LMFDB - Embedded newform 690.2.m.f.361.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(31,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 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("690.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.m (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:	$5.50967773947$
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} - 6 x^{19} + 36 x^{18} - 172 x^{17} + 691 x^{16} - 2342 x^{15} + 7870 x^{14} - 23240 x^{13} + \cdots + 123904 $ x^20 - 6x^19 + 36x^18 - 172x^17 + 691x^16 - 2342x^15 + 7870x^14 - 23240x^13 + 63837x^12 - 154607x^11 + 334467x^10 - 664202x^9 + 1099560x^8 - 1331000x^7 + 1218096x^6 + 395648x^5 - 588544x^4 + 665984x^3 + 2323200x^2 + 991232*x + 123904
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			361.1
Root			$1.05064 + 2.30058i$ of defining polynomial
Character	$\chi$	$=$	690.361
Dual form			690.2.m.f.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 - 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-3.76793 + 1.10637i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(0.654861 - 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-3.76793 + 1.10637i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-0.959493 - 0.281733i) q^{10} +(0.883071 + 1.01912i) q^{11} +(0.654861 + 0.755750i) q^{12} +(1.39104 + 0.408445i) q^{13} +(-1.63134 + 3.57213i) q^{14} +(0.841254 + 0.540641i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(-0.936163 + 6.51116i) q^{17} +(-0.415415 - 0.909632i) q^{18} +(0.354343 + 2.46451i) q^{19} +(-0.841254 + 0.540641i) q^{20} +(2.57164 - 2.96783i) q^{21} +1.34849 q^{22} +(-4.52426 + 1.59092i) q^{23} +1.00000 q^{24} +(-0.654861 + 0.755750i) q^{25} +(1.21962 - 0.783801i) q^{26} +(0.142315 + 0.989821i) q^{27} +(1.63134 + 3.57213i) q^{28} +(-1.10746 + 7.70255i) q^{29} +(0.959493 - 0.281733i) q^{30} +(2.10361 + 1.35191i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(-1.29386 - 0.379913i) q^{33} +(4.30775 + 4.97141i) q^{34} +(2.57164 + 2.96783i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(0.371911 - 0.814372i) q^{37} +(2.09460 + 1.34612i) q^{38} +(-1.39104 + 0.408445i) q^{39} +(-0.142315 + 0.989821i) q^{40} +(-4.24763 - 9.30102i) q^{41} +(-0.558871 - 3.88703i) q^{42} +(-6.59177 + 4.23627i) q^{43} +(0.883071 - 1.01912i) q^{44} -1.00000 q^{45} +(-1.76042 + 4.46104i) q^{46} -11.6523 q^{47} +(0.654861 - 0.755750i) q^{48} +(7.08450 - 4.55293i) q^{49} +(0.142315 + 0.989821i) q^{50} +(-2.73265 - 5.98366i) q^{51} +(0.206323 - 1.43501i) q^{52} +(12.1361 - 3.56348i) q^{53} +(0.841254 + 0.540641i) q^{54} +(0.560182 - 1.22663i) q^{55} +(3.76793 + 1.10637i) q^{56} +(-1.63051 - 1.88170i) q^{57} +(5.09597 + 5.88106i) q^{58} +(-8.65772 - 2.54214i) q^{59} +(0.415415 - 0.909632i) q^{60} +(6.74235 + 4.33305i) q^{61} +(2.39928 - 0.704491i) q^{62} +(-0.558871 + 3.88703i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-0.206323 - 1.43501i) q^{65} +(-1.13442 + 0.729047i) q^{66} +(-8.07285 + 9.31656i) q^{67} +6.57812 q^{68} +(2.94593 - 3.78437i) q^{69} +3.92700 q^{70} +(6.95423 - 8.02561i) q^{71} +(-0.841254 + 0.540641i) q^{72} +(-0.588681 - 4.09436i) q^{73} +(-0.371911 - 0.814372i) q^{74} +(0.142315 - 0.989821i) q^{75} +(2.38899 - 0.701472i) q^{76} +(-4.45487 - 2.86297i) q^{77} +(-0.602253 + 1.31875i) q^{78} +(8.99529 + 2.64126i) q^{79} +(0.654861 + 0.755750i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-9.81085 - 2.88072i) q^{82} +(2.61243 - 5.72042i) q^{83} +(-3.30361 - 2.12310i) q^{84} +(6.31166 - 1.85327i) q^{85} +(-1.11513 + 7.75590i) q^{86} +(-3.23266 - 7.07854i) q^{87} +(-0.191910 - 1.33476i) q^{88} +(-13.5298 + 8.69507i) q^{89} +(-0.654861 + 0.755750i) q^{90} -5.69322 q^{91} +(2.21860 + 4.25180i) q^{92} -2.50057 q^{93} +(-7.63065 + 8.80624i) q^{94} +(2.09460 - 1.34612i) q^{95} +(-0.142315 - 0.989821i) q^{96} +(2.33526 + 5.11350i) q^{97} +(1.19849 - 8.33565i) q^{98} +(1.29386 - 0.379913i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} - 2 q^{10} + 18 q^{11} + 2 q^{12} + 2 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} - 2 q^{17} + 2 q^{18} + 4 q^{19} + 2 q^{20} + 13 q^{21} + 26 q^{22} + 20 q^{24} - 2 q^{25} + 9 q^{26} + 2 q^{27} - 2 q^{28} + 6 q^{29} + 2 q^{30} + 8 q^{31} + 2 q^{32} + 4 q^{33} + 13 q^{34} + 13 q^{35} - 2 q^{36} + 16 q^{37} - 15 q^{38} - 2 q^{39} - 2 q^{40} + 3 q^{41} + 9 q^{42} - 16 q^{43} + 18 q^{44} - 20 q^{45} - 34 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} - 9 q^{51} + 2 q^{52} - 4 q^{53} - 2 q^{54} - 7 q^{55} + 2 q^{56} + 29 q^{57} + 16 q^{58} + 25 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 9 q^{63} - 2 q^{64} - 2 q^{65} - 15 q^{66} + 20 q^{67} - 2 q^{68} - 22 q^{69} - 2 q^{70} - q^{71} + 2 q^{72} - q^{73} - 16 q^{74} + 2 q^{75} + 4 q^{76} + 53 q^{77} + 2 q^{78} + 28 q^{79} + 2 q^{80} - 2 q^{81} - 25 q^{82} + 9 q^{83} - 9 q^{84} - 9 q^{85} - 28 q^{86} - 6 q^{87} - 7 q^{88} - 31 q^{89} - 2 q^{90} - 26 q^{91} + 11 q^{92} - 30 q^{93} + q^{94} - 15 q^{95} - 2 q^{96} - 35 q^{97} - 5 q^{98} - 4 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 - 2 * q^10 + 18 * q^11 + 2 * q^12 + 2 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 - 2 * q^17 + 2 * q^18 + 4 * q^19 + 2 * q^20 + 13 * q^21 + 26 * q^22 + 20 * q^24 - 2 * q^25 + 9 * q^26 + 2 * q^27 - 2 * q^28 + 6 * q^29 + 2 * q^30 + 8 * q^31 + 2 * q^32 + 4 * q^33 + 13 * q^34 + 13 * q^35 - 2 * q^36 + 16 * q^37 - 15 * q^38 - 2 * q^39 - 2 * q^40 + 3 * q^41 + 9 * q^42 - 16 * q^43 + 18 * q^44 - 20 * q^45 - 34 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 - 9 * q^51 + 2 * q^52 - 4 * q^53 - 2 * q^54 - 7 * q^55 + 2 * q^56 + 29 * q^57 + 16 * q^58 + 25 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 9 * q^63 - 2 * q^64 - 2 * q^65 - 15 * q^66 + 20 * q^67 - 2 * q^68 - 22 * q^69 - 2 * q^70 - q^71 + 2 * q^72 - q^73 - 16 * q^74 + 2 * q^75 + 4 * q^76 + 53 * q^77 + 2 * q^78 + 28 * q^79 + 2 * q^80 - 2 * q^81 - 25 * q^82 + 9 * q^83 - 9 * q^84 - 9 * q^85 - 28 * q^86 - 6 * q^87 - 7 * q^88 - 31 * q^89 - 2 * q^90 - 26 * q^91 + 11 * q^92 - 30 * q^93 + q^94 - 15 * q^95 - 2 * q^96 - 35 * q^97 - 5 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{11}\right)$

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
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$3$	−0.841254	+	0.540641i	−0.485698	+	0.312139i
$4$	−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
$6$	−0.142315	+	0.989821i	−0.0580998	+	0.404093i
$7$	−3.76793	+	1.10637i	−1.42414	+	0.418167i	−0.900904	−	0.434018i	$-0.857095\pi$
$7$	−3.76793	+	1.10637i	−1.42414	+	0.418167i	−0.523241	+	0.852185i	$0.675277\pi$
$8$	−0.841254	−	0.540641i	−0.297428	−	0.191145i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	−0.959493	−	0.281733i	−0.303418	−	0.0890917i
$11$	0.883071	+	1.01912i	0.266256	+	0.307276i	0.873096	−	0.487548i	$-0.162109\pi$
$11$	0.883071	+	1.01912i	0.266256	+	0.307276i	−0.606840	+	0.794824i	$0.707563\pi$
$12$	0.654861	+	0.755750i	0.189042	+	0.218166i
$13$	1.39104	+	0.408445i	0.385804	+	0.113282i	0.468882	−	0.883261i	$-0.344657\pi$
$13$	1.39104	+	0.408445i	0.385804	+	0.113282i	−0.0830780	+	0.996543i	$0.526475\pi$
$14$	−1.63134	+	3.57213i	−0.435993	+	0.954692i
$15$	0.841254	+	0.540641i	0.217211	+	0.139593i
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	−0.936163	+	6.51116i	−0.227053	+	1.57919i	0.483372	+	0.875415i	$0.339412\pi$
$17$	−0.936163	+	6.51116i	−0.227053	+	1.57919i	−0.710425	+	0.703773i	$0.751497\pi$
$18$	−0.415415	−	0.909632i	−0.0979143	−	0.214402i
$19$	0.354343	+	2.46451i	0.0812918	+	0.565397i	0.989239	+	0.146311i	$0.0467401\pi$
$19$	0.354343	+	2.46451i	0.0812918	+	0.565397i	−0.907947	+	0.419085i	$0.862351\pi$
$20$	−0.841254	+	0.540641i	−0.188110	+	0.120891i
$21$	2.57164	−	2.96783i	0.561178	−	0.647634i
$22$	1.34849			0.287498
$23$	−4.52426	+	1.59092i	−0.943374	+	0.331731i
$23$	−4.52426	+	1.59092i	−0.943374	+	0.331731i
$24$	1.00000			0.204124
$25$	−0.654861	+	0.755750i	−0.130972	+	0.151150i
$26$	1.21962	−	0.783801i	0.239187	−	0.153716i
$27$	0.142315	+	0.989821i	0.0273885	+	0.190491i
$28$	1.63134	+	3.57213i	0.308294	+	0.675069i
$29$	−1.10746	+	7.70255i	−0.205650	+	1.43033i	0.581490	+	0.813554i	$0.302470\pi$
$29$	−1.10746	+	7.70255i	−0.205650	+	1.43033i	−0.787140	+	0.616775i	$0.788439\pi$
$30$	0.959493	−	0.281733i	0.175179	−	0.0514371i
$31$	2.10361	+	1.35191i	0.377820	+	0.242810i	0.715743	−	0.698364i	$-0.246088\pi$
$31$	2.10361	+	1.35191i	0.377820	+	0.242810i	−0.337923	+	0.941174i	$0.609724\pi$
$32$	−0.415415	+	0.909632i	−0.0734357	+	0.160802i
$33$	−1.29386	−	0.379913i	−0.225233	−	0.0661343i
$34$	4.30775	+	4.97141i	0.738773	+	0.852589i
$35$	2.57164	+	2.96783i	0.434687	+	0.501655i
$36$	−0.959493	−	0.281733i	−0.159915	−	0.0469554i
$37$	0.371911	−	0.814372i	0.0611418	−	0.133882i	−0.876595	−	0.481230i	$-0.840190\pi$
$37$	0.371911	−	0.814372i	0.0611418	−	0.133882i	0.937736	+	0.347348i	$0.112918\pi$
$38$	2.09460	+	1.34612i	0.339788	+	0.218369i
$39$	−1.39104	+	0.408445i	−0.222744	+	0.0654036i
$40$	−0.142315	+	0.989821i	−0.0225020	+	0.156505i
$41$	−4.24763	−	9.30102i	−0.663369	−	1.45257i	−0.879349	−	0.476177i	$-0.842022\pi$
$41$	−4.24763	−	9.30102i	−0.663369	−	1.45257i	0.215981	−	0.976398i	$-0.430705\pi$
$42$	−0.558871	−	3.88703i	−0.0862357	−	0.599782i
$43$	−6.59177	+	4.23627i	−1.00524	+	0.646026i	−0.936156	−	0.351585i	$-0.885643\pi$
$43$	−6.59177	+	4.23627i	−1.00524	+	0.646026i	−0.0690799	+	0.997611i	$0.522006\pi$
$44$	0.883071	−	1.01912i	0.133128	−	0.153638i
$45$	−1.00000			−0.149071
$46$	−1.76042	+	4.46104i	−0.259560	+	0.657745i
$47$	−11.6523			−1.69967			−0.849833	−	0.527052i	$-0.823297\pi$
$47$	−11.6523			−1.69967			−0.849833	+	0.527052i	$0.823297\pi$
$48$	0.654861	−	0.755750i	0.0945210	−	0.109083i
$49$	7.08450	−	4.55293i	1.01207	−	0.650419i
$50$	0.142315	+	0.989821i	0.0201264	+	0.139982i
$51$	−2.73265	−	5.98366i	−0.382647	−	0.837881i
$52$	0.206323	−	1.43501i	0.0286118	−	0.198999i
$53$	12.1361	−	3.56348i	1.66702	−	0.489481i	0.693957	−	0.720017i	$-0.255866\pi$
$53$	12.1361	−	3.56348i	1.66702	−	0.489481i	0.973064	+	0.230535i	$0.0740477\pi$
$54$	0.841254	+	0.540641i	0.114480	+	0.0735719i
$55$	0.560182	−	1.22663i	0.0755349	−	0.165398i
$56$	3.76793	+	1.10637i	0.503511	+	0.147844i
$57$	−1.63051	−	1.88170i	−0.215966	−	0.249238i
$58$	5.09597	+	5.88106i	0.669134	+	0.772221i
$59$	−8.65772	−	2.54214i	−1.12714	−	0.330958i	−0.335557	−	0.942020i	$-0.608924\pi$
$59$	−8.65772	−	2.54214i	−1.12714	−	0.330958i	−0.791583	+	0.611062i	$0.790743\pi$
$60$	0.415415	−	0.909632i	0.0536298	−	0.117433i
$61$	6.74235	+	4.33305i	0.863269	+	0.554790i	0.895687	−	0.444685i	$-0.146684\pi$
$61$	6.74235	+	4.33305i	0.863269	+	0.554790i	−0.0324177	+	0.999474i	$0.510321\pi$
$62$	2.39928	−	0.704491i	0.304709	−	0.0894705i
$63$	−0.558871	+	3.88703i	−0.0704111	+	0.489720i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	−0.206323	−	1.43501i	−0.0255912	−	0.177991i
$66$	−1.13442	+	0.729047i	−0.139637	+	0.0897395i
$67$	−8.07285	+	9.31656i	−0.986256	+	1.13820i	0.00414768	+	0.999991i	$0.498680\pi$
$67$	−8.07285	+	9.31656i	−0.986256	+	1.13820i	−0.990403	+	0.138208i	$0.955866\pi$
$68$	6.57812			0.797714
$69$	2.94593	−	3.78437i	0.354649	−	0.455585i
$70$	3.92700			0.469367
$71$	6.95423	−	8.02561i	0.825315	−	0.952464i	−0.174165	−	0.984717i	$-0.555723\pi$
$71$	6.95423	−	8.02561i	0.825315	−	0.952464i	0.999480	+	0.0322523i	$0.0102680\pi$
$72$	−0.841254	+	0.540641i	−0.0991427	+	0.0637151i
$73$	−0.588681	−	4.09436i	−0.0688999	−	0.479209i	−0.994833	−	0.101522i	$-0.967629\pi$
$73$	−0.588681	−	4.09436i	−0.0688999	−	0.479209i	0.925933	−	0.377687i	$-0.123280\pi$
$74$	−0.371911	−	0.814372i	−0.0432338	−	0.0946688i
$75$	0.142315	−	0.989821i	0.0164331	−	0.114295i
$76$	2.38899	−	0.701472i	0.274036	−	0.0804644i
$77$	−4.45487	−	2.86297i	−0.507680	−	0.326266i
$78$	−0.602253	+	1.31875i	−0.0681917	+	0.149319i
$79$	8.99529	+	2.64126i	1.01205	+	0.297165i	0.745392	−	0.666627i	$-0.232262\pi$
$79$	8.99529	+	2.64126i	1.01205	+	0.297165i	0.266658	+	0.963791i	$0.414081\pi$
$80$	0.654861	+	0.755750i	0.0732157	+	0.0844954i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	−9.81085	−	2.88072i	−1.08343	−	0.318123i
$83$	2.61243	−	5.72042i	0.286751	−	0.627898i	−0.710361	−	0.703837i	$-0.751468\pi$
$83$	2.61243	−	5.72042i	0.286751	−	0.627898i	0.997112	+	0.0759395i	$0.0241956\pi$
$84$	−3.30361	−	2.12310i	−0.360453	−	0.231649i
$85$	6.31166	−	1.85327i	0.684595	−	0.201015i
$86$	−1.11513	+	7.75590i	−0.120248	+	0.836340i
$87$	−3.23266	−	7.07854i	−0.346578	−	0.758899i
$88$	−0.191910	−	1.33476i	−0.0204576	−	0.142286i
$89$	−13.5298	+	8.69507i	−1.43416	+	0.921676i	−0.434375	+	0.900732i	$0.643031\pi$
$89$	−13.5298	+	8.69507i	−1.43416	+	0.921676i	−0.999781	+	0.0209441i	$0.993333\pi$
$90$	−0.654861	+	0.755750i	−0.0690284	+	0.0796630i
$91$	−5.69322			−0.596812
$92$	2.21860	+	4.25180i	0.231305	+	0.443281i
$93$	−2.50057			−0.259297
$94$	−7.63065	+	8.80624i	−0.787042	+	0.908294i
$95$	2.09460	−	1.34612i	0.214901	−	0.138108i
$96$	−0.142315	−	0.989821i	−0.0145249	−	0.101023i
$97$	2.33526	+	5.11350i	0.237109	+	0.519197i	0.990357	−	0.138540i	$-0.0442410\pi$
$97$	2.33526	+	5.11350i	0.237109	+	0.519197i	−0.753247	+	0.657737i	$0.771514\pi$
$98$	1.19849	−	8.33565i	0.121065	−	0.842028i
$99$	1.29386	−	0.379913i	0.130038	−	0.0381827i
$100$	0.841254	+	0.540641i	0.0841254	+	0.0540641i
$101$	−3.03633	+	6.64864i	−0.302126	+	0.661564i	−0.998420	−	0.0561926i	$-0.982104\pi$
$101$	−3.03633	+	6.64864i	−0.302126	+	0.661564i	0.696294	+	0.717757i	$0.254831\pi$
$102$	−6.31166	−	1.85327i	−0.624947	−	0.183501i
$103$	7.32920	+	8.45835i	0.722167	+	0.833426i	0.991566	−	0.129603i	$-0.0413703\pi$
$103$	7.32920	+	8.45835i	0.722167	+	0.833426i	−0.269398	+	0.963029i	$0.586825\pi$
$104$	−0.949392	−	1.09566i	−0.0930956	−	0.107438i
$105$	−3.76793	−	1.10637i	−0.367713	−	0.107970i
$106$	5.25435	−	11.5054i	0.510348	−	1.11751i
$107$	−3.74479	−	2.40663i	−0.362023	−	0.232658i	0.346966	−	0.937878i	$-0.387212\pi$
$107$	−3.74479	−	2.40663i	−0.362023	−	0.232658i	−0.708989	+	0.705220i	$0.750848\pi$
$108$	0.959493	−	0.281733i	0.0923273	−	0.0271097i
$109$	1.29682	−	9.01957i	0.124213	−	0.863918i	−0.828488	−	0.560007i	$-0.810798\pi$
$109$	1.29682	−	9.01957i	0.124213	−	0.863918i	0.952700	−	0.303911i	$-0.0982926\pi$
$110$	−0.560182	−	1.22663i	−0.0534112	−	0.116954i
$111$	0.127411	+	0.886164i	0.0120933	+	0.0841109i
$112$	3.30361	−	2.12310i	0.312161	−	0.200614i
$113$	7.45593	−	8.60460i	0.701395	−	0.809453i	−0.287546	−	0.957767i	$-0.592839\pi$
$113$	7.45593	−	8.60460i	0.701395	−	0.809453i	0.988940	+	0.148314i	$0.0473847\pi$
$114$	−2.48985			−0.233196
$115$	3.32660	+	3.45452i	0.310207	+	0.322136i
$116$	7.78176			0.722518
$117$	0.949392	−	1.09566i	0.0877714	−	0.101294i
$118$	−7.59082	+	4.87832i	−0.698792	+	0.449086i
$119$	−3.67632	−	25.5694i	−0.337008	−	2.34394i
$120$	−0.415415	−	0.909632i	−0.0379220	−	0.0830377i
$121$	1.30668	−	9.08813i	0.118789	−	0.826193i
$122$	7.69000	−	2.25799i	0.696220	−	0.204429i
$123$	8.60185	+	5.52807i	0.775602	+	0.498449i
$124$	1.03877	−	2.27460i	0.0932846	−	0.204265i
$125$	0.959493	+	0.281733i	0.0858197	+	0.0251989i
$126$	2.57164	+	2.96783i	0.229100	+	0.264396i
$127$	−1.15377	−	1.33152i	−0.102381	−	0.118154i	0.702247	−	0.711934i	$-0.252180\pi$
$127$	−1.15377	−	1.33152i	−0.102381	−	0.118154i	−0.804627	+	0.593780i	$0.797635\pi$
$128$	0.959493	+	0.281733i	0.0848080	+	0.0249019i
$129$	3.25505	−	7.12756i	0.286591	−	0.627547i
$130$	−1.21962	−	0.783801i	−0.106968	−	0.0687439i
$131$	−21.3302	+	6.26312i	−1.86363	+	0.547211i	−0.864635	+	0.502400i	$0.832450\pi$
$131$	−21.3302	+	6.26312i	−1.86363	+	0.547211i	−0.998995	+	0.0448110i	$0.985731\pi$
$132$	−0.191910	+	1.33476i	−0.0167036	+	0.116176i
$133$	−4.06179	−	8.89407i	−0.352201	−	0.771214i
$134$	1.75440	+	12.2021i	0.151557	+	1.05410i
$135$	0.841254	−	0.540641i	0.0724036	−	0.0465310i
$136$	4.30775	−	4.97141i	0.369386	−	0.426295i
$137$	−9.12749			−0.779814			−0.389907	−	0.920854i	$-0.627493\pi$
$137$	−9.12749			−0.779814			−0.389907	+	0.920854i	$0.627493\pi$
$138$	−0.930861	−	4.70463i	−0.0792401	−	0.400484i
$139$	8.88648			0.753741			0.376871	−	0.926266i	$-0.377000\pi$
$139$	8.88648			0.753741			0.376871	+	0.926266i	$0.377000\pi$
$140$	2.57164	−	2.96783i	0.217343	−	0.250828i
$141$	9.80256	−	6.29972i	0.825525	−	0.530532i
$142$	−1.51130	−	10.5113i	−0.126825	−	0.882089i
$143$	0.812131	+	1.77832i	0.0679138	+	0.148710i
$144$	−0.142315	+	0.989821i	−0.0118596	+	0.0824851i
$145$	7.46654	−	2.19238i	0.620063	−	0.182067i
$146$	−3.47982	−	2.23634i	−0.287992	−	0.185081i
$147$	−3.49836	+	7.66034i	−0.288540	+	0.631815i
$148$	−0.859011	−	0.252229i	−0.0706103	−	0.0207331i
$149$	−8.23453	−	9.50315i	−0.674599	−	0.778529i	0.310490	−	0.950577i	$-0.399507\pi$
$149$	−8.23453	−	9.50315i	−0.674599	−	0.778529i	−0.985089	+	0.172048i	$0.944962\pi$
$150$	−0.654861	−	0.755750i	−0.0534692	−	0.0617067i
$151$	11.8710	+	3.48564i	0.966049	+	0.283657i	0.726454	−	0.687215i	$-0.241167\pi$
$151$	11.8710	+	3.48564i	0.966049	+	0.283657i	0.239595	+	0.970873i	$0.422985\pi$
$152$	1.03432	−	2.26485i	0.0838945	−	0.183703i
$153$	5.53386	+	3.55640i	0.447386	+	0.287518i
$154$	−5.08101	+	1.49192i	−0.409439	+	0.120222i
$155$	0.355868	−	2.47512i	0.0285840	−	0.198806i
$156$	0.602253	+	1.31875i	0.0482188	+	0.105585i
$157$	−0.964870	−	6.71082i	−0.0770050	−	0.535582i	−0.991411	−	0.130783i	$-0.958251\pi$
$157$	−0.964870	−	6.71082i	−0.0770050	−	0.535582i	0.914406	−	0.404798i	$-0.132658\pi$
$158$	7.88679	−	5.06853i	0.627440	−	0.403231i
$159$	−8.28297	+	9.55906i	−0.656882	+	0.758083i
$160$	1.00000			0.0790569
$161$	15.2870	−	11.0000i	1.20478	−	0.866920i
$162$	−1.00000			−0.0785674
$163$	4.06906	−	4.69595i	0.318714	−	0.367815i	−0.573675	−	0.819083i	$-0.694483\pi$
$163$	4.06906	−	4.69595i	0.318714	−	0.367815i	0.892389	+	0.451268i	$0.149028\pi$
$164$	−8.60185	+	5.52807i	−0.671691	+	0.431670i
$165$	0.191910	+	1.33476i	0.0149402	+	0.103911i
$166$	−2.61243	−	5.72042i	−0.202764	−	0.443991i
$167$	−1.50382	+	10.4593i	−0.116369	+	0.809362i	0.845132	+	0.534558i	$0.179522\pi$
$167$	−1.50382	+	10.4593i	−0.116369	+	0.809362i	−0.961500	+	0.274804i	$0.911387\pi$
$168$	−3.76793	+	1.10637i	−0.290702	+	0.0853579i
$169$	−9.16814	−	5.89201i	−0.705242	−	0.453231i
$170$	2.73265	−	5.98366i	0.209585	−	0.458926i
$171$	2.38899	+	0.701472i	0.182691	+	0.0536429i
$172$	5.13126	+	5.92179i	0.391255	+	0.451532i
$173$	2.35740	+	2.72059i	0.179230	+	0.206843i	0.838255	−	0.545279i	$-0.183576\pi$
$173$	2.35740	+	2.72059i	0.179230	+	0.206843i	−0.659025	+	0.752121i	$0.729031\pi$
$174$	−7.46654	−	2.19238i	−0.566037	−	0.166204i
$175$	1.63134	−	3.57213i	0.123317	−	0.270028i
$176$	−1.13442	−	0.729047i	−0.0855101	−	0.0549540i
$177$	8.65772	−	2.54214i	0.650754	−	0.191079i
$178$	−2.28884	+	15.9192i	−0.171556	+	1.19319i
$179$	−2.47106	−	5.41086i	−0.184696	−	0.404427i	0.794523	−	0.607234i	$-0.207721\pi$
$179$	−2.47106	−	5.41086i	−0.184696	−	0.404427i	−0.979219	+	0.202807i	$0.934994\pi$
$180$	0.142315	+	0.989821i	0.0106075	+	0.0737769i
$181$	−6.63510	+	4.26412i	−0.493183	+	0.316950i	−0.763484	−	0.645826i	$-0.776513\pi$
$181$	−6.63510	+	4.26412i	−0.493183	+	0.316950i	0.270301	+	0.962776i	$0.412877\pi$
$182$	−3.72827	+	4.30265i	−0.276358	+	0.318934i
$183$	−8.01465			−0.592460
$184$	4.66617	+	1.10763i	0.343995	+	0.0816557i
$185$	−0.895276			−0.0658220
$186$	−1.63752	+	1.88980i	−0.120069	+	0.138567i
$187$	−7.46234	+	4.79576i	−0.545701	+	0.350700i
$188$	1.65830	+	11.5337i	0.120944	+	0.841183i
$189$	−1.63134	−	3.57213i	−0.118662	−	0.259834i
$190$	0.354343	−	2.46451i	0.0257067	−	0.178794i
$191$	8.71297	−	2.55836i	0.630449	−	0.185116i	0.0491299	−	0.998792i	$-0.484355\pi$
$191$	8.71297	−	2.55836i	0.630449	−	0.185116i	0.581319	+	0.813676i	$0.302537\pi$
$192$	−0.841254	−	0.540641i	−0.0607122	−	0.0390174i
$193$	−7.74728	+	16.9642i	−0.557662	+	1.22111i	0.395450	+	0.918488i	$0.370589\pi$
$193$	−7.74728	+	16.9642i	−0.557662	+	1.22111i	−0.953111	+	0.302621i	$0.902138\pi$
$194$	5.39379	+	1.58376i	0.387252	+	0.113707i
$195$	0.949392	+	1.09566i	0.0679874	+	0.0784616i
$196$	−5.51482	−	6.36444i	−0.393916	−	0.454603i
$197$	0.727691	+	0.213669i	0.0518459	+	0.0152233i	0.307553	−	0.951531i	$-0.400490\pi$
$197$	0.727691	+	0.213669i	0.0518459	+	0.0152233i	−0.255707	+	0.966754i	$0.582308\pi$
$198$	0.560182	−	1.22663i	0.0398104	−	0.0871726i
$199$	14.0162	+	9.00766i	0.993582	+	0.638536i	0.933094	−	0.359633i	$-0.117098\pi$
$199$	14.0162	+	9.00766i	0.993582	+	0.638536i	0.0604877	+	0.998169i	$0.480734\pi$
$200$	0.959493	−	0.281733i	0.0678464	−	0.0199215i
$201$	1.75440	−	12.2021i	0.123746	−	0.860670i
$202$	3.03633	+	6.64864i	0.213636	+	0.467797i
$203$	−4.34900	−	30.2480i	−0.305240	−	2.12299i
$204$	−5.53386	+	3.55640i	−0.387448	+	0.248998i
$205$	−6.69597	+	7.72756i	−0.467667	+	0.539717i
$206$	11.1920			0.779783
$207$	−0.432292	+	4.77631i	−0.0300464	+	0.331976i
$208$	−1.44976			−0.100523
$209$	−2.19872	+	2.53745i	−0.152088	+	0.175519i
$210$	−3.30361	+	2.12310i	−0.227971	+	0.146508i
$211$	−0.315616	−	2.19516i	−0.0217279	−	0.151121i	0.976069	−	0.217460i	$-0.0697772\pi$
$211$	−0.315616	−	2.19516i	−0.0217279	−	0.151121i	−0.997797	+	0.0663390i	$0.978868\pi$
$212$	−5.25435	−	11.5054i	−0.360871	−	0.790196i
$213$	−1.51130	+	10.5113i	−0.103552	+	0.720223i
$214$	−4.27113	+	1.25412i	−0.291968	+	0.0857297i
$215$	6.59177	+	4.23627i	0.449555	+	0.288912i
$216$	0.415415	−	0.909632i	0.0282654	−	0.0618926i
$217$	−9.42197	−	2.76654i	−0.639605	−	0.187805i
$218$	−5.96730	−	6.88663i	−0.404157	−	0.466422i
$219$	2.70881	+	3.12613i	0.183044	+	0.211244i
$220$	−1.29386	−	0.379913i	−0.0872323	−	0.0256137i
$221$	−3.96169	+	8.67489i	−0.266492	+	0.583536i
$222$	0.753154	+	0.484023i	0.0505484	+	0.0324855i
$223$	−22.4739	+	6.59894i	−1.50497	+	0.441898i	−0.927282	−	0.374363i	$-0.877861\pi$
$223$	−22.4739	+	6.59894i	−1.50497	+	0.441898i	−0.577683	+	0.816261i	$0.696043\pi$
$224$	0.558871	−	3.88703i	0.0373411	−	0.259713i
$225$	0.415415	+	0.909632i	0.0276943	+	0.0606421i
$226$	−1.62033	−	11.2696i	−0.107783	−	0.749645i
$227$	−16.4214	+	10.5534i	−1.08993	+	0.700453i	−0.956829	−	0.290650i	$-0.906129\pi$
$227$	−16.4214	+	10.5534i	−1.08993	+	0.700453i	−0.133097	+	0.991103i	$0.542492\pi$
$228$	−1.63051	+	1.88170i	−0.107983	+	0.124619i
$229$	4.90533			0.324154			0.162077	−	0.986778i	$-0.448181\pi$
$229$	4.90533			0.324154			0.162077	+	0.986778i	$0.448181\pi$
$230$	4.78921	−	0.251848i	0.315791	−	0.0166064i
$231$	5.29552			0.348419
$232$	5.09597	−	5.88106i	0.334567	−	0.386111i
$233$	−13.6719	+	8.78640i	−0.895677	+	0.575616i	−0.905505	−	0.424335i	$-0.860508\pi$
$233$	−13.6719	+	8.78640i	−0.895677	+	0.575616i	0.00982854	+	0.999952i	$0.496871\pi$
$234$	−0.206323	−	1.43501i	−0.0134877	−	0.0938093i
$235$	4.84055	+	10.5993i	0.315763	+	0.691424i
$236$	−1.28414	+	8.93138i	−0.0835903	+	0.581383i
$237$	−8.99529	+	2.64126i	−0.584307	+	0.171568i
$238$	−21.7315	−	13.9660i	−1.40864	−	0.905281i
$239$	0.103886	−	0.227480i	0.00671986	−	0.0147144i	−0.906242	−	0.422759i	$-0.861062\pi$
$239$	0.103886	−	0.227480i	0.00671986	−	0.0147144i	0.912962	+	0.408044i	$0.133789\pi$
$240$	−0.959493	−	0.281733i	−0.0619350	−	0.0181858i
$241$	14.9279	+	17.2277i	0.961589	+	1.10973i	0.993903	+	0.110255i	$0.0351667\pi$
$241$	14.9279	+	17.2277i	0.961589	+	1.10973i	−0.0323145	+	0.999478i	$0.510288\pi$
$242$	−6.01266	−	6.93898i	−0.386508	−	0.446054i
$243$	0.959493	+	0.281733i	0.0615515	+	0.0180732i
$244$	3.32940	−	7.29038i	0.213143	−	0.466719i
$245$	−7.08450	−	4.55293i	−0.452612	−	0.290876i
$246$	9.81085	−	2.88072i	0.625517	−	0.183668i
$247$	−0.513713	+	3.57295i	−0.0326868	+	0.227341i
$248$	−1.03877	−	2.27460i	−0.0659622	−	0.144437i
$249$	0.894978	+	6.22471i	0.0567170	+	0.394475i
$250$	0.841254	−	0.540641i	0.0532055	−	0.0341931i
$251$	4.75346	−	5.48578i	0.300036	−	0.346260i	−0.585634	−	0.810576i	$-0.699154\pi$
$251$	4.75346	−	5.48578i	0.300036	−	0.346260i	0.885670	+	0.464316i	$0.153700\pi$
$252$	3.92700			0.247378
$253$	−5.61659	−	3.20586i	−0.353112	−	0.201551i
$254$	−1.76186			−0.110549
$255$	−4.30775	+	4.97141i	−0.269762	+	0.311322i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	1.63420	+	11.3661i	0.101938	+	0.708997i	0.975132	+	0.221624i	$0.0711358\pi$
$257$	1.63420	+	11.3661i	0.101938	+	0.708997i	−0.873194	+	0.487373i	$0.837955\pi$
$258$	−3.25505	−	7.12756i	−0.202650	−	0.443743i
$259$	−0.500344	+	3.47997i	−0.0310899	+	0.216235i
$260$	−1.39104	+	0.408445i	−0.0862684	+	0.0253307i
$261$	6.54643	+	4.20714i	0.405214	+	0.260415i
$262$	−9.23498	+	20.2218i	−0.570539	+	1.24931i
$263$	−0.551986	−	0.162078i	−0.0340369	−	0.00999415i	0.264670	−	0.964339i	$-0.414737\pi$
$263$	−0.551986	−	0.162078i	−0.0340369	−	0.00999415i	−0.298707	+	0.954345i	$0.596555\pi$
$264$	0.883071	+	1.01912i	0.0543493	+	0.0627224i
$265$	−8.28297	−	9.55906i	−0.508819	−	0.587208i
$266$	−9.38159	−	2.75468i	−0.575222	−	0.168901i
$267$	6.68108	−	14.6295i	0.408875	−	0.895312i
$268$	10.3706	+	6.66479i	0.633487	+	0.407117i
$269$	23.9780	−	7.04057i	1.46196	−	0.429271i	0.548486	−	0.836160i	$-0.315204\pi$
$269$	23.9780	−	7.04057i	1.46196	−	0.429271i	0.913478	+	0.406888i	$0.133386\pi$
$270$	0.142315	−	0.989821i	0.00866101	−	0.0602386i
$271$	7.75081	+	16.9719i	0.470828	+	1.03097i	0.984884	+	0.173214i	$0.0554151\pi$
$271$	7.75081	+	16.9719i	0.470828	+	1.03097i	−0.514056	+	0.857757i	$0.671858\pi$
$272$	−0.936163	−	6.51116i	−0.0567632	−	0.394797i
$273$	4.78944	−	3.07799i	0.289870	−	0.186288i
$274$	−5.97723	+	6.89809i	−0.361098	+	0.416729i
$275$	−1.34849			−0.0813168
$276$	−4.16510	−	2.37738i	−0.250710	−	0.143101i
$277$	18.8240			1.13102			0.565511	−	0.824741i	$-0.308679\pi$
$277$	18.8240			1.13102			0.565511	+	0.824741i	$0.308679\pi$
$278$	5.81941	−	6.71595i	0.349025	−	0.402796i
$279$	2.10361	−	1.35191i	0.125940	−	0.0809367i
$280$	−0.558871	−	3.88703i	−0.0333989	−	0.232295i
$281$	1.64392	+	3.59967i	0.0980678	+	0.214738i	0.952307	−	0.305142i	$-0.0987038\pi$
$281$	1.64392	+	3.59967i	0.0980678	+	0.214738i	−0.854239	+	0.519880i	$0.825977\pi$
$282$	1.65830	−	11.5337i	0.0987503	−	0.686823i
$283$	9.82424	−	2.88466i	0.583990	−	0.171475i	0.0236254	−	0.999721i	$-0.492479\pi$
$283$	9.82424	−	2.88466i	0.583990	−	0.171475i	0.560365	+	0.828246i	$0.310661\pi$
$284$	−8.93361	−	5.74128i	−0.530112	−	0.340682i
$285$	−1.03432	+	2.26485i	−0.0612679	+	0.134158i
$286$	1.87580	+	0.550783i	0.110918	+	0.0325685i
$287$	26.2951	+	30.3462i	1.55215	+	1.79128i
$288$	0.654861	+	0.755750i	0.0385880	+	0.0445330i
$289$	−25.2074	−	7.40157i	−1.48279	−	0.435386i
$290$	3.23266	−	7.07854i	0.189828	−	0.415666i
$291$	−4.72911	−	3.03921i	−0.277225	−	0.178162i
$292$	−3.96891	+	1.16538i	−0.232263	+	0.0681986i
$293$	0.403750	−	2.80814i	0.0235873	−	0.164053i	−0.974623	−	0.223852i	$-0.928137\pi$
$293$	0.403750	−	2.80814i	0.0235873	−	0.164053i	0.998210	+	0.0597986i	$0.0190459\pi$
$294$	3.49836	+	7.66034i	0.204029	+	0.446760i
$295$	1.28414	+	8.93138i	0.0747655	+	0.520005i
$296$	−0.753154	+	0.484023i	−0.0437762	+	0.0281333i
$297$	−0.883071	+	1.01912i	−0.0512410	+	0.0591353i
$298$	−12.5745			−0.728420
$299$	−6.94322	+	0.365120i	−0.401537	+	0.0211154i
$300$	−1.00000			−0.0577350
$301$	20.1505	−	23.2549i	1.16146	−	1.34039i
$302$	10.4081	−	6.68890i	0.598920	−	0.384903i
$303$	−1.04020	−	7.23476i	−0.0597580	−	0.415626i
$304$	−1.03432	−	2.26485i	−0.0593224	−	0.129898i
$305$	1.14060	−	7.93307i	0.0653107	−	0.454246i
$306$	6.31166	−	1.85327i	0.360813	−	0.105944i
$307$	7.71607	+	4.95882i	0.440379	+	0.283015i	0.741983	−	0.670419i	$-0.233886\pi$
$307$	7.71607	+	4.95882i	0.440379	+	0.283015i	−0.301604	+	0.953433i	$0.597522\pi$
$308$	−2.19984	+	4.81697i	−0.125347	+	0.274472i
$309$	−10.7386	−	3.15315i	−0.610900	−	0.179376i
$310$	−1.63752	−	1.88980i	−0.0930051	−	0.107334i
$311$	16.3657	+	18.8870i	0.928012	+	1.07098i	0.997304	+	0.0733868i	$0.0233808\pi$
$311$	16.3657	+	18.8870i	0.928012	+	1.07098i	−0.0692913	+	0.997596i	$0.522074\pi$
$312$	1.39104	+	0.408445i	0.0787519	+	0.0231237i
$313$	5.07641	−	11.1158i	0.286936	−	0.628302i	−0.710194	−	0.704006i	$-0.751393\pi$
$313$	5.07641	−	11.1158i	0.286936	−	0.628302i	0.997130	+	0.0757036i	$0.0241203\pi$
$314$	−5.70355	−	3.66545i	−0.321870	−	0.206853i
$315$	3.76793	−	1.10637i	0.212299	−	0.0623366i
$316$	1.33421	−	9.27963i	0.0750551	−	0.522020i
$317$	5.37886	+	11.7781i	0.302107	+	0.661522i	0.998419	−	0.0562176i	$-0.0179041\pi$
$317$	5.37886	+	11.7781i	0.302107	+	0.661522i	−0.696312	+	0.717740i	$0.745177\pi$
$318$	1.80006	+	12.5197i	0.100942	+	0.702070i
$319$	−8.82778	+	5.67327i	−0.494261	+	0.317642i
$320$	0.654861	−	0.755750i	0.0366078	−	0.0422477i
$321$	4.45144			0.248455
$322$	1.69761	−	18.7566i	0.0946042	−	1.04526i
$323$	−16.3785			−0.911326
$324$	−0.654861	+	0.755750i	−0.0363812	+	0.0419861i
$325$	−1.21962	+	0.783801i	−0.0676522	+	0.0434774i
$326$	−0.884292	−	6.15039i	−0.0489764	−	0.340638i
$327$	3.78540	+	8.28886i	0.209333	+	0.458375i
$328$	−1.45517	+	10.1210i	−0.0803485	+	0.558836i
$329$	43.9052	−	12.8917i	2.42057	−	0.710744i
$330$	1.13442	+	0.729047i	0.0624477	+	0.0401327i
$331$	−3.94087	+	8.62929i	−0.216610	+	0.474309i	−0.986478	−	0.163894i	$-0.947595\pi$
$331$	−3.94087	+	8.62929i	−0.216610	+	0.474309i	0.769868	+	0.638203i	$0.220322\pi$
$332$	−6.03398	−	1.77174i	−0.331158	−	0.0972367i
$333$	−0.586281	−	0.676605i	−0.0321280	−	0.0370777i
$334$	6.91980	+	7.98587i	0.378634	+	0.436967i
$335$	11.8282	+	3.47308i	0.646245	+	0.189755i
$336$	−1.63134	+	3.57213i	−0.0889967	+	0.194876i
$337$	28.0291	+	18.0132i	1.52684	+	0.981242i	0.990541	+	0.137214i	$0.0438149\pi$
$337$	28.0291	+	18.0132i	1.52684	+	0.981242i	0.536300	+	0.844027i	$0.319821\pi$
$338$	−10.4567	+	3.07037i	−0.568771	+	0.167006i
$339$	−1.62033	+	11.2696i	−0.0880041	+	0.612082i
$340$	−2.73265	−	5.98366i	−0.148199	−	0.324510i
$341$	0.479883	+	3.33766i	0.0259871	+	0.180745i
$342$	2.09460	−	1.34612i	0.113263	−	0.0727896i
$343$	−3.65524	+	4.21838i	−0.197365	+	0.227771i
$344$	7.83565			0.422470
$345$	−4.66617	−	1.10763i	−0.251218	−	0.0596329i
$346$	3.59986			0.193529
$347$	21.1681	−	24.4293i	1.13636	−	1.31143i	0.192427	−	0.981311i	$-0.438364\pi$
$347$	21.1681	−	24.4293i	1.13636	−	1.31143i	0.943938	−	0.330123i	$-0.107090\pi$
$348$	−6.54643	+	4.20714i	−0.350926	+	0.225526i
$349$	−1.94594	−	13.5343i	−0.104164	−	0.724474i	−0.973239	−	0.229794i	$-0.926195\pi$
$349$	−1.94594	−	13.5343i	−0.104164	−	0.724474i	0.869076	−	0.494679i	$-0.164714\pi$
$350$	−1.63134	−	3.57213i	−0.0871986	−	0.190938i
$351$	−0.206323	+	1.43501i	−0.0110127	+	0.0765949i
$352$	−1.29386	+	0.379913i	−0.0689632	+	0.0202494i
$353$	−4.93053	−	3.16866i	−0.262426	−	0.168651i	0.402811	−	0.915283i	$-0.368033\pi$
$353$	−4.93053	−	3.16866i	−0.262426	−	0.168651i	−0.665237	+	0.746632i	$0.731669\pi$
$354$	3.74838	−	8.20781i	0.199224	−	0.436240i
$355$	−10.1892	−	2.99183i	−0.540789	−	0.158790i
$356$	10.5321	+	12.1546i	0.558198	+	0.644195i
$357$	16.9166	+	19.5227i	0.895319	+	1.03325i
$358$	−5.70745	−	1.67586i	−0.301648	−	0.0885719i
$359$	−6.78985	+	14.8677i	−0.358354	+	0.784687i	0.641492	+	0.767130i	$0.278316\pi$
$359$	−6.78985	+	14.8677i	−0.358354	+	0.784687i	−0.999846	+	0.0175564i	$0.994411\pi$
$360$	0.841254	+	0.540641i	0.0443380	+	0.0284943i
$361$	12.2821	−	3.60636i	0.646428	−	0.189808i
$362$	−1.12246	+	7.80688i	−0.0589952	+	0.410320i
$363$	3.81417	+	8.35186i	0.200192	+	0.438359i
$364$	0.810230	+	5.63527i	0.0424676	+	0.295369i
$365$	−3.47982	+	2.23634i	−0.182142	+	0.117056i
$366$	−5.24848	+	6.05707i	−0.274342	+	0.316608i
$367$	−26.6776			−1.39256			−0.696279	−	0.717771i	$-0.745162\pi$
$367$	−26.6776			−1.39256			−0.696279	+	0.717771i	$0.745162\pi$
$368$	3.89278	−	2.80111i	0.202925	−	0.146018i
$369$	−10.2250			−0.532294
$370$	−0.586281	+	0.676605i	−0.0304793	+	0.0351750i
$371$	−41.7855	+	26.8539i	−2.16939	+	1.39419i
$372$	0.355868	+	2.47512i	0.0184509	+	0.128329i
$373$	−0.237776	−	0.520657i	−0.0123116	−	0.0269586i	0.903376	−	0.428849i	$-0.141081\pi$
$373$	−0.237776	−	0.520657i	−0.0123116	−	0.0269586i	−0.915688	+	0.401890i	$0.868353\pi$
$374$	−1.26240	+	8.78022i	−0.0652774	+	0.454014i
$375$	−0.959493	+	0.281733i	−0.0495480	+	0.0145486i
$376$	9.80256	+	6.29972i	0.505528	+	0.324883i
$377$	−4.68659	+	10.2622i	−0.241372	+	0.528530i
$378$	−3.76793	−	1.10637i	−0.193802	−	0.0569053i
$379$	−14.4525	−	16.6791i	−0.742375	−	0.856747i	0.251431	−	0.967875i	$-0.419099\pi$
$379$	−14.4525	−	16.6791i	−0.742375	−	0.856747i	−0.993806	+	0.111129i	$0.964553\pi$
$380$	−1.63051	−	1.88170i	−0.0836432	−	0.0965294i
$381$	1.69049	+	0.496372i	0.0866064	+	0.0254299i
$382$	3.77230	−	8.26019i	0.193008	−	0.422628i
$383$	7.16367	+	4.60381i	0.366046	+	0.235244i	0.710714	−	0.703481i	$-0.248372\pi$
$383$	7.16367	+	4.60381i	0.366046	+	0.235244i	−0.344668	+	0.938725i	$0.612008\pi$
$384$	−0.959493	+	0.281733i	−0.0489639	+	0.0143771i
$385$	−0.753631	+	5.24162i	−0.0384086	+	0.267137i
$386$	7.74728	+	16.9642i	0.394326	+	0.863454i
$387$	1.11513	+	7.75590i	0.0566852	+	0.394254i
$388$	4.72911	−	3.03921i	0.240084	−	0.154293i
$389$	−15.3721	+	17.7404i	−0.779398	+	0.899473i	−0.997066	−	0.0765499i	$-0.975610\pi$
$389$	−15.3721	+	17.7404i	−0.779398	+	0.899473i	0.217668	+	0.976023i	$0.430155\pi$
$390$	1.44976			0.0734116
$391$	−6.12331	−	30.9476i	−0.309669	−	1.56509i
$392$	−8.42137			−0.425343
$393$	14.5580	−	16.8009i	0.734356	−	0.847491i
$394$	0.638017	−	0.410029i	0.0321428	−	0.0206569i
$395$	−1.33421	−	9.27963i	−0.0671313	−	0.466909i
$396$	−0.560182	−	1.22663i	−0.0281502	−	0.0616403i
$397$	2.11402	−	14.7033i	0.106099	−	0.737938i	−0.865432	−	0.501027i	$-0.832956\pi$
$397$	2.11402	−	14.7033i	0.106099	−	0.737938i	0.971531	−	0.236911i	$-0.0761351\pi$
$398$	15.9862	−	4.69397i	0.801315	−	0.235287i
$399$	8.22549	+	5.28620i	0.411789	+	0.264641i
$400$	0.415415	−	0.909632i	0.0207708	−	0.0454816i
$401$	15.3237	+	4.49945i	0.765230	+	0.224692i	0.640979	−	0.767559i	$-0.278529\pi$
$401$	15.3237	+	4.49945i	0.765230	+	0.224692i	0.124252	+	0.992251i	$0.460347\pi$
$402$	−8.07285	−	9.31656i	−0.402637	−	0.464668i
$403$	2.37402	+	2.73977i	0.118258	+	0.136477i
$404$	7.01308	+	2.05923i	0.348914	+	0.102450i
$405$	−0.415415	+	0.909632i	−0.0206421	+	0.0452000i
$406$	−25.7079	−	16.5214i	−1.27586	−	0.819946i
$407$	1.15837	−	0.340127i	0.0574181	−	0.0168595i
$408$	−0.936163	+	6.51116i	−0.0463470	+	0.322350i
$409$	14.2449	+	31.1919i	0.704364	+	1.54234i	0.834599	+	0.550858i	$0.185699\pi$
$409$	14.2449	+	31.1919i	0.704364	+	1.54234i	−0.130235	+	0.991483i	$0.541573\pi$
$410$	1.45517	+	10.1210i	0.0718659	+	0.499838i
$411$	7.67853	−	4.93469i	0.378754	−	0.243410i
$412$	7.32920	−	8.45835i	0.361084	−	0.416713i
$413$	35.4343			1.74361
$414$	3.32660	+	3.45452i	0.163494	+	0.169780i
$415$	−6.28872			−0.308701
$416$	−0.949392	+	1.09566i	−0.0465478	+	0.0537190i
$417$	−7.47578	+	4.80439i	−0.366091	+	0.235272i
$418$	0.477827	+	3.32336i	0.0233713	+	0.162551i
$419$	14.1111	+	30.8991i	0.689374	+	1.50952i	0.852397	+	0.522896i	$0.175148\pi$
$419$	14.1111	+	30.8991i	0.689374	+	1.50952i	−0.163023	+	0.986622i	$0.552125\pi$
$420$	−0.558871	+	3.88703i	−0.0272701	+	0.189668i
$421$	−21.9886	+	6.45645i	−1.07166	+	0.314668i	−0.769538	−	0.638601i	$-0.779514\pi$
$421$	−21.9886	+	6.45645i	−1.07166	+	0.314668i	−0.302123	+	0.953269i	$0.597695\pi$
$422$	−1.86568	−	1.19900i	−0.0908197	−	0.0583663i
$423$	−4.84055	+	10.5993i	−0.235356	+	0.515357i
$424$	−12.1361	−	3.56348i	−0.589381	−	0.173058i
$425$	−4.30775	−	4.97141i	−0.208957	−	0.241149i
$426$	6.95423	+	8.02561i	0.336933	+	0.388842i
$427$	−30.1987	−	8.86713i	−1.46142	−	0.429110i
$428$	−1.84920	+	4.04918i	−0.0893843	+	0.195724i
$429$	−1.64464	−	1.05695i	−0.0794039	−	0.0510298i
$430$	7.51826	−	2.20756i	0.362562	−	0.106458i
$431$	1.63918	−	11.4008i	0.0789567	−	0.549156i	−0.911497	−	0.411308i	$-0.865072\pi$
$431$	1.63918	−	11.4008i	0.0789567	−	0.549156i	0.990453	−	0.137848i	$-0.0440187\pi$
$432$	−0.415415	−	0.909632i	−0.0199867	−	0.0437647i
$433$	0.724540	+	5.03928i	0.0348191	+	0.242172i	0.999797	−	0.0201597i	$-0.00641747\pi$
$433$	0.724540	+	5.03928i	0.0348191	+	0.242172i	−0.964978	+	0.262332i	$0.915508\pi$
$434$	−8.26089	+	5.30895i	−0.396536	+	0.254838i
$435$	−5.09597	+	5.88106i	−0.244333	+	0.281975i
$436$	−9.11232			−0.436401
$437$	−5.52398	−	10.5864i	−0.264248	−	0.506414i
$438$	4.13647			0.197648
$439$	2.40284	−	2.77303i	0.114682	−	0.132350i	−0.695506	−	0.718520i	$-0.744820\pi$
$439$	2.40284	−	2.77303i	0.114682	−	0.132350i	0.810188	+	0.586171i	$0.199365\pi$
$440$	−1.13442	+	0.729047i	−0.0540813	+	0.0347560i
$441$	−1.19849	−	8.33565i	−0.0570707	−	0.396936i
$442$	3.96169	+	8.67489i	0.188438	+	0.412622i
$443$	−0.494505	+	3.43936i	−0.0234946	+	0.163409i	−0.998191	−	0.0601248i	$-0.980850\pi$
$443$	−0.494505	+	3.43936i	−0.0234946	+	0.163409i	0.974696	+	0.223534i	$0.0717592\pi$
$444$	0.859011	−	0.252229i	0.0407669	−	0.0119702i
$445$	13.5298	+	8.69507i	0.641374	+	0.412186i
$446$	−9.73015	+	21.3060i	−0.460736	+	1.00887i
$447$	12.0651	+	3.54264i	0.570661	+	0.167561i
$448$	−2.57164	−	2.96783i	−0.121499	−	0.140217i
$449$	−15.5587	−	17.9557i	−0.734261	−	0.847383i	0.258683	−	0.965962i	$-0.416711\pi$
$449$	−15.5587	−	17.9557i	−0.734261	−	0.847383i	−0.992945	+	0.118579i	$0.962166\pi$
$450$	0.959493	+	0.281733i	0.0452309	+	0.0132810i
$451$	5.72788	−	12.5423i	0.269715	−	0.590594i
$452$	−9.57811	−	6.15547i	−0.450516	−	0.289529i
$453$	−11.8710	+	3.48564i	−0.557748	+	0.163770i
$454$	−2.77801	+	19.3215i	−0.130378	+	0.906801i
$455$	2.36505	+	5.17874i	0.110875	+	0.242783i
$456$	0.354343	+	2.46451i	0.0165936	+	0.115411i
$457$	−3.70556	+	2.38142i	−0.173339	+	0.111398i	−0.624433	−	0.781078i	$-0.714670\pi$
$457$	−3.70556	+	2.38142i	−0.173339	+	0.111398i	0.451095	+	0.892476i	$0.351034\pi$
$458$	3.21231	−	3.70720i	0.150101	−	0.173226i
$459$	−6.57812			−0.307040
$460$	2.94593	−	3.78437i	0.137355	−	0.176447i
$461$	−26.6274			−1.24016			−0.620080	−	0.784538i	$-0.712900\pi$
$461$	−26.6274			−1.24016			−0.620080	+	0.784538i	$0.712900\pi$
$462$	3.46783	−	4.00208i	0.161338	−	0.186194i
$463$	21.5113	−	13.8245i	0.999716	−	0.642478i	0.0650041	−	0.997885i	$-0.479294\pi$
$463$	21.5113	−	13.8245i	0.999716	−	0.642478i	0.934712	+	0.355407i	$0.115658\pi$
$464$	−1.10746	−	7.70255i	−0.0514125	−	0.357582i
$465$	1.03877	+	2.27460i	0.0481720	+	0.105482i
$466$	−2.31288	+	16.0864i	−0.107142	+	0.745189i
$467$	−35.3257	+	10.3726i	−1.63468	+	0.479985i	−0.964909	−	0.262584i	$-0.915425\pi$
$467$	−35.3257	+	10.3726i	−1.63468	+	0.479985i	−0.669770	+	0.742569i	$0.733607\pi$
$468$	−1.21962	−	0.783801i	−0.0563768	−	0.0362312i
$469$	20.1104	−	44.0357i	0.928614	−	2.03338i
$470$	11.1803	+	3.28284i	0.515710	+	0.151426i
$471$	4.43984	+	5.12385i	0.204577	+	0.236095i
$472$	5.90896	+	6.81930i	0.271982	+	0.313884i
$473$	−10.1383	−	2.97687i	−0.466158	−	0.136876i
$474$	−3.89454	+	8.52785i	−0.178882	+	0.391697i
$475$	−2.09460	−	1.34612i	−0.0961066	−	0.0617640i
$476$	−24.7859	+	7.27780i	−1.13606	+	0.333577i
$477$	1.80006	−	12.5197i	0.0824192	−	0.573238i
$478$	−0.103886	−	0.227480i	−0.00475166	−	0.0104047i
$479$	1.15617	+	8.04137i	0.0528269	+	0.367419i	0.999037	+	0.0438675i	$0.0139679\pi$
$479$	1.15617	+	8.04137i	0.0528269	+	0.367419i	−0.946210	+	0.323552i	$0.895123\pi$
$480$	−0.841254	+	0.540641i	−0.0383978	+	0.0246768i
$481$	0.849969	−	0.980916i	0.0387552	−	0.0447259i
$482$	22.7955			1.03831
$483$	−6.91319	+	17.5185i	−0.314561	+	0.797121i
$484$	−9.18158			−0.417345
$485$	3.68130	−	4.24845i	0.167159	−	0.192912i
$486$	0.841254	−	0.540641i	0.0381600	−	0.0245240i
$487$	−3.50767	−	24.3964i	−0.158948	−	1.10551i	−0.900577	−	0.434696i	$-0.856856\pi$
$487$	−3.50767	−	24.3964i	−0.158948	−	1.10551i	0.741630	−	0.670809i	$-0.234053\pi$
$488$	−3.32940	−	7.29038i	−0.150715	−	0.330020i
$489$	−0.884292	+	6.15039i	−0.0399891	+	0.278130i
$490$	−8.08024	+	2.37257i	−0.365028	+	0.107182i
$491$	−12.6672	−	8.14072i	−0.571663	−	0.367385i	0.222646	−	0.974899i	$-0.428531\pi$
$491$	−12.6672	−	8.14072i	−0.571663	−	0.367385i	−0.794309	+	0.607514i	$0.792167\pi$
$492$	4.24763	−	9.30102i	0.191498	−	0.419322i
$493$	−49.1158	−	14.4217i	−2.21206	−	0.649521i
$494$	2.36385	+	2.72802i	0.106354	+	0.122740i
$495$	−0.883071	−	1.01912i	−0.0396911	−	0.0458060i
$496$	−2.39928	−	0.704491i	−0.107731	−	0.0316326i
$497$	−17.3238	+	37.9339i	−0.777079	+	1.70157i
$498$	5.29041	+	3.39994i	0.237069	+	0.152355i
$499$	33.9719	−	9.97505i	1.52079	−	0.446544i	0.588573	−	0.808444i	$-0.299690\pi$
$499$	33.9719	−	9.97505i	1.52079	−	0.446544i	0.932217	+	0.361899i	$0.117872\pi$
$500$	0.142315	−	0.989821i	0.00636451	−	0.0442662i
$501$	−4.38962	−	9.61192i	−0.196114	−	0.429429i
$502$	−1.03303	−	7.18485i	−0.0461062	−	0.320676i
$503$	31.4938	−	20.2398i	1.40424	−	0.902449i	0.404312	−	0.914621i	$-0.367511\pi$
$503$	31.4938	−	20.2398i	1.40424	−	0.902449i	0.999926	+	0.0121725i	$0.00387474\pi$
$504$	2.57164	−	2.96783i	0.114550	−	0.132198i
$505$	7.30915			0.325253
$506$	−6.10091	+	2.14534i	−0.271219	+	0.0953720i
$507$	10.8982			0.484006
$508$	−1.15377	+	1.33152i	−0.0511903	+	0.0590768i
$509$	−15.7004	+	10.0900i	−0.695908	+	0.447233i	−0.840182	−	0.542305i	$-0.817552\pi$
$509$	−15.7004	+	10.0900i	−0.695908	+	0.447233i	0.144274	+	0.989538i	$0.453915\pi$
$510$	0.936163	+	6.51116i	0.0414540	+	0.288319i
$511$	6.74797	+	14.7760i	0.298513	+	0.653651i
$512$	0.142315	−	0.989821i	0.00628949	−	0.0437443i
$513$	−2.38899	+	0.701472i	−0.105477	+	0.0309707i
$514$	9.66009	+	6.20816i	0.426088	+	0.273830i
$515$	4.64932	−	10.1806i	0.204874	−	0.448611i
$516$	−7.51826	−	2.20756i	−0.330973	−	0.0971824i
$517$	−10.2898	−	11.8751i	−0.452546	−	0.522266i
$518$	2.30233	+	2.65703i	0.101159	+	0.116743i
$519$	−3.45404	−	1.01420i	−0.151615	−	0.0445183i
$520$	−0.602253	+	1.31875i	−0.0264105	+	0.0578310i
$521$	20.4088	+	13.1159i	0.894125	+	0.574619i	0.905042	−	0.425321i	$-0.139839\pi$
$521$	20.4088	+	13.1159i	0.894125	+	0.574619i	−0.0109178	+	0.999940i	$0.503475\pi$
$522$	7.46654	−	2.19238i	0.326802	−	0.0959577i
$523$	2.12796	−	14.8003i	0.0930491	−	0.647171i	−0.888911	−	0.458081i	$-0.848537\pi$
$523$	2.12796	−	14.8003i	0.0930491	−	0.647171i	0.981960	−	0.189090i	$-0.0605538\pi$
$524$	9.23498	+	20.2218i	0.403432	+	0.883393i
$525$	0.558871	+	3.88703i	0.0243911	+	0.169644i
$526$	−0.483964	+	0.311025i	−0.0211019	+	0.0135613i
$527$	−10.7718	+	12.4313i	−0.469228	+	0.541518i
$528$	1.34849			0.0586854
$529$	17.9379	−	14.3955i	0.779910	−	0.625892i
$530$	−12.6484			−0.549413
$531$	−5.90896	+	6.81930i	−0.256427	+	0.295932i
$532$	−8.22549	+	5.28620i	−0.356620	+	0.229186i
$533$	−2.10966	−	14.6730i	−0.0913794	−	0.635557i
$534$	−6.68108	−	14.6295i	−0.289119	−	0.633081i
$535$	−0.633507	+	4.40613i	−0.0273889	+	0.190494i
$536$	11.8282	−	3.47308i	0.510902	−	0.150014i
$537$	5.00412	+	3.21595i	0.215944	+	0.138779i
$538$	10.3813	−	22.7320i	0.447571	−	0.980044i
$539$	10.8961	+	3.19938i	0.469328	+	0.137807i
$540$	−0.654861	−	0.755750i	−0.0281807	−	0.0325223i
$541$	−6.65088	−	7.67553i	−0.285944	−	0.329997i	0.594546	−	0.804061i	$-0.297332\pi$
$541$	−6.65088	−	7.67553i	−0.285944	−	0.329997i	−0.880490	+	0.474065i	$0.842786\pi$
$542$	17.9022	+	5.25657i	0.768966	+	0.225789i
$543$	3.27644	−	7.17441i	0.140606	−	0.307883i
$544$	−5.53386	−	3.55640i	−0.237262	−	0.152479i
$545$	−8.74321	+	2.56724i	−0.374518	+	0.109968i
$546$	0.810230	−	5.63527i	0.0346746	−	0.241167i
$547$	−4.62044	−	10.1173i	−0.197556	−	0.432587i	0.784765	−	0.619794i	$-0.212784\pi$
$547$	−4.62044	−	10.1173i	−0.197556	−	0.432587i	−0.982320	+	0.187207i	$0.940056\pi$
$548$	1.29898	+	9.03458i	0.0554895	+	0.385938i
$549$	6.74235	−	4.33305i	0.287756	−	0.184930i
$550$	−0.883071	+	1.01912i	−0.0376543	+	0.0434554i
$551$	−19.3754			−0.825421
$552$	−4.52426	+	1.59092i	−0.192565	+	0.0677142i
$553$	−36.8159			−1.56557
$554$	12.3271	−	14.2262i	0.523727	−	0.604413i
$555$	0.753154	−	0.484023i	0.0319696	−	0.0205456i
$556$	−1.26468	−	8.79603i	−0.0536343	−	0.373035i
$557$	9.83917	+	21.5448i	0.416899	+	0.912881i	0.995274	+	0.0971101i	$0.0309599\pi$
$557$	9.83917	+	21.5448i	0.416899	+	0.912881i	−0.578375	+	0.815771i	$0.696313\pi$
$558$	0.355868	−	2.47512i	0.0150651	−	0.104780i
$559$	−10.8997	+	3.20044i	−0.461007	+	0.135364i
$560$	−3.30361	−	2.12310i	−0.139603	−	0.0897173i
$561$	3.68494	−	8.06889i	0.155578	−	0.340669i
$562$	3.79699	+	1.11490i	0.160166	+	0.0470290i
$563$	17.1893	+	19.8376i	0.724445	+	0.836054i	0.991834	−	0.127535i	$-0.0407064\pi$
$563$	17.1893	+	19.8376i	0.724445	+	0.836054i	−0.267389	+	0.963589i	$0.586161\pi$
$564$	−7.63065	−	8.80624i	−0.321308	−	0.370810i
$565$	−10.9243	−	3.20767i	−0.459590	−	0.134948i
$566$	4.25343	−	9.31371i	0.178785	−	0.391484i
$567$	3.30361	+	2.12310i	0.138738	+	0.0891618i
$568$	−10.1892	+	2.99183i	−0.427531	+	0.125534i
$569$	−2.55542	+	17.7733i	−0.107129	+	0.745097i	0.863471	+	0.504398i	$0.168286\pi$
$569$	−2.55542	+	17.7733i	−0.107129	+	0.745097i	−0.970600	+	0.240698i	$0.922624\pi$
$570$	1.03432	+	2.26485i	0.0433230	+	0.0948640i
$571$	2.45125	+	17.0488i	0.102582	+	0.713471i	0.974593	+	0.223985i	$0.0719066\pi$
$571$	2.45125	+	17.0488i	0.102582	+	0.713471i	−0.872011	+	0.489486i	$0.837184\pi$
$572$	1.64464	−	1.05695i	0.0687658	−	0.0441931i
$573$	−5.94667	+	6.86282i	−0.248425	+	0.286698i
$574$	40.1538			1.67599
$575$	1.76042	−	4.46104i	0.0734147	−	0.186038i
$576$	1.00000			0.0416667
$577$	6.20717	−	7.16346i	0.258408	−	0.298219i	−0.611690	−	0.791098i	$-0.709510\pi$
$577$	6.20717	−	7.16346i	0.258408	−	0.298219i	0.870098	+	0.492879i	$0.164055\pi$
$578$	−22.1011	+	14.2035i	−0.919284	+	0.590788i
$579$	−2.65410	−	18.4597i	−0.110301	−	0.767158i
$580$	−3.23266	−	7.07854i	−0.134229	−	0.293920i
$581$	−3.51458	+	24.4445i	−0.145810	+	1.01413i
$582$	−5.39379	+	1.58376i	−0.223580	+	0.0656490i
$583$	14.3486	+	9.22131i	0.594260	+	0.381908i
$584$	−1.71835	+	3.76266i	−0.0711058	+	0.155700i
$585$	−1.39104	−	0.408445i	−0.0575123	−	0.0168871i
$586$	−1.85785	−	2.14408i	−0.0767472	−	0.0885710i
$587$	0.353974	+	0.408507i	0.0146101	+	0.0168609i	0.763008	−	0.646390i	$-0.223722\pi$
$587$	0.353974	+	0.408507i	0.0146101	+	0.0168609i	−0.748398	+	0.663250i	$0.769176\pi$
$588$	8.08024	+	2.37257i	0.333224	+	0.0978433i
$589$	−2.58639	+	5.66341i	−0.106570	+	0.233357i
$590$	7.59082	+	4.87832i	0.312509	+	0.200837i
$591$	−0.727691	+	0.213669i	−0.0299332	+	0.00878919i
$592$	−0.127411	+	0.886164i	−0.00523656	+	0.0364211i
$593$	−5.97759	−	13.0891i	−0.245470	−	0.537504i	0.746289	−	0.665622i	$-0.231834\pi$
$593$	−5.97759	−	13.0891i	−0.245470	−	0.537504i	−0.991759	+	0.128118i	$0.959106\pi$
$594$	0.191910	+	1.33476i	0.00787415	+	0.0547659i
$595$	−21.7315	+	13.9660i	−0.890905	+	0.572550i
$596$	−8.23453	+	9.50315i	−0.337299	+	0.389264i
$597$	−16.6611			−0.681893
$598$	−4.27090	+	5.48644i	−0.174650	+	0.224357i
$599$	−9.84397			−0.402214			−0.201107	−	0.979569i	$-0.564454\pi$
$599$	−9.84397			−0.402214			−0.201107	+	0.979569i	$0.564454\pi$
$600$	−0.654861	+	0.755750i	−0.0267346	+	0.0308533i
$601$	1.09098	−	0.701128i	0.0445019	−	0.0285996i	−0.518201	−	0.855259i	$-0.673398\pi$
$601$	1.09098	−	0.701128i	0.0445019	−	0.0285996i	0.562703	+	0.826659i	$0.309762\pi$
$602$	−4.37912	−	30.4575i	−0.178480	−	1.24135i
$603$	5.12106	+	11.2136i	0.208546	+	0.456652i
$604$	1.76074	−	12.2462i	0.0716436	−	0.498292i
$605$	−8.80966	+	2.58675i	−0.358164	+	0.105166i
$606$	−6.14885	−	3.95163i	−0.249780	−	0.160524i
$607$	−2.79748	+	6.12563i	−0.113546	+	0.248632i	−0.957870	−	0.287201i	$-0.907275\pi$
$607$	−2.79748	+	6.12563i	−0.113546	+	0.248632i	0.844324	+	0.535833i	$0.180002\pi$
$608$	−2.38899	−	0.701472i	−0.0968865	−	0.0284484i
$609$	20.0119	+	23.0950i	0.810923	+	0.935855i
$610$	−5.24848	−	6.05707i	−0.212505	−	0.245243i
$611$	−16.2088	−	4.75934i	−0.655738	−	0.192542i
$612$	2.73265	−	5.98366i	0.110461	−	0.241875i
$613$	−6.06592	−	3.89833i	−0.245000	−	0.157452i	0.412378	−	0.911013i	$-0.364698\pi$
$613$	−6.06592	−	3.89833i	−0.245000	−	0.157452i	−0.657378	+	0.753561i	$0.728335\pi$
$614$	8.80057	−	2.58408i	0.355162	−	0.104285i
$615$	1.45517	−	10.1210i	0.0586783	−	0.408116i
$616$	2.19984	+	4.81697i	0.0886340	+	0.194081i
$617$	−3.12959	−	21.7668i	−0.125992	−	0.876297i	−0.950562	−	0.310536i	$-0.899492\pi$
$617$	−3.12959	−	21.7668i	−0.125992	−	0.876297i	0.824569	−	0.565761i	$-0.191418\pi$
$618$	−9.41531	+	6.05085i	−0.378739	+	0.243401i
$619$	−18.8116	+	21.7097i	−0.756101	+	0.872587i	−0.995145	−	0.0984216i	$-0.968621\pi$
$619$	−18.8116	+	21.7097i	−0.756101	+	0.872587i	0.239044	+	0.971009i	$0.423166\pi$
$620$	−2.50057			−0.100425
$621$	−2.21860	−	4.25180i	−0.0890294	−	0.170619i
$622$	24.9911			1.00205
$623$	41.3595	−	47.7314i	1.65703	−	1.91232i
$624$	1.21962	−	0.783801i	0.0488238	−	0.0313771i
$625$	−0.142315	−	0.989821i	−0.00569259	−	0.0395929i
$626$	−5.07641	−	11.1158i	−0.202894	−	0.444277i
$627$	0.477827	−	3.32336i	0.0190826	−	0.132722i
$628$	−6.50520	+	1.91010i	−0.259586	+	0.0762212i
$629$	4.95434	+	3.18396i	0.197542	+	0.126953i
$630$	1.63134	−	3.57213i	0.0649940	−	0.142317i
$631$	−9.50983	−	2.79234i	−0.378581	−	0.111161i	0.0869054	−	0.996217i	$-0.472302\pi$
$631$	−9.50983	−	2.79234i	−0.378581	−	0.111161i	−0.465486	+	0.885055i	$0.654120\pi$
$632$	−6.13935	−	7.08519i	−0.244210	−	0.281834i
$633$	1.45231	+	1.67605i	0.0577240	+	0.0666171i
$634$	12.4237	+	3.64792i	0.493407	+	0.144877i
$635$	−0.731902	+	1.60264i	−0.0290446	+	0.0635989i
$636$	10.6405	+	6.83827i	0.421925	+	0.271155i
$637$	11.7144	−	3.43967i	0.464143	−	0.136285i
$638$	−1.49340	+	10.3868i	−0.0591241	+	0.411217i
$639$	−4.41146	−	9.65974i	−0.174515	−	0.382134i
$640$	−0.142315	−	0.989821i	−0.00562549	−	0.0391261i
$641$	−3.12083	+	2.00564i	−0.123266	+	0.0792180i	−0.600821	−	0.799384i	$-0.705159\pi$
$641$	−3.12083	+	2.00564i	−0.123266	+	0.0792180i	0.477555	+	0.878602i	$0.341523\pi$
$642$	2.91508	−	3.36418i	0.115049	−	0.132773i
$643$	13.8582			0.546514			0.273257	−	0.961941i	$-0.411899\pi$
$643$	13.8582			0.546514			0.273257	+	0.961941i	$0.411899\pi$
$644$	−13.0636	−	13.5659i	−0.514777	−	0.534572i
$645$	−7.83565			−0.308529
$646$	−10.7257	+	12.3781i	−0.421995	+	0.487008i
$647$	19.9097	−	12.7952i	0.782731	−	0.503031i	−0.0872080	−	0.996190i	$-0.527794\pi$
$647$	19.9097	−	12.7952i	0.782731	−	0.503031i	0.869939	+	0.493159i	$0.164158\pi$
$648$	0.142315	+	0.989821i	0.00559065	+	0.0388839i
$649$	−5.05465	−	11.0681i	−0.198412	−	0.434462i
$650$	−0.206323	+	1.43501i	−0.00809264	+	0.0562856i
$651$	9.42197	−	2.76654i	0.369276	−	0.108429i
$652$	−5.22724	−	3.35934i	−0.204715	−	0.131562i
$653$	8.41634	−	18.4292i	0.329357	−	0.721191i	−0.670427	−	0.741975i	$-0.733889\pi$
$653$	8.41634	−	18.4292i	0.329357	−	0.721191i	0.999784	+	0.0207845i	$0.00661637\pi$
$654$	8.74321	+	2.56724i	0.341887	+	0.100387i
$655$	14.5580	+	16.8009i	0.568829	+	0.656464i
$656$	6.69597	+	7.72756i	0.261434	+	0.301711i
$657$	−3.96891	−	1.16538i	−0.154842	−	0.0454657i
$658$	19.0089	−	41.6236i	0.741043	−	1.62266i
$659$	−25.9290	−	16.6635i	−1.01005	−	0.649119i	−0.0726434	−	0.997358i	$-0.523143\pi$
$659$	−25.9290	−	16.6635i	−1.01005	−	0.649119i	−0.937406	+	0.348239i	$0.886780\pi$
$660$	1.29386	−	0.379913i	0.0503636	−	0.0147881i
$661$	1.30564	−	9.08091i	0.0507834	−	0.353207i	−0.948548	−	0.316635i	$-0.897447\pi$
$661$	1.30564	−	9.08091i	0.0507834	−	0.353207i	0.999331	−	0.0365720i	$-0.0116438\pi$
$662$	3.94087	+	8.62929i	0.153166	+	0.335387i
$663$	−1.35721	−	9.43963i	−0.0527098	−	0.366605i
$664$	−5.29041	+	3.39994i	−0.205308	+	0.131943i
$665$	−6.40300	+	7.38946i	−0.248298	+	0.286551i
$666$	−0.895276			−0.0346913
$667$	−7.24373	−	36.6103i	−0.280479	−	1.41756i
$668$	10.5668			0.408843
$669$	15.3386	−	17.7017i	0.593025	−	0.684387i
$670$	10.3706	−	6.66479i	0.400652	−	0.257483i
$671$	1.53809	+	10.6976i	0.0593773	+	0.412978i
$672$	1.63134	+	3.57213i	0.0629302	+	0.137798i
$673$	−1.00557	+	6.99392i	−0.0387620	+	0.269596i	−0.999981	−	0.00619114i	$-0.998029\pi$
$673$	−1.00557	+	6.99392i	−0.0387620	+	0.269596i	0.961219	+	0.275787i	$0.0889384\pi$
$674$	31.9686	−	9.38683i	1.23139	−	0.361567i
$675$	−0.841254	−	0.540641i	−0.0323799	−	0.0208093i
$676$	−4.52727	+	9.91334i	−0.174126	+	0.381282i
$677$	12.1459	+	3.56636i	0.466805	+	0.137066i	0.506672	−	0.862139i	$-0.330875\pi$
$677$	12.1459	+	3.56636i	0.466805	+	0.137066i	−0.0398674	+	0.999205i	$0.512694\pi$
$678$	7.45593	+	8.60460i	0.286343	+	0.330458i
$679$	−14.4565	−	16.6837i	−0.554789	−	0.640261i
$680$	−6.31166	−	1.85327i	−0.242041	−	0.0710696i
$681$	8.10896	−	17.7562i	0.310736	−	0.680417i
$682$	2.83669	+	1.82303i	0.108623	+	0.0698075i
$683$	−12.0677	+	3.54340i	−0.461759	+	0.135585i	−0.504334	−	0.863509i	$-0.668262\pi$
$683$	−12.0677	+	3.54340i	−0.461759	+	0.135585i	0.0425753	+	0.999093i	$0.486444\pi$
$684$	0.354343	−	2.46451i	0.0135486	−	0.0942328i
$685$	3.79169	+	8.30265i	0.144873	+	0.317228i
$686$	0.794361	+	5.52490i	0.0303288	+	0.210942i
$687$	−4.12663	+	2.65202i	−0.157441	+	0.101181i
$688$	5.13126	−	5.92179i	0.195628	−	0.225766i
$689$	18.3372			0.698593
$690$	−3.89278	+	2.80111i	−0.148196	+	0.106637i
$691$	4.81188			0.183052			0.0915262	−	0.995803i	$-0.470825\pi$
$691$	4.81188			0.183052			0.0915262	+	0.995803i	$0.470825\pi$
$692$	2.35740	−	2.72059i	0.0896151	−	0.103421i
$693$	−4.45487	+	2.86297i	−0.169227	+	0.108755i
$694$	−4.60027	−	31.9956i	−0.174624	−	1.21454i
$695$	−3.69158	−	8.08343i	−0.140029	−	0.306622i
$696$	−1.10746	+	7.70255i	−0.0419782	+	0.291965i
$697$	64.5369	−	18.9497i	2.44451	−	0.717773i
$698$	−11.5028	−	7.39243i	−0.435389	−	0.279808i
$699$	6.75125	−	14.7832i	0.255356	−	0.559151i
$700$	−3.76793	−	1.10637i	−0.142414	−	0.0418167i
$701$	7.20831	+	8.31884i	0.272254	+	0.314198i	0.875368	−	0.483457i	$-0.160619\pi$
$701$	7.20831	+	8.31884i	0.272254	+	0.314198i	−0.603114	+	0.797655i	$0.706074\pi$
$702$	0.949392	+	1.09566i	0.0358325	+	0.0413529i
$703$	2.13881	+	0.628011i	0.0806668	+	0.0236859i
$704$	−0.560182	+	1.22663i	−0.0211126	+	0.0462303i
$705$	−9.80256	−	6.29972i	−0.369186	−	0.237261i
$706$	−5.62353	+	1.65122i	−0.211644	+	0.0621444i
$707$	4.08487	−	28.4109i	0.153628	−	1.06850i
$708$	−3.74838	−	8.20781i	−0.140873	−	0.308469i
$709$	−0.774181	−	5.38455i	−0.0290750	−	0.202221i	0.970106	−	0.242681i	$-0.0780268\pi$
$709$	−0.774181	−	5.38455i	−0.0290750	−	0.202221i	−0.999181	+	0.0404600i	$0.987118\pi$
$710$	−8.93361	+	5.74128i	−0.335272	+	0.215466i
$711$	6.13935	−	7.08519i	0.230244	−	0.265715i
$712$	16.0829			0.602732
$713$	−11.6681	−	2.76971i	−0.436973	−	0.103726i
$714$	25.8323			0.966749
$715$	1.28024	−	1.47748i	0.0478784	−	0.0552546i
$716$	−5.00412	+	3.21595i	−0.187013	+	0.120186i
$717$	0.0355899	+	0.247533i	0.00132913	+	0.00924430i
$718$	6.78985	+	14.8677i	0.253395	+	0.554857i
$719$	6.95618	−	48.3813i	0.259422	−	1.80432i	−0.277542	−	0.960713i	$-0.589520\pi$
$719$	6.95618	−	48.3813i	0.259422	−	1.80432i	0.536964	−	0.843605i	$-0.319571\pi$
$720$	0.959493	−	0.281733i	0.0357582	−	0.0104996i
$721$	−36.9740	−	23.7617i	−1.37698	−	0.884933i
$722$	5.31758	−	11.6439i	0.197900	−	0.433340i
$723$	−21.8721	−	6.42223i	−0.813433	−	0.238845i
$724$	5.16499	+	5.96072i	0.191955	+	0.221528i
$725$	−5.09597	−	5.88106i	−0.189260	−	0.218417i
$726$	8.80966	+	2.58675i	0.326957	+	0.0960033i
$727$	13.2283	−	28.9659i	0.490610	−	1.07429i	−0.488798	−	0.872397i	$-0.662564\pi$
$727$	13.2283	−	28.9659i	0.490610	−	1.07429i	0.979408	−	0.201890i	$-0.0647083\pi$
$728$	4.78944	+	3.07799i	0.177509	+	0.114078i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	−0.588681	+	4.09436i	−0.0217880	+	0.151539i
$731$	−21.4121	−	46.8859i	−0.791955	−	1.73414i
$732$	1.14060	+	7.93307i	0.0421579	+	0.293215i
$733$	−36.6524	+	23.5551i	−1.35379	+	0.870027i	−0.997917	−	0.0645083i	$-0.979452\pi$
$733$	−36.6524	+	23.5551i	−1.35379	+	0.870027i	−0.355871	+	0.934535i	$0.615816\pi$
$734$	−17.4701	+	20.1616i	−0.644833	+	0.744177i
$735$	8.42137			0.310627
$736$	0.432292	−	4.77631i	0.0159345	−	0.176057i
$737$	−16.6236			−0.612338
$738$	−6.69597	+	7.72756i	−0.246482	+	0.284456i
$739$	−16.0574	+	10.3195i	−0.590681	+	0.379608i	−0.801569	−	0.597902i	$-0.796001\pi$
$739$	−16.0574	+	10.3195i	−0.590681	+	0.379608i	0.210887	+	0.977510i	$0.432365\pi$
$740$	0.127411	+	0.886164i	0.00468373	+	0.0325760i
$741$	−1.49952	−	3.28349i	−0.0550863	−	0.120622i
$742$	−7.06885	+	49.1649i	−0.259506	+	1.80490i
$743$	47.2159	−	13.8638i	1.73218	−	0.508615i	0.744844	−	0.667239i	$-0.232524\pi$
$743$	47.2159	−	13.8638i	1.73218	−	0.508615i	0.987339	+	0.158624i	$0.0507058\pi$
$744$	2.10361	+	1.35191i	0.0771221	+	0.0495634i
$745$	−5.22363	+	11.4381i	−0.191379	+	0.419061i
$746$	−0.549196	−	0.161259i	−0.0201075	−	0.00590409i
$747$	−4.11824	−	4.75270i	−0.150678	−	0.173892i
$748$	5.80895	+	6.70388i	0.212396	+	0.245118i
$749$	16.7727	+	4.92492i	0.612863	+	0.179953i
$750$	−0.415415	+	0.909632i	−0.0151688	+	0.0332151i
$751$	−22.0454	−	14.1677i	−0.804448	−	0.516987i	0.0726165	−	0.997360i	$-0.476865\pi$
$751$	−22.0454	−	14.1677i	−0.804448	−	0.516987i	−0.877065	+	0.480373i	$0.840501\pi$
$752$	11.1803	−	3.28284i	0.407705	−	0.119713i
$753$	−1.03303	+	7.18485i	−0.0376455	+	0.261830i
$754$	4.68659	+	10.2622i	0.170675	+	0.373727i
$755$	−1.76074	−	12.2462i	−0.0640800	−	0.445686i
$756$	−3.30361	+	2.12310i	−0.120151	+	0.0772164i
$757$	−1.26346	+	1.45811i	−0.0459212	+	0.0529958i	−0.778245	−	0.627960i	$-0.783890\pi$
$757$	−1.26346	+	1.45811i	−0.0459212	+	0.0529958i	0.732324	+	0.680956i	$0.238436\pi$
$758$	−22.0696			−0.801603
$759$	6.45819	−	0.339614i	0.234418	−	0.0123272i
$760$	−2.48985			−0.0903164
$761$	12.2104	−	14.0916i	0.442628	−	0.510820i	−0.489969	−	0.871740i	$-0.662992\pi$
$761$	12.2104	−	14.0916i	0.442628	−	0.510820i	0.932597	+	0.360920i	$0.117537\pi$
$762$	1.48217	−	0.952532i	0.0536933	−	0.0345066i
$763$	5.09261	+	35.4199i	0.184365	+	1.28229i
$764$	−3.77230	−	8.26019i	−0.136477	−	0.298843i
$765$	0.936163	−	6.51116i	0.0338471	−	0.235411i
$766$	8.17053	−	2.39908i	0.295213	−	0.0866825i
$767$	−11.0049	−	7.07241i	−0.397363	−	0.255370i
$768$	−0.415415	+	0.909632i	−0.0149900	+	0.0328235i
$769$	46.8938	+	13.7693i	1.69103	+	0.496532i	0.978697	−	0.205308i	$-0.0658195\pi$
$769$	46.8938	+	13.7693i	1.69103	+	0.496532i	0.712335	+	0.701840i	$0.247638\pi$
$770$	3.46783	+	4.00208i	0.124972	+	0.144225i
$771$	−7.51975	−	8.67825i	−0.270817	−	0.312540i
$772$	17.8941	+	5.25417i	0.644021	+	0.189102i
$773$	17.2826	−	37.8436i	0.621611	−	1.36114i	−0.292731	−	0.956195i	$-0.594564\pi$
$773$	17.2826	−	37.8436i	0.621611	−	1.36114i	0.914342	−	0.404943i	$-0.132709\pi$
$774$	6.59177	+	4.23627i	0.236936	+	0.152270i
$775$	−2.39928	+	0.704491i	−0.0861846	+	0.0253061i
$776$	0.800023	−	5.56428i	0.0287192	−	0.199746i
$777$	−1.46050	−	3.19804i	−0.0523951	−	0.114729i
$778$	3.34068	+	23.2350i	0.119769	+	0.833014i
$779$	21.4173	−	13.7641i	0.767355	−	0.493149i
$780$	0.949392	−	1.09566i	0.0339937	−	0.0392308i
$781$	14.3201			0.512414
$782$	−27.3985	−	15.6387i	−0.979769	−	0.559237i
$783$	−7.78176			−0.278097
$784$	−5.51482	+	6.36444i	−0.196958	+	0.227302i
$785$	−5.70355	+	3.66545i	−0.203569	+	0.130826i
$786$	−3.16376	−	22.0045i	−0.112848	−	0.784873i
$787$	1.62067	+	3.54878i	0.0577707	+	0.126500i	0.936316	−	0.351159i	$-0.114212\pi$
$787$	1.62067	+	3.54878i	0.0577707	+	0.126500i	−0.878545	+	0.477660i	$0.841485\pi$
$788$	0.107933	−	0.750693i	0.00384497	−	0.0267423i
$789$	0.551986	−	0.162078i	0.0196512	−	0.00577012i
$790$	−7.88679	−	5.06853i	−0.280600	−	0.180330i
$791$	−18.5736	+	40.6705i	−0.660402	+	1.44608i
$792$	−1.29386	−	0.379913i	−0.0459755	−	0.0134996i
$793$	7.60904	+	8.78131i	0.270205	+	0.311833i
$794$	−9.72764	−	11.2263i	−0.345221	−	0.398406i
$795$	12.1361	+	3.56348i	0.430423	+	0.126384i
$796$	6.92126	−	15.1555i	0.245318	−	0.537171i
$797$	5.53785	+	3.55896i	0.196161	+	0.126065i	0.635034	−	0.772484i	$-0.280986\pi$
$797$	5.53785	+	3.55896i	0.196161	+	0.126065i	−0.438873	+	0.898549i	$0.644622\pi$
$798$	9.38159	−	2.75468i	0.332105	−	0.0975148i
$799$	10.9085	−	75.8702i	0.385914	−	2.68409i
$800$	−0.415415	−	0.909632i	−0.0146871	−	0.0321603i
$801$	2.28884	+	15.9192i	0.0808720	+	0.562477i
$802$	13.4354	−	8.63439i	0.474419	−	0.304891i
$803$	3.65280	−	4.21555i	0.128904	−	0.148764i
$804$	−12.3276			−0.434760
$805$	−16.3564	−	9.33597i	−0.576487	−	0.329050i
$806$	3.62523			0.127693
$807$	−16.3652	+	18.8864i	−0.576081	+	0.664832i
$808$	6.14885	−	3.95163i	0.216316	−	0.139018i
$809$	6.26995	+	43.6084i	0.220440	+	1.53319i	0.736381	+	0.676567i	$0.236533\pi$
$809$	6.26995	+	43.6084i	0.220440	+	1.53319i	−0.515942	+	0.856624i	$0.672558\pi$
$810$	0.415415	+	0.909632i	0.0145962	+	0.0319612i
$811$	−4.30690	+	29.9551i	−0.151236	+	1.05187i	0.762917	+	0.646496i	$0.223766\pi$
$811$	−4.30690	+	29.9551i	−0.151236	+	1.05187i	−0.914153	+	0.405370i	$0.867143\pi$
$812$	−29.3212	+	8.60947i	−1.02897	+	0.302133i
$813$	−15.6961	−	10.0873i	−0.550487	−	0.353776i
$814$	0.501518	−	1.09817i	0.0175782	−	0.0384909i
$815$	−5.96194	−	1.75058i	−0.208838	−	0.0613202i
$816$	4.30775	+	4.97141i	0.150801	+	0.174034i
$817$	−12.7761	−	14.7444i	−0.446978	−	0.515841i
$818$	32.9017	+	9.66081i	1.15038	+	0.337782i
$819$	−2.36505	+	5.17874i	−0.0826416	+	0.180960i
$820$	8.60185	+	5.52807i	0.300389	+	0.193049i
$821$	11.2599	−	3.30621i	0.392974	−	0.115388i	−0.0792748	−	0.996853i	$-0.525260\pi$
$821$	11.2599	−	3.30621i	0.392974	−	0.115388i	0.472249	+	0.881465i	$0.343442\pi$
$822$	1.29898	−	9.03458i	0.0453070	−	0.315117i
$823$	15.4206	+	33.7664i	0.537527	+	1.17702i	0.962367	+	0.271752i	$0.0876032\pi$
$823$	15.4206	+	33.7664i	0.537527	+	1.17702i	−0.424840	+	0.905269i	$0.639670\pi$
$824$	−1.59279	−	11.0781i	−0.0554874	−	0.385923i
$825$	1.13442	−	0.729047i	0.0394954	−	0.0253822i
$826$	23.2045	−	26.7794i	0.807388	−	0.931775i
$827$	13.9885			0.486427			0.243214	−	0.969973i	$-0.421798\pi$
$827$	13.9885			0.486427			0.243214	+	0.969973i	$0.421798\pi$
$828$	4.78921	−	0.251848i	0.166437	−	0.00875232i
$829$	−57.5589			−1.99910			−0.999552	−	0.0299371i	$-0.990469\pi$
$829$	−57.5589			−1.99910			−0.999552	+	0.0299371i	$0.990469\pi$
$830$	−4.11824	+	4.75270i	−0.142946	+	0.164969i
$831$	−15.8357	+	10.1770i	−0.549335	+	0.353036i
$832$	0.206323	+	1.43501i	0.00715295	+	0.0497499i
$833$	23.0126	+	50.3906i	0.797340	+	1.74593i
$834$	−1.26468	+	8.79603i	−0.0437922	+	0.304582i
$835$	10.1388	−	2.97702i	0.350867	−	0.103024i
$836$	2.82454	+	1.81522i	0.0976886	+	0.0627807i
$837$	−1.03877	+	2.27460i	−0.0359053	+	0.0786216i
$838$	32.5928	+	9.57010i	1.12590	+	0.330594i
$839$	0.526028	+	0.607069i	0.0181605	+	0.0209583i	0.764757	−	0.644319i	$-0.222859\pi$
$839$	0.526028	+	0.607069i	0.0181605	+	0.0209583i	−0.746597	+	0.665277i	$0.768313\pi$
$840$	2.57164	+	2.96783i	0.0887301	+	0.102400i
$841$	−30.2776	−	8.89029i	−1.04405	−	0.306562i
$842$	−9.52004	+	20.8460i	−0.328082	+	0.718400i
$843$	−3.32908	−	2.13947i	−0.114660	−	0.0736872i
$844$	−2.12790	+	0.624808i	−0.0732453	+	0.0215068i
$845$	−1.55097	+	10.7873i	−0.0533551	+	0.371093i
$846$	4.84055	+	10.5993i	0.166422	+	0.364412i
$847$	5.13132	+	35.6891i	0.176314	+	1.22629i
$848$	−10.6405	+	6.83827i	−0.365398	+	0.234827i
$849$	−6.70511	+	7.73811i	−0.230119	+	0.265571i
$850$	−6.57812			−0.225627
$851$	−0.387021	+	4.27612i	−0.0132669	+	0.146583i
$852$	10.6194			0.363815
$853$	−11.4959	+	13.2670i	−0.393613	+	0.454253i	−0.917619	−	0.397461i	$-0.869891\pi$
$853$	−11.4959	+	13.2670i	−0.393613	+	0.454253i	0.524006	+	0.851714i	$0.324437\pi$
$854$	−26.4772	+	17.0159i	−0.906033	+	0.582272i
$855$	−0.354343	−	2.46451i	−0.0121183	−	0.0842844i
$856$	1.84920	+	4.04918i	0.0632042	+	0.138398i
$857$	1.02224	−	7.10986i	0.0349192	−	0.242868i	−0.964885	−	0.262674i	$-0.915396\pi$
$857$	1.02224	−	7.10986i	0.0349192	−	0.242868i	0.999804	+	0.0198057i	$0.00630476\pi$
$858$	−1.87580	+	0.550783i	−0.0640386	+	0.0188034i
$859$	−45.2651	−	29.0901i	−1.54443	−	0.992542i	−0.986706	−	0.162513i	$-0.948040\pi$
$859$	−45.2651	−	29.0901i	−1.54443	−	0.992542i	−0.557719	−	0.830030i	$-0.688323\pi$
$860$	3.25505	−	7.12756i	0.110996	−	0.243048i
$861$	−38.5272	−	11.3126i	−1.31300	−	0.385533i
$862$	−7.54269	−	8.70473i	−0.256905	−	0.296484i
$863$	14.3415	+	16.5509i	0.488189	+	0.563400i	0.945381	−	0.325968i	$-0.105690\pi$
$863$	14.3415	+	16.5509i	0.488189	+	0.563400i	−0.457192	+	0.889368i	$0.651145\pi$
$864$	−0.959493	−	0.281733i	−0.0326426	−	0.00958474i
$865$	1.49543	−	3.27454i	0.0508463	−	0.111338i
$866$	4.28291	+	2.75246i	0.145539	+	0.0935323i
$867$	25.2074	−	7.40157i	0.856089	−	0.251370i
$868$	−1.39750	+	9.71979i	−0.0474341	+	0.329911i
$869$	5.25173	+	11.4997i	0.178153	+	0.390100i
$870$	1.10746	+	7.70255i	0.0375464	+	0.261141i
$871$	−15.0349	+	9.66237i	−0.509439	+	0.327397i
$872$	−5.96730	+	6.88663i	−0.202078	+	0.233211i
$873$	5.62150			0.190259
$874$	−11.6181	−	2.75784i	−0.392987	−	0.0932852i
$875$	−3.92700			−0.132757
$876$	2.70881	−	3.12613i	0.0915222	−	0.105622i
$877$	37.0830	−	23.8318i	1.25220	−	0.804743i	0.265007	−	0.964247i	$-0.414626\pi$
$877$	37.0830	−	23.8318i	1.25220	−	0.804743i	0.987197	+	0.159504i	$0.0509895\pi$
$878$	−0.522188	−	3.63190i	−0.0176230	−	0.122571i
$879$	1.17854	+	2.58064i	0.0397512	+	0.0870429i
$880$	−0.191910	+	1.33476i	−0.00646928	+	0.0449948i
$881$	−41.7803	+	12.2678i	−1.40761	+	0.413312i	−0.895291	−	0.445481i	$-0.853033\pi$
$881$	−41.7803	+	12.2678i	−1.40761	+	0.413312i	−0.512321	+	0.858794i	$0.671214\pi$
$882$	−7.08450	−	4.55293i	−0.238548	−	0.153305i
$883$	7.34094	−	16.0744i	0.247042	−	0.540947i	−0.744969	−	0.667100i	$-0.767536\pi$
$883$	7.34094	−	16.0744i	0.247042	−	0.540947i	0.992011	+	0.126152i	$0.0402629\pi$
$884$	9.15040	+	2.68680i	0.307761	+	0.0903669i
$885$	−5.90896	−	6.81930i	−0.198627	−	0.229228i
$886$	2.27546	+	2.62602i	0.0764456	+	0.0882229i
$887$	7.24941	+	2.12862i	0.243411	+	0.0714720i	0.401163	−	0.916007i	$-0.368606\pi$
$887$	7.24941	+	2.12862i	0.243411	+	0.0714720i	−0.157751	+	0.987479i	$0.550424\pi$
$888$	0.371911	−	0.814372i	0.0124805	−	0.0273285i
$889$	5.82048	+	3.74060i	0.195213	+	0.125456i
$890$	15.4314	−	4.53108i	0.517263	−	0.151882i
$891$	0.191910	−	1.33476i	0.00642922	−	0.0447162i
$892$	9.73015	+	21.3060i	0.325789	+	0.713379i
$893$	−4.12892	−	28.7172i	−0.138169	−	0.960986i
$894$	10.5783	−	6.79827i	0.353792	−	0.227368i
$895$	−3.89538	+	4.49551i	−0.130208	+	0.150268i
$896$	−3.92700			−0.131192
$897$	5.64361	−	4.06095i	0.188435	−	0.135591i
$898$	−23.7588			−0.792842
$899$	−12.7428	+	14.7060i	−0.424997	+	0.490472i
$900$	0.841254	−	0.540641i	0.0280418	−	0.0180214i
$901$	11.8410	+	82.3560i	0.394481	+	2.74368i
$902$	−5.72788	−	12.5423i	−0.190717	−	0.417613i
$903$	−4.37912	+	30.4575i	−0.145728	+	1.01356i
$904$	−10.9243	+	3.20767i	−0.363338	+	0.106686i
$905$	6.63510	+	4.26412i	0.220558	+	0.141744i
$906$	−5.13958	+	11.2541i	−0.170751	+	0.373893i
$907$	−13.6512	−	4.00836i	−0.453281	−	0.133095i	0.0471198	−	0.998889i	$-0.484996\pi$
$907$	−13.6512	−	4.00836i	−0.453281	−	0.133095i	−0.500401	+	0.865794i	$0.666814\pi$
$908$	12.7830	+	14.7523i	0.424218	+	0.489574i
$909$	4.78648	+	5.52389i	0.158757	+	0.183216i
$910$	5.46261	+	1.60397i	0.181084	+	0.0531710i
$911$	−2.05180	+	4.49282i	−0.0679792	+	0.148854i	−0.940572	−	0.339595i	$-0.889710\pi$
$911$	−2.05180	+	4.49282i	−0.0679792	+	0.148854i	0.872592	+	0.488449i	$0.162437\pi$
$912$	2.09460	+	1.34612i	0.0693590	+	0.0445743i
$913$	8.13675	−	2.38917i	0.269287	−	0.0790698i
$914$	−0.626869	+	4.35997i	−0.0207350	+	0.144215i
$915$	3.32940	+	7.29038i	0.110067	+	0.241013i
$916$	−0.698102	−	4.85540i	−0.0230659	−	0.160427i
$917$	73.4416	−	47.1980i	2.42525	−	1.55862i
$918$	−4.30775	+	4.97141i	−0.142177	+	0.164081i
$919$	14.1836			0.467873			0.233936	−	0.972252i	$-0.424839\pi$
$919$	14.1836			0.467873			0.233936	+	0.972252i	$0.424839\pi$
$920$	−0.930861	−	4.70463i	−0.0306896	−	0.155107i
$921$	−9.17211			−0.302231
$922$	−17.4372	+	20.1236i	−0.574264	+	0.662736i
$923$	12.9516	−	8.32349i	0.426307	−	0.273971i
$924$	−0.753631	−	5.24162i	−0.0247926	−	0.172436i
$925$	0.371911	+	0.814372i	0.0122284	+	0.0267764i
$926$	3.63907	−	25.3103i	0.119587	−	0.831748i
$927$	10.7386	−	3.15315i	0.352703	−	0.103563i
$928$	−6.54643	−	4.20714i	−0.214897	−	0.138106i
$929$	−23.1166	+	50.6183i	−0.758432	+	1.66073i	−0.00783836	+	0.999969i	$0.502495\pi$
$929$	−23.1166	+	50.6183i	−0.758432	+	1.66073i	−0.750593	+	0.660764i	$0.770232\pi$
$930$	2.39928	+	0.704491i	0.0786754	+	0.0231012i
$931$	13.7311	+	15.8465i	0.450018	+	0.519349i
$932$	10.6427	+	12.2823i	0.348613	+	0.402321i
$933$	−23.9788	−	7.04080i	−0.785029	−	0.230505i
$934$	−15.2944	+	33.4900i	−0.500447	+	1.09583i
$935$	7.46234	+	4.79576i	0.244045	+	0.156838i
$936$	−1.39104	+	0.408445i	−0.0454675	+	0.0133504i
$937$	−7.02360	+	48.8502i	−0.229451	+	1.59587i	0.470977	+	0.882145i	$0.343901\pi$
$937$	−7.02360	+	48.8502i	−0.229451	+	1.59587i	−0.700428	+	0.713723i	$0.747008\pi$
$938$	−20.1104	−	44.0357i	−0.656629	−	1.43782i
$939$	1.73910	+	12.0957i	0.0567534	+	0.394729i
$940$	9.80256	−	6.29972i	0.319724	−	0.205474i
$941$	−21.1165	+	24.3698i	−0.688380	+	0.794432i	−0.987134	−	0.159898i	$-0.948884\pi$
$941$	−21.1165	+	24.3698i	−0.688380	+	0.794432i	0.298754	+	0.954330i	$0.403429\pi$
$942$	6.77983			0.220899
$943$	34.0146	+	35.3226i	1.10767	+	1.15026i
$944$	9.02323			0.293681
$945$	−2.57164	+	2.96783i	−0.0836555	+	0.0965436i
$946$	−8.88892	+	5.71256i	−0.289004	+	0.185731i
$947$	−6.85322	−	47.6652i	−0.222700	−	1.54891i	−0.727764	−	0.685828i	$-0.759440\pi$
$947$	−6.85322	−	47.6652i	−0.222700	−	1.54891i	0.505064	−	0.863082i	$-0.331469\pi$
$948$	3.89454	+	8.52785i	0.126489	+	0.276972i
$949$	0.853447	−	5.93585i	0.0277041	−	0.192686i
$950$	−2.38899	+	0.701472i	−0.0775092	+	0.0227588i
$951$	−10.8927	−	7.00031i	−0.353220	−	0.227001i
$952$	−10.7311	+	23.4979i	−0.347798	+	0.761571i
$953$	−36.7053	−	10.7776i	−1.18900	−	0.349122i	−0.373363	−	0.927685i	$-0.621795\pi$
$953$	−36.7053	−	10.7776i	−1.18900	−	0.349122i	−0.815637	+	0.578564i	$0.803613\pi$
$954$	−8.28297	−	9.55906i	−0.268171	−	0.309486i
$955$	−5.94667	−	6.86282i	−0.192430	−	0.222076i
$956$	−0.239949	−	0.0704553i	−0.00776050	−	0.00227869i
$957$	4.35920	−	9.54532i	0.140913	−	0.308556i
$958$	6.83439	+	4.39220i	0.220809	+	0.141905i
$959$	34.3918	−	10.0983i	1.11057	−	0.326092i
$960$	−0.142315	+	0.989821i	−0.00459319	+	0.0319463i
$961$	−10.2803	−	22.5108i	−0.331624	−	0.726155i
$962$	−0.184716	−	1.28473i	−0.00595548	−	0.0414213i
$963$	−3.74479	+	2.40663i	−0.120674	+	0.0775526i
$964$	14.9279	−	17.2277i	0.480794	−	0.554866i
$965$	18.6495			0.600349
$966$	8.71245	+	16.6968i	0.280319	+	0.537212i
$967$	15.1854			0.488330			0.244165	−	0.969734i	$-0.421486\pi$
$967$	15.1854			0.488330			0.244165	+	0.969734i	$0.421486\pi$
$968$	−6.01266	+	6.93898i	−0.193254	+	0.223027i
$969$	13.7785	−	8.85490i	0.442629	−	0.284460i
$970$	−0.800023	−	5.56428i	−0.0256872	−	0.178658i
$971$	−18.9417	−	41.4765i	−0.607868	−	1.33104i	−0.924023	−	0.382337i	$-0.875119\pi$
$971$	−18.9417	−	41.4765i	−0.607868	−	1.33104i	0.316155	−	0.948708i	$-0.397608\pi$
$972$	0.142315	−	0.989821i	0.00456475	−	0.0317485i
$973$	−33.4837	+	9.83169i	−1.07344	+	0.315190i
$974$	−20.7346	−	13.3253i	−0.664379	−	0.426970i
$975$	0.602253	−	1.31875i	0.0192875	−	0.0422338i
$976$	−7.69000	−	2.25799i	−0.246151	−	0.0722764i
$977$	31.4570	+	36.3034i	1.00640	+	1.16145i	0.986850	+	0.161639i	$0.0516779\pi$
$977$	31.4570	+	36.3034i	1.00640	+	1.16145i	0.0195499	+	0.999809i	$0.493777\pi$
$978$	4.06906	+	4.69595i	0.130114	+	0.150160i
$979$	−20.8091	−	6.11010i	−0.665061	−	0.195280i
$980$	−3.49836	+	7.66034i	−0.111751	+	0.244701i
$981$	−7.66577	−	4.92649i	−0.244749	−	0.157291i
$982$	−14.4476	+	4.24220i	−0.461041	+	0.135374i
$983$	−5.53833	+	38.5199i	−0.176645	+	1.22860i	0.687812	+	0.725889i	$0.258571\pi$
$983$	−5.53833	+	38.5199i	−0.176645	+	1.22860i	−0.864457	+	0.502706i	$0.832338\pi$
$984$	−4.24763	−	9.30102i	−0.135410	−	0.296506i
$985$	−0.107933	−	0.750693i	−0.00343904	−	0.0239191i
$986$	−43.0632	+	27.6750i	−1.37141	+	0.881353i
$987$	−29.9656	+	34.5821i	−0.953816	+	1.10076i
$988$	3.60969			0.114840
$989$	23.0833	−	29.6530i	0.734007	−	0.942911i
$990$	−1.34849			−0.0428577
$991$	−2.62029	+	3.02398i	−0.0832363	+	0.0960598i	−0.795840	−	0.605507i	$-0.792970\pi$
$991$	−2.62029	+	3.02398i	−0.0832363	+	0.0960598i	0.712604	+	0.701567i	$0.247516\pi$
$992$	−2.10361	+	1.35191i	−0.0667897	+	0.0429232i
$993$	−1.35008	−	9.39002i	−0.0428435	−	0.297983i
$994$	17.3238	+	37.9339i	0.549478	+	1.20319i
$995$	2.37112	−	16.4915i	0.0751695	−	0.522816i
$996$	6.03398	−	1.77174i	0.191194	−	0.0561397i
$997$	−19.6840	−	12.6502i	−0.623399	−	0.400634i	0.190461	−	0.981695i	$-0.439002\pi$
$997$	−19.6840	−	12.6502i	−0.623399	−	0.400634i	−0.813860	+	0.581060i	$0.802638\pi$
$998$	14.7082	−	32.2065i	0.465581	−	1.01948i
$999$	0.859011	+	0.252229i	0.0271779	+	0.00798016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.f.361.1	yes	20
23.13	even	11	inner	690.2.m.f.151.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.f.151.1	✓	20	23.13	even	11	inner
690.2.m.f.361.1	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.654861 - 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-3.76793 + 1.10637i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(0.654861 - 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(-0.415415 - 0.909632i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-3.76793 + 1.10637i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-0.959493 - 0.281733i) q^{10} +(0.883071 + 1.01912i) q^{11} +(0.654861 + 0.755750i) q^{12} +(1.39104 + 0.408445i) q^{13} +(-1.63134 + 3.57213i) q^{14} +(0.841254 + 0.540641i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(-0.936163 + 6.51116i) q^{17} +(-0.415415 - 0.909632i) q^{18} +(0.354343 + 2.46451i) q^{19} +(-0.841254 + 0.540641i) q^{20} +(2.57164 - 2.96783i) q^{21} +1.34849 q^{22} +(-4.52426 + 1.59092i) q^{23} +1.00000 q^{24} +(-0.654861 + 0.755750i) q^{25} +(1.21962 - 0.783801i) q^{26} +(0.142315 + 0.989821i) q^{27} +(1.63134 + 3.57213i) q^{28} +(-1.10746 + 7.70255i) q^{29} +(0.959493 - 0.281733i) q^{30} +(2.10361 + 1.35191i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(-1.29386 - 0.379913i) q^{33} +(4.30775 + 4.97141i) q^{34} +(2.57164 + 2.96783i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(0.371911 - 0.814372i) q^{37} +(2.09460 + 1.34612i) q^{38} +(-1.39104 + 0.408445i) q^{39} +(-0.142315 + 0.989821i) q^{40} +(-4.24763 - 9.30102i) q^{41} +(-0.558871 - 3.88703i) q^{42} +(-6.59177 + 4.23627i) q^{43} +(0.883071 - 1.01912i) q^{44} -1.00000 q^{45} +(-1.76042 + 4.46104i) q^{46} -11.6523 q^{47} +(0.654861 - 0.755750i) q^{48} +(7.08450 - 4.55293i) q^{49} +(0.142315 + 0.989821i) q^{50} +(-2.73265 - 5.98366i) q^{51} +(0.206323 - 1.43501i) q^{52} +(12.1361 - 3.56348i) q^{53} +(0.841254 + 0.540641i) q^{54} +(0.560182 - 1.22663i) q^{55} +(3.76793 + 1.10637i) q^{56} +(-1.63051 - 1.88170i) q^{57} +(5.09597 + 5.88106i) q^{58} +(-8.65772 - 2.54214i) q^{59} +(0.415415 - 0.909632i) q^{60} +(6.74235 + 4.33305i) q^{61} +(2.39928 - 0.704491i) q^{62} +(-0.558871 + 3.88703i) q^{63} +(0.415415 + 0.909632i) q^{64} +(-0.206323 - 1.43501i) q^{65} +(-1.13442 + 0.729047i) q^{66} +(-8.07285 + 9.31656i) q^{67} +6.57812 q^{68} +(2.94593 - 3.78437i) q^{69} +3.92700 q^{70} +(6.95423 - 8.02561i) q^{71} +(-0.841254 + 0.540641i) q^{72} +(-0.588681 - 4.09436i) q^{73} +(-0.371911 - 0.814372i) q^{74} +(0.142315 - 0.989821i) q^{75} +(2.38899 - 0.701472i) q^{76} +(-4.45487 - 2.86297i) q^{77} +(-0.602253 + 1.31875i) q^{78} +(8.99529 + 2.64126i) q^{79} +(0.654861 + 0.755750i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-9.81085 - 2.88072i) q^{82} +(2.61243 - 5.72042i) q^{83} +(-3.30361 - 2.12310i) q^{84} +(6.31166 - 1.85327i) q^{85} +(-1.11513 + 7.75590i) q^{86} +(-3.23266 - 7.07854i) q^{87} +(-0.191910 - 1.33476i) q^{88} +(-13.5298 + 8.69507i) q^{89} +(-0.654861 + 0.755750i) q^{90} -5.69322 q^{91} +(2.21860 + 4.25180i) q^{92} -2.50057 q^{93} +(-7.63065 + 8.80624i) q^{94} +(2.09460 - 1.34612i) q^{95} +(-0.142315 - 0.989821i) q^{96} +(2.33526 + 5.11350i) q^{97} +(1.19849 - 8.33565i) q^{98} +(1.29386 - 0.379913i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} - 2 q^{10} + 18 q^{11} + 2 q^{12} + 2 q^{13} + 2 q^{14} - 2 q^{15} - 2 q^{16} - 2 q^{17} + 2 q^{18} + 4 q^{19} + 2 q^{20} + 13 q^{21} + 26 q^{22} + 20 q^{24} - 2 q^{25} + 9 q^{26} + 2 q^{27} - 2 q^{28} + 6 q^{29} + 2 q^{30} + 8 q^{31} + 2 q^{32} + 4 q^{33} + 13 q^{34} + 13 q^{35} - 2 q^{36} + 16 q^{37} - 15 q^{38} - 2 q^{39} - 2 q^{40} + 3 q^{41} + 9 q^{42} - 16 q^{43} + 18 q^{44} - 20 q^{45} - 34 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} - 9 q^{51} + 2 q^{52} - 4 q^{53} - 2 q^{54} - 7 q^{55} + 2 q^{56} + 29 q^{57} + 16 q^{58} + 25 q^{59} - 2 q^{60} - 19 q^{61} - 8 q^{62} + 9 q^{63} - 2 q^{64} - 2 q^{65} - 15 q^{66} + 20 q^{67} - 2 q^{68} - 22 q^{69} - 2 q^{70} - q^{71} + 2 q^{72} - q^{73} - 16 q^{74} + 2 q^{75} + 4 q^{76} + 53 q^{77} + 2 q^{78} + 28 q^{79} + 2 q^{80} - 2 q^{81} - 25 q^{82} + 9 q^{83} - 9 q^{84} - 9 q^{85} - 28 q^{86} - 6 q^{87} - 7 q^{88} - 31 q^{89} - 2 q^{90} - 26 q^{91} + 11 q^{92} - 30 q^{93} + q^{94} - 15 q^{95} - 2 q^{96} - 35 q^{97} - 5 q^{98} - 4 q^{99}+O(q^{100}) \) 20 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 - 2 * q^9 - 2 * q^10 + 18 * q^11 + 2 * q^12 + 2 * q^13 + 2 * q^14 - 2 * q^15 - 2 * q^16 - 2 * q^17 + 2 * q^18 + 4 * q^19 + 2 * q^20 + 13 * q^21 + 26 * q^22 + 20 * q^24 - 2 * q^25 + 9 * q^26 + 2 * q^27 - 2 * q^28 + 6 * q^29 + 2 * q^30 + 8 * q^31 + 2 * q^32 + 4 * q^33 + 13 * q^34 + 13 * q^35 - 2 * q^36 + 16 * q^37 - 15 * q^38 - 2 * q^39 - 2 * q^40 + 3 * q^41 + 9 * q^42 - 16 * q^43 + 18 * q^44 - 20 * q^45 - 34 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 - 9 * q^51 + 2 * q^52 - 4 * q^53 - 2 * q^54 - 7 * q^55 + 2 * q^56 + 29 * q^57 + 16 * q^58 + 25 * q^59 - 2 * q^60 - 19 * q^61 - 8 * q^62 + 9 * q^63 - 2 * q^64 - 2 * q^65 - 15 * q^66 + 20 * q^67 - 2 * q^68 - 22 * q^69 - 2 * q^70 - q^71 + 2 * q^72 - q^73 - 16 * q^74 + 2 * q^75 + 4 * q^76 + 53 * q^77 + 2 * q^78 + 28 * q^79 + 2 * q^80 - 2 * q^81 - 25 * q^82 + 9 * q^83 - 9 * q^84 - 9 * q^85 - 28 * q^86 - 6 * q^87 - 7 * q^88 - 31 * q^89 - 2 * q^90 - 26 * q^91 + 11 * q^92 - 30 * q^93 + q^94 - 15 * q^95 - 2 * q^96 - 35 * q^97 - 5 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more