LMFDB - Embedded newform 690.2.m.e.361.2

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} + 21 x^{18} - 47 x^{17} + 44 x^{16} + 232 x^{15} - 1084 x^{14} + 1484 x^{13} + \cdots + 1849 $ x^20 - 6x^19 + 21x^18 - 47x^17 + 44x^16 + 232x^15 - 1084x^14 + 1484x^13 + 2670x^12 - 12826x^11 + 18393x^10 - 2728x^9 - 12654x^8 - 6818x^7 + 39054x^6 + 33738x^5 + 67716x^4 + 45635x^3 + 32892x^2 + 9761*x + 1849
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			361.2
Root			$-0.266817 - 0.584249i$ of defining polynomial
Character	$\chi$	$=$	690.361
Dual form			690.2.m.e.151.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 - 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.415415 + 0.909632i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-1.51668 + 0.445336i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(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} +(-1.51668 + 0.445336i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(0.959493 + 0.281733i) q^{10} +(2.10864 + 2.43350i) q^{11} +(0.654861 + 0.755750i) q^{12} +(2.52331 + 0.740910i) q^{13} +(-0.656649 + 1.43786i) q^{14} +(-0.841254 - 0.540641i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.365476 - 2.54194i) q^{17} +(-0.415415 - 0.909632i) q^{18} +(0.869552 + 6.04786i) q^{19} +(0.841254 - 0.540641i) q^{20} +(1.03514 - 1.19462i) q^{21} +3.21998 q^{22} +(2.96720 + 3.76772i) q^{23} +1.00000 q^{24} +(-0.654861 + 0.755750i) q^{25} +(2.21236 - 1.42180i) q^{26} +(0.142315 + 0.989821i) q^{27} +(0.656649 + 1.43786i) q^{28} +(0.0775433 - 0.539325i) q^{29} +(-0.959493 + 0.281733i) q^{30} +(7.09121 + 4.55724i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(-3.08955 - 0.907174i) q^{33} +(-1.68174 - 1.94083i) q^{34} +(-1.03514 - 1.19462i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(2.27539 - 4.98240i) q^{37} +(5.14011 + 3.30335i) q^{38} +(-2.52331 + 0.740910i) q^{39} +(0.142315 - 0.989821i) q^{40} +(3.64362 + 7.97841i) q^{41} +(-0.224958 - 1.56462i) q^{42} +(6.18008 - 3.97170i) q^{43} +(2.10864 - 2.43350i) q^{44} +1.00000 q^{45} +(4.79056 + 0.224872i) q^{46} -2.23198 q^{47} +(0.654861 - 0.755750i) q^{48} +(-3.78679 + 2.43362i) q^{49} +(0.142315 + 0.989821i) q^{50} +(1.06682 + 2.33601i) q^{51} +(0.374265 - 2.60307i) q^{52} +(-6.70514 + 1.96881i) q^{53} +(0.841254 + 0.540641i) q^{54} +(-1.33763 + 2.92900i) q^{55} +(1.51668 + 0.445336i) q^{56} +(-4.00124 - 4.61767i) q^{57} +(-0.356815 - 0.411786i) q^{58} +(-5.21081 - 1.53003i) q^{59} +(-0.415415 + 0.909632i) q^{60} +(-11.0885 - 7.12617i) q^{61} +(8.08789 - 2.37482i) q^{62} +(-0.224958 + 1.56462i) q^{63} +(0.415415 + 0.909632i) q^{64} +(0.374265 + 2.60307i) q^{65} +(-2.70882 + 1.74085i) q^{66} +(9.75167 - 11.2540i) q^{67} -2.56808 q^{68} +(-4.53315 - 1.56542i) q^{69} -1.58071 q^{70} +(-2.29674 + 2.65058i) q^{71} +(-0.841254 + 0.540641i) q^{72} +(0.103235 + 0.718016i) q^{73} +(-2.27539 - 4.98240i) q^{74} +(0.142315 - 0.989821i) q^{75} +(5.86255 - 1.72140i) q^{76} +(-4.28185 - 2.75178i) q^{77} +(-1.09247 + 2.39218i) q^{78} +(15.2327 + 4.47273i) q^{79} +(-0.654861 - 0.755750i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(8.41574 + 2.47108i) q^{82} +(-4.03791 + 8.84178i) q^{83} +(-1.32977 - 0.854594i) q^{84} +(2.46406 - 0.723512i) q^{85} +(1.04548 - 7.27150i) q^{86} +(0.226348 + 0.495632i) q^{87} +(-0.458251 - 3.18721i) q^{88} +(7.92235 - 5.09139i) q^{89} +(0.654861 - 0.755750i) q^{90} -4.15700 q^{91} +(3.30709 - 3.47320i) q^{92} -8.42934 q^{93} +(-1.46163 + 1.68681i) q^{94} +(-5.14011 + 3.30335i) q^{95} +(-0.142315 - 0.989821i) q^{96} +(-0.773395 - 1.69350i) q^{97} +(-0.640612 + 4.45555i) q^{98} +(3.08955 - 0.907174i) 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	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} - 13 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} + 26 q^{22} + 24 q^{23} + 20 q^{24} - 2 q^{25} + 13 q^{26} + 2 q^{27} - 2 q^{28} + 2 q^{29} - 2 q^{30} + 6 q^{31} + 2 q^{32} + 4 q^{33} + 5 q^{34} - 2 q^{35} - 2 q^{36} - 20 q^{37} + 4 q^{38} + 13 q^{39} + 2 q^{40} - 11 q^{41} - 13 q^{42} + 4 q^{43} - 4 q^{44} + 20 q^{45} - 2 q^{46} + 18 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} + 27 q^{51} - 2 q^{52} - 18 q^{53} - 2 q^{54} + 18 q^{55} + 2 q^{56} - 7 q^{57} + 9 q^{58} - 52 q^{59} + 2 q^{60} - 7 q^{61} + 16 q^{62} - 13 q^{63} - 2 q^{64} - 2 q^{65} + 7 q^{66} - 10 q^{67} + 28 q^{68} + 20 q^{69} - 20 q^{70} + 7 q^{71} + 2 q^{72} - 37 q^{73} + 20 q^{74} + 2 q^{75} - 4 q^{76} - 70 q^{77} + 9 q^{78} + 20 q^{79} - 2 q^{80} - 2 q^{81} - 11 q^{82} - 19 q^{83} - 9 q^{84} + 17 q^{85} - 26 q^{86} - 2 q^{87} + 4 q^{88} + 33 q^{89} + 2 q^{90} - 42 q^{91} - 9 q^{92} + 16 q^{93} - 7 q^{94} - 4 q^{95} - 2 q^{96} + 9 q^{97} + 6 q^{98} - 4 q^{99}+O(q^{100}) \) 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 - 4 * q^11 + 2 * q^12 - 13 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 2 * q^21 + 26 * q^22 + 24 * q^23 + 20 * q^24 - 2 * q^25 + 13 * q^26 + 2 * q^27 - 2 * q^28 + 2 * q^29 - 2 * q^30 + 6 * q^31 + 2 * q^32 + 4 * q^33 + 5 * q^34 - 2 * q^35 - 2 * q^36 - 20 * q^37 + 4 * q^38 + 13 * q^39 + 2 * q^40 - 11 * q^41 - 13 * q^42 + 4 * q^43 - 4 * q^44 + 20 * q^45 - 2 * q^46 + 18 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 + 27 * q^51 - 2 * q^52 - 18 * q^53 - 2 * q^54 + 18 * q^55 + 2 * q^56 - 7 * q^57 + 9 * q^58 - 52 * q^59 + 2 * q^60 - 7 * q^61 + 16 * q^62 - 13 * q^63 - 2 * q^64 - 2 * q^65 + 7 * q^66 - 10 * q^67 + 28 * q^68 + 20 * q^69 - 20 * q^70 + 7 * q^71 + 2 * q^72 - 37 * q^73 + 20 * q^74 + 2 * q^75 - 4 * q^76 - 70 * q^77 + 9 * q^78 + 20 * q^79 - 2 * q^80 - 2 * q^81 - 11 * q^82 - 19 * q^83 - 9 * q^84 + 17 * q^85 - 26 * q^86 - 2 * q^87 + 4 * q^88 + 33 * q^89 + 2 * q^90 - 42 * q^91 - 9 * q^92 + 16 * q^93 - 7 * q^94 - 4 * q^95 - 2 * q^96 + 9 * q^97 + 6 * 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
$7$	−1.51668	+	0.445336i	−0.573250	+	0.168321i	−0.555493	−	0.831521i	$-0.687471\pi$
$7$	−1.51668	+	0.445336i	−0.573250	+	0.168321i	−0.0177565	+	0.999842i	$0.505652\pi$
$8$	−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
$11$	2.10864	+	2.43350i	0.635779	+	0.733728i	0.978623	−	0.205665i	$-0.0659356\pi$
$11$	2.10864	+	2.43350i	0.635779	+	0.733728i	−0.342844	+	0.939392i	$0.611390\pi$
$12$	0.654861	+	0.755750i	0.189042	+	0.218166i
$13$	2.52331	+	0.740910i	0.699840	+	0.205492i	0.612249	−	0.790665i	$-0.290265\pi$
$13$	2.52331	+	0.740910i	0.699840	+	0.205492i	0.0875909	+	0.996157i	$0.472083\pi$
$14$	−0.656649	+	1.43786i	−0.175497	+	0.384284i
$15$	−0.841254	−	0.540641i	−0.217211	−	0.139593i
$16$	−0.959493	+	0.281733i	−0.239873	+	0.0704331i
$17$	0.365476	−	2.54194i	0.0886409	−	0.616511i	−0.896278	−	0.443493i	$-0.853739\pi$
$17$	0.365476	−	2.54194i	0.0886409	−	0.616511i	0.984919	−	0.173018i	$-0.0553519\pi$
$18$	−0.415415	−	0.909632i	−0.0979143	−	0.214402i
$19$	0.869552	+	6.04786i	0.199489	+	1.38748i	0.805772	+	0.592226i	$0.201751\pi$
$19$	0.869552	+	6.04786i	0.199489	+	1.38748i	−0.606283	+	0.795249i	$0.707340\pi$
$20$	0.841254	−	0.540641i	0.188110	−	0.120891i
$21$	1.03514	−	1.19462i	0.225887	−	0.260687i
$22$	3.21998			0.686503
$23$	2.96720	+	3.76772i	0.618704	+	0.785624i
$23$	2.96720	+	3.76772i	0.618704	+	0.785624i
$24$	1.00000			0.204124
$25$	−0.654861	+	0.755750i	−0.130972	+	0.151150i
$26$	2.21236	−	1.42180i	0.433879	−	0.278837i
$27$	0.142315	+	0.989821i	0.0273885	+	0.190491i
$28$	0.656649	+	1.43786i	0.124095	+	0.271730i
$29$	0.0775433	−	0.539325i	0.0143994	−	0.100150i	−0.981354	−	0.192208i	$-0.938435\pi$
$29$	0.0775433	−	0.539325i	0.0143994	−	0.100150i	0.995754	+	0.0920575i	$0.0293444\pi$
$30$	−0.959493	+	0.281733i	−0.175179	+	0.0514371i
$31$	7.09121	+	4.55724i	1.27362	+	0.818505i	0.990087	−	0.140458i	$-0.0448574\pi$
$31$	7.09121	+	4.55724i	1.27362	+	0.818505i	0.283532	+	0.958963i	$0.408494\pi$
$32$	−0.415415	+	0.909632i	−0.0734357	+	0.160802i
$33$	−3.08955	−	0.907174i	−0.537822	−	0.157919i
$34$	−1.68174	−	1.94083i	−0.288415	−	0.332849i
$35$	−1.03514	−	1.19462i	−0.174971	−	0.201927i
$36$	−0.959493	−	0.281733i	−0.159915	−	0.0469554i
$37$	2.27539	−	4.98240i	0.374071	−	0.819102i	−0.625183	−	0.780479i	$-0.714975\pi$
$37$	2.27539	−	4.98240i	0.374071	−	0.819102i	0.999254	−	0.0386233i	$-0.0122972\pi$
$38$	5.14011	+	3.30335i	0.833835	+	0.535873i
$39$	−2.52331	+	0.740910i	−0.404053	+	0.118641i
$40$	0.142315	−	0.989821i	0.0225020	−	0.156505i
$41$	3.64362	+	7.97841i	0.569037	+	1.24602i	0.947308	+	0.320323i	$0.103792\pi$
$41$	3.64362	+	7.97841i	0.569037	+	1.24602i	−0.378271	+	0.925695i	$0.623481\pi$
$42$	−0.224958	−	1.56462i	−0.0347118	−	0.241426i
$43$	6.18008	−	3.97170i	0.942454	−	0.605678i	0.0233643	−	0.999727i	$-0.492562\pi$
$43$	6.18008	−	3.97170i	0.942454	−	0.605678i	0.919090	+	0.394049i	$0.128926\pi$
$44$	2.10864	−	2.43350i	0.317889	−	0.366864i
$45$	1.00000			0.149071
$46$	4.79056	+	0.224872i	0.706329	+	0.0331556i
$47$	−2.23198			−0.325567			−0.162784	−	0.986662i	$-0.552047\pi$
$47$	−2.23198			−0.325567			−0.162784	+	0.986662i	$0.552047\pi$
$48$	0.654861	−	0.755750i	0.0945210	−	0.109083i
$49$	−3.78679	+	2.43362i	−0.540970	+	0.347661i
$50$	0.142315	+	0.989821i	0.0201264	+	0.139982i
$51$	1.06682	+	2.33601i	0.149385	+	0.327107i
$52$	0.374265	−	2.60307i	0.0519012	−	0.360981i
$53$	−6.70514	+	1.96881i	−0.921022	+	0.270437i	−0.707674	−	0.706539i	$-0.750255\pi$
$53$	−6.70514	+	1.96881i	−0.921022	+	0.270437i	−0.213349	+	0.976976i	$0.568437\pi$
$54$	0.841254	+	0.540641i	0.114480	+	0.0735719i
$55$	−1.33763	+	2.92900i	−0.180366	+	0.394946i
$56$	1.51668	+	0.445336i	0.202674	+	0.0595106i
$57$	−4.00124	−	4.61767i	−0.529977	−	0.611626i
$58$	−0.356815	−	0.411786i	−0.0468521	−	0.0540702i
$59$	−5.21081	−	1.53003i	−0.678390	−	0.199193i	−0.0756540	−	0.997134i	$-0.524104\pi$
$59$	−5.21081	−	1.53003i	−0.678390	−	0.199193i	−0.602736	+	0.797941i	$0.705923\pi$
$60$	−0.415415	+	0.909632i	−0.0536298	+	0.117433i
$61$	−11.0885	−	7.12617i	−1.41974	−	0.912412i	−0.999989	−	0.00477314i	$-0.998481\pi$
$61$	−11.0885	−	7.12617i	−1.41974	−	0.912412i	−0.419752	−	0.907639i	$-0.637883\pi$
$62$	8.08789	−	2.37482i	1.02716	−	0.301602i
$63$	−0.224958	+	1.56462i	−0.0283420	+	0.197123i
$64$	0.415415	+	0.909632i	0.0519269	+	0.113704i
$65$	0.374265	+	2.60307i	0.0464218	+	0.322871i
$66$	−2.70882	+	1.74085i	−0.333433	+	0.214284i
$67$	9.75167	−	11.2540i	1.19136	−	1.37490i	0.281717	−	0.959498i	$-0.409096\pi$
$67$	9.75167	−	11.2540i	1.19136	−	1.37490i	0.909639	−	0.415400i	$-0.136358\pi$
$68$	−2.56808			−0.311425
$69$	−4.53315	−	1.56542i	−0.545727	−	0.188454i
$70$	−1.58071			−0.188931
$71$	−2.29674	+	2.65058i	−0.272573	+	0.314566i	−0.875488	−	0.483239i	$-0.839460\pi$
$71$	−2.29674	+	2.65058i	−0.272573	+	0.314566i	0.602916	+	0.797805i	$0.294006\pi$
$72$	−0.841254	+	0.540641i	−0.0991427	+	0.0637151i
$73$	0.103235	+	0.718016i	0.0120828	+	0.0840374i	0.994971	−	0.100168i	$-0.0319380\pi$
$73$	0.103235	+	0.718016i	0.0120828	+	0.0840374i	−0.982888	+	0.184205i	$0.941029\pi$
$74$	−2.27539	−	4.98240i	−0.264508	−	0.579192i
$75$	0.142315	−	0.989821i	0.0164331	−	0.114295i
$76$	5.86255	−	1.72140i	0.672481	−	0.197458i
$77$	−4.28185	−	2.75178i	−0.487962	−	0.313594i
$78$	−1.09247	+	2.39218i	−0.123698	+	0.270861i
$79$	15.2327	+	4.47273i	1.71382	+	0.503222i	0.983657	−	0.180054i	$-0.0576274\pi$
$79$	15.2327	+	4.47273i	1.71382	+	0.503222i	0.730160	+	0.683276i	$0.239446\pi$
$80$	−0.654861	−	0.755750i	−0.0732157	−	0.0844954i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	8.41574	+	2.47108i	0.929363	+	0.272886i
$83$	−4.03791	+	8.84178i	−0.443218	+	0.970512i	0.547779	+	0.836623i	$0.315474\pi$
$83$	−4.03791	+	8.84178i	−0.443218	+	0.970512i	−0.990996	+	0.133888i	$0.957254\pi$
$84$	−1.32977	−	0.854594i	−0.145090	−	0.0932439i
$85$	2.46406	−	0.723512i	0.267264	−	0.0784759i
$86$	1.04548	−	7.27150i	0.112737	−	0.784107i
$87$	0.226348	+	0.495632i	0.0242670	+	0.0531374i
$88$	−0.458251	−	3.18721i	−0.0488497	−	0.339757i
$89$	7.92235	−	5.09139i	0.839768	−	0.539686i	−0.0486000	−	0.998818i	$-0.515476\pi$
$89$	7.92235	−	5.09139i	0.839768	−	0.539686i	0.888368	+	0.459132i	$0.151840\pi$
$90$	0.654861	−	0.755750i	0.0690284	−	0.0796630i
$91$	−4.15700			−0.435772
$92$	3.30709	−	3.47320i	0.344788	−	0.362106i
$93$	−8.42934			−0.874082
$94$	−1.46163	+	1.68681i	−0.150756	+	0.173982i
$95$	−5.14011	+	3.30335i	−0.527364	+	0.338916i
$96$	−0.142315	−	0.989821i	−0.0145249	−	0.101023i
$97$	−0.773395	−	1.69350i	−0.0785264	−	0.171949i	0.866297	−	0.499530i	$-0.166494\pi$
$97$	−0.773395	−	1.69350i	−0.0785264	−	0.171949i	−0.944823	+	0.327581i	$0.893767\pi$
$98$	−0.640612	+	4.45555i	−0.0647115	+	0.450079i
$99$	3.08955	−	0.907174i	0.310511	−	0.0911744i
$100$	0.841254	+	0.540641i	0.0841254	+	0.0540641i
$101$	−0.852925	+	1.86765i	−0.0848693	+	0.185838i	−0.947308	−	0.320323i	$-0.896209\pi$
$101$	−0.852925	+	1.86765i	−0.0848693	+	0.185838i	0.862439	+	0.506161i	$0.168936\pi$
$102$	2.46406	+	0.723512i	0.243978	+	0.0716384i
$103$	−6.72114	−	7.75661i	−0.662254	−	0.764282i	0.320890	−	0.947117i	$-0.396018\pi$
$103$	−6.72114	−	7.75661i	−0.662254	−	0.764282i	−0.983144	+	0.182835i	$0.941473\pi$
$104$	−1.72218	−	1.98750i	−0.168873	−	0.194890i
$105$	1.51668	+	0.445336i	0.148012	+	0.0434604i
$106$	−2.90301	+	6.35671i	−0.281965	+	0.617418i
$107$	−9.43013	−	6.06038i	−0.911645	−	0.585879i	−0.00142311	−	0.999999i	$-0.500453\pi$
$107$	−9.43013	−	6.06038i	−0.911645	−	0.585879i	−0.910222	+	0.414120i	$0.864089\pi$
$108$	0.959493	−	0.281733i	0.0923273	−	0.0271097i
$109$	1.00367	−	6.98071i	0.0961345	−	0.668630i	−0.883587	−	0.468267i	$-0.844879\pi$
$109$	1.00367	−	6.98071i	0.0961345	−	0.668630i	0.979722	−	0.200364i	$-0.0642123\pi$
$110$	1.33763	+	2.92900i	0.127538	+	0.279269i
$111$	0.779513	+	5.42163i	0.0739881	+	0.514598i
$112$	1.32977	−	0.854594i	0.125652	−	0.0807516i
$113$	−4.22722	+	4.87847i	−0.397663	+	0.458928i	−0.918904	−	0.394482i	$-0.870924\pi$
$113$	−4.22722	+	4.87847i	−0.397663	+	0.458928i	0.521240	+	0.853410i	$0.325470\pi$
$114$	−6.11006			−0.572259
$115$	−2.19462	+	4.26423i	−0.204649	+	0.397641i
$116$	−0.544871			−0.0505900
$117$	1.72218	−	1.98750i	0.159215	−	0.183744i
$118$	−4.56868	+	2.93611i	−0.420581	+	0.270291i
$119$	0.577710	+	4.01806i	0.0529586	+	0.368335i
$120$	0.415415	+	0.909632i	0.0379220	+	0.0830377i
$121$	0.0899023	−	0.625284i	0.00817294	−	0.0568440i
$122$	−12.6470	+	3.71351i	−1.14501	+	0.336205i
$123$	−7.37866	−	4.74198i	−0.665311	−	0.427570i
$124$	3.50167	−	7.66759i	0.314460	−	0.688570i
$125$	−0.959493	−	0.281733i	−0.0858197	−	0.0251989i
$126$	1.03514	+	1.19462i	0.0922178	+	0.106425i
$127$	−4.78452	−	5.52163i	−0.424557	−	0.489965i	0.502663	−	0.864483i	$-0.332354\pi$
$127$	−4.78452	−	5.52163i	−0.424557	−	0.489965i	−0.927220	+	0.374517i	$0.877808\pi$
$128$	0.959493	+	0.281733i	0.0848080	+	0.0249019i
$129$	−3.05175	+	6.68241i	−0.268692	+	0.588353i
$130$	2.21236	+	1.42180i	0.194037	+	0.124700i
$131$	−12.6750	+	3.72171i	−1.10742	+	0.325167i	−0.783795	−	0.621019i	$-0.786719\pi$
$131$	−12.6750	+	3.72171i	−1.10742	+	0.325167i	−0.323622	+	0.946186i	$0.604901\pi$
$132$	−0.458251	+	3.18721i	−0.0398857	+	0.277411i
$133$	−4.01216	−	8.78541i	−0.347899	−	0.761792i
$134$	−2.11924	−	14.7396i	−0.183074	−	1.27331i
$135$	−0.841254	+	0.540641i	−0.0724036	+	0.0465310i
$136$	−1.68174	+	1.94083i	−0.144208	+	0.166424i
$137$	−12.3486			−1.05501			−0.527505	−	0.849552i	$-0.676873\pi$
$137$	−12.3486			−1.05501			−0.527505	+	0.849552i	$0.676873\pi$
$138$	−4.15165	+	2.40080i	−0.353412	+	0.204369i
$139$	−10.7030			−0.907817			−0.453908	−	0.891048i	$-0.649971\pi$
$139$	−10.7030			−0.907817			−0.453908	+	0.891048i	$0.649971\pi$
$140$	−1.03514	+	1.19462i	−0.0874855	+	0.100964i
$141$	1.87766	−	1.20670i	0.158127	−	0.101622i
$142$	0.499129	+	3.47152i	0.0418860	+	0.291323i
$143$	3.51774	+	7.70279i	0.294169	+	0.644139i
$144$	−0.142315	+	0.989821i	−0.0118596	+	0.0824851i
$145$	0.522800	−	0.153508i	0.0434162	−	0.0127481i
$146$	0.610245	+	0.392181i	0.0505042	+	0.0324571i
$147$	1.86994	−	4.09459i	0.154230	−	0.337716i
$148$	−5.25551	−	1.54316i	−0.432000	−	0.126847i
$149$	−5.62093	−	6.48690i	−0.460484	−	0.531427i	0.477256	−	0.878764i	$-0.341631\pi$
$149$	−5.62093	−	6.48690i	−0.460484	−	0.531427i	−0.937740	+	0.347337i	$0.887086\pi$
$150$	−0.654861	−	0.755750i	−0.0534692	−	0.0617067i
$151$	17.8741	+	5.24831i	1.45457	+	0.427101i	0.911051	−	0.412293i	$-0.135272\pi$
$151$	17.8741	+	5.24831i	1.45457	+	0.427101i	0.543523	+	0.839395i	$0.317090\pi$
$152$	2.53821	−	5.55790i	0.205876	−	0.450805i
$153$	−2.16041	−	1.38841i	−0.174659	−	0.112246i
$154$	−4.88367	+	1.43398i	−0.393537	+	0.115553i
$155$	−1.19962	+	8.34354i	−0.0963558	+	0.670169i
$156$	1.09247	+	2.39218i	0.0874679	+	0.191528i
$157$	−0.732365	−	5.09371i	−0.0584491	−	0.406523i	−0.997951	−	0.0639794i	$-0.979621\pi$
$157$	−0.732365	−	5.09371i	−0.0584491	−	0.406523i	0.939502	−	0.342543i	$-0.111288\pi$
$158$	13.3556	−	8.58311i	1.06251	−	0.682836i
$159$	4.57631	−	5.28134i	0.362925	−	0.418838i
$160$	−1.00000			−0.0790569
$161$	−6.17819	−	4.39301i	−0.486909	−	0.346218i
$162$	−1.00000			−0.0785674
$163$	−7.72467	+	8.91475i	−0.605043	+	0.698257i	−0.972795	−	0.231667i	$-0.925582\pi$
$163$	−7.72467	+	8.91475i	−0.605043	+	0.698257i	0.367752	+	0.929924i	$0.380127\pi$
$164$	7.37866	−	4.74198i	0.576177	−	0.370286i
$165$	−0.458251	−	3.18721i	−0.0356748	−	0.248124i
$166$	4.03791	+	8.84178i	0.313402	+	0.686255i
$167$	1.53055	−	10.6452i	0.118438	−	0.823752i	−0.840839	−	0.541285i	$-0.817938\pi$
$167$	1.53055	−	10.6452i	0.118438	−	0.823752i	0.959277	−	0.282467i	$-0.0911527\pi$
$168$	−1.51668	+	0.445336i	−0.117014	+	0.0343584i
$169$	−5.11816	−	3.28924i	−0.393704	−	0.253018i
$170$	1.06682	−	2.33601i	0.0818213	−	0.179164i
$171$	5.86255	+	1.72140i	0.448321	+	0.131639i
$172$	−4.81079	−	5.55195i	−0.366819	−	0.423332i
$173$	9.12807	+	10.5344i	0.693995	+	0.800912i	0.987928	−	0.154913i	$-0.0495099\pi$
$173$	9.12807	+	10.5344i	0.693995	+	0.800912i	−0.293933	+	0.955826i	$0.594964\pi$
$174$	0.522800	+	0.153508i	0.0396334	+	0.0116374i
$175$	0.656649	−	1.43786i	0.0496380	−	0.108692i
$176$	−2.70882	−	1.74085i	−0.204185	−	0.131222i
$177$	5.21081	−	1.53003i	0.391668	−	0.115004i
$178$	1.34022	−	9.32147i	0.100454	−	0.698673i
$179$	3.64953	+	7.99135i	0.272779	+	0.597302i	0.995597	−	0.0937361i	$-0.0298810\pi$
$179$	3.64953	+	7.99135i	0.272779	+	0.597302i	−0.722818	+	0.691038i	$0.757154\pi$
$180$	−0.142315	−	0.989821i	−0.0106075	−	0.0737769i
$181$	7.56311	−	4.86051i	0.562161	−	0.361279i	−0.228490	−	0.973546i	$-0.573379\pi$
$181$	7.56311	−	4.86051i	0.562161	−	0.361279i	0.790651	+	0.612267i	$0.209742\pi$
$182$	−2.72225	+	3.14165i	−0.201787	+	0.232874i
$183$	13.1810			0.974365
$184$	−0.459184	−	4.77380i	−0.0338515	−	0.351929i
$185$	5.47738			0.402705
$186$	−5.52004	+	6.37047i	−0.404749	+	0.467105i
$187$	6.95647	−	4.47065i	0.508708	−	0.326927i
$188$	0.317643	+	2.20926i	0.0231665	+	0.161127i
$189$	−0.656649	−	1.43786i	−0.0477642	−	0.104589i
$190$	−0.869552	+	6.04786i	−0.0630839	+	0.438758i
$191$	−19.7759	+	5.80674i	−1.43094	+	0.420161i	−0.903190	−	0.429241i	$-0.858781\pi$
$191$	−19.7759	+	5.80674i	−1.43094	+	0.420161i	−0.527747	+	0.849402i	$0.676963\pi$
$192$	−0.841254	−	0.540641i	−0.0607122	−	0.0390174i
$193$	9.06137	−	19.8416i	0.652252	−	1.42823i	−0.237318	−	0.971432i	$-0.576268\pi$
$193$	9.06137	−	19.8416i	0.652252	−	1.42823i	0.889569	−	0.456800i	$-0.151004\pi$
$194$	−1.78633	−	0.524513i	−0.128251	−	0.0376579i
$195$	−1.72218	−	1.98750i	−0.123328	−	0.142328i
$196$	2.94777	+	3.40191i	0.210555	+	0.242993i
$197$	−8.27764	−	2.43053i	−0.589757	−	0.173168i	−0.0267810	−	0.999641i	$-0.508526\pi$
$197$	−8.27764	−	2.43053i	−0.589757	−	0.173168i	−0.562976	+	0.826473i	$0.690344\pi$
$198$	1.33763	−	2.92900i	0.0950612	−	0.208155i
$199$	12.4201	+	7.98193i	0.880440	+	0.565824i	0.900929	−	0.433966i	$-0.142886\pi$
$199$	12.4201	+	7.98193i	0.880440	+	0.565824i	−0.0204897	+	0.999790i	$0.506523\pi$
$200$	0.959493	−	0.281733i	0.0678464	−	0.0199215i
$201$	−2.11924	+	14.7396i	−0.149480	+	1.03965i
$202$	0.852925	+	1.86765i	0.0600116	+	0.131407i
$203$	0.122573	+	0.852515i	0.00860295	+	0.0598348i
$204$	2.16041	−	1.38841i	0.151259	−	0.0972081i
$205$	−5.74380	+	6.62870i	−0.401165	+	0.462969i
$206$	−10.2635			−0.715090
$207$	4.65986	−	1.13389i	0.323883	−	0.0788110i
$208$	−2.62984			−0.182346
$209$	−12.8839	+	14.8688i	−0.891198	+	1.02850i
$210$	1.32977	−	0.854594i	0.0917632	−	0.0589726i
$211$	3.65178	+	25.3987i	0.251399	+	1.74852i	0.589832	+	0.807526i	$0.299194\pi$
$211$	3.65178	+	25.3987i	0.251399	+	1.74852i	−0.338433	+	0.940990i	$0.609897\pi$
$212$	2.90301	+	6.35671i	0.199380	+	0.436580i
$213$	0.499129	−	3.47152i	0.0341997	−	0.237864i
$214$	−10.7556	+	3.15812i	−0.735234	+	0.215884i
$215$	6.18008	+	3.97170i	0.421478	+	0.270868i
$216$	0.415415	−	0.909632i	0.0282654	−	0.0618926i
$217$	−12.7846	−	3.75389i	−0.867874	−	0.254831i
$218$	−4.61840	−	5.32992i	−0.312797	−	0.360988i
$219$	−0.475036	−	0.548221i	−0.0320999	−	0.0370453i
$220$	3.08955	+	0.907174i	0.208297	+	0.0611616i
$221$	2.80556	−	6.14332i	0.188722	−	0.413244i
$222$	4.60787	+	2.96130i	0.309260	+	0.198749i
$223$	−2.41259	+	0.708400i	−0.161559	+	0.0474380i	−0.361512	−	0.932368i	$-0.617739\pi$
$223$	−2.41259	+	0.708400i	−0.161559	+	0.0474380i	0.199953	+	0.979806i	$0.435921\pi$
$224$	0.224958	−	1.56462i	0.0150306	−	0.104540i
$225$	0.415415	+	0.909632i	0.0276943	+	0.0606421i
$226$	0.918663	+	6.38944i	0.0611085	+	0.425019i
$227$	5.91472	−	3.80116i	0.392573	−	0.252292i	−0.329432	−	0.944179i	$-0.606857\pi$
$227$	5.91472	−	3.80116i	0.392573	−	0.252292i	0.722005	+	0.691888i	$0.243221\pi$
$228$	−4.00124	+	4.61767i	−0.264988	+	0.305813i
$229$	23.7846			1.57173			0.785866	−	0.618397i	$-0.212217\pi$
$229$	23.7846			1.57173			0.785866	+	0.618397i	$0.212217\pi$
$230$	1.78552	+	4.45106i	0.117734	+	0.293494i
$231$	5.08985			0.334887
$232$	−0.356815	+	0.411786i	−0.0234260	+	0.0270351i
$233$	11.8685	−	7.62742i	0.777531	−	0.499689i	−0.0906824	−	0.995880i	$-0.528905\pi$
$233$	11.8685	−	7.62742i	0.777531	−	0.499689i	0.868213	+	0.496191i	$0.165268\pi$
$234$	−0.374265	−	2.60307i	−0.0244664	−	0.170168i
$235$	−0.927196	−	2.03028i	−0.0604836	−	0.132441i
$236$	−0.772883	+	5.37552i	−0.0503104	+	0.349916i
$237$	−15.2327	+	4.47273i	−0.989472	+	0.290535i
$238$	3.41497	+	2.19467i	0.221359	+	0.142259i
$239$	9.98720	−	21.8689i	0.646018	−	1.41458i	−0.248978	−	0.968509i	$-0.580095\pi$
$239$	9.98720	−	21.8689i	0.646018	−	1.41458i	0.894996	−	0.446073i	$-0.147178\pi$
$240$	0.959493	+	0.281733i	0.0619350	+	0.0181858i
$241$	6.10835	+	7.04941i	0.393473	+	0.454092i	0.917575	−	0.397564i	$-0.130144\pi$
$241$	6.10835	+	7.04941i	0.393473	+	0.454092i	−0.524101	+	0.851656i	$0.675599\pi$
$242$	−0.413685	−	0.477418i	−0.0265927	−	0.0306896i
$243$	0.959493	+	0.281733i	0.0615515	+	0.0180732i
$244$	−5.47557	+	11.9898i	−0.350537	+	0.767570i
$245$	−3.78679	−	2.43362i	−0.241929	−	0.155479i
$246$	−8.41574	+	2.47108i	−0.536568	+	0.157551i
$247$	−2.28678	+	15.9049i	−0.145504	+	1.01200i
$248$	−3.50167	−	7.66759i	−0.222356	−	0.486893i
$249$	−1.38333	−	9.62124i	−0.0876647	−	0.609721i
$250$	−0.841254	+	0.540641i	−0.0532055	+	0.0341931i
$251$	12.5640	−	14.4996i	0.793033	−	0.915209i	−0.204945	−	0.978774i	$-0.565701\pi$
$251$	12.5640	−	14.4996i	0.793033	−	0.915209i	0.997978	+	0.0635645i	$0.0202469\pi$
$252$	1.58071			0.0995751
$253$	−2.91199	+	15.1654i	−0.183075	+	0.953444i
$254$	−7.30616			−0.458429
$255$	−1.68174	+	1.94083i	−0.105314	+	0.121539i
$256$	0.841254	−	0.540641i	0.0525783	−	0.0337901i
$257$	−0.0601582	−	0.418409i	−0.00375256	−	0.0260997i	0.987859	−	0.155352i	$-0.0496513\pi$
$257$	−0.0601582	−	0.418409i	−0.00375256	−	0.0260997i	−0.991612	+	0.129253i	$0.958742\pi$
$258$	3.05175	+	6.68241i	0.189994	+	0.416029i
$259$	−1.23218	+	8.57000i	−0.0765640	+	0.532514i
$260$	2.52331	−	0.740910i	0.156489	−	0.0459493i
$261$	−0.458375	−	0.294580i	−0.0283727	−	0.0182340i
$262$	−5.48766	+	12.0163i	−0.339029	+	0.742370i
$263$	−9.25301	−	2.71693i	−0.570565	−	0.167533i	−0.0162911	−	0.999867i	$-0.505186\pi$
$263$	−9.25301	−	2.71693i	−0.570565	−	0.167533i	−0.554274	+	0.832334i	$0.687004\pi$
$264$	2.10864	+	2.43350i	0.129778	+	0.149772i
$265$	−4.57631	−	5.28134i	−0.281120	−	0.324430i
$266$	−9.26698	−	2.72103i	−0.568195	−	0.166837i
$267$	−3.91210	+	8.56630i	−0.239416	+	0.524249i
$268$	−12.5273	−	8.05079i	−0.765225	−	0.491781i
$269$	17.6523	−	5.18319i	1.07628	−	0.316025i	0.304892	−	0.952387i	$-0.401380\pi$
$269$	17.6523	−	5.18319i	1.07628	−	0.316025i	0.771390	+	0.636362i	$0.219562\pi$
$270$	−0.142315	+	0.989821i	−0.00866101	+	0.0602386i
$271$	−6.58833	−	14.4264i	−0.400212	−	0.876343i	−0.997249	−	0.0741286i	$-0.976382\pi$
$271$	−6.58833	−	14.4264i	−0.400212	−	0.876343i	0.597036	−	0.802214i	$-0.296345\pi$
$272$	0.365476	+	2.54194i	0.0221602	+	0.154128i
$273$	3.49709	−	2.24744i	0.211653	−	0.136021i
$274$	−8.08660	+	9.33244i	−0.488530	+	0.563793i
$275$	−3.21998			−0.194172
$276$	−0.904351	+	4.70979i	−0.0544355	+	0.283496i
$277$	15.3957			0.925040			0.462520	−	0.886609i	$-0.346945\pi$
$277$	15.3957			0.925040			0.462520	+	0.886609i	$0.346945\pi$
$278$	−7.00898	+	8.08879i	−0.420370	+	0.485133i
$279$	7.09121	−	4.55724i	0.424540	−	0.272835i
$280$	0.224958	+	1.56462i	0.0134438	+	0.0935037i
$281$	−3.81114	−	8.34523i	−0.227353	−	0.497834i	0.761235	−	0.648476i	$-0.224593\pi$
$281$	−3.81114	−	8.34523i	−0.227353	−	0.497834i	−0.988588	+	0.150642i	$0.951866\pi$
$282$	0.317643	−	2.20926i	0.0189154	−	0.131559i
$283$	14.7103	−	4.31934i	0.874438	−	0.256758i	0.186436	−	0.982467i	$-0.440306\pi$
$283$	14.7103	−	4.31934i	0.874438	−	0.256758i	0.688002	+	0.725709i	$0.258488\pi$
$284$	2.95046	+	1.89614i	0.175077	+	0.112515i
$285$	2.53821	−	5.55790i	0.150351	−	0.329222i
$286$	8.12501	+	2.38572i	0.480442	+	0.141070i
$287$	−9.07926	−	10.4780i	−0.535932	−	0.618499i
$288$	0.654861	+	0.755750i	0.0385880	+	0.0445330i
$289$	9.98349	+	2.93142i	0.587264	+	0.172436i
$290$	0.226348	−	0.495632i	0.0132916	−	0.0291045i
$291$	1.56620	+	1.00653i	0.0918121	+	0.0590040i
$292$	0.696016	−	0.204369i	0.0407313	−	0.0119598i
$293$	0.145786	−	1.01397i	0.00851693	−	0.0592366i	−0.985120	−	0.171869i	$-0.945019\pi$
$293$	0.145786	−	1.01397i	0.00851693	−	0.0592366i	0.993637	+	0.112633i	$0.0359284\pi$
$294$	−1.86994	−	4.09459i	−0.109057	−	0.238801i
$295$	−0.772883	−	5.37552i	−0.0449990	−	0.312975i
$296$	−4.60787	+	2.96130i	−0.267827	+	0.172122i
$297$	−2.10864	+	2.43350i	−0.122356	+	0.141206i
$298$	−8.58339			−0.497223
$299$	4.69562	+	11.7056i	0.271555	+	0.676950i
$300$	−1.00000			−0.0577350
$301$	−7.60444	+	8.77600i	−0.438313	+	0.505840i
$302$	15.6715	−	10.0714i	0.901791	−	0.579546i
$303$	−0.292199	−	2.03229i	−0.0167864	−	0.116752i
$304$	−2.53821	−	5.55790i	−0.145576	−	0.318768i
$305$	1.87585	−	13.0468i	0.107411	−	0.747057i
$306$	−2.46406	+	0.723512i	−0.140861	+	0.0413604i
$307$	−5.33718	−	3.43000i	−0.304609	−	0.195760i	0.379402	−	0.925232i	$-0.376130\pi$
$307$	−5.33718	−	3.43000i	−0.304609	−	0.195760i	−0.684011	+	0.729471i	$0.739766\pi$
$308$	−2.11440	+	4.62989i	−0.120479	+	0.263812i
$309$	9.84773	+	2.89155i	0.560218	+	0.164495i
$310$	5.52004	+	6.37047i	0.313517	+	0.361818i
$311$	0.635431	+	0.733327i	0.0360320	+	0.0415831i	0.773480	−	0.633821i	$-0.218515\pi$
$311$	0.635431	+	0.733327i	0.0360320	+	0.0415831i	−0.737448	+	0.675404i	$0.763969\pi$
$312$	2.52331	+	0.740910i	0.142854	+	0.0419458i
$313$	9.76100	−	21.3736i	0.551724	−	1.20811i	−0.404248	−	0.914650i	$-0.632467\pi$
$313$	9.76100	−	21.3736i	0.551724	−	1.20811i	0.955972	−	0.293458i	$-0.0948061\pi$
$314$	−4.32917	−	2.78219i	−0.244309	−	0.157008i
$315$	−1.51668	+	0.445336i	−0.0854550	+	0.0250919i
$316$	2.25936	−	15.7142i	0.127099	−	0.883994i
$317$	−5.09471	−	11.1559i	−0.286147	−	0.626575i	0.710906	−	0.703287i	$-0.248285\pi$
$317$	−5.09471	−	11.1559i	−0.286147	−	0.626575i	−0.997053	+	0.0767118i	$0.975558\pi$
$318$	−0.994527	−	6.91709i	−0.0557703	−	0.387891i
$319$	1.47596	−	0.948541i	0.0826378	−	0.0531081i
$320$	−0.654861	+	0.755750i	−0.0366078	+	0.0422477i
$321$	11.2096			0.625660
$322$	−7.36587	+	1.79235i	−0.410484	+	0.0998838i
$323$	15.6911			0.873077
$324$	−0.654861	+	0.755750i	−0.0363812	+	0.0419861i
$325$	−2.21236	+	1.42180i	−0.122720	+	0.0788671i
$326$	1.67873	+	11.6758i	0.0929763	+	0.646665i
$327$	2.92971	+	6.41517i	0.162013	+	0.354760i
$328$	1.24825	−	8.68175i	0.0689230	−	0.479370i
$329$	3.38518	−	0.993980i	0.186631	−	0.0547999i
$330$	−2.70882	−	1.74085i	−0.149116	−	0.0958308i
$331$	−4.48504	+	9.82087i	−0.246520	+	0.539804i	−0.991928	−	0.126805i	$-0.959528\pi$
$331$	−4.48504	+	9.82087i	−0.246520	+	0.539804i	0.745407	+	0.666609i	$0.232255\pi$
$332$	9.32644	+	2.73849i	0.511855	+	0.150294i
$333$	−3.58692	−	4.13953i	−0.196562	−	0.226845i
$334$	−7.04282	−	8.12785i	−0.385366	−	0.444736i
$335$	14.2880	+	4.19534i	0.780637	+	0.229216i
$336$	−0.656649	+	1.43786i	−0.0358231	+	0.0784417i
$337$	−11.5692	−	7.43509i	−0.630216	−	0.405015i	0.186174	−	0.982517i	$-0.440391\pi$
$337$	−11.5692	−	7.43509i	−0.630216	−	0.405015i	−0.816389	+	0.577502i	$0.804028\pi$
$338$	−5.83752	+	1.71405i	−0.317519	+	0.0932321i
$339$	0.918663	−	6.38944i	0.0498949	−	0.347027i
$340$	−1.06682	−	2.33601i	−0.0578564	−	0.126688i
$341$	3.86275	+	26.8660i	0.209180	+	1.45488i
$342$	5.14011	−	3.30335i	0.277945	−	0.178624i
$343$	11.9056	−	13.7397i	0.642839	−	0.741876i
$344$	−7.34628			−0.396085
$345$	−0.459184	−	4.77380i	−0.0247216	−	0.257013i
$346$	13.9390			0.749363
$347$	−10.9533	+	12.6407i	−0.588001	+	0.678590i	−0.969305	−	0.245860i	$-0.920930\pi$
$347$	−10.9533	+	12.6407i	−0.588001	+	0.678590i	0.381304	+	0.924450i	$0.375475\pi$
$348$	0.458375	−	0.294580i	0.0245715	−	0.0157911i
$349$	1.08548	+	7.54967i	0.0581044	+	0.404125i	0.998030	+	0.0627445i	$0.0199853\pi$
$349$	1.08548	+	7.54967i	0.0581044	+	0.404125i	−0.939925	+	0.341380i	$0.889106\pi$
$350$	−0.656649	−	1.43786i	−0.0350994	−	0.0768569i
$351$	−0.374265	+	2.60307i	−0.0199768	+	0.138941i
$352$	−3.08955	+	0.907174i	−0.164674	+	0.0483525i
$353$	24.7846	+	15.9281i	1.31915	+	0.847768i	0.995158	−	0.0982907i	$-0.0313375\pi$
$353$	24.7846	+	15.9281i	1.31915	+	0.847768i	0.323995	+	0.946059i	$0.394974\pi$
$354$	2.25603	−	4.94002i	0.119907	−	0.262559i
$355$	−3.36515	−	0.988097i	−0.178604	−	0.0524427i
$356$	−6.16703	−	7.11714i	−0.326852	−	0.377207i
$357$	−2.65833	−	3.06787i	−0.140694	−	0.162369i
$358$	8.42940	+	2.47509i	0.445507	+	0.130813i
$359$	0.883649	−	1.93492i	0.0466372	−	0.102121i	−0.884879	−	0.465821i	$-0.845759\pi$
$359$	0.883649	−	1.93492i	0.0466372	−	0.102121i	0.931516	+	0.363699i	$0.118486\pi$
$360$	−0.841254	−	0.540641i	−0.0443380	−	0.0284943i
$361$	−17.5902	+	5.16494i	−0.925798	+	0.271839i
$362$	1.27945	−	8.89877i	0.0672464	−	0.467709i
$363$	0.262424	+	0.574628i	0.0137737	+	0.0301601i
$364$	0.591602	+	4.11468i	0.0310084	+	0.215668i
$365$	−0.610245	+	0.392181i	−0.0319417	+	0.0205277i
$366$	8.63169	−	9.96151i	0.451186	−	0.520696i
$367$	6.91883			0.361160			0.180580	−	0.983560i	$-0.442203\pi$
$367$	6.91883			0.361160			0.180580	+	0.983560i	$0.442203\pi$
$368$	−3.90850	−	2.77915i	−0.203745	−	0.144873i
$369$	8.77103			0.456602
$370$	3.58692	−	4.13953i	0.186475	−	0.215204i
$371$	9.29275	−	5.97209i	0.482456	−	0.310055i
$372$	1.19962	+	8.34354i	0.0621974	+	0.432592i
$373$	−11.0791	−	24.2597i	−0.573652	−	1.25612i	−0.944830	−	0.327561i	$-0.893773\pi$
$373$	−11.0791	−	24.2597i	−0.573652	−	1.25612i	0.371178	−	0.928562i	$-0.378954\pi$
$374$	1.17683	−	8.18501i	0.0608522	−	0.423237i
$375$	0.959493	−	0.281733i	0.0495480	−	0.0145486i
$376$	1.87766	+	1.20670i	0.0968328	+	0.0622307i
$377$	0.595257	−	1.30343i	0.0306573	−	0.0671301i
$378$	−1.51668	−	0.445336i	−0.0780094	−	0.0229056i
$379$	−21.6559	−	24.9923i	−1.11239	−	1.28377i	−0.955123	−	0.296211i	$-0.904277\pi$
$379$	−21.6559	−	24.9923i	−1.11239	−	1.28377i	−0.157267	−	0.987556i	$-0.550268\pi$
$380$	4.00124	+	4.61767i	0.205259	+	0.236882i
$381$	7.01021	+	2.05838i	0.359144	+	0.105454i
$382$	−8.56204	+	18.7483i	−0.438072	+	0.959244i
$383$	12.6173	+	8.10866i	0.644715	+	0.414333i	0.821732	−	0.569875i	$-0.193008\pi$
$383$	12.6173	+	8.10866i	0.644715	+	0.414333i	−0.177017	+	0.984208i	$0.556645\pi$
$384$	−0.959493	+	0.281733i	−0.0489639	+	0.0143771i
$385$	0.724360	−	5.03804i	0.0369168	−	0.256762i
$386$	−9.06137	−	19.8416i	−0.461212	−	1.00991i
$387$	−1.04548	−	7.27150i	−0.0531450	−	0.369631i
$388$	−1.56620	+	1.00653i	−0.0795116	+	0.0510990i
$389$	1.74277	−	2.01126i	0.0883619	−	0.101975i	−0.709847	−	0.704356i	$-0.751236\pi$
$389$	1.74277	−	2.01126i	0.0883619	−	0.101975i	0.798209	+	0.602381i	$0.205781\pi$
$390$	−2.62984			−0.133167
$391$	10.6618	−	6.16544i	0.539189	−	0.311800i
$392$	4.50137			0.227353
$393$	8.65075	−	9.98350i	0.436373	−	0.503601i
$394$	−7.25758	+	4.66416i	−0.365631	+	0.234977i
$395$	2.25936	+	15.7142i	0.113681	+	0.790668i
$396$	−1.33763	−	2.92900i	−0.0672184	−	0.147188i
$397$	−1.95917	+	13.6263i	−0.0983278	+	0.683885i	0.879718	+	0.475496i	$0.157731\pi$
$397$	−1.95917	+	13.6263i	−0.0983278	+	0.683885i	−0.978046	+	0.208389i	$0.933178\pi$
$398$	14.1658	−	4.15945i	0.710067	−	0.208495i
$399$	8.12500	+	5.22162i	0.406759	+	0.261408i
$400$	0.415415	−	0.909632i	0.0207708	−	0.0454816i
$401$	11.8706	+	3.48553i	0.592790	+	0.174059i	0.564349	−	0.825537i	$-0.309127\pi$
$401$	11.8706	+	3.48553i	0.592790	+	0.174059i	0.0284414	+	0.999595i	$0.490946\pi$
$402$	9.75167	+	11.2540i	0.486369	+	0.561300i
$403$	14.5168	+	16.7533i	0.723133	+	0.834540i
$404$	1.97002	+	0.578450i	0.0980122	+	0.0287790i
$405$	0.415415	−	0.909632i	0.0206421	−	0.0452000i
$406$	0.724556	+	0.465644i	0.0359591	+	0.0231095i
$407$	16.9226	−	4.96894i	0.838824	−	0.246301i
$408$	0.365476	−	2.54194i	0.0180938	−	0.125845i
$409$	−4.36561	−	9.55935i	−0.215865	−	0.472679i	0.770460	−	0.637488i	$-0.220027\pi$
$409$	−4.36561	−	9.55935i	−0.215865	−	0.472679i	−0.986326	+	0.164809i	$0.947299\pi$
$410$	1.24825	+	8.68175i	0.0616466	+	0.428761i
$411$	10.3883	−	6.67615i	0.512417	−	0.329310i
$412$	−6.72114	+	7.75661i	−0.331127	+	0.382141i
$413$	8.58449			0.422415
$414$	2.19462	−	4.26423i	0.107860	−	0.209575i
$415$	−9.72018			−0.477145
$416$	−1.72218	+	1.98750i	−0.0844366	+	0.0974451i
$417$	9.00394	−	5.78648i	0.440925	−	0.283365i
$418$	2.79994	+	19.4740i	0.136950	+	0.952505i
$419$	3.20012	+	7.00728i	0.156336	+	0.342328i	0.971551	−	0.236830i	$-0.0761086\pi$
$419$	3.20012	+	7.00728i	0.156336	+	0.342328i	−0.815215	+	0.579158i	$0.803381\pi$
$420$	0.224958	−	1.56462i	0.0109768	−	0.0763455i
$421$	−35.3598	+	10.3826i	−1.72333	+	0.506016i	−0.985602	−	0.169080i	$-0.945921\pi$
$421$	−35.3598	+	10.3826i	−1.72333	+	0.506016i	−0.737730	+	0.675096i	$0.764102\pi$
$422$	21.5864	+	13.8728i	1.05081	+	0.675316i
$423$	−0.927196	+	2.03028i	−0.0450818	+	0.0987154i
$424$	6.70514	+	1.96881i	0.325631	+	0.0956138i
$425$	1.68174	+	1.94083i	0.0815761	+	0.0941439i
$426$	−2.29674	−	2.65058i	−0.111277	−	0.128421i
$427$	19.9912	+	5.86996i	0.967444	+	0.284067i
$428$	−4.65664	+	10.1966i	−0.225087	+	0.492873i
$429$	−7.12375	−	4.57816i	−0.343938	−	0.221036i
$430$	7.04870	−	2.06969i	0.339919	−	0.0998091i
$431$	3.96469	−	27.5750i	0.190972	−	1.32824i	−0.638469	−	0.769648i	$-0.720432\pi$
$431$	3.96469	−	27.5750i	0.190972	−	1.32824i	0.829441	−	0.558594i	$-0.188659\pi$
$432$	−0.415415	−	0.909632i	−0.0199867	−	0.0437647i
$433$	−1.75596	−	12.2130i	−0.0843859	−	0.586917i	−0.987512	−	0.157542i	$-0.949643\pi$
$433$	−1.75596	−	12.2130i	−0.0843859	−	0.586917i	0.903126	−	0.429375i	$-0.141266\pi$
$434$	−11.2091	+	7.20366i	−0.538055	+	0.345787i
$435$	−0.356815	+	0.411786i	−0.0171080	+	0.0197436i
$436$	−7.05249			−0.337753
$437$	−20.2065	+	21.2214i	−0.966609	+	1.01516i
$438$	−0.725400			−0.0346609
$439$	−18.0727	+	20.8570i	−0.862561	+	0.995449i	0.137426	+	0.990512i	$0.456117\pi$
$439$	−18.0727	+	20.8570i	−0.862561	+	0.995449i	−0.999988	+	0.00493696i	$0.998429\pi$
$440$	2.70882	−	1.74085i	0.129138	−	0.0829920i
$441$	0.640612	+	4.45555i	0.0305053	+	0.212169i
$442$	−2.80556	−	6.14332i	−0.133447	−	0.292208i
$443$	−3.33413	+	23.1894i	−0.158409	+	1.10176i	0.743156	+	0.669118i	$0.233328\pi$
$443$	−3.33413	+	23.1894i	−0.158409	+	1.10176i	−0.901566	+	0.432642i	$0.857581\pi$
$444$	5.25551	−	1.54316i	0.249415	−	0.0732350i
$445$	7.92235	+	5.09139i	0.375556	+	0.241355i
$446$	−1.04454	+	2.28722i	−0.0494603	+	0.108303i
$447$	8.23571	+	2.41822i	0.389536	+	0.114378i
$448$	−1.03514	−	1.19462i	−0.0489059	−	0.0564404i
$449$	−22.1467	−	25.5587i	−1.04517	−	1.20619i	−0.978034	−	0.208444i	$-0.933160\pi$
$449$	−22.1467	−	25.5587i	−1.04517	−	1.20619i	−0.0671337	−	0.997744i	$-0.521385\pi$
$450$	0.959493	+	0.281733i	0.0452309	+	0.0132810i
$451$	−11.7324	+	25.6903i	−0.552456	+	1.20971i
$452$	5.43041	+	3.48991i	0.255425	+	0.164152i
$453$	−17.8741	+	5.24831i	−0.839799	+	0.246587i
$454$	1.00059	−	6.95927i	0.0469601	−	0.326615i
$455$	−1.72688	−	3.78134i	−0.0809573	−	0.177272i
$456$	0.869552	+	6.04786i	0.0407205	+	0.283217i
$457$	13.0302	−	8.37403i	0.609529	−	0.391721i	−0.199151	−	0.979969i	$-0.563819\pi$
$457$	13.0302	−	8.37403i	0.609529	−	0.391721i	0.808680	+	0.588248i	$0.200182\pi$
$458$	15.5756	−	17.9752i	0.727801	−	0.839927i
$459$	2.56808			0.119868
$460$	4.53315	+	1.56542i	0.211359	+	0.0729881i
$461$	20.9484			0.975667			0.487833	−	0.872937i	$-0.337787\pi$
$461$	20.9484			0.975667			0.487833	+	0.872937i	$0.337787\pi$
$462$	3.33314	−	3.84665i	0.155072	−	0.178962i
$463$	−6.35765	+	4.08581i	−0.295465	+	0.189884i	−0.679972	−	0.733238i	$-0.738008\pi$
$463$	−6.35765	+	4.08581i	−0.295465	+	0.189884i	0.384507	+	0.923122i	$0.374372\pi$
$464$	0.0775433	+	0.539325i	0.00359986	+	0.0250375i
$465$	−3.50167	−	7.66759i	−0.162386	−	0.355576i
$466$	2.00779	−	13.9645i	0.0930092	−	0.646893i
$467$	−35.4164	+	10.3992i	−1.63887	+	0.481217i	−0.966001	−	0.258540i	$-0.916759\pi$
$467$	−35.4164	+	10.3992i	−1.63887	+	0.481217i	−0.672874	+	0.739757i	$0.734940\pi$
$468$	−2.21236	−	1.42180i	−0.102266	−	0.0657226i
$469$	−9.77830	+	21.4115i	−0.451520	+	0.988690i
$470$	−2.14157	−	0.628820i	−0.0987830	−	0.0290053i
$471$	3.36997	+	3.88916i	0.155280	+	0.179203i
$472$	3.55641	+	4.10432i	0.163697	+	0.188917i
$473$	22.6967	+	6.66435i	1.04360	+	0.306427i
$474$	−6.59505	+	14.4412i	−0.302921	+	0.663304i
$475$	−5.14011	−	3.30335i	−0.235844	−	0.151568i
$476$	3.89495	−	1.14366i	0.178525	−	0.0524195i
$477$	−0.994527	+	6.91709i	−0.0455363	+	0.316712i
$478$	−9.98720	−	21.8689i	−0.456804	−	1.00026i
$479$	3.72749	+	25.9252i	0.170313	+	1.18455i	0.878223	+	0.478252i	$0.158729\pi$
$479$	3.72749	+	25.9252i	0.170313	+	1.18455i	−0.707910	+	0.706303i	$0.750362\pi$
$480$	0.841254	−	0.540641i	0.0383978	−	0.0246768i
$481$	9.43302	−	10.8863i	0.430108	−	0.496372i
$482$	9.32770			0.424865
$483$	7.57246	+	0.355457i	0.344559	+	0.0161739i
$484$	−0.631714			−0.0287143
$485$	1.21918	−	1.40701i	0.0553602	−	0.0638891i
$486$	0.841254	−	0.540641i	0.0381600	−	0.0245240i
$487$	−3.39794	−	23.6332i	−0.153975	−	1.07092i	−0.909471	−	0.415768i	$-0.863513\pi$
$487$	−3.39794	−	23.6332i	−0.153975	−	1.07092i	0.755496	−	0.655154i	$-0.227396\pi$
$488$	5.47557	+	11.9898i	0.247867	+	0.542754i
$489$	1.67873	−	11.6758i	0.0759149	−	0.528000i
$490$	−4.31903	+	1.26818i	−0.195114	+	0.0572906i
$491$	−28.1177	−	18.0701i	−1.26893	−	0.815494i	−0.279453	−	0.960159i	$-0.590153\pi$
$491$	−28.1177	−	18.0701i	−1.26893	−	0.815494i	−0.989481	+	0.144665i	$0.953789\pi$
$492$	−3.64362	+	7.97841i	−0.164267	+	0.359694i
$493$	−1.34259	−	0.394221i	−0.0604673	−	0.0177548i
$494$	10.5226	+	12.1437i	0.473434	+	0.546372i
$495$	2.10864	+	2.43350i	0.0947763	+	0.109378i
$496$	−8.08789	−	2.37482i	−0.363157	−	0.106633i
$497$	2.30301	−	5.04289i	0.103304	−	0.226204i
$498$	−8.17713	−	5.25512i	−0.366426	−	0.235488i
$499$	17.6425	−	5.18030i	0.789786	−	0.231902i	0.138127	−	0.990414i	$-0.455892\pi$
$499$	17.6425	−	5.18030i	0.789786	−	0.231902i	0.651659	+	0.758512i	$0.274073\pi$
$500$	−0.142315	+	0.989821i	−0.00636451	+	0.0442662i
$501$	4.46766	+	9.78280i	0.199600	+	0.437063i
$502$	−2.73042	−	18.9905i	−0.121865	−	0.847587i
$503$	0.0109218	−	0.00701903i	0.000486980	−	0.000312963i	−0.540397	−	0.841410i	$-0.681726\pi$
$503$	0.0109218	−	0.00701903i	0.000486980	−	0.000312963i	0.540884	+	0.841097i	$0.318090\pi$
$504$	1.03514	−	1.19462i	0.0461089	−	0.0532125i
$505$	−2.05319			−0.0913657
$506$	9.55433	+	12.1320i	0.424742	+	0.539333i
$507$	6.08397			0.270198
$508$	−4.78452	+	5.52163i	−0.212279	+	0.244983i
$509$	6.26834	−	4.02842i	0.277839	−	0.178557i	−0.394299	−	0.918982i	$-0.629012\pi$
$509$	6.26834	−	4.02842i	0.277839	−	0.178557i	0.672138	+	0.740426i	$0.265376\pi$
$510$	0.365476	+	2.54194i	0.0161835	+	0.112559i
$511$	−0.476333	−	1.04302i	−0.0210717	−	0.0461407i
$512$	0.142315	−	0.989821i	0.00628949	−	0.0437443i
$513$	−5.86255	+	1.72140i	−0.258838	+	0.0760017i
$514$	−0.355608	−	0.228535i	−0.0156852	−	0.0100803i
$515$	4.26360	−	9.33598i	0.187877	−	0.411392i
$516$	7.04870	+	2.06969i	0.310302	+	0.0911128i
$517$	−4.70643	−	5.43151i	−0.206989	−	0.238878i
$518$	5.66987	+	6.54338i	0.249120	+	0.287500i
$519$	−13.3743	−	3.92706i	−0.587068	−	0.172379i
$520$	1.09247	−	2.39218i	0.0479081	−	0.104904i
$521$	13.2139	+	8.49205i	0.578911	+	0.372043i	0.797086	−	0.603866i	$-0.206374\pi$
$521$	13.2139	+	8.49205i	0.578911	+	0.372043i	−0.218175	+	0.975910i	$0.570010\pi$
$522$	−0.522800	+	0.153508i	−0.0228823	+	0.00671886i
$523$	−6.12885	+	42.6271i	−0.267996	+	1.86395i	0.199420	+	0.979914i	$0.436094\pi$
$523$	−6.12885	+	42.6271i	−0.267996	+	1.86395i	−0.467416	+	0.884038i	$0.654815\pi$
$524$	5.48766	+	12.0163i	0.239730	+	0.524935i
$525$	0.224958	+	1.56462i	0.00981797	+	0.0682855i
$526$	−8.11275	+	5.21375i	−0.353733	+	0.227330i
$527$	14.1759	−	16.3599i	0.617512	−	0.712647i
$528$	3.21998			0.140132
$529$	−5.39145	+	22.3592i	−0.234411	+	0.972138i
$530$	−6.98822			−0.303549
$531$	−3.55641	+	4.10432i	−0.154335	+	0.178112i
$532$	−8.12500	+	5.22162i	−0.352263	+	0.226386i
$533$	3.28269	+	22.8316i	0.142189	+	0.988946i
$534$	3.91210	+	8.56630i	0.169293	+	0.370700i
$535$	1.59530	−	11.0955i	0.0689706	−	0.479701i
$536$	−14.2880	+	4.19534i	−0.617148	+	0.181211i
$537$	−7.39063	−	4.74967i	−0.318929	−	0.204963i
$538$	7.64263	−	16.7350i	0.329497	−	0.721498i
$539$	−13.9072	−	4.08352i	−0.599026	−	0.175890i
$540$	0.654861	+	0.755750i	0.0281807	+	0.0325223i
$541$	−11.1835	−	12.9064i	−0.480815	−	0.554890i	0.462573	−	0.886581i	$-0.346926\pi$
$541$	−11.1835	−	12.9064i	−0.480815	−	0.554890i	−0.943388	+	0.331691i	$0.892381\pi$
$542$	−15.2172	−	4.46817i	−0.653635	−	0.191924i
$543$	−3.73470	+	8.17785i	−0.160271	+	0.350945i
$544$	2.16041	+	1.38841i	0.0926267	+	0.0595275i
$545$	6.76682	−	1.98692i	0.289859	−	0.0851101i
$546$	0.591602	−	4.11468i	0.0253182	−	0.176092i
$547$	9.09272	+	19.9103i	0.388777	+	0.851302i	0.998286	+	0.0585232i	$0.0186392\pi$
$547$	9.09272	+	19.9103i	0.388777	+	0.851302i	−0.609509	+	0.792779i	$0.708634\pi$
$548$	1.75739	+	12.2229i	0.0750718	+	0.522136i
$549$	−11.0885	+	7.12617i	−0.473247	+	0.304137i
$550$	−2.10864	+	2.43350i	−0.0899127	+	0.103765i
$551$	3.32919			0.141828
$552$	2.96720	+	3.76772i	0.126292	+	0.160365i
$553$	−25.0950			−1.06715
$554$	10.0821	−	11.6353i	0.428346	−	0.494337i
$555$	−4.60787	+	2.96130i	−0.195593	+	0.125700i
$556$	1.52320	+	10.5941i	0.0645979	+	0.449288i
$557$	−5.75997	−	12.6126i	−0.244058	−	0.534412i	0.747472	−	0.664294i	$-0.231267\pi$
$557$	−5.75997	−	12.6126i	−0.244058	−	0.534412i	−0.991529	+	0.129882i	$0.958540\pi$
$558$	1.19962	−	8.34354i	0.0507840	−	0.353210i
$559$	18.5369	−	5.44293i	0.784029	−	0.230212i
$560$	1.32977	+	0.854594i	0.0561932	+	0.0361132i
$561$	−3.43514	+	7.52190i	−0.145032	+	0.317575i
$562$	−8.80266	−	2.58470i	−0.371318	−	0.109029i
$563$	−0.0674388	−	0.0778285i	−0.00284221	−	0.00328008i	0.754327	−	0.656499i	$-0.227963\pi$
$563$	−0.0674388	−	0.0778285i	−0.00284221	−	0.00328008i	−0.757169	+	0.653219i	$0.773418\pi$
$564$	−1.46163	−	1.68681i	−0.0615459	−	0.0710277i
$565$	−6.19366	−	1.81862i	−0.260569	−	0.0765101i
$566$	6.36887	−	13.9459i	0.267704	−	0.586189i
$567$	1.32977	+	0.854594i	0.0558453	+	0.0358896i
$568$	3.36515	−	0.988097i	0.141198	−	0.0414596i
$569$	−4.40581	+	30.6431i	−0.184701	+	1.28462i	0.660764	+	0.750594i	$0.270232\pi$
$569$	−4.40581	+	30.6431i	−0.184701	+	1.28462i	−0.845465	+	0.534031i	$0.820677\pi$
$570$	−2.53821	−	5.55790i	−0.106314	−	0.232795i
$571$	−5.09855	−	35.4612i	−0.213368	−	1.48400i	−0.761801	−	0.647811i	$-0.775685\pi$
$571$	−5.09855	−	35.4612i	−0.213368	−	1.48400i	0.548434	−	0.836194i	$-0.315224\pi$
$572$	7.12375	−	4.57816i	0.297859	−	0.191422i
$573$	13.4972	−	15.5766i	0.563854	−	0.650723i
$574$	−13.8644			−0.578690
$575$	−4.79056	−	0.224872i	−0.199780	−	0.00937783i
$576$	1.00000			0.0416667
$577$	−26.3691	+	30.4315i	−1.09776	+	1.26688i	−0.136677	+	0.990616i	$0.543642\pi$
$577$	−26.3691	+	30.4315i	−1.09776	+	1.26688i	−0.961081	+	0.276265i	$0.910903\pi$
$578$	8.75321	−	5.62535i	0.364086	−	0.233984i
$579$	3.10429	+	21.5908i	0.129010	+	0.897283i
$580$	−0.226348	−	0.495632i	−0.00939858	−	0.0205800i
$581$	2.18663	−	15.2083i	0.0907167	−	0.630949i
$582$	1.78633	−	0.524513i	0.0740457	−	0.0217418i
$583$	−18.9298	−	12.1655i	−0.783993	−	0.503842i
$584$	0.301342	−	0.659847i	0.0124696	−	0.0273047i
$585$	2.52331	+	0.740910i	0.104326	+	0.0306329i
$586$	−0.670835	−	0.774185i	−0.0277119	−	0.0319813i
$587$	7.11577	+	8.21203i	0.293699	+	0.338947i	0.883352	−	0.468710i	$-0.155281\pi$
$587$	7.11577	+	8.21203i	0.293699	+	0.338947i	−0.589653	+	0.807657i	$0.700736\pi$
$588$	−4.31903	−	1.26818i	−0.178114	−	0.0522989i
$589$	−21.3954	+	46.8494i	−0.881583	+	1.93040i
$590$	−4.56868	−	2.93611i	−0.188089	−	0.120878i
$591$	8.27764	−	2.43053i	0.340497	−	0.0999788i
$592$	−0.779513	+	5.42163i	−0.0320378	+	0.222828i
$593$	6.26478	+	13.7180i	0.257264	+	0.563329i	0.993557	−	0.113334i	$-0.0361529\pi$
$593$	6.26478	+	13.7180i	0.257264	+	0.563329i	−0.736293	+	0.676662i	$0.763426\pi$
$594$	0.458251	+	3.18721i	0.0188023	+	0.130773i
$595$	−3.41497	+	2.19467i	−0.140000	+	0.0899726i
$596$	−5.62093	+	6.48690i	−0.230242	+	0.265714i
$597$	−14.7638			−0.604244
$598$	11.9214	+	4.11680i	0.487504	+	0.168348i
$599$	36.8338			1.50499			0.752493	−	0.658600i	$-0.228851\pi$
$599$	36.8338			1.50499			0.752493	+	0.658600i	$0.228851\pi$
$600$	−0.654861	+	0.755750i	−0.0267346	+	0.0308533i
$601$	−12.3170	+	7.91566i	−0.502421	+	0.322886i	−0.767184	−	0.641427i	$-0.778343\pi$
$601$	−12.3170	+	7.91566i	−0.502421	+	0.322886i	0.264763	+	0.964314i	$0.414706\pi$
$602$	1.65260	+	11.4941i	0.0673551	+	0.468465i
$603$	−6.18603	−	13.5455i	−0.251915	−	0.551616i
$604$	2.65114	−	18.4391i	0.107873	−	0.750276i
$605$	0.606125	−	0.177974i	0.0246425	−	0.00723569i
$606$	−1.72725	−	1.11004i	−0.0701648	−	0.0450922i
$607$	2.45752	−	5.38121i	0.0997476	−	0.218417i	−0.853179	−	0.521619i	$-0.825328\pi$
$607$	2.45752	−	5.38121i	0.0997476	−	0.218417i	0.952926	+	0.303202i	$0.0980557\pi$
$608$	−5.86255	−	1.72140i	−0.237758	−	0.0698120i
$609$	−0.564019	−	0.650913i	−0.0228552	−	0.0263763i
$610$	−8.63169	−	9.96151i	−0.349487	−	0.403330i
$611$	−5.63196	−	1.65369i	−0.227845	−	0.0669013i
$612$	−1.06682	+	2.33601i	−0.0431236	+	0.0944275i
$613$	−6.47537	−	4.16147i	−0.261538	−	0.168080i	0.403300	−	0.915068i	$-0.367863\pi$
$613$	−6.47537	−	4.16147i	−0.261538	−	0.168080i	−0.664838	+	0.746988i	$0.731499\pi$
$614$	−6.08733	+	1.78740i	−0.245665	+	0.0721337i
$615$	1.24825	−	8.68175i	0.0503342	−	0.350082i
$616$	2.11440	+	4.62989i	0.0851915	+	0.186543i
$617$	1.06203	+	7.38659i	0.0427558	+	0.297373i	0.999968	+	0.00798647i	$0.00254220\pi$
$617$	1.06203	+	7.38659i	0.0427558	+	0.297373i	−0.957212	+	0.289387i	$0.906549\pi$
$618$	8.63418	−	5.54885i	0.347318	−	0.223208i
$619$	10.9989	−	12.6934i	0.442084	−	0.510192i	−0.490354	−	0.871524i	$-0.663132\pi$
$619$	10.9989	−	12.6934i	0.442084	−	0.510192i	0.932437	+	0.361332i	$0.117678\pi$
$620$	8.42934			0.338530
$621$	−3.30709	+	3.47320i	−0.132709	+	0.139375i
$622$	0.970330			0.0389067
$623$	−9.74827	+	11.2501i	−0.390556	+	0.450726i
$624$	2.21236	−	1.42180i	0.0885652	−	0.0569174i
$625$	−0.142315	−	0.989821i	−0.00569259	−	0.0395929i
$626$	−9.76100	−	21.3736i	−0.390128	−	0.854261i
$627$	2.79994	−	19.4740i	0.111819	−	0.777717i
$628$	−4.93764	+	1.44982i	−0.197033	+	0.0578542i
$629$	−11.8334	−	7.60485i	−0.471827	−	0.303225i
$630$	−0.656649	+	1.43786i	−0.0261615	+	0.0572857i
$631$	0.550363	+	0.161601i	0.0219096	+	0.00643324i	0.292669	−	0.956214i	$-0.405457\pi$
$631$	0.550363	+	0.161601i	0.0219096	+	0.00643324i	−0.270759	+	0.962647i	$0.587275\pi$
$632$	−10.3964	−	11.9981i	−0.413549	−	0.477260i
$633$	−16.8036	−	19.3924i	−0.667884	−	0.770780i
$634$	−11.7674	−	3.45521i	−0.467341	−	0.137224i
$635$	3.03509	−	6.64592i	0.120444	−	0.263735i
$636$	−5.87886	−	3.77812i	−0.233112	−	0.149812i
$637$	−11.3583	+	3.33511i	−0.450034	+	0.132142i
$638$	0.249688	−	1.73662i	0.00988524	−	0.0687534i
$639$	1.45695	+	3.19028i	0.0576360	+	0.126205i
$640$	0.142315	+	0.989821i	0.00562549	+	0.0391261i
$641$	−4.08725	+	2.62672i	−0.161437	+	0.103749i	−0.618865	−	0.785498i	$-0.712407\pi$
$641$	−4.08725	+	2.62672i	−0.161437	+	0.103749i	0.457428	+	0.889247i	$0.348771\pi$
$642$	7.34074	−	8.47167i	0.289716	−	0.334350i
$643$	−28.7688			−1.13453			−0.567266	−	0.823535i	$-0.691999\pi$
$643$	−28.7688			−1.13453			−0.567266	+	0.823535i	$0.691999\pi$
$644$	−3.46905	+	6.74049i	−0.136700	+	0.265613i
$645$	−7.34628			−0.289259
$646$	10.2755	−	11.8586i	0.404284	−	0.466568i
$647$	24.7036	−	15.8760i	0.971199	−	0.624151i	0.0441230	−	0.999026i	$-0.485951\pi$
$647$	24.7036	−	15.8760i	0.971199	−	0.624151i	0.927075	+	0.374875i	$0.122314\pi$
$648$	0.142315	+	0.989821i	0.00559065	+	0.0388839i
$649$	−7.26439	−	15.9068i	−0.285152	−	0.624396i
$650$	−0.374265	+	2.60307i	−0.0146799	+	0.102101i
$651$	12.7846	−	3.75389i	0.501067	−	0.147127i
$652$	9.92334	+	6.37735i	0.388628	+	0.249756i
$653$	21.0833	−	46.1660i	0.825054	−	1.80662i	0.305454	−	0.952207i	$-0.401192\pi$
$653$	21.0833	−	46.1660i	0.825054	−	1.80662i	0.519600	−	0.854410i	$-0.326081\pi$
$654$	6.76682	+	1.98692i	0.264603	+	0.0776946i
$655$	−8.65075	−	9.98350i	−0.338013	−	0.390088i
$656$	−5.74380	−	6.62870i	−0.224258	−	0.258807i
$657$	0.696016	+	0.204369i	0.0271542	+	0.00797318i
$658$	1.46562	−	3.20927i	0.0571360	−	0.125110i
$659$	−23.9462	−	15.3893i	−0.932811	−	0.599481i	−0.0164632	−	0.999864i	$-0.505241\pi$
$659$	−23.9462	−	15.3893i	−0.932811	−	0.599481i	−0.916348	+	0.400383i	$0.868877\pi$
$660$	−3.08955	+	0.907174i	−0.120261	+	0.0353117i
$661$	3.78674	−	26.3374i	0.147287	−	1.02440i	−0.773348	−	0.633981i	$-0.781420\pi$
$661$	3.78674	−	26.3374i	0.147287	−	1.02440i	0.920636	−	0.390423i	$-0.127671\pi$
$662$	4.48504	+	9.82087i	0.174316	+	0.381699i
$663$	0.961142	+	6.68489i	0.0373276	+	0.259619i
$664$	8.17713	−	5.25512i	0.317334	−	0.203938i
$665$	6.32478	−	7.29918i	0.245264	−	0.283050i
$666$	−5.47738			−0.212244
$667$	2.26211	−	1.30812i	0.0875894	−	0.0506508i
$668$	−10.7547			−0.416111
$669$	1.64661	−	1.90029i	0.0636616	−	0.0734694i
$670$	12.5273	−	8.05079i	0.483971	−	0.311029i
$671$	−6.04019	−	42.0105i	−0.233179	−	1.62180i
$672$	0.656649	+	1.43786i	0.0253308	+	0.0554667i
$673$	0.588107	−	4.09038i	0.0226699	−	0.157672i	−0.975342	−	0.220699i	$-0.929166\pi$
$673$	0.588107	−	4.09038i	0.0226699	−	0.157672i	0.998012	+	0.0630265i	$0.0200753\pi$
$674$	−13.1953	+	3.87449i	−0.508264	+	0.149240i
$675$	−0.841254	−	0.540641i	−0.0323799	−	0.0208093i
$676$	−2.52737	+	5.53417i	−0.0972066	+	0.212853i
$677$	−17.4782	−	5.13206i	−0.671741	−	0.197241i	−0.0719631	−	0.997407i	$-0.522926\pi$
$677$	−17.4782	−	5.13206i	−0.671741	−	0.197241i	−0.599778	+	0.800166i	$0.704745\pi$
$678$	−4.22722	−	4.87847i	−0.162345	−	0.187357i
$679$	1.92717	+	2.22407i	0.0739579	+	0.0853520i
$680$	−2.46406	−	0.723512i	−0.0944922	−	0.0277454i
$681$	−2.92071	+	6.39547i	−0.111922	+	0.245075i
$682$	22.8336	+	14.6742i	0.874343	+	0.561906i
$683$	−47.7914	+	14.0328i	−1.82869	+	0.536951i	−0.999749	−	0.0223913i	$-0.992872\pi$
$683$	−47.7914	+	14.0328i	−1.82869	+	0.536951i	−0.828937	+	0.559342i	$0.811054\pi$
$684$	0.869552	−	6.04786i	0.0332481	−	0.231246i
$685$	−5.12979	−	11.2327i	−0.195999	−	0.429178i
$686$	−2.58732	−	17.9952i	−0.0987845	−	0.687061i
$687$	−20.0089	+	12.8589i	−0.763387	+	0.490599i
$688$	−4.81079	+	5.55195i	−0.183410	+	0.211666i
$689$	−18.3779			−0.700141
$690$	−3.90850	−	2.77915i	−0.148794	−	0.105800i
$691$	−9.55400			−0.363451			−0.181726	−	0.983349i	$-0.558168\pi$
$691$	−9.55400			−0.363451			−0.181726	+	0.983349i	$0.558168\pi$
$692$	9.12807	−	10.5344i	0.346997	−	0.400456i
$693$	−4.28185	+	2.75178i	−0.162654	+	0.104531i
$694$	2.38037	+	16.5558i	0.0903576	+	0.628451i
$695$	−4.44619	−	9.73579i	−0.168653	−	0.369300i
$696$	0.0775433	−	0.539325i	0.00293927	−	0.0204431i
$697$	21.6123	−	6.34594i	0.818624	−	0.240370i
$698$	6.41650	+	4.12363i	0.242868	+	0.156082i
$699$	−5.86072	+	12.8332i	−0.221673	+	0.485396i
$700$	−1.51668	−	0.445336i	−0.0573250	−	0.0168321i
$701$	−26.9457	−	31.0970i	−1.01772	−	1.17452i	−0.984557	−	0.175067i	$-0.943986\pi$
$701$	−26.9457	−	31.0970i	−1.01772	−	1.17452i	−0.0331677	−	0.999450i	$-0.510560\pi$
$702$	1.72218	+	1.98750i	0.0649993	+	0.0750132i
$703$	32.1115	+	9.42877i	1.21111	+	0.355613i
$704$	−1.33763	+	2.92900i	−0.0504138	+	0.110391i
$705$	1.87766	+	1.20670i	0.0707167	+	0.0454468i
$706$	28.2681	−	8.30028i	1.06389	−	0.312385i
$707$	0.461881	−	3.21245i	0.0173708	−	0.120817i
$708$	−2.25603	−	4.94002i	−0.0847869	−	0.185658i
$709$	−1.20665	−	8.39246i	−0.0453169	−	0.315186i	−0.999854	−	0.0170933i	$-0.994559\pi$
$709$	−1.20665	−	8.39246i	−0.0453169	−	0.315186i	0.954537	−	0.298092i	$-0.0963503\pi$
$710$	−2.95046	+	1.89614i	−0.110729	+	0.0711610i
$711$	10.3964	−	11.9981i	0.389897	−	0.449965i
$712$	−9.41732			−0.352929
$713$	3.87061	+	40.2400i	0.144956	+	1.50700i
$714$	−4.05938			−0.151918
$715$	−5.54538	+	6.39971i	−0.207385	+	0.239335i
$716$	7.39063	−	4.74967i	0.276201	−	0.177504i
$717$	3.42146	+	23.7968i	0.127777	+	0.888707i
$718$	−0.883649	−	1.93492i	−0.0329775	−	0.0722106i
$719$	0.645117	−	4.48688i	0.0240588	−	0.167333i	−0.974250	−	0.225472i	$-0.927608\pi$
$719$	0.645117	−	4.48688i	0.0240588	−	0.167333i	0.998308	+	0.0581393i	$0.0185167\pi$
$720$	−0.959493	+	0.281733i	−0.0357582	+	0.0104996i
$721$	13.6481	+	8.77110i	0.508282	+	0.326653i
$722$	−7.61571	+	16.6761i	−0.283427	+	0.620619i
$723$	−8.94987	−	2.62792i	−0.332849	−	0.0977333i
$724$	−5.88738	−	6.79440i	−0.218803	−	0.252512i
$725$	0.356815	+	0.411786i	0.0132518	+	0.0152934i
$726$	0.606125	+	0.177974i	0.0224954	+	0.00660525i
$727$	−11.2546	+	24.6442i	−0.417411	+	0.914002i	0.577793	+	0.816183i	$0.303914\pi$
$727$	−11.2546	+	24.6442i	−0.417411	+	0.914002i	−0.995204	+	0.0978192i	$0.968813\pi$
$728$	3.49709	+	2.24744i	0.129611	+	0.0832957i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	−0.103235	+	0.718016i	−0.00382090	+	0.0265750i
$731$	−7.83715	−	17.1610i	−0.289868	−	0.634721i
$732$	−1.87585	−	13.0468i	−0.0693333	−	0.482223i
$733$	2.14989	−	1.38165i	0.0794081	−	0.0510325i	−0.500334	−	0.865832i	$-0.666790\pi$
$733$	2.14989	−	1.38165i	0.0794081	−	0.0510325i	0.579742	+	0.814800i	$0.303153\pi$
$734$	4.53087	−	5.22890i	0.167237	−	0.193002i
$735$	4.50137			0.166035
$736$	−4.65986	+	1.13389i	−0.171765	+	0.0417958i
$737$	47.9494			1.76624
$738$	5.74380	−	6.62870i	0.211432	−	0.244006i
$739$	21.3024	−	13.6902i	0.783620	−	0.503602i	−0.0866130	−	0.996242i	$-0.527604\pi$
$739$	21.3024	−	13.6902i	0.783620	−	0.503602i	0.870233	+	0.492640i	$0.163968\pi$
$740$	−0.779513	−	5.42163i	−0.0286555	−	0.199303i
$741$	−6.67507	−	14.6164i	−0.245215	−	0.536946i
$742$	1.57205	−	10.9339i	0.0577119	−	0.401395i
$743$	−18.9152	+	5.55401i	−0.693932	+	0.203757i	−0.609633	−	0.792684i	$-0.708683\pi$
$743$	−18.9152	+	5.55401i	−0.693932	+	0.203757i	−0.0842989	+	0.996441i	$0.526865\pi$
$744$	7.09121	+	4.55724i	0.259976	+	0.167077i
$745$	3.56567	−	7.80773i	0.130636	−	0.286053i
$746$	−25.5895	−	7.51377i	−0.936899	−	0.275098i
$747$	6.36536	+	7.34602i	0.232896	+	0.268777i
$748$	−5.41516	−	6.24942i	−0.197998	−	0.228502i
$749$	17.0014	+	4.99205i	0.621216	+	0.182406i
$750$	0.415415	−	0.909632i	0.0151688	−	0.0332151i
$751$	−35.1856	−	22.6124i	−1.28394	−	0.825139i	−0.292573	−	0.956243i	$-0.594511\pi$
$751$	−35.1856	−	22.6124i	−1.28394	−	0.825139i	−0.991369	+	0.131104i	$0.958148\pi$
$752$	2.14157	−	0.628820i	0.0780948	−	0.0229307i
$753$	−2.73042	+	18.9905i	−0.0995020	+	0.692052i
$754$	−0.595257	−	1.30343i	−0.0216780	−	0.0474682i
$755$	2.65114	+	18.4391i	0.0964849	+	0.671067i
$756$	−1.32977	+	0.854594i	−0.0483634	+	0.0310813i
$757$	−31.1181	+	35.9123i	−1.13101	+	1.30525i	−0.184406	+	0.982850i	$0.559036\pi$
$757$	−31.1181	+	35.9123i	−1.13101	+	1.30525i	−0.946603	+	0.322403i	$0.895509\pi$
$758$	−33.0695			−1.20114
$759$	−5.74934	−	14.3323i	−0.208688	−	0.520231i
$760$	6.11006			0.221635
$761$	−19.8853	+	22.9489i	−0.720842	+	0.831896i	−0.991408	−	0.130805i	$-0.958244\pi$
$761$	−19.8853	+	22.9489i	−0.720842	+	0.831896i	0.270566	+	0.962701i	$0.412789\pi$
$762$	6.14633	−	3.95001i	0.222658	−	0.143094i
$763$	1.58651	+	11.0344i	0.0574356	+	0.399474i
$764$	8.56204	+	18.7483i	0.309764	+	0.678288i
$765$	0.365476	−	2.54194i	0.0132138	−	0.0919041i
$766$	14.3907	−	4.22549i	0.519957	−	0.152673i
$767$	−12.0149	−	7.72148i	−0.433832	−	0.278807i
$768$	−0.415415	+	0.909632i	−0.0149900	+	0.0328235i
$769$	−11.4816	−	3.37131i	−0.414039	−	0.121573i	0.0680775	−	0.997680i	$-0.478313\pi$
$769$	−11.4816	−	3.37131i	−0.414039	−	0.121573i	−0.482116	+	0.876107i	$0.660132\pi$
$770$	−3.33314	−	3.84665i	−0.120118	−	0.138624i
$771$	0.276817	+	0.319464i	0.00996934	+	0.0115052i
$772$	−20.9292	−	6.14538i	−0.753260	−	0.221177i
$773$	14.1769	−	31.0431i	0.509908	−	1.11654i	−0.463212	−	0.886247i	$-0.653303\pi$
$773$	14.1769	−	31.0431i	0.509908	−	1.11654i	0.973121	−	0.230296i	$-0.0739694\pi$
$774$	−6.18008	−	3.97170i	−0.222139	−	0.142760i
$775$	−8.08789	+	2.37482i	−0.290526	+	0.0853060i
$776$	−0.264953	+	1.84279i	−0.00951128	+	0.0661524i
$777$	−3.59672	−	7.87571i	−0.129032	−	0.282540i
$778$	−0.378740	−	2.63419i	−0.0135785	−	0.0944405i
$779$	−45.0840	+	28.9737i	−1.61530	+	1.03809i
$780$	−1.72218	+	1.98750i	−0.0616638	+	0.0711638i
$781$	−11.2932			−0.404101
$782$	2.32245	−	12.0951i	0.0830505	−	0.432521i
$783$	0.544871			0.0194721
$784$	2.94777	−	3.40191i	0.105277	−	0.121497i
$785$	4.32917	−	2.78219i	0.154515	−	0.0993005i
$786$	−1.87999	−	13.0756i	−0.0670570	−	0.466392i
$787$	−10.4270	−	22.8320i	−0.371683	−	0.813873i	−0.999373	−	0.0354092i	$-0.988727\pi$
$787$	−10.4270	−	22.8320i	−0.371683	−	0.813873i	0.627690	−	0.778464i	$-0.284001\pi$
$788$	−1.22776	+	8.53929i	−0.0437373	+	0.304200i
$789$	9.25301	−	2.71693i	0.329416	−	0.0967252i
$790$	13.3556	+	8.58311i	0.475170	+	0.305374i
$791$	4.23876	−	9.28160i	0.150713	−	0.330016i
$792$	−3.08955	−	0.907174i	−0.109782	−	0.0322350i
$793$	−22.6999	−	26.1971i	−0.806098	−	0.930287i
$794$	9.01510	+	10.4040i	0.319934	+	0.369223i
$795$	6.70514	+	1.96881i	0.237807	+	0.0698264i
$796$	6.13312	−	13.4297i	0.217383	−	0.476002i
$797$	24.7853	+	15.9286i	0.877942	+	0.564219i	0.900172	−	0.435534i	$-0.143440\pi$
$797$	24.7853	+	15.9286i	0.877942	+	0.564219i	−0.0222306	+	0.999753i	$0.507077\pi$
$798$	9.26698	−	2.72103i	0.328047	−	0.0963234i
$799$	−0.815734	+	5.67355i	−0.0288586	+	0.200716i
$800$	−0.415415	−	0.909632i	−0.0146871	−	0.0321603i
$801$	−1.34022	−	9.32147i	−0.0473545	−	0.329358i
$802$	10.4078	−	6.68867i	0.367512	−	0.236185i
$803$	−1.52961	+	1.76526i	−0.0539787	+	0.0622947i
$804$	14.8912			0.525172
$805$	1.42951	−	7.44480i	0.0503837	−	0.262395i
$806$	22.1678			0.780826
$807$	−12.0478	+	13.9040i	−0.424104	+	0.489442i
$808$	1.72725	−	1.11004i	0.0607645	−	0.0390510i
$809$	−3.25031	−	22.6064i	−0.114275	−	0.794799i	−0.963680	−	0.267058i	$-0.913948\pi$
$809$	−3.25031	−	22.6064i	−0.114275	−	0.794799i	0.849406	−	0.527741i	$-0.176961\pi$
$810$	−0.415415	−	0.909632i	−0.0145962	−	0.0319612i
$811$	−2.88058	+	20.0349i	−0.101151	+	0.703520i	0.874633	+	0.484785i	$0.161102\pi$
$811$	−2.88058	+	20.0349i	−0.101151	+	0.703520i	−0.975784	+	0.218735i	$0.929807\pi$
$812$	0.826393	−	0.242651i	0.0290007	−	0.00851538i
$813$	13.3420	+	8.57436i	0.467923	+	0.300716i
$814$	7.32670	−	16.0432i	0.256801	−	0.562315i
$815$	−11.3181	−	3.32329i	−0.396455	−	0.116410i
$816$	−1.68174	−	1.94083i	−0.0588725	−	0.0679425i
$817$	29.3942	+	33.9227i	1.02837	+	1.18681i
$818$	−10.0833	−	2.96073i	−0.352556	−	0.103520i
$819$	−1.72688	+	3.78134i	−0.0603420	+	0.132131i
$820$	7.37866	+	4.74198i	0.257674	+	0.165597i
$821$	−27.4557	+	8.06172i	−0.958211	+	0.281356i	−0.723202	−	0.690637i	$-0.757330\pi$
$821$	−27.4557	+	8.06172i	−0.958211	+	0.281356i	−0.235009	+	0.971993i	$0.575512\pi$
$822$	1.75739	−	12.2229i	0.0612959	−	0.426322i
$823$	−2.67595	−	5.85951i	−0.0932777	−	0.204250i	0.857242	−	0.514913i	$-0.172176\pi$
$823$	−2.67595	−	5.85951i	−0.0932777	−	0.204250i	−0.950520	+	0.310664i	$0.899449\pi$
$824$	1.46064	+	10.1590i	0.0508839	+	0.353906i
$825$	2.70882	−	1.74085i	0.0943091	−	0.0606088i
$826$	5.62165	−	6.48772i	0.195602	−	0.225737i
$827$	−28.8919			−1.00467			−0.502336	−	0.864673i	$-0.667526\pi$
$827$	−28.8919			−1.00467			−0.502336	+	0.864673i	$0.667526\pi$
$828$	−1.78552	−	4.45106i	−0.0620510	−	0.154685i
$829$	35.9162			1.24742			0.623710	−	0.781656i	$-0.285625\pi$
$829$	35.9162			1.24742			0.623710	+	0.781656i	$0.285625\pi$
$830$	−6.36536	+	7.34602i	−0.220945	+	0.254984i
$831$	−12.9517	+	8.32356i	−0.449290	+	0.288741i
$832$	0.374265	+	2.60307i	0.0129753	+	0.0902451i
$833$	4.80215	+	10.5152i	0.166385	+	0.364331i
$834$	1.52320	−	10.5941i	0.0527440	−	0.366842i
$835$	10.3190	−	3.02994i	0.357105	−	0.104856i
$836$	16.5510	+	10.6367i	0.572430	+	0.367878i
$837$	−3.50167	+	7.66759i	−0.121036	+	0.265031i
$838$	7.39138	+	2.17030i	0.255331	+	0.0749719i
$839$	−28.3491	−	32.7166i	−0.978718	−	1.12950i	−0.991569	−	0.129583i	$-0.958636\pi$
$839$	−28.3491	−	32.7166i	−0.978718	−	1.12950i	0.0128504	−	0.999917i	$-0.495909\pi$
$840$	−1.03514	−	1.19462i	−0.0357158	−	0.0412182i
$841$	27.5404	+	8.08660i	0.949670	+	0.278848i
$842$	−15.3091	+	33.5223i	−0.527587	+	1.15526i
$843$	7.71790	+	4.95999i	0.265819	+	0.170831i
$844$	24.6204	−	7.22922i	0.847471	−	0.248840i
$845$	0.865839	−	6.02204i	0.0297858	−	0.207164i
$846$	0.927196	+	2.03028i	0.0318777	+	0.0698024i
$847$	0.142109	+	0.988391i	0.00488293	+	0.0339615i
$848$	5.87886	−	3.77812i	0.201881	−	0.129741i
$849$	−10.0399	+	11.5867i	−0.344568	+	0.397653i
$850$	2.56808			0.0880844
$851$	25.5238	−	6.21076i	0.874946	−	0.212902i
$852$	−3.50722			−0.120155
$853$	15.8117	−	18.2477i	0.541382	−	0.624788i	−0.417471	−	0.908690i	$-0.637084\pi$
$853$	15.8117	−	18.2477i	0.541382	−	0.624788i	0.958853	+	0.283902i	$0.0916290\pi$
$854$	17.5277	−	11.2644i	0.599786	−	0.385459i
$855$	0.869552	+	6.04786i	0.0297380	+	0.206833i
$856$	4.65664	+	10.1966i	0.159161	+	0.348514i
$857$	−0.693269	+	4.82179i	−0.0236816	+	0.164709i	−0.998230	−	0.0594667i	$-0.981060\pi$
$857$	−0.693269	+	4.82179i	−0.0236816	+	0.164709i	0.974549	+	0.224176i	$0.0719691\pi$
$858$	−8.12501	+	2.38572i	−0.277383	+	0.0814471i
$859$	−23.6185	−	15.1787i	−0.805853	−	0.517891i	0.0716677	−	0.997429i	$-0.477168\pi$
$859$	−23.6185	−	15.1787i	−0.805853	−	0.517891i	−0.877521	+	0.479538i	$0.840804\pi$
$860$	3.05175	−	6.68241i	0.104064	−	0.227868i
$861$	13.3028	+	3.90606i	0.453359	+	0.133118i
$862$	−18.2435	−	21.0541i	−0.621376	−	0.717106i
$863$	2.17738	+	2.51283i	0.0741188	+	0.0855376i	0.791598	−	0.611042i	$-0.209250\pi$
$863$	2.17738	+	2.51283i	0.0741188	+	0.0855376i	−0.717479	+	0.696580i	$0.754704\pi$
$864$	−0.959493	−	0.281733i	−0.0326426	−	0.00958474i
$865$	−5.79045	+	12.6793i	−0.196881	+	0.431110i
$866$	−10.3798	−	6.67072i	−0.352721	−	0.226680i
$867$	−9.98349	+	2.93142i	−0.339057	+	0.0995561i
$868$	−1.89625	+	13.1887i	−0.0643628	+	0.447653i
$869$	21.2360	+	46.5003i	0.720380	+	1.57741i
$870$	0.0775433	+	0.539325i	0.00262896	+	0.0182848i
$871$	32.9447	−	21.1723i	1.11629	−	0.717395i
$872$	−4.61840	+	5.32992i	−0.156399	+	0.180494i
$873$	−1.86174			−0.0630104
$874$	2.80564	+	29.1682i	0.0949021	+	0.986628i
$875$	1.58071			0.0534376
$876$	−0.475036	+	0.548221i	−0.0160500	+	0.0185227i
$877$	−19.0729	+	12.2574i	−0.644046	+	0.413903i	−0.821486	−	0.570229i	$-0.806855\pi$
$877$	−19.0729	+	12.2574i	−0.644046	+	0.413903i	0.177441	+	0.984132i	$0.443218\pi$
$878$	3.92757	+	27.3168i	0.132549	+	0.921898i
$879$	0.425549	+	0.931821i	0.0143534	+	0.0314296i
$880$	0.458251	−	3.18721i	0.0154476	−	0.107441i
$881$	33.4155	−	9.81167i	1.12580	−	0.330564i	0.334742	−	0.942310i	$-0.391351\pi$
$881$	33.4155	−	9.81167i	1.12580	−	0.330564i	0.791054	+	0.611746i	$0.209533\pi$
$882$	3.78679	+	2.43362i	0.127508	+	0.0819444i
$883$	−18.7737	+	41.1087i	−0.631785	+	1.38342i	0.274844	+	0.961489i	$0.411374\pi$
$883$	−18.7737	+	41.1087i	−0.631785	+	1.38342i	−0.906629	+	0.421928i	$0.861353\pi$
$884$	−6.48006	−	1.90272i	−0.217948	−	0.0639953i
$885$	3.55641	+	4.10432i	0.119548	+	0.137965i
$886$	15.3420	+	17.7056i	0.515423	+	0.594830i
$887$	−31.3473	−	9.20441i	−1.05254	−	0.309054i	−0.290697	−	0.956815i	$-0.593887\pi$
$887$	−31.3473	−	9.20441i	−1.05254	−	0.309054i	−0.761844	+	0.647761i	$0.775705\pi$
$888$	2.27539	−	4.98240i	0.0763570	−	0.167198i
$889$	9.71555	+	6.24380i	0.325849	+	0.209410i
$890$	9.03585	−	2.65317i	0.302883	−	0.0889343i
$891$	0.458251	−	3.18721i	0.0153520	−	0.106775i
$892$	1.04454	+	2.28722i	0.0349737	+	0.0765817i
$893$	−1.94082	−	13.4987i	−0.0649470	−	0.451716i
$894$	7.22081	−	4.64053i	0.241500	−	0.155203i
$895$	−5.75312	+	6.63946i	−0.192306	+	0.221933i
$896$	−1.58071			−0.0528077
$897$	−10.2787	−	7.30869i	−0.343196	−	0.244030i
$898$	−33.8190			−1.12855
$899$	3.00771	−	3.47108i	0.100313	−	0.115767i
$900$	0.841254	−	0.540641i	0.0280418	−	0.0180214i
$901$	2.55403	+	17.7636i	0.0850869	+	0.591792i
$902$	11.7324	+	25.6903i	0.390646	+	0.855395i
$903$	1.65260	−	11.4941i	0.0549952	−	0.382500i
$904$	6.19366	−	1.81862i	0.205998	−	0.0604865i
$905$	7.56311	+	4.86051i	0.251406	+	0.161569i
$906$	−7.73864	+	16.9453i	−0.257099	+	0.562969i
$907$	39.6152	+	11.6321i	1.31540	+	0.386237i	0.862831	−	0.505492i	$-0.168689\pi$
$907$	39.6152	+	11.6321i	1.31540	+	0.386237i	0.452570	+	0.891729i	$0.350507\pi$
$908$	−4.60422	−	5.31355i	−0.152796	−	0.176336i
$909$	1.34455	+	1.55170i	0.0445960	+	0.0514665i
$910$	−3.98861	−	1.17116i	−0.132221	−	0.0388236i
$911$	−7.07597	+	15.4942i	−0.234437	+	0.513346i	−0.989887	−	0.141861i	$-0.954691\pi$
$911$	−7.07597	+	15.4942i	−0.234437	+	0.513346i	0.755449	+	0.655207i	$0.227419\pi$
$912$	5.14011	+	3.30335i	0.170206	+	0.109385i
$913$	−30.0310	+	8.81789i	−0.993880	+	0.291830i
$914$	2.20433	−	15.3314i	0.0729126	−	0.507119i
$915$	5.47557	+	11.9898i	0.181017	+	0.396371i
$916$	−3.38490	−	23.5425i	−0.111840	−	0.777867i
$917$	17.5664	−	11.2892i	0.580094	−	0.372804i
$918$	1.68174	−	1.94083i	0.0555055	−	0.0640568i
$919$	32.1900			1.06185			0.530925	−	0.847419i	$-0.321844\pi$
$919$	32.1900			1.06185			0.530925	+	0.847419i	$0.321844\pi$
$920$	4.15165	−	2.40080i	0.136876	−	0.0791519i
$921$	6.34432			0.209053
$922$	13.7183	−	15.8318i	0.451789	−	0.521392i
$923$	−7.75922	+	4.98655i	−0.255398	+	0.164134i
$924$	−0.724360	−	5.03804i	−0.0238297	−	0.165739i
$925$	2.27539	+	4.98240i	0.0748143	+	0.163820i
$926$	−1.07552	+	7.48043i	−0.0353439	+	0.245822i
$927$	−9.84773	+	2.89155i	−0.323442	+	0.0949711i
$928$	0.458375	+	0.294580i	0.0150469	+	0.00967005i
$929$	2.72150	−	5.95924i	0.0892894	−	0.195516i	−0.859719	−	0.510767i	$-0.829361\pi$
$929$	2.72150	−	5.95924i	0.0892894	−	0.195516i	0.949008	+	0.315251i	$0.102089\pi$
$930$	−8.08789	−	2.37482i	−0.265212	−	0.0778734i
$931$	−18.0110	−	20.7858i	−0.590288	−	0.681228i
$932$	−9.23885	−	10.6622i	−0.302628	−	0.349252i
$933$	−0.931025	−	0.273374i	−0.0304804	−	0.00894985i
$934$	−15.3336	+	33.5759i	−0.501731	+	1.09864i
$935$	6.95647	+	4.47065i	0.227501	+	0.146206i
$936$	−2.52331	+	0.740910i	−0.0824769	+	0.0242174i
$937$	−1.12233	+	7.80600i	−0.0366650	+	0.255011i	−0.999907	−	0.0136237i	$-0.995663\pi$
$937$	−1.12233	+	7.80600i	−0.0366650	+	0.255011i	0.963242	+	0.268635i	$0.0865724\pi$
$938$	9.77830	+	21.4115i	0.319273	+	0.699110i
$939$	3.34397	+	23.2578i	0.109126	+	0.758990i
$940$	−1.87766	+	1.20670i	−0.0612424	+	0.0393581i
$941$	29.6840	−	34.2572i	0.967671	−	1.11675i	−0.0254524	−	0.999676i	$-0.508103\pi$
$941$	29.6840	−	34.2572i	0.967671	−	1.11675i	0.993123	−	0.117075i	$-0.0373519\pi$
$942$	5.14609			0.167669
$943$	−19.2491	+	37.4017i	−0.626836	+	1.21797i
$944$	5.43079			0.176757
$945$	1.03514	−	1.19462i	0.0336732	−	0.0388609i
$946$	19.8998	−	12.7888i	0.646997	−	0.415800i
$947$	4.91759	+	34.2026i	0.159800	+	1.11144i	0.899000	+	0.437949i	$0.144295\pi$
$947$	4.91759	+	34.2026i	0.159800	+	1.11144i	−0.739200	+	0.673486i	$0.764796\pi$
$948$	6.59505	+	14.4412i	0.214197	+	0.469027i
$949$	−0.271491	+	1.88826i	−0.00881299	+	0.0612957i
$950$	−5.86255	+	1.72140i	−0.190206	+	0.0558496i
$951$	10.3173	+	6.63050i	0.334560	+	0.215009i
$952$	1.68633	−	3.69254i	0.0546542	−	0.119676i
$953$	−6.08662	−	1.78719i	−0.197165	−	0.0578929i	0.181659	−	0.983362i	$-0.441853\pi$
$953$	−6.08662	−	1.78719i	−0.197165	−	0.0578929i	−0.378824	+	0.925469i	$0.623671\pi$
$954$	4.57631	+	5.28134i	0.148163	+	0.170990i
$955$	−13.4972	−	15.5766i	−0.436760	−	0.504048i
$956$	−23.0676	−	6.77327i	−0.746061	−	0.219063i
$957$	−0.728836	+	1.59593i	−0.0235599	+	0.0515890i
$958$	22.0340	+	14.1604i	0.711885	+	0.457501i
$959$	18.7288	−	5.49927i	0.604785	−	0.177581i
$960$	0.142315	−	0.989821i	0.00459319	−	0.0319463i
$961$	16.6389	+	36.4341i	0.536739	+	1.17529i
$962$	−2.04999	−	14.2580i	−0.0660943	−	0.459696i
$963$	−9.43013	+	6.06038i	−0.303882	+	0.195293i
$964$	6.10835	−	7.04941i	0.196737	−	0.227046i
$965$	21.8128			0.702179
$966$	5.22754	−	5.49011i	0.168193	−	0.176641i
$967$	57.9099			1.86226			0.931128	−	0.364693i	$-0.118826\pi$
$967$	57.9099			1.86226			0.931128	+	0.364693i	$0.118826\pi$
$968$	−0.413685	+	0.477418i	−0.0132963	+	0.0153448i
$969$	−13.2002	+	8.48326i	−0.424052	+	0.272521i
$970$	−0.264953	−	1.84279i	−0.00850714	−	0.0591685i
$971$	−23.6008	−	51.6784i	−0.757384	−	1.65844i	−0.752623	−	0.658452i	$-0.771212\pi$
$971$	−23.6008	−	51.6784i	−0.757384	−	1.65844i	−0.00476125	−	0.999989i	$-0.501516\pi$
$972$	0.142315	−	0.989821i	0.00456475	−	0.0317485i
$973$	16.2330	−	4.76644i	0.520406	−	0.152805i
$974$	−20.0859	−	12.9084i	−0.643595	−	0.413613i
$975$	1.09247	−	2.39218i	0.0349871	−	0.0766112i
$976$	12.6470	+	3.71351i	0.404822	+	0.118866i
$977$	15.2410	+	17.5890i	0.487602	+	0.562723i	0.945223	−	0.326424i	$-0.105844\pi$
$977$	15.2410	+	17.5890i	0.487602	+	0.562723i	−0.457621	+	0.889147i	$0.651298\pi$
$978$	−7.72467	−	8.91475i	−0.247008	−	0.285062i
$979$	29.0953	+	8.54315i	0.929889	+	0.273040i
$980$	−1.86994	+	4.09459i	−0.0597329	+	0.130797i
$981$	−5.93293	−	3.81286i	−0.189424	−	0.121735i
$982$	−32.0697	+	9.41650i	−1.02338	+	0.300493i
$983$	−3.03692	+	21.1222i	−0.0968626	+	0.673694i	0.882311	+	0.470667i	$0.155987\pi$
$983$	−3.03692	+	21.1222i	−0.0968626	+	0.673694i	−0.979173	+	0.203026i	$0.934922\pi$
$984$	3.64362	+	7.97841i	0.116154	+	0.254342i
$985$	−1.22776	−	8.53929i	−0.0391198	−	0.272084i
$986$	−1.17714	+	0.756504i	−0.0374879	+	0.0240920i
$987$	−2.31041	+	2.66636i	−0.0735412	+	0.0848711i
$988$	16.0684			0.511205
$989$	33.3018	+	11.5000i	1.05894	+	0.365679i
$990$	3.21998			0.102338
$991$	39.3914	−	45.4601i	1.25131	−	1.44409i	0.402470	−	0.915433i	$-0.368152\pi$
$991$	39.3914	−	45.4601i	1.25131	−	1.44409i	0.848838	−	0.528653i	$-0.177303\pi$
$992$	−7.09121	+	4.55724i	−0.225146	+	0.144693i
$993$	−1.53651	−	10.6866i	−0.0487596	−	0.339130i
$994$	−2.30301	−	5.04289i	−0.0730470	−	0.159951i
$995$	−2.10111	+	14.6136i	−0.0666098	+	0.463281i
$996$	−9.32644	+	2.73849i	−0.295520	+	0.0867724i
$997$	36.8387	+	23.6748i	1.16669	+	0.749788i	0.972894	−	0.231254i	$-0.0742827\pi$
$997$	36.8387	+	23.6748i	1.16669	+	0.749788i	0.193799	+	0.981041i	$0.437919\pi$
$998$	7.63836	−	16.7257i	0.241788	−	0.529442i
$999$	5.25551	+	1.54316i	0.166277	+	0.0488233i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.m.e.361.2	yes	20
23.13	even	11	inner	690.2.m.e.151.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.m.e.151.2	✓	20	23.13	even	11	inner
690.2.m.e.361.2	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)

\(f(q)\)	\(=\)	\(q+(0.654861 - 0.755750i) q^{2} +(-0.841254 + 0.540641i) q^{3} +(-0.142315 - 0.989821i) q^{4} +(0.415415 + 0.909632i) q^{5} +(-0.142315 + 0.989821i) q^{6} +(-1.51668 + 0.445336i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(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} +(-1.51668 + 0.445336i) q^{7} +(-0.841254 - 0.540641i) q^{8} +(0.415415 - 0.909632i) q^{9} +(0.959493 + 0.281733i) q^{10} +(2.10864 + 2.43350i) q^{11} +(0.654861 + 0.755750i) q^{12} +(2.52331 + 0.740910i) q^{13} +(-0.656649 + 1.43786i) q^{14} +(-0.841254 - 0.540641i) q^{15} +(-0.959493 + 0.281733i) q^{16} +(0.365476 - 2.54194i) q^{17} +(-0.415415 - 0.909632i) q^{18} +(0.869552 + 6.04786i) q^{19} +(0.841254 - 0.540641i) q^{20} +(1.03514 - 1.19462i) q^{21} +3.21998 q^{22} +(2.96720 + 3.76772i) q^{23} +1.00000 q^{24} +(-0.654861 + 0.755750i) q^{25} +(2.21236 - 1.42180i) q^{26} +(0.142315 + 0.989821i) q^{27} +(0.656649 + 1.43786i) q^{28} +(0.0775433 - 0.539325i) q^{29} +(-0.959493 + 0.281733i) q^{30} +(7.09121 + 4.55724i) q^{31} +(-0.415415 + 0.909632i) q^{32} +(-3.08955 - 0.907174i) q^{33} +(-1.68174 - 1.94083i) q^{34} +(-1.03514 - 1.19462i) q^{35} +(-0.959493 - 0.281733i) q^{36} +(2.27539 - 4.98240i) q^{37} +(5.14011 + 3.30335i) q^{38} +(-2.52331 + 0.740910i) q^{39} +(0.142315 - 0.989821i) q^{40} +(3.64362 + 7.97841i) q^{41} +(-0.224958 - 1.56462i) q^{42} +(6.18008 - 3.97170i) q^{43} +(2.10864 - 2.43350i) q^{44} +1.00000 q^{45} +(4.79056 + 0.224872i) q^{46} -2.23198 q^{47} +(0.654861 - 0.755750i) q^{48} +(-3.78679 + 2.43362i) q^{49} +(0.142315 + 0.989821i) q^{50} +(1.06682 + 2.33601i) q^{51} +(0.374265 - 2.60307i) q^{52} +(-6.70514 + 1.96881i) q^{53} +(0.841254 + 0.540641i) q^{54} +(-1.33763 + 2.92900i) q^{55} +(1.51668 + 0.445336i) q^{56} +(-4.00124 - 4.61767i) q^{57} +(-0.356815 - 0.411786i) q^{58} +(-5.21081 - 1.53003i) q^{59} +(-0.415415 + 0.909632i) q^{60} +(-11.0885 - 7.12617i) q^{61} +(8.08789 - 2.37482i) q^{62} +(-0.224958 + 1.56462i) q^{63} +(0.415415 + 0.909632i) q^{64} +(0.374265 + 2.60307i) q^{65} +(-2.70882 + 1.74085i) q^{66} +(9.75167 - 11.2540i) q^{67} -2.56808 q^{68} +(-4.53315 - 1.56542i) q^{69} -1.58071 q^{70} +(-2.29674 + 2.65058i) q^{71} +(-0.841254 + 0.540641i) q^{72} +(0.103235 + 0.718016i) q^{73} +(-2.27539 - 4.98240i) q^{74} +(0.142315 - 0.989821i) q^{75} +(5.86255 - 1.72140i) q^{76} +(-4.28185 - 2.75178i) q^{77} +(-1.09247 + 2.39218i) q^{78} +(15.2327 + 4.47273i) q^{79} +(-0.654861 - 0.755750i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(8.41574 + 2.47108i) q^{82} +(-4.03791 + 8.84178i) q^{83} +(-1.32977 - 0.854594i) q^{84} +(2.46406 - 0.723512i) q^{85} +(1.04548 - 7.27150i) q^{86} +(0.226348 + 0.495632i) q^{87} +(-0.458251 - 3.18721i) q^{88} +(7.92235 - 5.09139i) q^{89} +(0.654861 - 0.755750i) q^{90} -4.15700 q^{91} +(3.30709 - 3.47320i) q^{92} -8.42934 q^{93} +(-1.46163 + 1.68681i) q^{94} +(-5.14011 + 3.30335i) q^{95} +(-0.142315 - 0.989821i) q^{96} +(-0.773395 - 1.69350i) q^{97} +(-0.640612 + 4.45555i) q^{98} +(3.08955 - 0.907174i) 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	\( 20 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{12} - 13 q^{13} + 2 q^{14} + 2 q^{15} - 2 q^{16} + 6 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 2 q^{21} + 26 q^{22} + 24 q^{23} + 20 q^{24} - 2 q^{25} + 13 q^{26} + 2 q^{27} - 2 q^{28} + 2 q^{29} - 2 q^{30} + 6 q^{31} + 2 q^{32} + 4 q^{33} + 5 q^{34} - 2 q^{35} - 2 q^{36} - 20 q^{37} + 4 q^{38} + 13 q^{39} + 2 q^{40} - 11 q^{41} - 13 q^{42} + 4 q^{43} - 4 q^{44} + 20 q^{45} - 2 q^{46} + 18 q^{47} + 2 q^{48} - 6 q^{49} + 2 q^{50} + 27 q^{51} - 2 q^{52} - 18 q^{53} - 2 q^{54} + 18 q^{55} + 2 q^{56} - 7 q^{57} + 9 q^{58} - 52 q^{59} + 2 q^{60} - 7 q^{61} + 16 q^{62} - 13 q^{63} - 2 q^{64} - 2 q^{65} + 7 q^{66} - 10 q^{67} + 28 q^{68} + 20 q^{69} - 20 q^{70} + 7 q^{71} + 2 q^{72} - 37 q^{73} + 20 q^{74} + 2 q^{75} - 4 q^{76} - 70 q^{77} + 9 q^{78} + 20 q^{79} - 2 q^{80} - 2 q^{81} - 11 q^{82} - 19 q^{83} - 9 q^{84} + 17 q^{85} - 26 q^{86} - 2 q^{87} + 4 q^{88} + 33 q^{89} + 2 q^{90} - 42 q^{91} - 9 q^{92} + 16 q^{93} - 7 q^{94} - 4 q^{95} - 2 q^{96} + 9 q^{97} + 6 q^{98} - 4 q^{99}+O(q^{100}) \) 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 - 4 * q^11 + 2 * q^12 - 13 * q^13 + 2 * q^14 + 2 * q^15 - 2 * q^16 + 6 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 2 * q^21 + 26 * q^22 + 24 * q^23 + 20 * q^24 - 2 * q^25 + 13 * q^26 + 2 * q^27 - 2 * q^28 + 2 * q^29 - 2 * q^30 + 6 * q^31 + 2 * q^32 + 4 * q^33 + 5 * q^34 - 2 * q^35 - 2 * q^36 - 20 * q^37 + 4 * q^38 + 13 * q^39 + 2 * q^40 - 11 * q^41 - 13 * q^42 + 4 * q^43 - 4 * q^44 + 20 * q^45 - 2 * q^46 + 18 * q^47 + 2 * q^48 - 6 * q^49 + 2 * q^50 + 27 * q^51 - 2 * q^52 - 18 * q^53 - 2 * q^54 + 18 * q^55 + 2 * q^56 - 7 * q^57 + 9 * q^58 - 52 * q^59 + 2 * q^60 - 7 * q^61 + 16 * q^62 - 13 * q^63 - 2 * q^64 - 2 * q^65 + 7 * q^66 - 10 * q^67 + 28 * q^68 + 20 * q^69 - 20 * q^70 + 7 * q^71 + 2 * q^72 - 37 * q^73 + 20 * q^74 + 2 * q^75 - 4 * q^76 - 70 * q^77 + 9 * q^78 + 20 * q^79 - 2 * q^80 - 2 * q^81 - 11 * q^82 - 19 * q^83 - 9 * q^84 + 17 * q^85 - 26 * q^86 - 2 * q^87 + 4 * q^88 + 33 * q^89 + 2 * q^90 - 42 * q^91 - 9 * q^92 + 16 * q^93 - 7 * q^94 - 4 * q^95 - 2 * q^96 + 9 * q^97 + 6 * q^98 - 4 * q^99

Introduction

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