924i) q^{66} +(6.56894 - 7.58097i) q^{67} +3.34394 q^{68} +(-3.47204 - 9.14297i) q^{69} +3.23485 q^{70} +(0.633599 - 0.731212i) q^{71} +(-0.974718 + 0.626414i) q^{72} +(-0.492094 - 3.42259i) q^{73} +(4.04484 + 8.85697i) q^{74} +(0.290219 - 2.01852i) q^{75} +(-7.16090 + 2.10263i) q^{76} +(7.69918 + 4.94796i) q^{77} +(-5.22182 + 11.4342i) q^{78} +(-11.6597 - 3.42359i) q^{79} +(-0.654861 - 0.755750i) q^{80} +(7.29088 + 8.41412i) q^{81} +(-2.10316 - 0.617544i) q^{82} +(0.439078 - 0.961447i) q^{83} +(5.54954 + 3.56647i) q^{84} +(-3.20849 + 0.942097i) q^{85} +(0.00379051 - 0.0263636i) q^{86} +(3.90689 + 8.55490i) q^{87} +(-0.402637 - 2.80040i) q^{88} +(-8.63158 + 5.54718i) q^{89} +(0.758754 - 0.875649i) q^{90} +19.9396 q^{91} +(4.78556 + 0.313763i) q^{92} +15.4405 q^{93} +(-5.23710 + 6.04394i) q^{94} +(6.27845 - 4.03492i) q^{95} +(-0.290219 - 2.01852i) q^{96} +(-6.28698 - 13.7666i) q^{97} +(0.493014 - 3.42899i) q^{98} +(3.14527 - 0.923534i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9	\( 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9} + 2 q^{10} + 7 q^{11} + 8 q^{12} + 8 q^{13} + 3 q^{14} - 3 q^{15} - 2 q^{16} + 8 q^{17} + 27 q^{18} - q^{19} - 2 q^{20} - 31 q^{21} - 18 q^{22} - 9 q^{23} - 8 q^{24} - 2 q^{25} - 8 q^{26} - 18 q^{27} - 3 q^{28} + 20 q^{29} + 3 q^{30} - 17 q^{31} + 2 q^{32} + 17 q^{33} + 3 q^{34} - 3 q^{35} + 17 q^{36} + 6 q^{37} - 21 q^{38} - 75 q^{39} + 2 q^{40} - 2 q^{41} + 42 q^{42} - 18 q^{43} + 7 q^{44} + 28 q^{45} - 2 q^{46} + 42 q^{47} + 8 q^{48} - 19 q^{49} + 2 q^{50} + 26 q^{51} + 19 q^{52} + 19 q^{53} - 26 q^{54} - 15 q^{55} - 19 q^{56} + 7 q^{57} - 9 q^{58} + 25 q^{59} - 3 q^{60} - 49 q^{61} - 38 q^{62} - 87 q^{63} - 2 q^{64} + 19 q^{65} - 6 q^{66} + 19 q^{67} - 36 q^{68} + 36 q^{69} + 14 q^{70} + 7 q^{71} - 17 q^{72} - 10 q^{73} - 6 q^{74} - 3 q^{75} - q^{76} - 29 q^{77} - 2 q^{78} - 33 q^{79} - 2 q^{80} + 72 q^{81} + 2 q^{82} - 41 q^{83} + 13 q^{84} - 14 q^{85} - 48 q^{86} - 16 q^{87} - 7 q^{88} + 55 q^{89} + 5 q^{90} + 13 q^{92} + 10 q^{93} + 13 q^{94} + 21 q^{95} + 3 q^{96} - 9 q^{97} + 41 q^{98} + 59 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9 + 2 * q^10 + 7 * q^11 + 8 * q^12 + 8 * q^13 + 3 * q^14 - 3 * q^15 - 2 * q^16 + 8 * q^17 + 27 * q^18 - q^19 - 2 * q^20 - 31 * q^21 - 18 * q^22 - 9 * q^23 - 8 * q^24 - 2 * q^25 - 8 * q^26 - 18 * q^27 - 3 * q^28 + 20 * q^29 + 3 * q^30 - 17 * q^31 + 2 * q^32 + 17 * q^33 + 3 * q^34 - 3 * q^35 + 17 * q^36 + 6 * q^37 - 21 * q^38 - 75 * q^39 + 2 * q^40 - 2 * q^41 + 42 * q^42 - 18 * q^43 + 7 * q^44 + 28 * q^45 - 2 * q^46 + 42 * q^47 + 8 * q^48 - 19 * q^49 + 2 * q^50 + 26 * q^51 + 19 * q^52 + 19 * q^53 - 26 * q^54 - 15 * q^55 - 19 * q^56 + 7 * q^57 - 9 * q^58 + 25 * q^59 - 3 * q^60 - 49 * q^61 - 38 * q^62 - 87 * q^63 - 2 * q^64 + 19 * q^65 - 6 * q^66 + 19 * q^67 - 36 * q^68 + 36 * q^69 + 14 * q^70 + 7 * q^71 - 17 * q^72 - 10 * q^73 - 6 * q^74 - 3 * q^75 - q^76 - 29 * q^77 - 2 * q^78 - 33 * q^79 - 2 * q^80 + 72 * q^81 + 2 * q^82 - 41 * q^83 + 13 * q^84 - 14 * q^85 - 48 * q^86 - 16 * q^87 - 7 * q^88 + 55 * q^89 + 5 * q^90 + 13 * q^92 + 10 * q^93 + 13 * q^94 + 21 * q^95 + 3 * q^96 - 9 * q^97 + 41 * q^98 + 59 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	0.654861	−	0.755750i	0.463056	−	0.534396i
$2$	0.654861	−	0.755750i	0.463056	−	0.534396i
$3$	−1.71555	+	1.10252i	−0.990473	+	0.636538i	−0.932269	−	0.361767i	$-0.882174\pi$
$3$	−1.71555	+	1.10252i	−0.990473	+	0.636538i	−0.0582039	+	0.998305i	$0.518537\pi$
$4$	−0.142315	−	0.989821i	−0.0711574	−	0.494911i
$5$	0.415415	+	0.909632i	0.185779	+	0.406800i
$5$	0.415415	+	0.909632i	0.185779	+	0.406800i
$6$	−0.290219	+	2.01852i	−0.118482	+	0.824057i
$7$	3.10381	−	0.911362i	1.17313	−	0.344463i	0.363609	−	0.931552i	$-0.381544\pi$
$7$	3.10381	−	0.911362i	1.17313	−	0.344463i	0.809522	+	0.587089i	$0.199726\pi$
$8$	−0.841254	−	0.540641i	−0.297428	−	0.191145i
$9$	0.481321	−	1.05395i	0.160440	−	0.351315i
$10$	0.959493	+	0.281733i	0.303418	+	0.0890917i
$11$	1.85273	+	2.13817i	0.558620	+	0.644682i	0.962870	−	0.269967i	$-0.0870128\pi$
$11$	1.85273	+	2.13817i	0.558620	+	0.644682i	−0.404250	+	0.914649i	$0.632467\pi$
$12$	1.33544	+	1.54118i	0.385509	+	0.444901i
$13$	5.91432	+	1.73660i	1.64034	+	0.481647i	0.966379	−	0.257122i	$-0.0827743\pi$
$13$	5.91432	+	1.73660i	1.64034	+	0.481647i	0.673959	+	0.738769i	$0.264592\pi$
$14$	1.34380	−	2.94252i	0.359147	−	0.786422i
$15$	−1.71555	−	1.10252i	−0.442953	−	0.284668i
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	−0.475893	+	3.30991i	−0.115421	+	0.802770i	0.847075	+	0.531474i	$0.178361\pi$
$17$	−0.475893	+	3.30991i	−0.115421	+	0.802770i	−0.962496	+	0.271297i	$0.912548\pi$
$18$	−0.481321	−	1.05395i	−0.113448	−	0.248417i
$19$	−1.06213	−	7.38724i	−0.243668	−	1.69475i	−0.633402	−	0.773823i	$-0.718342\pi$
$19$	−1.06213	−	7.38724i	−0.243668	−	1.69475i	0.389734	−	0.920927i	$-0.372567\pi$
$20$	0.841254	−	0.540641i	0.188110	−	0.120891i
$21$	−4.31995	+	4.98549i	−0.942691	+	1.08792i
$22$	2.82920			0.603187
$23$	−0.991625	+	4.69219i	−0.206768	+	0.978390i
$23$	−0.991625	+	4.69219i	−0.206768	+	0.978390i
$24$	2.03928			0.416266
$25$	−0.654861	+	0.755750i	−0.130972	+	0.151150i
$26$	5.18549	−	3.33251i	1.01696	−	0.653560i
$27$	−0.534395	−	3.71680i	−0.102844	−	0.715299i
$28$	−1.34380	−	2.94252i	−0.253955	−	0.556084i
$29$	0.656331	−	4.56488i	0.121878	−	0.847678i	−0.833548	−	0.552447i	$-0.813694\pi$
$29$	0.656331	−	4.56488i	0.121878	−	0.847678i	0.955426	−	0.295231i	$-0.0953966\pi$
$30$	−1.95667	+	0.574531i	−0.357238	+	0.104894i
$31$	−6.36959	−	4.09348i	−1.14401	−	0.735211i	−0.175573	−	0.984466i	$-0.556178\pi$
$31$	−6.36959	−	4.09348i	−1.14401	−	0.735211i	−0.968438	+	0.249255i	$0.919814\pi$
$32$	−0.415415	+	0.909632i	−0.0734357	+	0.160802i
$33$	−5.53582	−	1.62546i	−0.963662	−	0.282957i
$34$	2.18982	+	2.52718i	0.375550	+	0.433408i
$35$	2.11838	+	2.44474i	0.358071	+	0.413236i
$36$	−1.11172	−	0.326429i	−0.185286	−	0.0544049i
$37$	−4.04484	+	8.85697i	−0.664968	+	1.45608i	0.212851	+	0.977085i	$0.431725\pi$
$37$	−4.04484	+	8.85697i	−0.664968	+	1.45608i	−0.877819	+	0.478993i	$0.841002\pi$
$38$	−6.27845	−	4.03492i	−1.01850	−	0.654550i
$39$	−12.0609	+	3.54141i	−1.93130	+	0.567080i
$40$	0.142315	−	0.989821i	0.0225020	−	0.156505i
$41$	−0.910569	−	1.99387i	−0.142207	−	0.311390i	0.825105	−	0.564980i	$-0.191116\pi$
$41$	−0.910569	−	1.99387i	−0.142207	−	0.311390i	−0.967312	+	0.253590i	$0.918389\pi$
$42$	0.938816	+	6.52961i	0.144862	+	1.00754i
$43$	0.0224065	−	0.0143998i	0.00341696	−	0.00219595i	−0.538931	−	0.842350i	$-0.681172\pi$
$43$	0.0224065	−	0.0143998i	0.00341696	−	0.00219595i	0.542348	+	0.840154i	$0.317535\pi$
$44$	1.85273	−	2.13817i	0.279310	−	0.322341i
$45$	1.15865			0.172721
$46$	2.89675	+	3.82215i	0.427102	+	0.563546i
$47$	−7.99727			−1.16652			−0.583261	−	0.812285i	$-0.698224\pi$
$47$	−7.99727			−1.16652			−0.583261	+	0.812285i	$0.698224\pi$
$48$	1.33544	−	1.54118i	0.192754	−	0.222451i
$49$	2.91431	−	1.87291i	0.416330	−	0.267559i
$50$	0.142315	+	0.989821i	0.0201264	+	0.139982i
$51$	−2.83281	−	6.20298i	−0.396672	−	0.868592i
$52$	0.877230	−	6.10127i	0.121650	−	0.846093i
$53$	10.5990	−	3.11216i	1.45589	−	0.427488i	0.544406	−	0.838822i	$-0.316755\pi$
$53$	10.5990	−	3.11216i	1.45589	−	0.427488i	0.911485	+	0.411334i	$0.134937\pi$
$54$	−3.15893	−	2.03012i	−0.429875	−	0.276264i
$55$	−1.17529	+	2.57353i	−0.158476	+	0.347015i
$56$	−3.10381	−	0.911362i	−0.414765	−	0.121786i
$57$	9.96668	+	11.5022i	1.32012	+	1.52350i
$58$	−3.02010	−	3.48539i	−0.396559	−	0.457654i
$59$	0.649652	+	0.190755i	0.0845775	+	0.0248342i	0.323748	−	0.946144i	$-0.395057\pi$
$59$	0.649652	+	0.190755i	0.0845775	+	0.0248342i	−0.239170	+	0.970978i	$0.576875\pi$
$60$	−0.847146	+	1.85499i	−0.109366	+	0.239478i
$61$	1.17992	+	0.758288i	0.151073	+	0.0970888i	0.613994	−	0.789311i	$-0.289562\pi$
$61$	1.17992	+	0.758288i	0.151073	+	0.0970888i	−0.462920	+	0.886400i	$0.653198\pi$
$62$	−7.26484	+	2.13315i	−0.922636	+	0.270910i
$63$	0.533404	−	3.70991i	0.0672026	−	0.467404i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	0.877230	+	6.10127i	0.108807	+	0.756769i
$66$	−4.85363	+	3.11924i	−0.597441	+	0.383952i
$67$	6.56894	−	7.58097i	0.802524	−	0.926162i	−0.195993	−	0.980605i	$-0.562793\pi$
$67$	6.56894	−	7.58097i	0.802524	−	0.926162i	0.998517	+	0.0544429i	$0.0173383\pi$
$68$	3.34394			0.405513
$69$	−3.47204	−	9.14297i	−0.417984	−	1.10068i
$70$	3.23485			0.386638
$71$	0.633599	−	0.731212i	0.0751943	−	0.0867789i	−0.716906	−	0.697170i	$-0.754442\pi$
$71$	0.633599	−	0.731212i	0.0751943	−	0.0867789i	0.792100	+	0.610391i	$0.208988\pi$
$72$	−0.974718	+	0.626414i	−0.114872	+	0.0738235i
$73$	−0.492094	−	3.42259i	−0.0575953	−	0.400584i	−0.998143	−	0.0609213i	$-0.980596\pi$
$73$	−0.492094	−	3.42259i	−0.0575953	−	0.400584i	0.940547	−	0.339663i	$-0.110313\pi$
$74$	4.04484	+	8.85697i	0.470204	+	1.02960i
$75$	0.290219	−	2.01852i	0.0335116	−	0.233079i
$76$	−7.16090	+	2.10263i	−0.821411	+	0.241188i
$77$	7.69918	+	4.94796i	0.877403	+	0.563873i
$78$	−5.22182	+	11.4342i	−0.591254	+	1.29467i
$79$	−11.6597	−	3.42359i	−1.31182	−	0.385184i	−0.450283	−	0.892886i	$-0.648677\pi$
$79$	−11.6597	−	3.42359i	−1.31182	−	0.385184i	−0.861533	+	0.507702i	$0.830495\pi$
$80$	−0.654861	−	0.755750i	−0.0732157	−	0.0844954i
$81$	7.29088	+	8.41412i	0.810098	+	0.934903i
$82$	−2.10316	−	0.617544i	−0.232255	−	0.0681963i
$83$	0.439078	−	0.961447i	0.0481951	−	0.105532i	−0.884003	−	0.467482i	$-0.845161\pi$
$83$	0.439078	−	0.961447i	0.0481951	−	0.105532i	0.932198	+	0.361949i	$0.117889\pi$
$84$	5.54954	+	3.56647i	0.605505	+	0.389134i
$85$	−3.20849	+	0.942097i	−0.348009	+	0.102185i
$86$	0.00379051	−	0.0263636i	0.000408741	−	0.00284286i
$87$	3.90689	+	8.55490i	0.418863	+	0.917181i
$88$	−0.402637	−	2.80040i	−0.0429213	−	0.298524i
$89$	−8.63158	+	5.54718i	−0.914946	+	0.588000i	−0.911187	−	0.411993i	$-0.864833\pi$
$89$	−8.63158	+	5.54718i	−0.914946	+	0.588000i	−0.00375857	+	0.999993i	$0.501196\pi$
$90$	0.758754	−	0.875649i	0.0799797	−	0.0923015i
$91$	19.9396			2.09024
$92$	4.78556	+	0.313763i	0.498929	+	0.0327120i
$93$	15.4405			1.60110
$94$	−5.23710	+	6.04394i	−0.540166	+	0.623384i
$95$	6.27845	−	4.03492i	0.644155	−	0.413974i
$96$	−0.290219	−	2.01852i	−0.0296204	−	0.206014i
$97$	−6.28698	−	13.7666i	−0.638346	−	1.39778i	−0.901394	−	0.433000i	$-0.857455\pi$
$97$	−6.28698	−	13.7666i	−0.638346	−	1.39778i	0.263047	−	0.964783i	$-0.415272\pi$
$98$	0.493014	−	3.42899i	0.0498019	−	0.346380i
$99$	3.14527	−	0.923534i	0.316111	−	0.0928187i
$100$	0.841254	+	0.540641i	0.0841254	+	0.0540641i
$101$	−1.39034	+	3.04443i	−0.138344	+	0.302932i	−0.966105	−	0.258150i	$-0.916887\pi$
$101$	−1.39034	+	3.04443i	−0.138344	+	0.302932i	0.827761	+	0.561081i	$0.189615\pi$
$102$	−6.54300	−	1.92120i	−0.647853	−	0.190227i
$103$	−7.21601	−	8.32772i	−0.711014	−	0.820554i	0.279182	−	0.960238i	$-0.409937\pi$
$103$	−7.21601	−	8.32772i	−0.711014	−	0.820554i	−0.990196	+	0.139684i	$0.955391\pi$
$104$	−4.03657	−	4.65845i	−0.395818	−	0.456798i
$105$	−6.32954	−	1.85852i	−0.617700	−	0.181373i
$106$	4.58888	−	10.0483i	0.445712	−	0.975973i
$107$	−1.39394	−	0.895830i	−0.134757	−	0.0866031i	0.471525	−	0.881852i	$-0.343704\pi$
$107$	−1.39394	−	0.895830i	−0.134757	−	0.0866031i	−0.606282	+	0.795249i	$0.707340\pi$
$108$	−3.60292	+	1.05791i	−0.346691	+	0.101798i
$109$	0.254441	−	1.76968i	0.0243711	−	0.169505i	−0.974001	−	0.226544i	$-0.927257\pi$
$109$	0.254441	−	1.76968i	0.0243711	−	0.169505i	0.998372	+	0.0570399i	$0.0181662\pi$
$110$	1.17529	+	2.57353i	0.112060	+	0.245377i
$111$	−2.82583	−	19.6541i	−0.268216	−	1.86548i
$112$	−2.72133	+	1.74889i	−0.257141	+	0.165255i
$113$	−1.33332	+	1.53873i	−0.125428	+	0.144752i	−0.814990	−	0.579475i	$-0.803258\pi$
$113$	−1.33332	+	1.53873i	−0.125428	+	0.144752i	0.689562	+	0.724227i	$0.257803\pi$
$114$	15.2195			1.42544
$115$	−4.68011	+	1.04719i	−0.436422	+	0.0976514i
$116$	−4.61183			−0.428197
$117$	4.67697	−	5.39751i	0.432386	−	0.499000i
$118$	0.569595	−	0.366056i	0.0524354	−	0.0336982i
$119$	1.53944	+	10.7070i	0.141120	+	0.981513i
$120$	0.847146	+	1.85499i	0.0773335	+	0.169337i
$121$	0.426322	−	2.96514i	0.0387566	−	0.269558i
$122$	1.34576	−	0.395150i	0.121839	−	0.0357752i
$123$	3.76040	+	2.41666i	0.339064	+	0.217903i
$124$	−3.14533	+	6.88732i	−0.282459	+	0.618499i
$125$	−0.959493	−	0.281733i	−0.0858197	−	0.0251989i
$126$	−2.45446	−	2.83259i	−0.218660	−	0.252347i
$127$	10.1410	+	11.7033i	0.899865	+	1.03850i	0.999056	+	0.0434317i	$0.0138291\pi$
$127$	10.1410	+	11.7033i	0.899865	+	1.03850i	−0.0991910	+	0.995068i	$0.531625\pi$
$128$	0.959493	+	0.281733i	0.0848080	+	0.0249019i
$129$	−0.0225635	+	0.0494071i	−0.00198660	+	0.00435005i
$130$	5.18549	+	3.33251i	0.454798	+	0.292281i
$131$	−7.20709	+	2.11619i	−0.629686	+	0.184892i	−0.580976	−	0.813920i	$-0.697329\pi$
$131$	−7.20709	+	2.11619i	−0.629686	+	0.184892i	−0.0487097	+	0.998813i	$0.515511\pi$
$132$	−0.821089	+	5.71080i	−0.0714666	+	0.497061i
$133$	−10.0291	−	21.9607i	−0.869633	−	1.90423i
$134$	−1.42757	−	9.92895i	−0.123323	−	0.857731i
$135$	3.15893	−	2.03012i	0.271877	−	0.174725i
$136$	2.18982	−	2.52718i	0.187775	−	0.216704i
$137$	−6.34200			−0.541834			−0.270917	−	0.962603i	$-0.587327\pi$
$137$	−6.34200			−0.541834			−0.270917	+	0.962603i	$0.587327\pi$
$138$	−9.18350	−	3.36338i	−0.781751	−	0.286310i
$139$	14.4328			1.22418			0.612088	−	0.790790i	$-0.290330\pi$
$139$	14.4328			1.22418			0.612088	+	0.790790i	$0.290330\pi$
$140$	2.11838	−	2.44474i	0.179035	−	0.206618i
$141$	13.7197	−	8.81712i	1.15541	−	0.742536i
$142$	−0.137694	−	0.957684i	−0.0115550	−	0.0803670i
$143$	7.24451	+	15.8633i	0.605816	+	1.32655i
$144$	−0.164893	+	1.14686i	−0.0137411	+	0.0955714i
$145$	4.42502	−	1.29930i	0.367478	−	0.107901i
$146$	−2.90888	−	1.86942i	−0.240740	−	0.154714i
$147$	−2.93472	+	6.42615i	−0.242052	+	0.530020i
$148$	9.34246	+	2.74319i	0.767946	+	0.225489i
$149$	−3.01928	−	3.48443i	−0.247349	−	0.285456i	0.618475	−	0.785804i	$-0.287751\pi$
$149$	−3.01928	−	3.48443i	−0.247349	−	0.285456i	−0.865824	+	0.500348i	$0.833205\pi$
$150$	−1.33544	−	1.54118i	−0.109038	−	0.125837i
$151$	9.47907	+	2.78330i	0.771395	+	0.226502i	0.643666	−	0.765307i	$-0.277413\pi$
$151$	9.47907	+	2.78330i	0.771395	+	0.226502i	0.127730	+	0.991809i	$0.459231\pi$
$152$	−3.10033	+	6.78877i	−0.251470	+	0.550642i
$153$	3.25940	+	2.09469i	0.263507	+	0.169346i
$154$	8.78131	−	2.57843i	0.707618	−	0.207775i
$155$	1.07754	−	7.49447i	0.0865503	−	0.601971i
$156$	5.22182	+	11.4342i	0.418080	+	0.915467i
$157$	−1.84742	−	12.8491i	−0.147440	−	1.02547i	−0.920390	−	0.391001i	$-0.872129\pi$
$157$	−1.84742	−	12.8491i	−0.147440	−	1.02547i	0.772950	−	0.634467i	$-0.218780\pi$
$158$	−10.2228	+	6.56982i	−0.813285	+	0.522667i
$159$	−14.7520	+	17.0247i	−1.16991	+	1.35014i
$160$	−1.00000			−0.0790569
$161$	1.19847	+	15.4674i	0.0944526	+	1.21900i
$162$	11.1335			0.874729
$163$	−9.46528	+	10.9235i	−0.741378	+	0.855596i	−0.993703	−	0.112047i	$-0.964259\pi$
$163$	−9.46528	+	10.9235i	−0.741378	+	0.855596i	0.252325	+	0.967643i	$0.418805\pi$
$164$	−1.84399	+	1.18506i	−0.143991	+	0.0925375i
$165$	−0.821089	−	5.71080i	−0.0639217	−	0.444585i
$166$	−0.439078	−	0.961447i	−0.0340791	−	0.0746227i
$167$	−1.67500	+	11.6499i	−0.129616	+	0.901496i	0.816426	+	0.577450i	$0.195952\pi$
$167$	−1.67500	+	11.6499i	−0.129616	+	0.901496i	−0.946041	+	0.324046i	$0.894957\pi$
$168$	6.32954	−	1.85852i	0.488334	−	0.143388i
$169$	21.0271	+	13.5133i	1.61747	+	1.03949i
$170$	−1.38912	+	3.04176i	−0.106541	+	0.233292i
$171$	−8.29697	−	2.43621i	−0.634485	−	0.186302i
$172$	−0.0174420	−	0.0201292i	−0.00132994	−	0.00153483i
$173$	13.3783	+	15.4394i	1.01713	+	1.17383i	0.984682	+	0.174360i	$0.0557856\pi$
$173$	13.3783	+	15.4394i	1.01713	+	1.17383i	0.0324503	+	0.999473i	$0.489669\pi$
$174$	9.02383	+	2.64964i	0.684095	+	0.200868i
$175$	−1.34380	+	2.94252i	−0.101582	+	0.222434i
$176$	−2.38007	−	1.52958i	−0.179405	−	0.115297i
$177$	−1.32482	+	0.389002i	−0.0995796	+	0.0292392i
$178$	−1.46020	+	10.1559i	−0.109447	+	0.761220i
$179$	−3.83268	−	8.39240i	−0.286468	−	0.627278i	0.710617	−	0.703579i	$-0.248416\pi$
$179$	−3.83268	−	8.39240i	−0.286468	−	0.627278i	−0.997085	+	0.0763018i	$0.975689\pi$
$180$	−0.164893	−	1.14686i	−0.0122904	−	0.0854816i
$181$	5.43140	−	3.49055i	0.403713	−	0.259451i	−0.322990	−	0.946402i	$-0.604688\pi$
$181$	5.43140	−	3.49055i	0.403713	−	0.259451i	0.726703	+	0.686952i	$0.241052\pi$
$182$	13.0577	−	15.0694i	0.967900	−	1.11702i
$183$	−2.86023			−0.211435
$184$	3.37100	−	3.41121i	0.248513	−	0.251478i
$185$	−9.73688			−0.715869
$186$	10.1114	−	11.6691i	0.741401	−	0.855622i
$187$	−7.95883	+	5.11483i	−0.582007	+	0.374033i
$188$	1.13813	+	7.91587i	0.0830067	+	0.577324i
$189$	−5.04602	−	11.0492i	−0.367044	−	0.803714i
$190$	1.06213	−	7.38724i	0.0770547	−	0.535927i
$191$	5.34096	−	1.56825i	0.386458	−	0.113474i	−0.0827312	−	0.996572i	$-0.526364\pi$
$191$	5.34096	−	1.56825i	0.386458	−	0.113474i	0.469190	+	0.883097i	$0.344546\pi$
$192$	−1.71555	−	1.10252i	−0.123809	−	0.0795673i
$193$	−7.74158	+	16.9517i	−0.557251	+	1.22021i	0.396062	+	0.918224i	$0.370377\pi$
$193$	−7.74158	+	16.9517i	−0.557251	+	1.22021i	−0.953313	+	0.301985i	$0.902351\pi$
$194$	−14.5212	−	4.26380i	−1.04256	−	0.306123i
$195$	−8.23168	−	9.49986i	−0.589483	−	0.680299i
$196$	−2.26860	−	2.61810i	−0.162043	−	0.187007i
$197$	−25.0109	−	7.34385i	−1.78195	−	0.523228i	−0.786421	−	0.617690i	$-0.788069\pi$
$197$	−25.0109	−	7.34385i	−1.78195	−	0.523228i	−0.995528	+	0.0944627i	$0.969887\pi$
$198$	1.36175	−	2.98182i	0.0967755	−	0.211909i
$199$	−13.4631	−	8.65219i	−0.954372	−	0.613337i	−0.0319366	−	0.999490i	$-0.510167\pi$
$199$	−13.4631	−	8.65219i	−0.954372	−	0.613337i	−0.922435	+	0.386153i	$0.873804\pi$
$200$	0.959493	−	0.281733i	0.0678464	−	0.0199215i
$201$	−2.91121	+	20.2479i	−0.205341	+	1.42818i
$202$	1.39034	+	3.04443i	0.0978242	+	0.214205i
$203$	−2.12313	−	14.7667i	−0.149015	−	1.03642i
$204$	−5.73670	+	3.68675i	−0.401649	+	0.258124i
$205$	1.43542	−	1.65657i	0.100254	−	0.115700i
$206$	−11.0192			−0.767741
$207$	4.46803	+	3.30357i	0.310549	+	0.229614i
$208$	−6.16401			−0.427397
$209$	13.8273	−	15.9576i	0.956456	−	1.10381i
$210$	−5.54954	+	3.56647i	−0.382955	+	0.246110i
$211$	−0.713636	−	4.96344i	−0.0491287	−	0.341698i	−0.999530	−	0.0306700i	$-0.990236\pi$
$211$	−0.713636	−	4.96344i	−0.0491287	−	0.341698i	0.950401	−	0.311028i	$-0.100673\pi$
$212$	−4.58888	−	10.0483i	−0.315166	−	0.690117i
$213$	−0.280796	+	1.95298i	−0.0192399	+	0.133816i
$214$	−1.58986	+	0.466824i	−0.108680	+	0.0319115i
$215$	0.0224065	+	0.0143998i	0.00152811	+	0.000982058i
$216$	−1.55989	+	3.41569i	−0.106137	+	0.232408i
$217$	−23.5007	−	6.90042i	−1.59533	−	0.468431i
$218$	−1.17081	−	1.35119i	−0.0792973	−	0.0915140i
$219$	4.61768	+	5.32908i	0.312034	+	0.360106i
$220$	2.71460	+	0.797078i	0.183018	+	0.0537390i
$221$	−8.56257	+	18.7494i	−0.575981	+	1.26122i
$222$	−16.7041	−	10.7351i	−1.12110	−	0.720490i
$223$	3.97269	−	1.16649i	0.266031	−	0.0781137i	−0.145997	−	0.989285i	$-0.546639\pi$
$223$	3.97269	−	1.16649i	0.266031	−	0.0781137i	0.412028	+	0.911171i	$0.364821\pi$
$224$	−0.460367	+	3.20192i	−0.0307596	+	0.213937i
$225$	0.481321	+	1.05395i	0.0320880	+	0.0702630i
$226$	0.289758	+	2.01531i	0.0192744	+	0.134057i
$227$	−5.47854	+	3.52085i	−0.363624	+	0.233687i	−0.709676	−	0.704529i	$-0.751158\pi$
$227$	−5.47854	+	3.52085i	−0.363624	+	0.233687i	0.346052	+	0.938215i	$0.387522\pi$
$228$	9.96668	−	11.5022i	0.660060	−	0.761750i
$229$	3.15078			0.208209			0.104105	−	0.994566i	$-0.466802\pi$
$229$	3.15078			0.208209			0.104105	+	0.994566i	$0.466802\pi$
$230$	−2.27340	+	4.22275i	−0.149904	+	0.278440i
$231$	−18.6635			−1.22797
$232$	−3.02010	+	3.48539i	−0.198280	+	0.228827i
$233$	−1.28899	+	0.828387i	−0.0844448	+	0.0542694i	−0.582182	−	0.813059i	$-0.697801\pi$
$233$	−1.28899	+	0.828387i	−0.0844448	+	0.0542694i	0.497737	+	0.867328i	$0.334164\pi$
$234$	−1.01640	−	7.06923i	−0.0664443	−	0.462130i
$235$	−3.32219	−	7.27457i	−0.216716	−	0.474541i
$236$	0.0963583	−	0.670187i	0.00627239	−	0.0436254i
$237$	23.7773	−	6.98165i	1.54450	−	0.453507i
$238$	9.09996	+	5.84819i	0.589863	+	0.379082i
$239$	3.83962	−	8.40760i	0.248364	−	0.543842i	−0.743855	−	0.668341i	$-0.767005\pi$
$239$	3.83962	−	8.40760i	0.248364	−	0.543842i	0.992220	+	0.124498i	$0.0397321\pi$
$240$	1.95667	+	0.574531i	0.126303	+	0.0370858i
$241$	−6.14550	−	7.09229i	−0.395867	−	0.456854i	0.522468	−	0.852659i	$-0.325011\pi$
$241$	−6.14550	−	7.09229i	−0.395867	−	0.456854i	−0.918335	+	0.395804i	$0.870466\pi$
$242$	−1.96172	−	2.26394i	−0.126104	−	0.145532i
$243$	−10.9758	−	3.22279i	−0.704099	−	0.206742i
$244$	0.582650	−	1.27582i	0.0373003	−	0.0816763i
$245$	2.91431	+	1.87291i	0.186188	+	0.119656i
$246$	4.28893	−	1.25934i	0.273452	−	0.0802928i
$247$	6.54695	−	45.5350i	0.416572	−	2.89732i
$248$	3.14533	+	6.88732i	0.199729	+	0.437345i
$249$	0.306751	+	2.13350i	0.0194396	+	0.135205i
$250$	−0.841254	+	0.540641i	−0.0532055	+	0.0341931i
$251$	−11.8690	+	13.6975i	−0.749162	+	0.864579i	−0.994487	−	0.104862i	$-0.966560\pi$
$251$	−11.8690	+	13.6975i	−0.749162	+	0.864579i	0.245325	+	0.969441i	$0.421105\pi$
$252$	−3.74806			−0.236105
$253$	−11.8699	+	6.57312i	−0.746255	+	0.413248i
$254$	15.4857			0.971658
$255$	4.46564	−	5.15363i	0.279649	−	0.322733i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	−1.94984	−	13.5614i	−0.121628	−	0.845938i	−0.955712	−	0.294302i	$-0.904913\pi$
$257$	−1.94984	−	13.5614i	−0.121628	−	0.845938i	0.834085	−	0.551636i	$-0.185996\pi$
$258$	0.0225635	+	0.0494071i	0.00140474	+	0.00307595i
$259$	−4.48254	+	31.1767i	−0.278531	+	1.93723i
$260$	5.91432	−	1.73660i	0.366791	−	0.107699i
$261$	−4.49523	−	2.88891i	−0.278248	−	0.178819i
$262$	−3.12033	+	6.83256i	−0.192774	+	0.422117i
$263$	23.8221	+	6.99480i	1.46893	+	0.431318i	0.915752	−	0.401744i	$-0.131596\pi$
$263$	23.8221	+	6.99480i	1.46893	+	0.431318i	0.553181	+	0.833061i	$0.313414\pi$
$264$	3.77823	+	4.36031i	0.232534	+	0.268359i
$265$	7.23392	+	8.34839i	0.444376	+	0.512838i
$266$	−23.1644	−	6.80169i	−1.42030	−	0.417038i
$267$	8.69204	−	19.0329i	0.531944	−	1.16480i
$268$	−8.43866	−	5.42320i	−0.515473	−	0.331275i
$269$	−5.23960	+	1.53848i	−0.319464	+	0.0938030i	−0.437533	−	0.899202i	$-0.644148\pi$
$269$	−5.23960	+	1.53848i	−0.319464	+	0.0938030i	0.118069	+	0.993005i	$0.462330\pi$
$270$	0.534395	−	3.71680i	0.0325223	−	0.226197i
$271$	10.4409	+	22.8623i	0.634238	+	1.38879i	0.904697	+	0.426056i	$0.140097\pi$
$271$	10.4409	+	22.8623i	0.634238	+	1.38879i	−0.270459	+	0.962732i	$0.587175\pi$
$272$	−0.475893	−	3.30991i	−0.0288552	−	0.200693i
$273$	−34.2074	+	21.9838i	−2.07033	+	1.33052i
$274$	−4.15313	+	4.79297i	−0.250900	+	0.289554i
$275$	−2.82920			−0.170607
$276$	−8.55578	+	4.73788i	−0.514998	+	0.285187i
$277$	−7.77758			−0.467309			−0.233655	−	0.972320i	$-0.575069\pi$
$277$	−7.77758			−0.467309			−0.233655	+	0.972320i	$0.575069\pi$
$278$	9.45148	−	10.9076i	0.566862	−	0.654194i
$279$	−7.38012	+	4.74292i	−0.441836	+	0.283951i
$280$	−0.460367	−	3.20192i	−0.0275122	−	0.191351i
$281$	3.73349	+	8.17520i	0.222721	+	0.487692i	0.987699	−	0.156365i	$-0.0499775\pi$
$281$	3.73349	+	8.17520i	0.222721	+	0.487692i	−0.764978	+	0.644056i	$0.777250\pi$
$282$	2.32096	−	16.1427i	0.138211	−	0.961281i
$283$	4.93858	−	1.45010i	0.293568	−	0.0861994i	−0.131632	−	0.991299i	$-0.542022\pi$
$283$	4.93858	−	1.45010i	0.293568	−	0.0861994i	0.425200	+	0.905099i	$0.360204\pi$
$284$	−0.813939	−	0.523087i	−0.0482984	−	0.0310395i
$285$	−6.32243	+	13.8442i	−0.374508	+	0.820059i
$286$	16.7328	+	4.91319i	0.989431	+	0.290523i
$287$	−4.64337	−	5.35874i	−0.274090	−	0.316316i
$288$	0.758754	+	0.875649i	0.0447100	+	0.0515981i
$289$	5.58238	+	1.63913i	0.328375	+	0.0964197i
$290$	1.91582	−	4.19507i	0.112501	−	0.246343i
$291$	25.9635	+	16.6857i	1.52201	+	0.978134i
$292$	−3.31772	+	0.974171i	−0.194155	+	0.0570091i
$293$	4.60464	−	32.0259i	0.269006	−	1.87098i	−0.188930	−	0.981991i	$-0.560502\pi$
$293$	4.60464	−	32.0259i	0.269006	−	1.87098i	0.457936	−	0.888985i	$-0.348589\pi$
$294$	2.93472	+	6.42615i	0.171157	+	0.374781i
$295$	0.0963583	+	0.670187i	0.00561020	+	0.0390198i
$296$	8.19118	−	5.26415i	0.476103	−	0.305973i
$297$	6.95705	−	8.02886i	0.403689	−	0.465882i
$298$	−4.61057			−0.267083
$299$	−14.0133	+	26.0291i	−0.810408	+	1.50530i
$300$	−2.03928			−0.117738
$301$	0.0564223	−	0.0651148i	0.00325213	−	0.00375315i
$302$	8.31095	−	5.34112i	0.478241	−	0.307347i
$303$	−0.971329	−	6.75574i	−0.0558014	−	0.388107i
$304$	3.10033	+	6.78877i	0.177816	+	0.389363i
$305$	−0.199607	+	1.38830i	−0.0114295	+	0.0794936i
$306$	3.71752	−	1.09156i	0.212516	−	0.0624004i
$307$	17.5984	+	11.3098i	1.00439	+	0.645485i	0.935936	−	0.352169i	$-0.114556\pi$
$307$	17.5984	+	11.3098i	1.00439	+	0.645485i	0.0684578	+	0.997654i	$0.478192\pi$
$308$	3.80189	−	8.32498i	0.216633	−	0.474360i
$309$	21.5609	+	6.33084i	1.22655	+	0.360149i
$310$	−4.95831	−	5.72219i	−0.281613	−	0.324998i
$311$	−21.4065	−	24.7044i	−1.21385	−	1.40086i	−0.890750	−	0.454494i	$-0.849820\pi$
$311$	−21.4065	−	24.7044i	−1.21385	−	1.40086i	−0.323101	−	0.946365i	$-0.604725\pi$
$312$	12.0609	+	3.54141i	0.682816	+	0.200493i
$313$	5.48394	−	12.0082i	0.309971	−	0.678741i	−0.688968	−	0.724791i	$-0.741936\pi$
$313$	5.48394	−	12.0082i	0.309971	−	0.678741i	0.998939	+	0.0460501i	$0.0146634\pi$
$314$	−10.9205	−	7.01817i	−0.616278	−	0.396058i
$315$	3.59624	−	1.05595i	0.202625	−	0.0594960i
$316$	−1.72940	+	12.0282i	−0.0972862	+	0.676640i
$317$	8.25259	+	18.0706i	0.463512	+	1.01495i	0.986673	+	0.162715i	$0.0520252\pi$
$317$	8.25259	+	18.0706i	0.463512	+	1.01495i	−0.523162	+	0.852234i	$0.675248\pi$
$318$	3.20591	+	22.2976i	0.179778	+	1.25039i
$319$	10.9765	−	7.05416i	0.614566	−	0.394957i
$320$	−0.654861	+	0.755750i	−0.0366078	+	0.0422477i
$321$	3.37904			0.188599
$322$	12.4743	+	9.22327i	0.695167	+	0.513993i
$323$	24.9565			1.38862
$324$	7.29088	−	8.41412i	0.405049	−	0.467451i
$325$	−5.18549	+	3.33251i	−0.287639	+	0.184855i
$326$	2.05700	+	14.3068i	0.113927	+	0.792379i
$327$	1.51459	+	3.31650i	0.0837572	+	0.183403i
$328$	−0.311947	+	2.16964i	−0.0172244	+	0.119798i
$329$	−24.8221	+	7.28841i	−1.36848	+	0.401823i
$330$	−4.85363	−	3.11924i	−0.267184	−	0.171708i
$331$	2.13156	−	4.66748i	0.117161	−	0.256548i	−0.841961	−	0.539538i	$-0.818599\pi$
$331$	2.13156	−	4.66748i	0.117161	−	0.256548i	0.959123	+	0.282990i	$0.0913263\pi$
$332$	−1.01415	−	0.297781i	−0.0556586	−	0.0163428i
$333$	7.38790	+	8.52609i	0.404854	+	0.467227i
$334$	7.70751	+	8.89494i	0.421736	+	0.486710i
$335$	9.62473	+	2.82608i	0.525855	+	0.154405i
$336$	2.74039	−	6.00062i	0.149501	−	0.327360i
$337$	23.9639	+	15.4007i	1.30540	+	0.838927i	0.993789	−	0.111284i	$-0.0354962\pi$
$337$	23.9639	+	15.4007i	1.30540	+	0.838927i	0.311608	+	0.950211i	$0.399133\pi$
$338$	23.9825	−	7.04190i	1.30448	−	0.383029i
$339$	0.590897	−	4.10978i	0.0320931	−	0.223213i
$340$	1.38912	+	3.04176i	0.0753358	+	0.164962i
$341$	−3.04858	−	21.2034i	−0.165090	−	1.14823i
$342$	−7.27453	+	4.67505i	−0.393361	+	0.252798i
$343$	−7.49005	+	8.64398i	−0.404425	+	0.466731i
$344$	−0.0266347			−0.00143605
$345$	6.87440	−	6.95641i	0.370105	−	0.374520i
$346$	20.4292			1.09828
$347$	−22.3434	+	25.7857i	−1.19946	+	1.38425i	−0.296215	+	0.955121i	$0.595725\pi$
$347$	−22.3434	+	25.7857i	−1.19946	+	1.38425i	−0.903244	+	0.429128i	$0.858821\pi$
$348$	7.91181	−	5.08461i	0.424118	−	0.272564i
$349$	2.75999	+	19.1961i	0.147739	+	1.02755i	0.919910	+	0.392130i	$0.128262\pi$
$349$	2.75999	+	19.1961i	0.147739	+	1.02755i	−0.772171	+	0.635415i	$0.780829\pi$
$350$	1.34380	+	2.94252i	0.0718294	+	0.157284i
$351$	3.29402	−	22.9104i	0.175822	−	1.22287i
$352$	−2.71460	+	0.797078i	−0.144689	+	0.0424844i
$353$	14.2242	+	9.14131i	0.757075	+	0.486543i	0.861354	−	0.508005i	$-0.169617\pi$
$353$	14.2242	+	9.14131i	0.757075	+	0.486543i	−0.104279	+	0.994548i	$0.533253\pi$
$354$	−0.573584	+	1.25597i	−0.0304857	+	0.0667543i
$355$	0.928340	+	0.272585i	0.0492712	+	0.0144673i
$356$	6.71912	+	7.75428i	0.356113	+	0.410976i
$357$	−14.4457	−	16.6712i	−0.764546	−	0.882333i
$358$	−8.85243	−	2.59931i	−0.467865	−	0.137378i
$359$	9.78634	−	21.4291i	0.516503	−	1.13098i	−0.454243	−	0.890878i	$-0.650090\pi$
$359$	9.78634	−	21.4291i	0.516503	−	1.13098i	0.970746	−	0.240107i	$-0.0771825\pi$
$360$	−0.974718	−	0.626414i	−0.0513722	−	0.0330149i
$361$	−35.2129	+	10.3394i	−1.85331	+	0.544181i
$362$	0.918830	−	6.39061i	0.0482927	−	0.335883i
$363$	2.53773	+	5.55686i	0.133197	+	0.291660i
$364$	−2.83771	−	19.7367i	−0.148736	−	1.03448i
$365$	2.90888	−	1.86942i	0.152258	−	0.0978500i
$366$	−1.87305	+	2.16162i	−0.0979061	+	0.112990i
$367$	−4.67596			−0.244083			−0.122041	−	0.992525i	$-0.538944\pi$
$367$	−4.67596			−0.244083			−0.122041	+	0.992525i	$0.538944\pi$
$368$	−0.370487	−	4.78150i	−0.0193130	−	0.249253i
$369$	−2.53970			−0.132212
$370$	−6.37630	+	7.35864i	−0.331488	+	0.382557i
$371$	30.0612	−	19.3191i	1.56070	−	1.00300i
$372$	−2.19741	−	15.2833i	−0.113930	−	0.792403i
$373$	−3.12140	−	6.83490i	−0.161620	−	0.353898i	0.811445	−	0.584428i	$-0.198681\pi$
$373$	−3.12140	−	6.83490i	−0.161620	−	0.353898i	−0.973065	+	0.230530i	$0.925954\pi$
$374$	−1.34640	+	9.36439i	−0.0696204	+	0.484221i
$375$	1.95667	−	0.574531i	0.101042	−	0.0296686i
$376$	6.72773	+	4.32365i	0.346956	+	0.222975i
$377$	11.8091	−	25.8584i	0.608202	−	1.33178i
$378$	−11.6549	−	3.42219i	−0.599463	−	0.176018i
$379$	18.8077	+	21.7052i	0.966086	+	1.11492i	0.993331	+	0.115294i	$0.0367811\pi$
$379$	18.8077	+	21.7052i	0.966086	+	1.11492i	−0.0272451	+	0.999629i	$0.508673\pi$
$380$	−4.88736	−	5.64032i	−0.250716	−	0.289342i
$381$	−30.3004	−	8.89700i	−1.55234	−	0.455807i
$382$	2.31238	−	5.06341i	0.118312	−	0.259067i
$383$	14.4427	+	9.28176i	0.737988	+	0.474276i	0.854852	−	0.518872i	$-0.173648\pi$
$383$	14.4427	+	9.28176i	0.737988	+	0.474276i	−0.116864	+	0.993148i	$0.537284\pi$
$384$	−1.95667	+	0.574531i	−0.0998510	+	0.0293189i
$385$	−1.30247	+	9.05888i	−0.0663800	+	0.461683i
$386$	7.74158	+	16.9517i	0.394036	+	0.862818i
$387$	−0.00439188	−	0.0305462i	−0.000223252	−	0.00155275i
$388$	−12.7317	+	8.18218i	−0.646355	+	0.415387i
$389$	5.00364	−	5.77451i	0.253694	−	0.292779i	−0.614589	−	0.788848i	$-0.710678\pi$
$389$	5.00364	−	5.77451i	0.253694	−	0.292779i	0.868283	+	0.496069i	$0.165224\pi$
$390$	−12.5701			−0.636513
$391$	−15.0588	−	5.51516i	−0.761557	−	0.278914i
$392$	−3.46425			−0.174971
$393$	10.0310	−	11.5764i	0.505996	−	0.583950i
$394$	−21.9287	+	14.0927i	−1.10475	+	0.709982i
$395$	−1.72940	−	12.0282i	−0.0870154	−	0.605206i
$396$	−1.36175	−	2.98182i	−0.0684306	−	0.149842i
$397$	4.17402	−	29.0309i	0.209488	−	1.45702i	−0.565345	−	0.824855i	$-0.691257\pi$
$397$	4.17402	−	29.0309i	0.209488	−	1.45702i	0.774833	−	0.632167i	$-0.217834\pi$
$398$	−15.3553	+	4.50873i	−0.769693	+	0.226002i
$399$	41.4174	+	26.6173i	2.07346	+	1.33253i
$400$	0.415415	−	0.909632i	0.0207708	−	0.0454816i
$401$	16.6370	+	4.88505i	0.830810	+	0.243948i	0.669365	−	0.742934i	$-0.266566\pi$
$401$	16.6370	+	4.88505i	0.830810	+	0.243948i	0.161445	+	0.986882i	$0.448385\pi$
$402$	13.3959	+	15.4597i	0.668127	+	0.771059i
$403$	−30.5630	−	35.2716i	−1.52245	−	1.75700i
$404$	3.21131	+	0.942925i	0.159768	+	0.0469123i
$405$	−4.62501	+	10.1274i	−0.229819	+	0.503233i
$406$	−12.5503	−	8.06558i	−0.622861	−	0.400288i
$407$	−26.4317	+	7.76105i	−1.31017	+	0.384701i
$408$	−0.970477	+	6.74981i	−0.0480458	+	0.334166i
$409$	−3.28957	−	7.20315i	−0.162659	−	0.356173i	0.810700	−	0.585462i	$-0.199087\pi$
$409$	−3.28957	−	7.20315i	−0.162659	−	0.356173i	−0.973358	+	0.229290i	$0.926360\pi$
$410$	−0.311947	−	2.16964i	−0.0154060	−	0.107151i
$411$	10.8800	−	6.99216i	0.536672	−	0.344898i
$412$	−7.21601	+	8.32772i	−0.355507	+	0.410277i
$413$	2.19025			0.107775
$414$	5.42260	−	1.21333i	0.266506	−	0.0596320i
$415$	1.05696			0.0518842
$416$	−4.03657	+	4.65845i	−0.197909	+	0.228399i
$417$	−24.7602	+	15.9124i	−1.21251	+	0.779234i
$418$	−3.00496	−	20.9000i	−0.146978	−	1.02225i
$419$	−1.24563	−	2.72754i	−0.0608528	−	0.133249i	0.876762	−	0.480924i	$-0.159699\pi$
$419$	−1.24563	−	2.72754i	−0.0608528	−	0.133249i	−0.937615	+	0.347675i	$0.886971\pi$
$420$	−0.938816	+	6.52961i	−0.0458095	+	0.318612i
$421$	11.3990	−	3.34704i	0.555552	−	0.163125i	0.00810798	−	0.999967i	$-0.497419\pi$
$421$	11.3990	−	3.34704i	0.555552	−	0.163125i	0.547444	+	0.836842i	$0.315601\pi$
$422$	−4.21845	−	2.71103i	−0.205351	−	0.131971i
$423$	−3.84925	+	8.42869i	−0.187157	+	0.409817i
$424$	−10.5990	−	3.11216i	−0.514735	−	0.151140i
$425$	−2.18982	−	2.52718i	−0.106222	−	0.122586i
$426$	1.29208	+	1.49114i	0.0626016	+	0.0722461i
$427$	4.35332	+	1.27825i	0.210672	+	0.0618589i
$428$	−0.688333	+	1.50724i	−0.0332718	+	0.0728552i
$429$	−29.9178	−	19.2270i	−1.44445	−	0.928289i
$430$	0.0255558	−	0.00750386i	0.00123241	−	0.000361868i
$431$	1.65762	−	11.5290i	0.0798450	−	0.555334i	−0.910155	−	0.414268i	$-0.864038\pi$
$431$	1.65762	−	11.5290i	0.0798450	−	0.555334i	0.990000	−	0.141066i	$-0.0450531\pi$
$432$	1.55989	+	3.41569i	0.0750504	+	0.164337i
$433$	−2.08236	−	14.4831i	−0.100072	−	0.696015i	−0.976663	−	0.214779i	$-0.931097\pi$
$433$	−2.08236	−	14.4831i	−0.100072	−	0.696015i	0.876591	−	0.481236i	$-0.159812\pi$
$434$	−20.6046	+	13.2418i	−0.989055	+	0.635627i
$435$	−6.15883	+	7.10767i	−0.295293	+	0.340787i
$436$	−1.78788			−0.0856238
$437$	35.7156	+	2.34167i	1.70851	+	0.112018i
$438$	7.05139			0.336928
$439$	15.7201	−	18.1419i	0.750279	−	0.865868i	−0.244317	−	0.969696i	$-0.578564\pi$
$439$	15.7201	−	18.1419i	0.750279	−	0.865868i	0.994595	+	0.103828i	$0.0331091\pi$
$440$	2.38007	−	1.52958i	0.113466	−	0.0729199i
$441$	−0.571230	−	3.97300i	−0.0272014	−	0.189190i
$442$	8.56257	+	18.7494i	0.407280	+	0.891819i
$443$	−4.10524	+	28.5526i	−0.195046	+	1.35657i	0.623361	+	0.781934i	$0.285767\pi$
$443$	−4.10524	+	28.5526i	−0.195046	+	1.35657i	−0.818407	+	0.574639i	$0.805142\pi$
$444$	−19.0519	+	5.59413i	−0.904162	+	0.265486i
$445$	−8.63158	−	5.54718i	−0.409176	−	0.262961i
$446$	1.71999	−	3.76624i	0.0814437	−	0.178337i
$447$	9.02137	+	2.64891i	0.426696	+	0.125289i
$448$	2.11838	+	2.44474i	0.100084	+	0.115503i
$449$	4.98964	+	5.75835i	0.235476	+	0.271753i	0.861172	−	0.508313i	$-0.169731\pi$
$449$	4.98964	+	5.75835i	0.235476	+	0.271753i	−0.625697	+	0.780066i	$0.715185\pi$
$450$	1.11172	+	0.326429i	0.0524068	+	0.0153880i
$451$	2.57618	−	5.64105i	0.121308	−	0.265627i
$452$	1.71282	+	1.10076i	0.0805644	+	0.0517756i
$453$	−19.3304	+	5.67593i	−0.908223	+	0.266678i
$454$	−0.926805	+	6.44607i	−0.0434971	+	0.302529i
$455$	8.28322	+	18.1377i	0.388323	+	0.850310i
$456$	−2.16597	−	15.0646i	−0.101431	−	0.705466i
$457$	−8.90307	+	5.72166i	−0.416468	+	0.267648i	−0.732050	−	0.681250i	$-0.761436\pi$
$457$	−8.90307	+	5.72166i	−0.416468	+	0.267648i	0.315582	+	0.948898i	$0.397800\pi$
$458$	2.06332	−	2.38120i	0.0964127	−	0.111266i
$459$	12.5566			0.586091
$460$	1.70258	+	4.48344i	0.0793834	+	0.209041i
$461$	34.2388			1.59466			0.797331	−	0.603543i	$-0.206245\pi$
$461$	34.2388			1.59466			0.797331	+	0.603543i	$0.206245\pi$
$462$	−12.2220	+	14.1050i	−0.568620	+	0.656222i
$463$	6.39192	−	4.10784i	0.297058	−	0.190907i	−0.383619	−	0.923492i	$-0.625322\pi$
$463$	6.39192	−	4.10784i	0.297058	−	0.190907i	0.680677	+	0.732584i	$0.261686\pi$
$464$	0.656331	+	4.56488i	0.0304694	+	0.211919i
$465$	6.41420	+	14.0451i	0.297452	+	0.651328i
$466$	−0.218059	+	1.51663i	−0.0101014	+	0.0702568i
$467$	−6.60384	+	1.93906i	−0.305589	+	0.0897291i	−0.430932	−	0.902384i	$-0.641815\pi$
$467$	−6.60384	+	1.93906i	−0.305589	+	0.0897291i	0.125343	+	0.992114i	$0.459997\pi$
$468$	−6.00817	−	3.86122i	−0.277728	−	0.178485i
$469$	13.4798	−	29.5166i	0.622438	−	1.36295i
$470$	−7.67333	−	2.25309i	−0.353944	−	0.103927i
$471$	17.3356	+	20.0064i	0.798784	+	0.921846i
$472$	−0.443392	−	0.511702i	−0.0204088	−	0.0235530i
$473$	0.0723024	+	0.0212299i	0.00332447	+	0.000976152i
$474$	10.2944	−	22.5417i	0.472840	−	1.03537i
$475$	6.27845	+	4.03492i	0.288075	+	0.185135i
$476$	10.3790	−	3.04754i	0.475720	−	0.139684i
$477$	1.82149	−	12.6688i	0.0834004	−	0.580062i
$478$	−3.83962	−	8.40760i	−0.175620	−	0.384555i
$479$	3.21639	+	22.3705i	0.146961	+	1.02213i	0.921158	+	0.389189i	$0.127245\pi$
$479$	3.21639	+	22.3705i	0.146961	+	1.02213i	−0.774197	+	0.632944i	$0.781846\pi$
$480$	1.71555	−	1.10252i	0.0783037	−	0.0503228i
$481$	−39.3035	+	45.3587i	−1.79209	+	2.06818i
$482$	−9.38444			−0.427450
$483$	−19.1091	−	25.2138i	−0.869495	−	1.14727i
$484$	−2.99563			−0.136165
$485$	9.91081	−	11.4377i	0.450026	−	0.519358i
$486$	−9.62325	+	6.18449i	−0.436520	+	0.280534i
$487$	5.25186	+	36.5275i	0.237985	+	1.65522i	0.661956	+	0.749543i	$0.269727\pi$
$487$	5.25186	+	36.5275i	0.237985	+	1.65522i	−0.423971	+	0.905676i	$0.639364\pi$
$488$	−0.582650	−	1.27582i	−0.0263753	−	0.0577539i
$489$	4.19480	−	29.1755i	0.189695	−	1.31936i
$490$	3.32392	−	0.975991i	0.150159	−	0.0440908i
$491$	−10.1453	−	6.52000i	−0.457852	−	0.294244i	0.291312	−	0.956628i	$-0.405908\pi$
$491$	−10.1453	−	6.52000i	−0.457852	−	0.294244i	−0.749164	+	0.662385i	$0.769545\pi$
$492$	1.85690	−	4.06605i	0.0837156	−	0.183312i
$493$	14.7970	+	4.34479i	0.666423	+	0.195679i
$494$	−30.1257	−	34.7670i	−1.35542	−	1.56424i
$495$	2.14667	+	2.47739i	0.0964856	+	0.111350i
$496$	7.26484	+	2.13315i	0.326201	+	0.0957812i
$497$	1.30017	−	2.84698i	0.0583208	−	0.127705i
$498$	1.81327	+	1.16532i	0.0812546	+	0.0522192i
$499$	3.57477	−	1.04965i	0.160029	−	0.0469887i	−0.200737	−	0.979645i	$-0.564334\pi$
$499$	3.57477	−	1.04965i	0.160029	−	0.0469887i	0.360766	+	0.932656i	$0.382515\pi$
$500$	−0.142315	+	0.989821i	−0.00636451	+	0.0442662i
$501$	−9.97065	−	21.8327i	−0.445456	−	0.975412i
$502$	2.57937	+	17.9399i	0.115123	+	0.800698i
$503$	10.3678	−	6.66295i	0.462275	−	0.297086i	−0.288696	−	0.957421i	$-0.593222\pi$
$503$	10.3678	−	6.66295i	0.462275	−	0.297086i	0.750972	+	0.660334i	$0.229585\pi$
$504$	−2.45446	+	2.83259i	−0.109330	+	0.126174i
$505$	−3.34688			−0.148934
$506$	−2.80550	+	13.2752i	−0.124720	+	0.590153i
$507$	−50.9717			−2.26373
$508$	10.1410	−	11.7033i	0.449933	−	0.519250i
$509$	1.48354	−	0.953413i	0.0657568	−	0.0422593i	−0.507349	−	0.861740i	$-0.669375\pi$
$509$	1.48354	−	0.953413i	0.0657568	−	0.0422593i	0.573106	+	0.819481i	$0.305738\pi$
$510$	−0.970477	−	6.74981i	−0.0429734	−	0.298887i
$511$	−4.64659	−	10.1746i	−0.205553	−	0.450099i
$512$	0.142315	−	0.989821i	0.00628949	−	0.0437443i
$513$	−26.8893	+	7.89542i	−1.18719	+	0.348591i
$514$	−11.5259	−	7.40725i	−0.508386	−	0.326720i
$515$	4.57752	−	10.0234i	0.201710	−	0.441683i
$516$	0.0521153	+	0.0153024i	0.00229425	+	0.000673652i
$517$	−14.8168	−	17.0995i	−0.651642	−	0.752035i
$518$	20.6264	+	23.8041i	0.906270	+	1.04589i
$519$	−39.9733	−	11.7372i	−1.75463	−	0.515206i
$520$	2.56062	−	5.60698i	0.112291	−	0.245882i
$521$	−23.0215	−	14.7950i	−1.00859	−	0.648181i	−0.0715618	−	0.997436i	$-0.522798\pi$
$521$	−23.0215	−	14.7950i	−1.00859	−	0.648181i	−0.937028	+	0.349255i	$0.886435\pi$
$522$	−5.12704	+	1.50544i	−0.224405	+	0.0658911i
$523$	−2.48216	+	17.2638i	−0.108537	+	0.754894i	0.860761	+	0.509009i	$0.169988\pi$
$523$	−2.48216	+	17.2638i	−0.108537	+	0.754894i	−0.969299	+	0.245886i	$0.920921\pi$
$524$	3.12033	+	6.83256i	0.136312	+	0.298482i
$525$	−0.938816	−	6.52961i	−0.0409733	−	0.284975i
$526$	20.8865	−	13.4229i	0.910693	−	0.585267i
$527$	16.5803	−	19.1347i	0.722249	−	0.833519i
$528$	5.76952			0.251086
$529$	−21.0334	−	9.30579i	−0.914494	−	0.404600i
$530$	11.0465			0.479829
$531$	0.513736	−	0.592883i	0.0222943	−	0.0257289i
$532$	−20.3098	+	13.0523i	−0.880543	+	0.565891i
$533$	−1.92284	−	13.3737i	−0.0832876	−	0.579278i
$534$	−8.69204	−	19.0329i	−0.376141	−	0.823635i
$535$	0.235812	−	1.64011i	0.0101951	−	0.0709082i
$536$	−9.62473	+	2.82608i	−0.415725	+	0.122068i
$537$	15.8279	+	10.1720i	0.683025	+	0.438953i
$538$	−2.26850	+	4.96731i	−0.0978018	+	0.214156i
$539$	9.40404	+	2.76127i	0.405061	+	0.118937i
$540$	−2.45902	−	2.83786i	−0.105819	−	0.122122i
$541$	24.4803	+	28.2517i	1.05249	+	1.21464i	0.976046	+	0.217563i	$0.0698109\pi$
$541$	24.4803	+	28.2517i	1.05249	+	1.21464i	0.0764431	+	0.997074i	$0.475644\pi$
$542$	24.1155	+	7.08095i	1.03585	+	0.304153i
$543$	−5.46945	+	11.9764i	−0.234716	+	0.513957i
$544$	−2.81310	−	1.80787i	−0.120611	−	0.0775119i
$545$	1.71546	−	0.503703i	0.0734820	−	0.0215763i
$546$	−5.78687	+	40.2485i	−0.247655	+	1.72248i
$547$	19.0842	+	41.7886i	0.815983	+	1.78675i	0.579188	+	0.815194i	$0.303370\pi$
$547$	19.0842	+	41.7886i	0.815983	+	1.78675i	0.236795	+	0.971560i	$0.423903\pi$
$548$	0.902561	+	6.27745i	0.0385555	+	0.268159i
$549$	1.36711	−	0.878590i	0.0583470	−	0.0374973i
$550$	−1.85273	+	2.13817i	−0.0790008	+	0.0911717i
$551$	−34.4190			−1.46630
$552$	−2.02220	+	9.56868i	−0.0860704	+	0.407270i
$553$	−39.3096			−1.67161
$554$	−5.09323	+	5.87790i	−0.216391	+	0.249728i
$555$	16.7041	−	10.7351i	0.709049	−	0.455678i
$556$	−2.05400	−	14.2859i	−0.0871092	−	0.605857i
$557$	−15.6071	−	34.1748i	−0.661295	−	1.44803i	−0.881310	−	0.472538i	$-0.843338\pi$
$557$	−15.6071	−	34.1748i	−0.661295	−	1.44803i	0.220015	−	0.975496i	$-0.429389\pi$
$558$	−1.24849	+	8.68347i	−0.0528530	+	0.367601i
$559$	0.157526	−	0.0462538i	0.00666264	−	0.00195633i
$560$	−2.72133	−	1.74889i	−0.114997	−	0.0739041i
$561$	8.01458	−	17.5495i	0.338376	−	0.740940i
$562$	8.62332	+	2.53204i	0.363753	+	0.106807i
$563$	−13.3983	−	15.4625i	−0.564672	−	0.651667i	0.399566	−	0.916705i	$-0.369161\pi$
$563$	−13.3983	−	15.4625i	−0.564672	−	0.651667i	−0.964238	+	0.265038i	$0.914615\pi$
$564$	−10.6799	−	12.3253i	−0.449705	−	0.518987i
$565$	−1.95356	−	0.573618i	−0.0821870	−	0.0241323i
$566$	2.13817	−	4.68194i	0.0898740	−	0.196797i
$567$	30.2979	+	19.4712i	1.27239	+	0.817716i
$568$	−0.928340	+	0.272585i	−0.0389523	+	0.0114374i
$569$	1.20403	−	8.37424i	0.0504757	−	0.351066i	−0.948895	−	0.315592i	$-0.897797\pi$
$569$	1.20403	−	8.37424i	0.0504757	−	0.351066i	0.999371	−	0.0354740i	$-0.0112941\pi$
$570$	6.32243	+	13.8442i	0.264817	+	0.579869i
$571$	2.04552	+	14.2269i	0.0856022	+	0.595377i	0.986797	+	0.161962i	$0.0517823\pi$
$571$	2.04552	+	14.2269i	0.0856022	+	0.595377i	−0.901195	+	0.433414i	$0.857309\pi$
$572$	14.6708	−	9.42835i	0.613417	−	0.394219i
$573$	−7.43366	+	8.57890i	−0.310546	+	0.358389i
$574$	−7.09063			−0.295957
$575$	−2.89675	−	3.82215i	−0.120803	−	0.159395i
$576$	1.15865			0.0482771
$577$	−24.1575	+	27.8792i	−1.00569	+	1.16063i	−0.0187023	+	0.999825i	$0.505953\pi$
$577$	−24.1575	+	27.8792i	−1.00569	+	1.16063i	−0.986987	+	0.160802i	$0.948592\pi$
$578$	4.89446	−	3.14548i	0.203583	−	0.130835i
$579$	−5.40846	−	37.6167i	−0.224768	−	1.56330i
$580$	−1.91582	−	4.19507i	−0.0795502	−	0.174191i
$581$	0.486591	−	3.38431i	0.0201872	−	0.140405i
$582$	29.6127	−	8.69507i	1.22749	−	0.360422i
$583$	26.2915	+	16.8965i	1.08888	+	0.699782i
$584$	−1.43642	+	3.14531i	−0.0594394	+	0.130154i
$585$	6.85263	+	2.01211i	0.283321	+	0.0831907i
$586$	−21.1882	−	24.4525i	−0.875276	−	1.01012i
$587$	2.71286	+	3.13081i	0.111972	+	0.129222i	0.808969	−	0.587852i	$-0.200026\pi$
$587$	2.71286	+	3.13081i	0.111972	+	0.129222i	−0.696997	+	0.717074i	$0.745481\pi$
$588$	6.77839	+	1.99032i	0.279536	+	0.0820793i
$589$	−23.4743	+	51.4015i	−0.967240	+	2.11796i
$590$	0.569595	+	0.366056i	0.0234498	+	0.0150703i
$591$	51.0041	−	14.9761i	2.09803	−	0.616036i
$592$	1.38570	−	9.63777i	0.0569520	−	0.396110i
$593$	−0.897957	−	1.96625i	−0.0368747	−	0.0807443i	0.890298	−	0.455378i	$-0.150496\pi$
$593$	−0.897957	−	1.96625i	−0.0368747	−	0.0807443i	−0.927173	+	0.374634i	$0.877769\pi$
$594$	−1.51191	−	10.5156i	−0.0620345	−	0.431459i
$595$	−9.09996	+	5.84819i	−0.373062	+	0.239752i
$596$	−3.01928	+	3.48443i	−0.123675	+	0.142728i
$597$	32.6357			1.33569
$598$	10.4947	+	27.6359i	0.429162	+	1.13012i
$599$	33.3912			1.36433			0.682164	−	0.731200i	$-0.261039\pi$
$599$	33.3912			1.36433			0.682164	+	0.731200i	$0.261039\pi$
$600$	−1.33544	+	1.54118i	−0.0545192	+	0.0629185i
$601$	−3.66320	+	2.35420i	−0.149425	+	0.0960297i	−0.613217	−	0.789914i	$-0.710125\pi$
$601$	−3.66320	+	2.35420i	−0.149425	+	0.0960297i	0.463792	+	0.885944i	$0.346489\pi$
$602$	−0.0122617	−	0.0852822i	−0.000499751	−	0.00347584i
$603$	−4.82815	−	10.5722i	−0.196618	−	0.430533i
$604$	1.40596	−	9.77869i	0.0572078	−	0.397889i
$605$	2.87428	−	0.843966i	0.116856	−	0.0343121i
$606$	−5.74173	−	3.68999i	−0.233242	−	0.149896i
$607$	−7.09496	+	15.5358i	−0.287975	+	0.630578i	−0.997230	−	0.0743737i	$-0.976304\pi$
$607$	−7.09496	+	15.5358i	−0.287975	+	0.630578i	0.709255	+	0.704952i	$0.249032\pi$
$608$	7.16090	+	2.10263i	0.290413	+	0.0852729i
$609$	19.9229	+	22.9922i	0.807316	+	0.931692i
$610$	0.918490	+	1.05999i	0.0371886	+	0.0429179i
$611$	−47.2984	−	13.8881i	−1.91349	−	0.561851i
$612$	1.60951	−	3.52433i	0.0650605	−	0.142463i
$613$	2.70217	+	1.73658i	0.109139	+	0.0701397i	0.594072	−	0.804412i	$-0.297519\pi$
$613$	2.70217	+	1.73658i	0.109139	+	0.0701397i	−0.484932	+	0.874552i	$0.661156\pi$
$614$	20.0719	−	5.89364i	0.810036	−	0.237848i
$615$	−0.636146	+	4.42450i	−0.0256519	+	0.178413i
$616$	−3.80189	−	8.32498i	−0.153183	−	0.335423i
$617$	5.79531	+	40.3073i	0.233310	+	1.62271i	0.683621	+	0.729838i	$0.260404\pi$
$617$	5.79531	+	40.3073i	0.233310	+	1.62271i	−0.450310	+	0.892872i	$0.648687\pi$
$618$	18.9039	−	12.1488i	0.760426	−	0.488696i
$619$	12.0933	−	13.9564i	0.486072	−	0.560957i	−0.458740	−	0.888571i	$-0.651699\pi$
$619$	12.0933	−	13.9564i	0.486072	−	0.560957i	0.944812	+	0.327614i	$0.106245\pi$
$620$	−7.57154			−0.304080
$621$	17.9699	+	1.17819i	0.721106	+	0.0472789i
$622$	−32.6886			−1.31069
$623$	−21.7353	+	25.0839i	−0.870808	+	1.00497i
$624$	10.5747	−	6.79592i	0.423325	−	0.272054i
$625$	−0.142315	−	0.989821i	−0.00569259	−	0.0395929i
$626$	−5.48394	−	12.0082i	−0.219182	−	0.479943i
$627$	−6.12796	+	42.6209i	−0.244727	+	1.70211i
$628$	−12.4554	+	3.65723i	−0.497023	+	0.145939i
$629$	−27.3908	−	17.6030i	−1.09214	−	0.701878i
$630$	1.55700	−	3.40935i	0.0620323	−	0.135832i
$631$	−33.4895	−	9.83340i	−1.33320	−	0.391462i	−0.463958	−	0.885857i	$-0.653571\pi$
$631$	−33.4895	−	9.83340i	−1.33320	−	0.391462i	−0.869237	+	0.494395i	$0.835389\pi$
$632$	7.95781	+	9.18380i	0.316545	+	0.365312i
$633$	6.69655	+	7.72824i	0.266164	+	0.307170i
$634$	19.0612	+	5.59687i	0.757016	+	0.222280i
$635$	−6.43299	+	14.0863i	−0.255285	+	0.558997i
$636$	18.9508	+	12.1789i	0.751449	+	0.482927i
$637$	20.4887	−	6.01602i	0.811791	−	0.238363i
$638$	1.85689	−	12.9150i	0.0735151	−	0.511309i
$639$	−0.465693	−	1.01973i	−0.0184225	−	0.0403397i
$640$	0.142315	+	0.989821i	0.00562549	+	0.0391261i
$641$	6.87637	−	4.41918i	0.271600	−	0.174547i	−0.397750	−	0.917494i	$-0.630209\pi$
$641$	6.87637	−	4.41918i	0.271600	−	0.174547i	0.669350	+	0.742947i	$0.266573\pi$
$642$	2.21280	−	2.55370i	0.0873322	−	0.100787i
$643$	−21.3316			−0.841234			−0.420617	−	0.907238i	$-0.638186\pi$
$643$	−21.3316			−0.841234			−0.420617	+	0.907238i	$0.638186\pi$
$644$	15.1394	−	3.38752i	0.596577	−	0.133487i
$645$	−0.0543155			−0.00213867
$646$	16.3431	−	18.8609i	0.643009	−	0.742072i
$647$	−30.9521	+	19.8917i	−1.21685	+	0.782025i	−0.981793	−	0.189956i	$-0.939166\pi$
$647$	−30.9521	+	19.8917i	−1.21685	+	0.782025i	−0.235062	+	0.971980i	$0.575529\pi$
$648$	−1.58446	−	11.0202i	−0.0622434	−	0.432913i
$649$	0.795765	+	1.74248i	0.0312365	+	0.0683984i
$650$	−0.877230	+	6.10127i	−0.0344078	+	0.239311i
$651$	47.9244	−	14.0719i	1.87830	−	0.551520i
$652$	12.1594	+	7.81436i	0.476198	+	0.306034i
$653$	16.7475	−	36.6718i	0.655378	−	1.43508i	−0.231388	−	0.972861i	$-0.574327\pi$
$653$	16.7475	−	36.6718i	0.655378	−	1.43508i	0.886767	−	0.462217i	$-0.152946\pi$
$654$	3.49829	+	1.02719i	0.136794	+	0.0401663i
$655$	−4.91889	−	5.67670i	−0.192197	−	0.221807i
$656$	1.43542	+	1.65657i	0.0560438	+	0.0646780i
$657$	−3.84408	−	1.12872i	−0.149972	−	0.0440357i
$658$	−10.7468	+	23.5321i	−0.418953	+	0.917379i
$659$	−15.1899	−	9.76195i	−0.591714	−	0.380271i	0.210247	−	0.977648i	$-0.432573\pi$
$659$	−15.1899	−	9.76195i	−0.591714	−	0.380271i	−0.801961	+	0.597377i	$0.796210\pi$
$660$	−5.53582	+	1.62546i	−0.215481	+	0.0632710i
$661$	−6.75458	+	46.9791i	−0.262723	+	1.82728i	0.249442	+	0.968390i	$0.419753\pi$
$661$	−6.75458	+	46.9791i	−0.262723	+	1.82728i	−0.512165	+	0.858887i	$0.671156\pi$
$662$	−2.13156	−	4.66748i	−0.0828456	−	0.181407i
$663$	−5.98203	−	41.6059i	−0.232323	−	1.61584i
$664$	−0.889173	+	0.571437i	−0.0345066	+	0.0221761i
$665$	15.8099	−	18.2456i	0.613081	−	0.707533i
$666$	11.2816			0.437154
$667$	20.7685	+	7.60629i	0.804159	+	0.294517i
$668$	11.7697			0.455383
$669$	−5.52927	+	6.38112i	−0.213774	+	0.246708i
$670$	8.43866	−	5.42320i	0.326014	−	0.209516i
$671$	0.564728	+	3.92777i	0.0218011	+	0.151630i
$672$	−2.74039	−	6.00062i	−0.105713	−	0.231479i
$673$	0.0327930	−	0.228080i	0.00126408	−	0.00879184i	−0.989180	−	0.146709i	$-0.953132\pi$
$673$	0.0327930	−	0.228080i	0.00126408	−	0.00879184i	0.990444	+	0.137918i	$0.0440409\pi$
$674$	27.3321	−	8.02541i	1.05279	−	0.309127i
$675$	3.15893	+	2.03012i	0.121587	+	0.0781393i
$676$	10.3833	−	22.7362i	0.399357	−	0.874471i
$677$	−11.6632	−	3.42464i	−0.448255	−	0.131619i	0.0498112	−	0.998759i	$-0.484138\pi$
$677$	−11.6632	−	3.42464i	−0.448255	−	0.131619i	−0.498066	+	0.867139i	$0.665956\pi$
$678$	−2.71901	−	3.13790i	−0.104423	−	0.120510i
$679$	−32.0600	−	36.9992i	−1.23035	−	1.41990i
$680$	3.20849	+	0.942097i	0.123040	+	0.0361278i
$681$	5.51692	−	12.0804i	0.211409	−	0.462921i
$682$	−18.0208	−	11.5813i	−0.690053	−	0.443470i
$683$	−21.9277	+	6.43857i	−0.839042	+	0.246365i	−0.672897	−	0.739736i	$-0.734950\pi$
$683$	−21.9277	+	6.43857i	−0.839042	+	0.246365i	−0.166145	+	0.986101i	$0.553132\pi$
$684$	−1.23063	+	8.55923i	−0.0470544	+	0.327270i
$685$	−2.63456	−	5.76889i	−0.100661	−	0.220418i
$686$	1.62774	+	11.3212i	0.0621476	+	0.432246i
$687$	−5.40532	+	3.47379i	−0.206226	+	0.132533i
$688$	−0.0174420	+	0.0201292i	−0.000664970	+	0.000767417i
$689$	68.0907			2.59405
$690$	−0.755525	−	9.75080i	−0.0287624	−	0.371207i
$691$	24.7352			0.940971			0.470485	−	0.882408i	$-0.344079\pi$
$691$	24.7352			0.940971			0.470485	+	0.882408i	$0.344079\pi$
$692$	13.3783	−	15.4394i	0.508566	−	0.586917i
$693$	8.92066	−	5.73296i	0.338868	−	0.217777i
$694$	4.85569	+	33.7721i	0.184320	+	1.28197i
$695$	5.99561	+	13.1285i	0.227426	+	0.497994i
$696$	1.33844	−	9.30906i	0.0507335	−	0.352859i
$697$	7.03285	−	2.06503i	0.266388	−	0.0782186i
$698$	16.3149	+	10.4849i	0.617527	+	0.396861i
$699$	1.29802	−	2.84228i	0.0490958	−	0.107505i
$700$	3.10381	+	0.911362i	0.117313	+	0.0344463i
$701$	−32.2453	−	37.2130i	−1.21789	−	1.40552i	−0.886952	−	0.461862i	$-0.847182\pi$
$701$	−32.2453	−	37.2130i	−1.21789	−	1.40552i	−0.330935	−	0.943654i	$-0.607364\pi$
$702$	−15.1574	−	17.4926i	−0.572079	−	0.660214i
$703$	69.7248	+	20.4730i	2.62972	+	0.772155i
$704$	−1.17529	+	2.57353i	−0.0442955	+	0.0969936i
$705$	13.7197	+	8.81712i	0.516714	+	0.332072i
$706$	16.2234	−	4.76361i	0.610575	−	0.179281i
$707$	−1.54079	+	10.7164i	−0.0579475	+	0.403033i
$708$	0.573584	+	1.25597i	0.0215566	+	0.0472024i
$709$	0.434583	+	3.02259i	0.0163211	+	0.113516i	0.996353	−	0.0853228i	$-0.0271922\pi$
$709$	0.434583	+	3.02259i	0.0163211	+	0.113516i	−0.980032	+	0.198839i	$0.936283\pi$
$710$	0.813939	−	0.523087i	0.0305466	−	0.0196311i
$711$	−9.22032	+	10.6408i	−0.345789	+	0.399062i
$712$	10.2604			0.384524
$713$	25.5237	−	25.8281i	0.955869	−	0.967271i
$714$	−22.0592			−0.825543
$715$	−11.4203	+	13.1797i	−0.427093	+	0.492892i
$716$	−7.76153	+	4.98803i	−0.290062	+	0.186412i
$717$	2.68246	+	18.6569i	0.100178	+	0.696754i
$718$	−9.78634	−	21.4291i	−0.365223	−	0.799727i
$719$	−2.35575	+	16.3846i	−0.0878546	+	0.611042i	0.897563	+	0.440887i	$0.145336\pi$
$719$	−2.35575	+	16.3846i	−0.0878546	+	0.611042i	−0.985417	+	0.170155i	$0.945573\pi$
$720$	−1.11172	+	0.326429i	−0.0414312	+	0.0121653i
$721$	−29.9867	−	19.2713i	−1.11676	−	0.717701i
$722$	−15.2455	+	33.3830i	−0.567379	+	1.24239i
$723$	18.3623	+	5.39165i	0.682900	+	0.200518i
$724$	−4.22799	−	4.87936i	−0.157132	−	0.181340i
$725$	3.02010	+	3.48539i	0.112164	+	0.129444i
$726$	5.86146	+	1.72108i	0.217539	+	0.0638753i
$727$	1.96264	−	4.29758i	0.0727903	−	0.159389i	−0.869739	−	0.493512i	$-0.835713\pi$
$727$	1.96264	−	4.29758i	0.0727903	−	0.159389i	0.942529	+	0.334123i	$0.108440\pi$
$728$	−16.7743	−	10.7802i	−0.621696	−	0.399540i
$729$	−9.66476	+	2.83783i	−0.357954	+	0.105105i
$730$	0.492094	−	3.42259i	0.0182132	−	0.126676i
$731$	0.0369989	+	0.0810162i	0.00136845	+	0.00299649i
$732$	0.407054	+	2.83112i	0.0150451	+	0.104641i
$733$	−18.6574	+	11.9904i	−0.689127	+	0.442875i	−0.837775	−	0.546015i	$-0.816144\pi$
$733$	−18.6574	+	11.9904i	−0.689127	+	0.442875i	0.148649	+	0.988890i	$0.452508\pi$
$734$	−3.06210	+	3.53385i	−0.113024	+	0.130437i
$735$	−7.06456			−0.260580
$736$	−3.85623	−	2.85122i	−0.142143	−	0.105097i
$737$	28.3799			1.04539
$738$	−1.66315	+	1.91938i	−0.0612215	+	0.0706533i
$739$	−1.47044	+	0.944996i	−0.0540911	+	0.0347622i	−0.567407	−	0.823438i	$-0.692053\pi$
$739$	−1.47044	+	0.944996i	−0.0540911	+	0.0347622i	0.513316	+	0.858200i	$0.328417\pi$
$740$	1.38570	+	9.63777i	0.0509394	+	0.354291i
$741$	38.9715	+	85.3357i	1.43165	+	3.13488i
$742$	5.08545	−	35.3701i	0.186693	−	1.29848i
$743$	−18.8151	+	5.52460i	−0.690258	+	0.202678i	−0.608005	−	0.793933i	$-0.708030\pi$
$743$	−18.8151	+	5.52460i	−0.690258	+	0.202678i	−0.0822532	+	0.996611i	$0.526212\pi$
$744$	−12.9893	−	8.34775i	−0.476213	−	0.306043i
$745$	1.91530	−	4.19392i	0.0701711	−	0.153653i
$746$	−7.20955	−	2.11692i	−0.263961	−	0.0775058i
$747$	−0.801975	−	0.925528i	−0.0293427	−	0.0338633i
$748$	6.19543	+	7.14991i	0.226527	+	0.261426i
$749$	−5.14295	−	1.51011i	−0.187919	−	0.0551781i
$750$	0.847146	−	1.85499i	0.0309334	−	0.0677347i
$751$	−14.6207	−	9.39618i	−0.533518	−	0.342871i	0.245981	−	0.969275i	$-0.420890\pi$
$751$	−14.6207	−	9.39618i	−0.533518	−	0.342871i	−0.779499	+	0.626403i	$0.784526\pi$
$752$	7.67333	−	2.25309i	0.279817	−	0.0821618i
$753$	5.26005	−	36.5845i	0.191687	−	1.33321i
$754$	−11.8091	−	25.8584i	−0.430064	−	0.941708i
$755$	1.40596	+	9.77869i	0.0511682	+	0.355883i
$756$	−10.2186	+	6.56713i	−0.371649	+	0.238844i
$757$	13.1429	−	15.1677i	0.477688	−	0.551281i	−0.464846	−	0.885391i	$-0.653890\pi$
$757$	13.1429	−	15.1677i	0.477688	−	0.551281i	0.942534	+	0.334110i	$0.108436\pi$
$758$	28.7201			1.04316
$759$	13.1164	−	24.3633i	0.476096	−	0.884331i
$760$	−7.46321			−0.270719
$761$	−31.6219	+	36.4936i	−1.14629	+	1.32289i	−0.207569	+	0.978220i	$0.566555\pi$
$761$	−31.6219	+	36.4936i	−1.14629	+	1.32289i	−0.938723	+	0.344672i	$0.887990\pi$
$762$	−26.5665	+	17.0732i	−0.962401	+	0.618498i
$763$	−0.823080	−	5.72464i	−0.0297975	−	0.207246i
$764$	−2.31238	−	5.06341i	−0.0836591	−	0.183188i
$765$	−0.551393	+	3.83502i	−0.0199357	+	0.138656i
$766$	16.4726	−	4.83681i	0.595181	−	0.174761i
$767$	3.51099	+	2.25637i	0.126774	+	0.0814729i
$768$	−0.847146	+	1.85499i	−0.0305688	+	0.0669362i
$769$	10.7169	+	3.14677i	0.386462	+	0.113475i	0.469191	−	0.883097i	$-0.344546\pi$
$769$	10.7169	+	3.14677i	0.386462	+	0.113475i	−0.0827294	+	0.996572i	$0.526364\pi$
$770$	5.99331	+	6.91665i	0.215984	+	0.249259i
$771$	18.2967	+	21.1155i	0.658940	+	0.760458i
$772$	17.8809	+	5.25030i	0.643547	+	0.188963i
$773$	−1.65555	+	3.62516i	−0.0595461	+	0.130388i	−0.937066	−	0.349153i	$-0.886469\pi$
$773$	−1.65555	+	3.62516i	−0.0595461	+	0.130388i	0.877520	+	0.479541i	$0.159197\pi$
$774$	−0.0259613	−	0.0166843i	−0.000933160	−	0.000599706i
$775$	7.26484	−	2.13315i	0.260961	−	0.0766250i
$776$	−2.15382	+	14.9802i	−0.0773178	+	0.537757i
$777$	−26.6828	−	58.4273i	−0.957241	−	2.09607i
$778$	−1.08739	−	7.56299i	−0.0389850	−	0.271146i
$779$	−13.7621	+	8.84433i	−0.493077	+	0.316881i
$780$	−8.23168	+	9.49986i	−0.294741	+	0.340150i
$781$	2.73734			0.0979498
$782$	−14.0295	+	7.76903i	−0.501694	+	0.277820i
$783$	−17.3175			−0.618877
$784$	−2.26860	+	2.61810i	−0.0810214	+	0.0935037i
$785$	10.9205	−	7.01817i	0.389769	−	0.250489i
$786$	−2.17994	−	15.1618i	−0.0777558	−	0.540804i
$787$	−2.23251	−	4.88852i	−0.0795805	−	0.174257i	0.865659	−	0.500633i	$-0.166900\pi$
$787$	−2.23251	−	4.88852i	−0.0795805	−	0.174257i	−0.945240	+	0.326377i	$0.894172\pi$
$788$	−3.70968	+	25.8014i	−0.132152	+	0.919138i
$789$	−48.5798	+	14.2643i	−1.72949	+	0.507823i
$790$	−10.2228	−	6.56982i	−0.363712	−	0.233744i
$791$	−2.73603	+	5.99108i	−0.0972822	+	0.213018i
$792$	−3.14527	−	0.923534i	−0.111762	−	0.0328164i
$793$	5.66158	+	6.53381i	0.201048	+	0.232022i
$794$	−19.2067	−	22.1657i	−0.681621	−	0.786633i
$795$	−21.6144	−	6.34655i	−0.766583	−	0.225089i
$796$	−6.64813	+	14.5574i	−0.235637	+	0.515972i
$797$	4.74735	+	3.05094i	0.168160	+	0.108070i	0.622014	−	0.783006i	$-0.286315\pi$
$797$	4.74735	+	3.05094i	0.168160	+	0.108070i	−0.453854	+	0.891076i	$0.649951\pi$
$798$	47.2387	−	13.8705i	1.67223	−	0.491011i
$799$	3.80584	−	26.4702i	0.134641	−	0.936449i
$800$	−0.415415	−	0.909632i	−0.0146871	−	0.0321603i
$801$	1.69187	+	11.7672i	0.0597791	+	0.415773i
$802$	14.5868	−	9.37434i	0.515077	−	0.331020i
$803$	6.40635	−	7.39333i	0.226075	−	0.260905i
$804$	20.4561			0.721431
$805$	−13.5718	+	7.51557i	−0.478343	+	0.264889i
$806$	−46.6710			−1.64392
$807$	7.29258	−	8.41608i	0.256711	−	0.296260i
$808$	2.81557	−	1.80946i	0.0990515	−	0.0636565i
$809$	4.22344	+	29.3747i	0.148488	+	1.03276i	0.918696	+	0.394966i	$0.129244\pi$
$809$	4.22344	+	29.3747i	0.148488	+	1.03276i	−0.770207	+	0.637794i	$0.779847\pi$
$810$	4.62501	+	10.1274i	0.162506	+	0.355840i
$811$	2.28820	−	15.9148i	0.0803497	−	0.558844i	−0.909388	−	0.415949i	$-0.863450\pi$
$811$	2.28820	−	15.9148i	0.0803497	−	0.558844i	0.989738	−	0.142896i	$-0.0456413\pi$
$812$	−14.3143	+	4.20304i	−0.502332	+	0.147498i
$813$	−43.1179	−	27.7102i	−1.51221	−	0.971839i
$814$	−11.4437	+	25.0582i	−0.401101	+	0.878288i
$815$	−13.8684	−	4.07213i	−0.485789	−	0.142641i
$816$	4.46564	+	5.15363i	0.156329	+	0.180413i
$817$	−0.130173	−	0.150228i	−0.00455419	−	0.00525581i
$818$	−7.59798	−	2.23097i	−0.265657	−	0.0780040i
$819$	9.59736	−	21.0153i	0.335359	−	0.734333i
$820$	−1.84399	−	1.18506i	−0.0643948	−	0.0413840i
$821$	8.95706	−	2.63003i	0.312604	−	0.0917887i	−0.121668	−	0.992571i	$-0.538824\pi$
$821$	8.95706	−	2.63003i	0.312604	−	0.0917887i	0.434271	+	0.900782i	$0.357006\pi$
$822$	1.84057	−	12.8015i	0.0641973	−	0.446502i
$823$	−14.5820	−	31.9301i	−0.508296	−	1.11301i	−0.973683	−	0.227906i	$-0.926812\pi$
$823$	−14.5820	−	31.9301i	−0.508296	−	1.11301i	0.465387	−	0.885107i	$-0.345915\pi$
$824$	1.56819	+	10.9070i	0.0546304	+	0.379963i
$825$	4.85363	−	3.11924i	0.168982	−	0.108598i
$826$	1.43431	−	1.65528i	0.0499059	−	0.0575945i
$827$	40.2836			1.40080			0.700400	−	0.713751i	$-0.253005\pi$
$827$	40.2836			1.40080			0.700400	+	0.713751i	$0.253005\pi$
$828$	2.63408	−	4.89269i	0.0915405	−	0.170033i
$829$	5.27401			0.183174			0.0915870	−	0.995797i	$-0.470806\pi$
$829$	5.27401			0.183174			0.0915870	+	0.995797i	$0.470806\pi$
$830$	0.692163	−	0.798799i	0.0240253	−	0.0277267i
$831$	13.3428	−	8.57491i	0.462857	−	0.297460i
$832$	0.877230	+	6.10127i	0.0304125	+	0.211523i
$833$	4.81227	+	10.5374i	0.166735	+	0.365099i
$834$	−4.18868	+	29.1329i	−0.145042	+	1.00879i
$835$	−11.2929	+	3.31591i	−0.390808	+	0.114752i
$836$	−17.7630	−	11.4156i	−0.614346	−	0.394816i
$837$	−11.8108	+	25.8620i	−0.408241	+	0.893922i
$838$	−2.87705	−	0.844777i	−0.0993860	−	0.0291824i
$839$	14.8940	+	17.1885i	0.514197	+	0.593415i	0.952168	−	0.305574i	$-0.0988484\pi$
$839$	14.8940	+	17.1885i	0.514197	+	0.593415i	−0.437972	+	0.898989i	$0.644303\pi$
$840$	4.31995	+	4.98549i	0.149053	+	0.172016i
$841$	7.41789	+	2.17809i	0.255789	+	0.0751065i
$842$	4.93521	−	10.8066i	0.170079	−	0.372420i
$843$	−15.4183	−	9.90873i	−0.531034	−	0.341275i
$844$	−4.81136	+	1.41274i	−0.165614	+	0.0486286i
$845$	−3.55716	+	24.7406i	−0.122370	+	0.851102i
$846$	3.84925	+	8.42869i	0.132340	+	0.289784i
$847$	−1.37909	−	9.59177i	−0.0473860	−	0.329577i
$848$	−9.29291	+	5.97219i	−0.319120	+	0.205086i
$849$	−6.87362	+	7.93258i	−0.235902	+	0.272245i
$850$	−3.34394			−0.114696
$851$	−37.5477	−	27.7620i	−1.28712	−	0.951669i
$852$	1.97307			0.0675961
$853$	−18.5515	+	21.4096i	−0.635192	+	0.733051i	−0.978517	−	0.206166i	$-0.933901\pi$
$853$	−18.5515	+	21.4096i	−0.635192	+	0.733051i	0.343325	+	0.939217i	$0.388447\pi$
$854$	3.81686	−	2.45295i	0.130610	−	0.0839381i
$855$	−1.23063	−	8.55923i	−0.0420867	−	0.292720i
$856$	0.688333	+	1.50724i	0.0235267	+	0.0515164i
$857$	1.70639	−	11.8682i	0.0582892	−	0.405410i	−0.939699	−	0.342004i	$-0.888894\pi$
$857$	1.70639	−	11.8682i	0.0582892	−	0.405410i	0.997988	−	0.0634065i	$-0.0201965\pi$
$858$	−34.1228	+	10.0194i	−1.16493	+	0.342055i
$859$	−6.19747	−	3.98287i	−0.211455	−	0.135894i	0.430627	−	0.902530i	$-0.358293\pi$
$859$	−6.19747	−	3.98287i	−0.211455	−	0.135894i	−0.642082	+	0.766636i	$0.721929\pi$
$860$	0.0110644	−	0.0242278i	0.000377295	−	0.000826160i
$861$	13.8740	+	4.07378i	0.472826	+	0.138834i
$862$	−7.62755	−	8.80266i	−0.259795	−	0.299820i
$863$	−20.1055	−	23.2030i	−0.684398	−	0.789838i	0.302158	−	0.953258i	$-0.402293\pi$
$863$	−20.1055	−	23.2030i	−0.684398	−	0.789838i	−0.986557	+	0.163420i	$0.947747\pi$
$864$	3.60292	+	1.05791i	0.122574	+	0.0359909i
$865$	−8.48660	+	18.5831i	−0.288553	+	0.631843i
$866$	−12.3093	−	7.91069i	−0.418286	−	0.268816i
$867$	−11.3840	+	3.34265i	−0.386621	+	0.113522i
$868$	−3.48569	+	24.2435i	−0.118312	+	0.822878i
$869$	−14.2820	−	31.2733i	−0.484485	−	1.06087i
$870$	1.33844	+	9.30906i	0.0453774	+	0.315607i
$871$	52.0160	−	33.4286i	1.76249	−	1.13269i
$872$	−1.17081	+	1.35119i	−0.0396486	+	0.0457570i
$873$	−17.5353			−0.593479
$874$	25.1585	−	25.4586i	0.850998	−	0.861149i
$875$	−3.23485			−0.109358
$876$	4.61768	−	5.32908i	0.156017	−	0.180053i
$877$	39.0357	−	25.0867i	1.31814	−	0.847119i	0.323080	−	0.946372i	$-0.395282\pi$
$877$	39.0357	−	25.0867i	1.31814	−	0.847119i	0.995062	+	0.0992531i	$0.0316454\pi$
$878$	−3.41630	−	23.7609i	−0.115295	−	0.801891i
$879$	27.4096	+	60.0188i	0.924505	+	2.02438i
$880$	0.402637	−	2.80040i	0.0135729	−	0.0944016i
$881$	13.1438	−	3.85937i	0.442826	−	0.130026i	−0.0527156	−	0.998610i	$-0.516788\pi$
$881$	13.1438	−	3.85937i	0.442826	−	0.130026i	0.495542	+	0.868584i	$0.334970\pi$
$882$	−3.37667	−	2.17005i	−0.113698	−	0.0730694i
$883$	4.17966	−	9.15217i	0.140657	−	0.307995i	−0.826173	−	0.563416i	$-0.809487\pi$
$883$	4.17966	−	9.15217i	0.140657	−	0.307995i	0.966830	+	0.255421i	$0.0822141\pi$
$884$	19.7772	+	5.80710i	0.665178	+	0.195314i
$885$	−0.904199	−	1.04350i	−0.0303943	−	0.0350769i
$886$	18.8902	+	21.8005i	0.634629	+	0.732401i
$887$	−52.8414	−	15.5156i	−1.77424	−	0.520964i	−0.779779	−	0.626055i	$-0.784669\pi$
$887$	−52.8414	−	15.5156i	−1.77424	−	0.520964i	−0.994463	+	0.105090i	$0.966487\pi$
$888$	−8.24856	+	18.0618i	−0.276803	+	0.606115i
$889$	42.1416	+	27.0828i	1.41339	+	0.908327i
$890$	−9.84476	+	2.89068i	−0.329997	+	0.0968959i
$891$	−4.48275	+	31.1782i	−0.150178	+	1.04451i
$892$	−1.71999	−	3.76624i	−0.0575894	−	0.126103i
$893$	8.49411	+	59.0778i	0.284244	+	1.97696i
$894$	7.90965	−	5.08323i	0.264538	−	0.170008i
$895$	6.04184	−	6.97266i	0.201957	−	0.233070i
$896$	3.23485			0.108069
$897$	−4.65706	−	60.1040i	−0.155495	−	2.00681i
$898$	7.61939			0.254262
$899$	−22.8668	+	26.3897i	−0.762652	+	0.880147i
$900$	0.974718	−	0.626414i	0.0324906	−	0.0208805i
$901$	5.25695	+	36.5629i	0.175134	+	1.21809i
$902$	−2.57618	−	5.64105i	−0.0857775	−	0.187826i
$903$	−0.0250051	+	0.173914i	−0.000832116	+	0.00578750i
$904$	1.95356	−	0.573618i	0.0649745	−	0.0190782i
$905$	5.43140	+	3.49055i	0.180546	+	0.116030i
$906$	−8.36917	+	18.3259i	−0.278047	+	0.608838i
$907$	18.0391	+	5.29676i	0.598979	+	0.175876i	0.567146	−	0.823617i	$-0.308048\pi$
$907$	18.0391	+	5.29676i	0.598979	+	0.175876i	0.0318325	+	0.999493i	$0.489866\pi$
$908$	4.26469	+	4.92171i	0.141529	+	0.163333i
$909$	2.53946	+	2.93069i	0.0842285	+	0.0972049i
$910$	19.1319	+	5.61764i	0.634218	+	0.186223i
$911$	5.02498	−	11.0032i	0.166485	−	0.364551i	−0.807940	−	0.589265i	$-0.799417\pi$
$911$	5.02498	−	11.0032i	0.166485	−	0.364551i	0.974425	+	0.224714i	$0.0721447\pi$
$912$	−12.8035	−	8.22831i	−0.423966	−	0.272467i
$913$	2.86923	−	0.842481i	0.0949576	−	0.0278821i
$914$	−1.50613	+	10.4754i	−0.0498184	+	0.346495i
$915$	−1.18818	−	2.60176i	−0.0392801	−	0.0860115i
$916$	−0.448403	−	3.11871i	−0.0148156	−	0.103045i
$917$	−20.4408	+	13.1365i	−0.675016	+	0.433806i
$918$	8.22281	−	9.48963i	0.271393	−	0.313204i
$919$	−18.1443			−0.598525			−0.299262	−	0.954171i	$-0.596741\pi$
$919$	−18.1443			−0.598525			−0.299262	+	0.954171i	$0.596741\pi$
$920$	4.50331	+	1.64930i	0.148470	+	0.0543758i
$921$	−42.6602			−1.40570
$922$	22.4217	−	25.8760i	0.738418	−	0.852180i
$923$	5.01713	−	3.22431i	0.165141	−	0.106130i
$924$	2.65610	+	18.4736i	0.0873792	+	0.607736i
$925$	−4.04484	−	8.85697i	−0.132994	−	0.291216i
$926$	1.08132	−	7.52076i	0.0355344	−	0.247147i
$927$	−12.2502	+	3.59698i	−0.402348	+	0.118140i
$928$	3.87972	+	2.49334i	0.127358	+	0.0818480i
$929$	−10.4276	+	22.8333i	−0.342119	+	0.749136i	−0.999992	−	0.00399252i	$-0.998729\pi$
$929$	−10.4276	+	22.8333i	−0.342119	+	0.749136i	0.657873	+	0.753129i	$0.271456\pi$
$930$	14.8150	+	4.35008i	0.485804	+	0.142645i
$931$	−16.9310	−	19.5395i	−0.554892	−	0.640380i
$932$	1.00340	+	1.15798i	0.0328674	+	0.0379310i
$933$	63.9609	+	18.7806i	2.09399	+	0.614850i
$934$	−2.85915	+	6.26067i	−0.0935543	+	0.204855i
$935$	−7.95883	−	5.11483i	−0.260282	−	0.167273i
$936$	−6.85263	+	2.01211i	−0.223985	+	0.0657680i
$937$	3.49749	−	24.3256i	0.114258	−	0.794683i	−0.849439	−	0.527686i	$-0.823060\pi$
$937$	3.49749	−	24.3256i	0.114258	−	0.794683i	0.963697	−	0.266997i	$-0.0860312\pi$
$938$	−13.4798	−	29.5166i	−0.440130	−	0.963751i
$939$	3.83122	+	26.6467i	0.125027	+	0.869583i
$940$	−6.72773	+	4.32365i	−0.219434	+	0.141022i
$941$	6.76973	−	7.81268i	0.220687	−	0.254686i	−0.634600	−	0.772840i	$-0.718835\pi$
$941$	6.76973	−	7.81268i	0.220687	−	0.254686i	0.855287	+	0.518154i	$0.173381\pi$
$942$	26.4723			0.862513
$943$	10.2586	−	2.29540i	0.334065	−	0.0747484i
$944$	−0.677078			−0.0220370
$945$	7.95455	−	9.18004i	0.258761	−	0.298627i
$946$	0.0633925	−	0.0407399i	0.00206107	−	0.00132457i
$947$	−1.40123	−	9.74574i	−0.0455337	−	0.316694i	−0.999840	−	0.0178651i	$-0.994313\pi$
$947$	−1.40123	−	9.74574i	−0.0455337	−	0.316694i	0.954307	−	0.298829i	$-0.0965960\pi$
$948$	−10.2944	−	22.5417i	−0.334348	−	0.732120i
$949$	3.03327	−	21.0969i	0.0984642	−	0.684834i
$950$	7.16090	−	2.10263i	0.232330	−	0.0682183i
$951$	−34.0809	−	21.9025i	−1.10515	−	0.710236i
$952$	4.49361	−	9.83962i	0.145639	−	0.318904i
$953$	−57.5926	−	16.9107i	−1.86561	−	0.547792i	−0.998791	−	0.0491675i	$-0.984343\pi$
$953$	−57.5926	−	16.9107i	−1.86561	−	0.547792i	−0.866818	−	0.498625i	$-0.833839\pi$
$954$	−8.38158	−	9.67286i	−0.271364	−	0.313170i
$955$	3.64524	+	4.20684i	0.117957	+	0.136130i
$956$	−8.86846	−	2.60401i	−0.286826	−	0.0842198i
$957$	−11.0534	+	24.2035i	−0.357305	+	0.782389i
$958$	19.0128	+	12.2188i	0.614275	+	0.394770i
$959$	−19.6844	+	5.77986i	−0.635643	+	0.186641i
$960$	0.290219	−	2.01852i	0.00936679	−	0.0651475i
$961$	10.9371	+	23.9490i	0.352811	+	0.772549i
$962$	8.54148	+	59.4073i	0.275388	+	1.91537i
$963$	−1.61509	+	1.03795i	−0.0520454	+	0.0334476i
$964$	−6.14550	+	7.09229i	−0.197933	+	0.228427i
$965$	−18.6358			−0.599907
$966$	−31.5691	−	2.06981i	−1.01572	−	0.0665952i
$967$	−44.7785			−1.43998			−0.719990	−	0.693985i	$-0.755853\pi$
$967$	−44.7785			−1.43998			−0.719990	+	0.693985i	$0.755853\pi$
$968$	−1.96172	+	2.26394i	−0.0630520	+	0.0727659i
$969$	−42.8142	+	27.5150i	−1.37539	+	0.883909i
$970$	−2.15382	−	14.9802i	−0.0691551	−	0.480984i
$971$	10.5359	+	23.0705i	0.338114	+	0.740366i	0.999957	−	0.00927625i	$-0.00295277\pi$
$971$	10.5359	+	23.0705i	0.338114	+	0.740366i	−0.661843	+	0.749642i	$0.730225\pi$
$972$	−1.62797	+	11.3227i	−0.0522170	+	0.363177i
$973$	44.7968	−	13.1535i	1.43612	−	0.421683i
$974$	31.0449	+	19.9513i	0.994742	+	0.639282i
$975$	5.22182	−	11.4342i	0.167232	−	0.366187i
$976$	−1.34576	−	0.395150i	−0.0430767	−	0.0126485i
$977$	21.6926	+	25.0346i	0.694008	+	0.800928i	0.987930	−	0.154902i	$-0.0495061\pi$
$977$	21.6926	+	25.0346i	0.694008	+	0.800928i	−0.293922	+	0.955829i	$0.594961\pi$
$978$	−19.3023	−	22.2761i	−0.617221	−	0.712310i
$979$	−27.8528	−	8.17832i	−0.890179	−	0.261380i
$980$	1.43910	−	3.15119i	0.0459704	−	0.100661i
$981$	−1.74268	−	1.11995i	−0.0556394	−	0.0357573i
$982$	−11.5713	+	3.39763i	−0.369254	+	0.108423i
$983$	−2.71819	+	18.9054i	−0.0866967	+	0.602989i	0.899439	+	0.437047i	$0.143976\pi$
$983$	−2.71819	+	18.9054i	−0.0866967	+	0.602989i	−0.986135	+	0.165942i	$0.946933\pi$
$984$	−1.85690	−	4.06605i	−0.0591959	−	0.129621i
$985$	−3.70968	−	25.8014i	−0.118200	−	0.822102i
$986$	12.9735	−	8.33759i	0.413162	−	0.265523i
$987$	34.5478	−	39.8703i	1.09967	−	1.26909i
$988$	−46.0033			−1.46356
$989$	0.0453478	+	0.119415i	0.00144198	+	0.00379717i
$990$	3.27805			0.104183
$991$	−7.11920	+	8.21600i	−0.226149	+	0.260990i	−0.857473	−	0.514530i	$-0.827967\pi$
$991$	−7.11920	+	8.21600i	−0.226149	+	0.260990i	0.631324	+	0.775519i	$0.282512\pi$
$992$	6.36959	−	4.09348i	0.202235	−	0.129968i
$993$	1.48916	+	10.3574i	0.0472572	+	0.328681i
$994$	−1.30017	−	2.84698i	−0.0412390	−	0.0903008i
$995$	2.27755	−	15.8407i	0.0722031	−	0.502183i
$996$	2.06813	−	0.607257i	0.0655312	−	0.0192417i
$997$	18.7405	+	12.0438i	0.593518	+	0.381431i	0.802644	−	0.596458i	$-0.203426\pi$
$997$	18.7405	+	12.0438i	0.593518	+	0.381431i	−0.209127	+	0.977889i	$0.567062\pi$
$998$	1.54771	−	3.38901i	0.0489918	−	0.107277i
$999$	35.0812	+	10.3008i	1.10992	+	0.325902i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.g.b.131.1	✓	20
23.6	even	11		5290.2.a.bj.1.3		10
23.13	even	11	inner	230.2.g.b.151.1	yes	20
23.17	odd	22		5290.2.a.bi.1.3		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.b.131.1	✓	20	1.1	even	1	trivial
230.2.g.b.151.1	yes	20	23.13	even	11	inner
5290.2.a.bi.1.3		10	23.17	odd	22
5290.2.a.bj.1.3		10	23.6	even	11

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 - 0.755750i) q^{2} +(-1.71555 + 1.10252i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.415415 + 0.909632i) q^{5} +(-0.290219 + 2.01852i) q^{6} +(3.10381 - 0.911362i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.481321 - 1.05395i) q^{9} +O(q^{10})\)	\(q+(0.654861 - 0.755750i) q^{2} +(-1.71555 + 1.10252i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.415415 + 0.909632i) q^{5} +(-0.290219 + 2.01852i) q^{6} +(3.10381 - 0.911362i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.481321 - 1.05395i) q^{9} +(0.959493 + 0.281733i) q^{10} +(1.85273 + 2.13817i) q^{11} +(1.33544 + 1.54118i) q^{12} +(5.91432 + 1.73660i) q^{13} +(1.34380 - 2.94252i) q^{14} +(-1.71555 - 1.10252i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(-0.475893 + 3.30991i) q^{17} +(-0.481321 - 1.05395i) q^{18} +(-1.06213 - 7.38724i) q^{19} +(0.841254 - 0.540641i) q^{20} +(-4.31995 + 4.98549i) q^{21} +2.82920 q^{22} +(-0.991625 + 4.69219i) q^{23} +2.03928 q^{24} +(-0.654861 + 0.755750i) q^{25} +(5.18549 - 3.33251i) q^{26} +(-0.534395 - 3.71680i) q^{27} +(-1.34380 - 2.94252i) q^{28} +(0.656331 - 4.56488i) q^{29} +(-1.95667 + 0.574531i) q^{30} +(-6.36959 - 4.09348i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(-5.53582 - 1.62546i) q^{33} +(2.18982 + 2.52718i) q^{34} +(2.11838 + 2.44474i) q^{35} +(-1.11172 - 0.326429i) q^{36} +(-4.04484 + 8.85697i) q^{37} +(-6.27845 - 4.03492i) q^{38} +(-12.0609 + 3.54141i) q^{39} +(0.142315 - 0.989821i) q^{40} +(-0.910569 - 1.99387i) q^{41} +(0.938816 + 6.52961i) q^{42} +(0.0224065 - 0.0143998i) q^{43} +(1.85273 - 2.13817i) q^{44} +1.15865 q^{45} +(2.89675 + 3.82215i) q^{46} -7.99727 q^{47} +(1.33544 - 1.54118i) q^{48} +(2.91431 - 1.87291i) q^{49} +(0.142315 + 0.989821i) q^{50} +(-2.83281 - 6.20298i) q^{51} +(0.877230 - 6.10127i) q^{52} +(10.5990 - 3.11216i) q^{53} +(-3.15893 - 2.03012i) q^{54} +(-1.17529 + 2.57353i) q^{55} +(-3.10381 - 0.911362i) q^{56} +(9.96668 + 11.5022i) q^{57} +(-3.02010 - 3.48539i) q^{58} +(0.649652 + 0.190755i) q^{59} +(-0.847146 + 1.85499i) q^{60} +(1.17992 + 0.758288i) q^{61} +(-7.26484 + 2.13315i) q^{62} +(0.533404 - 3.70991i) q^{63} +(0.415415 + 0.909632i) q^{64} +(0.877230 + 6.10127i) q^{65} +(-4.85363 + 3.11924i) q^{66} +(6.56894 - 7.58097i) q^{67} +3.34394 q^{68} +(-3.47204 - 9.14297i) q^{69} +3.23485 q^{70} +(0.633599 - 0.731212i) q^{71} +(-0.974718 + 0.626414i) q^{72} +(-0.492094 - 3.42259i) q^{73} +(4.04484 + 8.85697i) q^{74} +(0.290219 - 2.01852i) q^{75} +(-7.16090 + 2.10263i) q^{76} +(7.69918 + 4.94796i) q^{77} +(-5.22182 + 11.4342i) q^{78} +(-11.6597 - 3.42359i) q^{79} +(-0.654861 - 0.755750i) q^{80} +(7.29088 + 8.41412i) q^{81} +(-2.10316 - 0.617544i) q^{82} +(0.439078 - 0.961447i) q^{83} +(5.54954 + 3.56647i) q^{84} +(-3.20849 + 0.942097i) q^{85} +(0.00379051 - 0.0263636i) q^{86} +(3.90689 + 8.55490i) q^{87} +(-0.402637 - 2.80040i) q^{88} +(-8.63158 + 5.54718i) q^{89} +(0.758754 - 0.875649i) q^{90} +19.9396 q^{91} +(4.78556 + 0.313763i) q^{92} +15.4405 q^{93} +(-5.23710 + 6.04394i) q^{94} +(6.27845 - 4.03492i) q^{95} +(-0.290219 - 2.01852i) q^{96} +(-6.28698 - 13.7666i) q^{97} +(0.493014 - 3.42899i) q^{98} +(3.14527 - 0.923534i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9	\( 20 q + 2 q^{2} - 3 q^{3} - 2 q^{4} - 2 q^{5} + 3 q^{6} + 19 q^{7} + 2 q^{8} - 27 q^{9} + 2 q^{10} + 7 q^{11} + 8 q^{12} + 8 q^{13} + 3 q^{14} - 3 q^{15} - 2 q^{16} + 8 q^{17} + 27 q^{18} - q^{19} - 2 q^{20} - 31 q^{21} - 18 q^{22} - 9 q^{23} - 8 q^{24} - 2 q^{25} - 8 q^{26} - 18 q^{27} - 3 q^{28} + 20 q^{29} + 3 q^{30} - 17 q^{31} + 2 q^{32} + 17 q^{33} + 3 q^{34} - 3 q^{35} + 17 q^{36} + 6 q^{37} - 21 q^{38} - 75 q^{39} + 2 q^{40} - 2 q^{41} + 42 q^{42} - 18 q^{43} + 7 q^{44} + 28 q^{45} - 2 q^{46} + 42 q^{47} + 8 q^{48} - 19 q^{49} + 2 q^{50} + 26 q^{51} + 19 q^{52} + 19 q^{53} - 26 q^{54} - 15 q^{55} - 19 q^{56} + 7 q^{57} - 9 q^{58} + 25 q^{59} - 3 q^{60} - 49 q^{61} - 38 q^{62} - 87 q^{63} - 2 q^{64} + 19 q^{65} - 6 q^{66} + 19 q^{67} - 36 q^{68} + 36 q^{69} + 14 q^{70} + 7 q^{71} - 17 q^{72} - 10 q^{73} - 6 q^{74} - 3 q^{75} - q^{76} - 29 q^{77} - 2 q^{78} - 33 q^{79} - 2 q^{80} + 72 q^{81} + 2 q^{82} - 41 q^{83} + 13 q^{84} - 14 q^{85} - 48 q^{86} - 16 q^{87} - 7 q^{88} + 55 q^{89} + 5 q^{90} + 13 q^{92} + 10 q^{93} + 13 q^{94} + 21 q^{95} + 3 q^{96} - 9 q^{97} + 41 q^{98} + 59 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 - 3 * q^3 - 2 * q^4 - 2 * q^5 + 3 * q^6 + 19 * q^7 + 2 * q^8 - 27 * q^9 + 2 * q^10 + 7 * q^11 + 8 * q^12 + 8 * q^13 + 3 * q^14 - 3 * q^15 - 2 * q^16 + 8 * q^17 + 27 * q^18 - q^19 - 2 * q^20 - 31 * q^21 - 18 * q^22 - 9 * q^23 - 8 * q^24 - 2 * q^25 - 8 * q^26 - 18 * q^27 - 3 * q^28 + 20 * q^29 + 3 * q^30 - 17 * q^31 + 2 * q^32 + 17 * q^33 + 3 * q^34 - 3 * q^35 + 17 * q^36 + 6 * q^37 - 21 * q^38 - 75 * q^39 + 2 * q^40 - 2 * q^41 + 42 * q^42 - 18 * q^43 + 7 * q^44 + 28 * q^45 - 2 * q^46 + 42 * q^47 + 8 * q^48 - 19 * q^49 + 2 * q^50 + 26 * q^51 + 19 * q^52 + 19 * q^53 - 26 * q^54 - 15 * q^55 - 19 * q^56 + 7 * q^57 - 9 * q^58 + 25 * q^59 - 3 * q^60 - 49 * q^61 - 38 * q^62 - 87 * q^63 - 2 * q^64 + 19 * q^65 - 6 * q^66 + 19 * q^67 - 36 * q^68 + 36 * q^69 + 14 * q^70 + 7 * q^71 - 17 * q^72 - 10 * q^73 - 6 * q^74 - 3 * q^75 - q^76 - 29 * q^77 - 2 * q^78 - 33 * q^79 - 2 * q^80 + 72 * q^81 + 2 * q^82 - 41 * q^83 + 13 * q^84 - 14 * q^85 - 48 * q^86 - 16 * q^87 - 7 * q^88 + 55 * q^89 + 5 * q^90 + 13 * q^92 + 10 * q^93 + 13 * q^94 + 21 * q^95 + 3 * q^96 - 9 * q^97 + 41 * q^98 + 59 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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