LMFDB - Embedded newform 403.2.bs.a.101.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(4,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 18]))

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

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

chi := DirichletCharacter("403.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.bs (of order $30$, degree $8$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$36$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			101.3
Character	$\chi$	$=$	403.101
Dual form			403.2.bs.a.4.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.518746 - 2.44051i) q^{2} +(-1.86014 + 2.06590i) q^{3} +(-3.85989 + 1.71854i) q^{4} -2.00004i q^{5} +(6.00678 + 3.46802i) q^{6} +(-1.59632 - 3.58539i) q^{7} +(3.26332 + 4.49158i) q^{8} +(-0.494216 - 4.70215i) q^{9} +O(q^{10})$	\(q+(-0.518746 - 2.44051i) q^{2} +(-1.86014 + 2.06590i) q^{3} +(-3.85989 + 1.71854i) q^{4} -2.00004i q^{5} +(6.00678 + 3.46802i) q^{6} +(-1.59632 - 3.58539i) q^{7} +(3.26332 + 4.49158i) q^{8} +(-0.494216 - 4.70215i) q^{9} +(-4.88112 + 1.03751i) q^{10} +(-1.84978 - 0.194419i) q^{11} +(3.62963 - 11.1709i) q^{12} +(0.726405 + 3.53162i) q^{13} +(-7.92208 + 5.75573i) q^{14} +(4.13188 + 3.72036i) q^{15} +(3.61450 - 4.01431i) q^{16} +(0.706683 + 6.72364i) q^{17} +(-11.2193 + 3.64536i) q^{18} +(0.410670 - 0.369769i) q^{19} +(3.43714 + 7.71995i) q^{20} +(10.3764 + 3.37150i) q^{21} +(0.485083 + 4.61525i) q^{22} +(0.0161603 + 0.00719504i) q^{23} +(-15.3494 - 1.61328i) q^{24} +0.999830 q^{25} +(8.24213 - 3.60481i) q^{26} +(3.88642 + 2.82365i) q^{27} +(12.3232 + 11.0959i) q^{28} +(-8.78316 + 1.86692i) q^{29} +(6.93618 - 12.0138i) q^{30} +(5.34893 + 1.54562i) q^{31} +(-2.05581 - 1.18692i) q^{32} +(3.84250 - 3.45980i) q^{33} +(16.0425 - 5.21253i) q^{34} +(-7.17093 + 3.19270i) q^{35} +(9.98844 + 17.3005i) q^{36} +(-0.381900 + 0.220490i) q^{37} +(-1.11546 - 0.810427i) q^{38} +(-8.64718 - 5.06863i) q^{39} +(8.98335 - 6.52678i) q^{40} +(2.16483 + 10.1847i) q^{41} +(2.84545 - 27.0727i) q^{42} +(-0.304383 - 0.338052i) q^{43} +(7.47406 - 2.42847i) q^{44} +(-9.40451 + 0.988454i) q^{45} +(0.00917645 - 0.0431718i) q^{46} +(-11.7978 + 3.83334i) q^{47} +(1.56967 + 14.9344i) q^{48} +(-5.62285 + 6.24481i) q^{49} +(-0.518658 - 2.44009i) q^{50} +(-15.2049 - 11.0470i) q^{51} +(-8.87306 - 12.3833i) q^{52} +(2.34914 - 1.70675i) q^{53} +(4.87508 - 10.9496i) q^{54} +(-0.388847 + 3.69963i) q^{55} +(10.8947 - 18.8703i) q^{56} +1.53622i q^{57} +(9.11246 + 20.4669i) q^{58} +(1.67919 - 7.89999i) q^{59} +(-22.3422 - 7.25942i) q^{60} +(1.55585 - 2.69482i) q^{61} +(0.997366 - 13.8559i) q^{62} +(-16.0701 + 9.27808i) q^{63} +(1.50824 - 4.64188i) q^{64} +(7.06339 - 1.45284i) q^{65} +(-10.4370 - 7.58289i) q^{66} +(-12.0733 + 6.97053i) q^{67} +(-14.2825 - 24.7381i) q^{68} +(-0.0449247 + 0.0200018i) q^{69} +(11.5117 + 15.8445i) q^{70} +(4.69760 - 0.493738i) q^{71} +(19.5073 - 17.5645i) q^{72} +(0.843917 - 1.16155i) q^{73} +(0.736216 + 0.817651i) q^{74} +(-1.85982 + 2.06554i) q^{75} +(-0.949681 + 2.13302i) q^{76} +(2.25576 + 6.94252i) q^{77} +(-7.88436 + 23.7328i) q^{78} +(5.23589 - 3.80410i) q^{79} +(-8.02880 - 7.22916i) q^{80} +(0.811534 - 0.172497i) q^{81} +(23.7329 - 10.5666i) q^{82} +(-8.15388 - 2.64936i) q^{83} +(-45.8459 + 4.81860i) q^{84} +(13.4476 - 1.41340i) q^{85} +(-0.667121 + 0.918213i) q^{86} +(12.4811 - 21.6178i) q^{87} +(-5.16317 - 8.94288i) q^{88} +(-3.42737 - 0.360231i) q^{89} +(7.29088 + 22.4390i) q^{90} +(11.5026 - 8.24203i) q^{91} -0.0747420 q^{92} +(-13.1429 + 8.17526i) q^{93} +(15.4754 + 26.8041i) q^{94} +(-0.739553 - 0.821357i) q^{95} +(6.27616 - 2.03925i) q^{96} +(5.35306 + 12.0232i) q^{97} +(18.1574 + 10.4832i) q^{98} +8.79403i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 9 q^{2} - q^{3} - 39 q^{4} - 42 q^{6} - 15 q^{7} + 31 q^{9}+O(q^{10}) $ 288 * q - 9 * q^2 - q^3 - 39 * q^4 - 42 * q^6 - 15 * q^7 + 31 * q^9	$ 288 q - 9 q^{2} - q^{3} - 39 q^{4} - 42 q^{6} - 15 q^{7} + 31 q^{9} + 3 q^{10} - 18 q^{11} - 46 q^{12} - q^{13} - 32 q^{14} + 18 q^{15} + 21 q^{16} - 15 q^{17} - 15 q^{19} + 51 q^{20} - 10 q^{22} - 4 q^{23} - 51 q^{24} - 296 q^{25} - 6 q^{26} - 52 q^{27} + 21 q^{28} + q^{29} + 60 q^{30} + 138 q^{32} + 69 q^{33} - 10 q^{35} + 128 q^{36} - 18 q^{37} + 32 q^{38} - 14 q^{39} + 60 q^{40} - 15 q^{41} - 49 q^{42} - 36 q^{43} + 6 q^{45} - 69 q^{46} + 21 q^{48} - 23 q^{49} + 117 q^{50} + 8 q^{51} + 26 q^{52} - 48 q^{53} + 75 q^{54} + 46 q^{55} - 98 q^{56} - 21 q^{58} - 105 q^{59} - 74 q^{61} - 3 q^{62} - 90 q^{63} + 90 q^{64} + 89 q^{65} - 8 q^{66} + 6 q^{67} - 182 q^{68} + 29 q^{69} + 3 q^{71} - 183 q^{72} - 53 q^{74} - 38 q^{75} + 144 q^{76} - 128 q^{78} - 72 q^{79} - 72 q^{80} + 11 q^{81} - 11 q^{82} - 33 q^{84} + 72 q^{85} - 18 q^{87} - 14 q^{88} + 81 q^{89} - 34 q^{90} - 48 q^{91} + 8 q^{92} + 72 q^{93} - 6 q^{94} + 141 q^{97} + 96 q^{98}+O(q^{100}) $ 288 * q - 9 * q^2 - q^3 - 39 * q^4 - 42 * q^6 - 15 * q^7 + 31 * q^9 + 3 * q^10 - 18 * q^11 - 46 * q^12 - q^13 - 32 * q^14 + 18 * q^15 + 21 * q^16 - 15 * q^17 - 15 * q^19 + 51 * q^20 - 10 * q^22 - 4 * q^23 - 51 * q^24 - 296 * q^25 - 6 * q^26 - 52 * q^27 + 21 * q^28 + q^29 + 60 * q^30 + 138 * q^32 + 69 * q^33 - 10 * q^35 + 128 * q^36 - 18 * q^37 + 32 * q^38 - 14 * q^39 + 60 * q^40 - 15 * q^41 - 49 * q^42 - 36 * q^43 + 6 * q^45 - 69 * q^46 + 21 * q^48 - 23 * q^49 + 117 * q^50 + 8 * q^51 + 26 * q^52 - 48 * q^53 + 75 * q^54 + 46 * q^55 - 98 * q^56 - 21 * q^58 - 105 * q^59 - 74 * q^61 - 3 * q^62 - 90 * q^63 + 90 * q^64 + 89 * q^65 - 8 * q^66 + 6 * q^67 - 182 * q^68 + 29 * q^69 + 3 * q^71 - 183 * q^72 - 53 * q^74 - 38 * q^75 + 144 * q^76 - 128 * q^78 - 72 * q^79 - 72 * q^80 + 11 * q^81 - 11 * q^82 - 33 * q^84 + 72 * q^85 - 18 * q^87 - 14 * q^88 + 81 * q^89 - 34 * q^90 - 48 * q^91 + 8 * q^92 + 72 * q^93 - 6 * q^94 + 141 * q^97 + 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.518746	−	2.44051i	−0.366809	−	1.72570i	−0.644124	−	0.764921i	$-0.722778\pi$
$2$	−0.518746	−	2.44051i	−0.366809	−	1.72570i	0.277315	−	0.960779i	$-0.410555\pi$
$3$	−1.86014	+	2.06590i	−1.07395	+	1.19275i	−0.0935766	+	0.995612i	$0.529830\pi$
$3$	−1.86014	+	2.06590i	−1.07395	+	1.19275i	−0.980377	+	0.197134i	$0.936837\pi$
$4$	−3.85989	+	1.71854i	−1.92995	+	0.859268i
$5$		−	2.00004i		−	0.894446i	−0.894422	−	0.447223i	$-0.852413\pi$
$5$		−	2.00004i		−	0.894446i	0.894422	−	0.447223i	$-0.147587\pi$
$6$	6.00678	+	3.46802i	2.45226	+	1.41581i
$7$	−1.59632	−	3.58539i	−0.603351	−	1.35515i	−0.914422	−	0.404762i	$-0.867354\pi$
$7$	−1.59632	−	3.58539i	−0.603351	−	1.35515i	0.311071	−	0.950387i	$-0.399312\pi$
$8$	3.26332	+	4.49158i	1.15376	+	1.58801i
$9$	−0.494216	−	4.70215i	−0.164739	−	1.56738i
$10$	−4.88112	+	1.03751i	−1.54355	+	0.328091i
$11$	−1.84978	−	0.194419i	−0.557729	−	0.0586197i	−0.178529	−	0.983935i	$-0.557134\pi$
$11$	−1.84978	−	0.194419i	−0.557729	−	0.0586197i	−0.379200	+	0.925315i	$0.623801\pi$
$12$	3.62963	−	11.1709i	1.04778	−	3.22475i
$13$	0.726405	+	3.53162i	0.201468	+	0.979495i
$13$	0.726405	+	3.53162i	0.201468	+	0.979495i
$14$	−7.92208	+	5.75573i	−2.11727	+	1.53828i
$15$	4.13188	+	3.72036i	1.06685	+	0.960593i
$16$	3.61450	−	4.01431i	0.903626	−	1.00358i
$17$	0.706683	+	6.72364i	0.171396	+	1.63072i	0.655136	+	0.755511i	$0.272611\pi$
$17$	0.706683	+	6.72364i	0.171396	+	1.63072i	−0.483741	+	0.875211i	$0.660722\pi$
$18$	−11.2193	+	3.64536i	−2.64441	+	0.859220i
$19$	0.410670	−	0.369769i	0.0942141	−	0.0848307i	−0.620678	−	0.784066i	$-0.713143\pi$
$19$	0.410670	−	0.369769i	0.0942141	−	0.0848307i	0.714892	+	0.699235i	$0.246476\pi$
$20$	3.43714	+	7.71995i	0.768569	+	1.72623i
$21$	10.3764	+	3.37150i	2.26432	+	0.735722i
$22$	0.485083	+	4.61525i	0.103420	+	0.983975i
$23$	0.0161603	+	0.00719504i	0.00336966	+	0.00150027i	0.408421	−	0.912794i	$-0.366080\pi$
$23$	0.0161603	+	0.00719504i	0.00336966	+	0.00150027i	−0.405051	+	0.914294i	$0.632746\pi$
$24$	−15.3494	−	1.61328i	−3.13318	−	0.329310i
$25$	0.999830			0.199966
$26$	8.24213	−	3.60481i	1.61641	−	0.706962i
$27$	3.88642	+	2.82365i	0.747943	+	0.543412i
$28$	12.3232	+	11.0959i	2.32887	+	2.09693i
$29$	−8.78316	+	1.86692i	−1.63099	+	0.346678i	−0.930304	−	0.366790i	$-0.880457\pi$
$29$	−8.78316	+	1.86692i	−1.63099	+	0.346678i	−0.700688	+	0.713468i	$0.747123\pi$
$30$	6.93618	−	12.0138i	1.26637	−	2.19341i
$31$	5.34893	+	1.54562i	0.960696	+	0.277602i
$31$	5.34893	+	1.54562i	0.960696	+	0.277602i
$32$	−2.05581	−	1.18692i	−0.363420	−	0.209820i
$33$	3.84250	−	3.45980i	0.668893	−	0.602274i
$34$	16.0425	−	5.21253i	2.75127	−	0.893941i
$35$	−7.17093	+	3.19270i	−1.21211	+	0.539665i
$36$	9.98844	+	17.3005i	1.66474	+	2.88341i
$37$	−0.381900	+	0.220490i	−0.0627839	+	0.0362483i	−0.531063	−	0.847332i	$-0.678207\pi$
$37$	−0.381900	+	0.220490i	−0.0627839	+	0.0362483i	0.468279	+	0.883580i	$0.344874\pi$
$38$	−1.11546	−	0.810427i	−0.180951	−	0.131469i
$39$	−8.64718	−	5.06863i	−1.38466	−	0.811631i
$40$	8.98335	−	6.52678i	1.42039	−	1.03198i
$41$	2.16483	+	10.1847i	0.338090	+	1.59059i	0.738501	+	0.674252i	$0.235534\pi$
$41$	2.16483	+	10.1847i	0.338090	+	1.59059i	−0.400412	+	0.916335i	$0.631133\pi$
$42$	2.84545	−	27.0727i	0.439063	−	4.17741i
$43$	−0.304383	−	0.338052i	−0.0464180	−	0.0515524i	0.719489	−	0.694504i	$-0.244376\pi$
$43$	−0.304383	−	0.338052i	−0.0464180	−	0.0515524i	−0.765907	+	0.642952i	$0.777710\pi$
$44$	7.47406	−	2.42847i	1.12676	−	0.366106i
$45$	−9.40451	+	0.988454i	−1.40194	+	0.147350i
$46$	0.00917645	−	0.0431718i	0.00135299	−	0.00636533i
$47$	−11.7978	+	3.83334i	−1.72089	+	0.559151i	−0.992085	−	0.125572i	$-0.959924\pi$
$47$	−11.7978	+	3.83334i	−1.72089	+	0.559151i	−0.728804	+	0.684722i	$0.759924\pi$
$48$	1.56967	+	14.9344i	0.226562	+	2.15559i
$49$	−5.62285	+	6.24481i	−0.803265	+	0.892116i
$50$	−0.518658	−	2.44009i	−0.0733493	−	0.345081i
$51$	−15.2049	−	11.0470i	−2.12911	−	1.54689i
$52$	−8.87306	−	12.3833i	−1.23047	−	1.71726i
$53$	2.34914	−	1.70675i	0.322679	−	0.234440i	−0.414639	−	0.909986i	$-0.636092\pi$
$53$	2.34914	−	1.70675i	0.322679	−	0.234440i	0.737318	+	0.675546i	$0.236092\pi$
$54$	4.87508	−	10.9496i	0.663414	−	1.49005i
$55$	−0.388847	+	3.69963i	−0.0524322	+	0.498859i
$56$	10.8947	−	18.8703i	1.45587	−	2.52164i
$57$			1.53622i			0.203478i
$58$	9.11246	+	20.4669i	1.19652	+	2.68744i
$59$	1.67919	−	7.89999i	0.218612	−	1.02849i	−0.722754	−	0.691105i	$-0.757124\pi$
$59$	1.67919	−	7.89999i	0.218612	−	1.02849i	0.941367	−	0.337386i	$-0.109543\pi$
$60$	−22.3422	−	7.25942i	−2.88437	−	0.937187i
$61$	1.55585	−	2.69482i	0.199207	−	0.345036i	−0.749065	−	0.662497i	$-0.769497\pi$
$61$	1.55585	−	2.69482i	0.199207	−	0.345036i	0.948271	+	0.317461i	$0.102830\pi$
$62$	0.997366	−	13.8559i	0.126666	−	1.75970i
$63$	−16.0701	+	9.27808i	−2.02464	+	1.16893i
$64$	1.50824	−	4.64188i	0.188530	−	0.580235i
$65$	7.06339	−	1.45284i	0.876106	−	0.180203i
$66$	−10.4370	−	7.58289i	−1.28470	−	0.933390i
$67$	−12.0733	+	6.97053i	−1.47499	+	0.851585i	−0.999603	−	0.0281914i	$-0.991025\pi$
$67$	−12.0733	+	6.97053i	−1.47499	+	0.851585i	−0.475387	+	0.879777i	$0.657692\pi$
$68$	−14.2825	−	24.7381i	−1.73201	−	2.99993i
$69$	−0.0449247	+	0.0200018i	−0.00540829	+	0.00240793i
$70$	11.5117	+	15.8445i	1.37591	+	1.89378i
$71$	4.69760	−	0.493738i	0.557503	−	0.0585959i	0.178413	−	0.983956i	$-0.442904\pi$
$71$	4.69760	−	0.493738i	0.557503	−	0.0585959i	0.379090	+	0.925360i	$0.376237\pi$
$72$	19.5073	−	17.5645i	2.29896	−	2.06999i
$73$	0.843917	−	1.16155i	0.0987731	−	0.135949i	−0.756770	−	0.653682i	$-0.773224\pi$
$73$	0.843917	−	1.16155i	0.0987731	−	0.135949i	0.855543	+	0.517732i	$0.173224\pi$
$74$	0.736216	+	0.817651i	0.0855834	+	0.0950500i
$75$	−1.85982	+	2.06554i	−0.214754	+	0.238509i
$76$	−0.949681	+	2.13302i	−0.108936	+	0.244674i
$77$	2.25576	+	6.94252i	0.257068	+	0.791174i
$78$	−7.88436	+	23.7328i	−0.892728	+	2.68722i
$79$	5.23589	−	3.80410i	0.589084	−	0.427994i	−0.252904	−	0.967491i	$-0.581386\pi$
$79$	5.23589	−	3.80410i	0.589084	−	0.427994i	0.841987	+	0.539497i	$0.181386\pi$
$80$	−8.02880	−	7.22916i	−0.897647	−	0.808245i
$81$	0.811534	−	0.172497i	0.0901705	−	0.0191663i
$82$	23.7329	−	10.5666i	2.62086	−	1.16688i
$83$	−8.15388	−	2.64936i	−0.895004	−	0.290805i	−0.174831	−	0.984598i	$-0.555938\pi$
$83$	−8.15388	−	2.64936i	−0.895004	−	0.290805i	−0.720174	+	0.693794i	$0.755938\pi$
$84$	−45.8459	+	4.81860i	−5.00220	+	0.525752i
$85$	13.4476	−	1.41340i	1.45859	−	0.153304i
$86$	−0.667121	+	0.918213i	−0.0719375	+	0.0990134i
$87$	12.4811	−	21.6178i	1.33811	−	2.31767i
$88$	−5.16317	−	8.94288i	−0.550396	−	0.953314i
$89$	−3.42737	−	0.360231i	−0.363300	−	0.0381844i	−0.0788799	−	0.996884i	$-0.525134\pi$
$89$	−3.42737	−	0.360231i	−0.363300	−	0.0381844i	−0.284420	+	0.958700i	$0.591801\pi$
$90$	7.29088	+	22.4390i	0.768526	+	2.36528i
$91$	11.5026	−	8.24203i	1.20581	−	0.863999i
$92$	−0.0747420			−0.00779240
$93$	−13.1429	+	8.17526i	−1.36285	+	0.847735i
$94$	15.4754	+	26.8041i	1.59616	+	2.76464i
$95$	−0.739553	−	0.821357i	−0.0758765	−	0.0842694i
$96$	6.27616	−	2.03925i	0.640558	−	0.208130i
$97$	5.35306	+	12.0232i	0.543521	+	1.22077i	0.951464	+	0.307760i	$0.0995794\pi$
$97$	5.35306	+	12.0232i	0.543521	+	1.22077i	−0.407943	+	0.913007i	$0.633754\pi$
$98$	18.1574	+	10.4832i	1.83417	+	1.05896i
$99$			8.79403i			0.883833i
$100$	−3.85924	+	1.71824i	−0.385924	+	0.171824i
$101$	0.898845	+	0.400192i	0.0894385	+	0.0398206i	0.450968	−	0.892540i	$-0.351079\pi$
$101$	0.898845	+	0.400192i	0.0894385	+	0.0398206i	−0.361530	+	0.932361i	$0.617745\pi$
$102$	−19.0728	+	42.8382i	−1.88849	+	4.24161i
$103$	−3.44356	+	10.5982i	−0.339304	+	1.04427i	0.625259	+	0.780417i	$0.284993\pi$
$103$	−3.44356	+	10.5982i	−0.339304	+	1.04427i	−0.964563	+	0.263853i	$0.915007\pi$
$104$	−13.4921	+	14.7875i	−1.32300	+	1.45004i
$105$	6.74315	−	20.7533i	0.658064	−	2.02531i
$106$	−5.38394	−	4.84772i	−0.522934	−	0.470852i
$107$	−8.84570	−	3.93836i	−0.855146	−	0.380736i	−0.0681365	−	0.997676i	$-0.521705\pi$
$107$	−8.84570	−	3.93836i	−0.855146	−	0.380736i	−0.787010	+	0.616940i	$0.788372\pi$
$108$	−19.8537	−	4.22004i	−1.91043	−	0.406074i
$109$	1.72280	−	0.559773i	0.165015	−	0.0536165i	−0.225345	−	0.974279i	$-0.572351\pi$
$109$	1.72280	−	0.559773i	0.165015	−	0.0536165i	0.390359	+	0.920663i	$0.372351\pi$
$110$	9.23070	−	0.970186i	0.880113	−	0.0925036i
$111$	0.254878	−	1.19911i	0.0241920	−	0.113814i
$112$	−20.1628	−	6.55128i	−1.90520	−	0.619038i
$113$	−15.3417	+	6.83055i	−1.44322	+	0.642564i	−0.971036	−	0.238934i	$-0.923202\pi$
$113$	−15.3417	+	6.83055i	−1.44322	+	0.642564i	−0.472187	+	0.881498i	$0.656535\pi$
$114$	3.74917	−	0.796910i	0.351142	−	0.0746374i
$115$	0.0143904	−	0.0323213i	0.00134191	−	0.00301398i
$116$	30.6937	−	22.3003i	2.84984	−	2.07053i
$117$	16.2472	−	5.16105i	1.50206	−	0.477139i
$118$	−20.1511			−1.85506
$119$	22.9788	−	13.2668i	2.10646	−	1.21616i
$120$	−3.22664	+	30.6994i	−0.294550	+	2.80246i
$121$	−7.37574	−	1.56776i	−0.670522	−	0.142524i
$122$	−7.38382	−	2.39915i	−0.668500	−	0.217209i
$123$	−25.0675	−	14.4727i	−2.26026	−	1.30496i
$124$	−23.3025	+	3.22639i	−2.09263	+	0.289739i
$125$		−	11.9999i		−	1.07331i
$126$	30.9796	+	34.4063i	2.75988	+	3.06516i
$127$	−7.07211	+	7.85437i	−0.627548	+	0.696963i	−0.970147	−	0.242519i	$-0.922026\pi$
$127$	−7.07211	+	7.85437i	−0.627548	+	0.696963i	0.342598	+	0.939482i	$0.388693\pi$
$128$	−16.8326	−	1.76918i	−1.48781	−	0.156375i
$129$	1.26458			0.111340
$130$	−7.20978	−	16.4846i	−0.632339	−	1.44580i
$131$	−1.88889	−	1.37236i	−0.165033	−	0.119903i	0.502203	−	0.864749i	$-0.332523\pi$
$131$	−1.88889	−	1.37236i	−0.165033	−	0.119903i	−0.667236	+	0.744846i	$0.732523\pi$
$132$	−8.88585	+	19.9579i	−0.773414	+	1.73712i
$133$	−1.98132	−	0.882142i	−0.171802	−	0.0764914i
$134$	23.2746	+	25.8491i	2.01062	+	2.23302i
$135$	5.64742	−	7.77301i	0.486053	−	0.668994i
$136$	−27.8936	+	25.1155i	−2.39186	+	2.15364i
$137$	−0.759231	+	3.57190i	−0.0648655	+	0.305168i	−0.998606	−	0.0527823i	$-0.983191\pi$
$137$	−0.759231	+	3.57190i	−0.0648655	+	0.305168i	0.933741	+	0.357951i	$0.116524\pi$
$138$	0.0721189	+	0.0992632i	0.00613917	+	0.00844985i
$139$	−2.65634	−	0.564623i	−0.225308	−	0.0478907i	0.0938742	−	0.995584i	$-0.470075\pi$
$139$	−2.65634	−	0.564623i	−0.225308	−	0.0478907i	−0.319182	+	0.947693i	$0.603408\pi$
$140$	22.1922	−	24.6470i	1.87559	−	2.08305i
$141$	14.0263	−	31.5036i	1.18123	−	2.65308i
$142$	−3.64184	−	11.2084i	−0.305616	−	0.940590i
$143$	−0.657072	−	6.67394i	−0.0549471	−	0.558103i
$144$	−20.6623	−	15.0120i	−1.72186	−	1.25100i
$145$	3.73392	+	17.5667i	0.310085	+	1.45883i
$146$	−3.27256	−	1.45704i	−0.270839	−	0.120585i
$147$	−2.44183	−	23.2325i	−0.201399	−	1.91618i
$148$	1.09517	−	1.50738i	0.0900226	−	0.123906i
$149$	4.35571	+	2.51477i	0.356834	+	0.206018i	0.667691	−	0.744438i	$-0.267283\pi$
$149$	4.35571	+	2.51477i	0.356834	+	0.206018i	−0.310857	+	0.950457i	$0.600616\pi$
$150$	6.00576	+	3.46742i	0.490368	+	0.283114i
$151$	1.47037	−	2.02379i	0.119657	−	0.164693i	−0.744987	−	0.667079i	$-0.767544\pi$
$151$	1.47037	−	2.02379i	0.119657	−	0.164693i	0.864644	+	0.502386i	$0.167544\pi$
$152$	3.00099	+	0.637881i	0.243413	+	0.0517389i
$153$	31.2663	−	6.64586i	2.52773	−	0.537286i
$154$	15.7731	−	9.10662i	1.27103	−	0.733832i
$155$	3.09131	−	10.6981i	0.248300	−	0.859291i
$156$	42.0878	+	4.70391i	3.36972	+	0.376615i
$157$	−2.54396	+	7.82949i	−0.203030	+	0.624861i	0.796759	+	0.604298i	$0.206546\pi$
$157$	−2.54396	+	7.82949i	−0.203030	+	0.624861i	−0.999789	+	0.0205639i	$0.993454\pi$
$158$	−12.0000	−	10.8049i	−0.954671	−	0.859590i
$159$	−0.843763	+	8.02787i	−0.0669147	+	0.636651i
$160$	−2.37390	+	4.11171i	−0.187673	+	0.325059i
$161$		−	0.0694265i		−	0.00547158i
$162$	−0.841961	−	1.89107i	−0.0661507	−	0.148577i
$163$	−11.1015	+	1.16682i	−0.869539	+	0.0913922i	−0.528780	−	0.848759i	$-0.677350\pi$
$163$	−11.1015	+	1.16682i	−0.869539	+	0.0913922i	−0.340758	+	0.940151i	$0.610684\pi$
$164$	−25.8588	−	35.5916i	−2.01924	−	2.77924i
$165$	−6.91975	−	7.68516i	−0.538702	−	0.598289i
$166$	−2.23598	+	21.2740i	−0.173546	+	1.65118i
$167$	4.24678	+	19.9795i	0.328625	+	1.54606i	0.763643	+	0.645639i	$0.223409\pi$
$167$	4.24678	+	19.9795i	0.328625	+	1.54606i	−0.435017	+	0.900422i	$0.643258\pi$
$168$	18.7182	+	57.6088i	1.44414	+	4.44461i
$169$	−11.9447	+	5.13077i	−0.918821	+	0.394675i
$170$	−10.4253	−	32.0857i	−0.799582	−	2.46086i
$171$	−1.94167	−	1.74829i	−0.148483	−	0.133695i
$172$	1.75584	+	0.781751i	0.133882	+	0.0596079i
$173$	1.57313	+	0.334380i	0.119603	+	0.0254224i	0.267324	−	0.963607i	$-0.413860\pi$
$173$	1.57313	+	0.334380i	0.119603	+	0.0254224i	−0.147721	+	0.989029i	$0.547194\pi$
$174$	−59.2330	−	19.2460i	−4.49044	−	1.45903i
$175$	−1.59604	−	3.58478i	−0.120650	−	0.270984i
$176$	−7.46649	+	6.72286i	−0.562808	+	0.506755i
$177$	13.1970	+	18.1641i	0.991949	+	1.36530i
$178$	0.898787	+	8.55138i	0.0673669	+	0.640953i
$179$	−0.452348	+	4.30380i	−0.0338101	+	0.321681i	0.964525	+	0.263993i	$0.0850396\pi$
$179$	−0.452348	+	4.30380i	−0.0338101	+	0.321681i	−0.998335	+	0.0576882i	$0.981627\pi$
$180$	34.6017	−	19.9773i	2.57906	−	1.48902i
$181$	2.75510			0.204785			0.102393	−	0.994744i	$-0.467350\pi$
$181$	2.75510			0.204785			0.102393	+	0.994744i	$0.467350\pi$
$182$	−26.0817	−	23.7968i	−1.93330	−	1.76394i
$183$	2.67311	+	8.22698i	0.197602	+	0.608156i
$184$	0.0204193	+	0.0960650i	0.00150533	+	0.00708201i
$185$	0.440989	+	0.763815i	0.0324222	+	0.0561568i
$186$	26.7696	+	27.8344i	1.96284	+	2.04092i
$187$		−	12.5746i		−	0.919548i
$188$	38.9506	−	35.0713i	2.84076	−	2.55784i
$189$	3.91992	−	18.4418i	0.285132	−	1.34144i
$190$	−1.62089	+	2.23096i	−0.117592	+	0.161851i
$191$	−7.32411	+	12.6857i	−0.529954	+	0.917907i	0.469436	+	0.882967i	$0.344457\pi$
$191$	−7.32411	+	12.6857i	−0.529954	+	0.917907i	−0.999389	+	0.0349402i	$0.988876\pi$
$192$	6.78411	+	11.7504i	0.489601	+	0.848013i
$193$	24.0057	+	2.52310i	1.72797	+	0.181617i	0.915752	−	0.401743i	$-0.131596\pi$
$193$	24.0057	+	2.52310i	1.72797	+	0.181617i	0.812214	+	0.583360i	$0.198262\pi$
$194$	26.5658	−	19.3012i	1.90731	−	1.38574i
$195$	−10.1375	+	17.2947i	−0.725960	+	1.23850i
$196$	10.9717	−	33.7674i	0.783692	−	2.41196i
$197$	−22.9923	−	2.41658i	−1.63813	−	0.172174i	−0.759776	−	0.650185i	$-0.774691\pi$
$197$	−22.9923	−	2.41658i	−1.63813	−	0.172174i	−0.878354	+	0.478010i	$0.841358\pi$
$198$	21.4619	−	4.56187i	1.52523	−	0.324198i
$199$	−0.117033	−	0.0248761i	−0.00829623	−	0.00176342i	0.203762	−	0.979021i	$-0.434683\pi$
$199$	−0.117033	−	0.0248761i	−0.00829623	−	0.00176342i	−0.212058	+	0.977257i	$0.568017\pi$
$200$	3.26277	+	4.49081i	0.230712	+	0.317548i
$201$	8.05767	−	37.9084i	0.568344	−	2.67385i
$202$	0.510399	−	2.40124i	0.0359115	−	0.168951i
$203$	20.7143	+	28.5108i	1.45386	+	2.00107i
$204$	77.6739	+	16.5101i	5.43826	+	1.15594i
$205$	20.3699	−	4.32975i	1.42269	−	0.302403i
$206$	27.6513	+	2.90627i	1.92656	+	0.202489i
$207$	0.0258455	−	0.0795442i	0.00179638	−	0.00552870i
$208$	16.8026	+	9.84904i	1.16505	+	0.682908i
$209$	−0.831538	+	0.604148i	−0.0575187	+	0.0417898i
$210$	−54.1465	−	5.69103i	−3.73646	−	0.392718i
$211$	−7.64963	−	13.2495i	−0.526622	−	0.912137i	−0.999519	−	0.0310186i	$-0.990125\pi$
$211$	−7.64963	−	13.2495i	−0.526622	−	0.912137i	0.472897	−	0.881118i	$-0.343208\pi$
$212$	−6.13431	+	10.6249i	−0.421306	+	0.729724i
$213$	−7.71820	+	10.6232i	−0.528842	+	0.727889i
$214$	−5.02293	+	23.6310i	−0.343360	+	1.61538i
$215$	−0.676118	+	0.608779i	−0.0461109	+	0.0415184i
$216$			26.6707i			1.81471i
$217$	−2.99694	−	21.6453i	−0.203445	−	1.46938i
$218$	−2.25983	−	3.91414i	−0.153055	−	0.265099i
$219$	0.829842	+	3.90410i	0.0560755	+	0.263815i
$220$	−4.85705	−	14.9484i	−0.327462	−	1.00782i
$221$	−23.2320	+	7.37982i	−1.56275	+	0.496420i
$222$	−3.05865			−0.205283
$223$	22.6944	−	13.1026i	1.51973	−	0.877417i	0.520001	−	0.854166i	$-0.325932\pi$
$223$	22.6944	−	13.1026i	1.51973	−	0.877417i	0.999730	−	0.0232511i	$-0.00740174\pi$
$224$	−0.973852	+	9.26559i	−0.0650683	+	0.619083i
$225$	−0.494132	−	4.70135i	−0.0329421	−	0.313423i
$226$	24.6284	+	33.8982i	1.63826	+	2.25487i
$227$	12.5226	−	11.2754i	0.831154	−	0.748375i	−0.139147	−	0.990272i	$-0.544436\pi$
$227$	12.5226	−	11.2754i	0.831154	−	0.748375i	0.970302	+	0.241897i	$0.0777695\pi$
$228$	−2.64005	−	5.92966i	−0.174842	−	0.392701i
$229$	8.29219	+	2.69430i	0.547964	+	0.178044i	0.569898	−	0.821715i	$-0.306983\pi$
$229$	8.29219	+	2.69430i	0.547964	+	0.178044i	−0.0219347	+	0.999759i	$0.506983\pi$
$230$	−0.0863454	−	0.0183533i	−0.00569345	−	0.00121018i
$231$	−18.5386	−	8.25390i	−1.21975	−	0.543067i
$232$	−37.0477	−	33.3579i	−2.43230	−	2.19005i
$233$	−4.22847	−	13.0139i	−0.277017	−	0.852569i	−0.988679	−	0.150048i	$-0.952057\pi$
$233$	−4.22847	−	13.0139i	−0.277017	−	0.852569i	0.711662	−	0.702522i	$-0.247943\pi$
$234$	−21.0238	−	36.9742i	−1.37437	−	2.41708i
$235$	7.66685	+	23.5961i	0.500130	+	1.53924i
$236$	7.09490	+	33.3789i	0.461839	+	2.17278i
$237$	−1.88063	+	17.8930i	−0.122160	+	1.16227i
$238$	−44.2979	−	49.1978i	−2.87140	−	3.18902i
$239$	6.30218	+	8.67421i	0.407654	+	0.561088i	0.962644	−	0.270769i	$-0.0872780\pi$
$239$	6.30218	+	8.67421i	0.407654	+	0.561088i	−0.554990	+	0.831857i	$0.687278\pi$
$240$	29.8694	−	3.13940i	1.92806	−	0.202647i
$241$	−10.1389	−	22.7723i	−0.653102	−	1.46689i	−0.871182	−	0.490961i	$-0.836646\pi$
$241$	−10.1389	−	22.7723i	−0.653102	−	1.46689i	0.218080	−	0.975931i	$-0.430021\pi$
$242$			18.8138i			1.20940i
$243$	−8.35903	+	14.4783i	−0.536232	+	0.928782i
$244$	−1.37429	+	13.0755i	−0.0879800	+	0.837074i
$245$	12.4899	+	11.2459i	0.797950	+	0.718477i
$246$	−22.3171	+	68.6851i	−1.42289	+	4.37920i
$247$	1.60419	+	1.18173i	0.102072	+	0.0751915i
$248$	10.5130	+	29.0690i	0.667576	+	1.84588i
$249$	20.6407	−	11.9169i	1.30805	−	0.755202i
$250$	−29.2859	+	6.22491i	−1.85220	+	0.393698i
$251$	−14.6174	−	3.10703i	−0.922643	−	0.196114i	−0.277985	−	0.960585i	$-0.589667\pi$
$251$	−14.6174	−	3.10703i	−0.922643	−	0.196114i	−0.644657	+	0.764472i	$0.723000\pi$
$252$	46.0842	−	63.4295i	2.90303	−	3.99568i
$253$	−0.0284941	−	0.0164511i	−0.00179141	−	0.00103427i
$254$	22.8373	+	13.1851i	1.43294	+	0.827308i
$255$	−22.0944	+	30.4104i	−1.38361	+	1.90437i
$256$	3.39380	+	32.2899i	0.212113	+	2.01812i
$257$	−13.2059	−	5.87963i	−0.823759	−	0.366761i	−0.0488282	−	0.998807i	$-0.515549\pi$
$257$	−13.2059	−	5.87963i	−0.823759	−	0.366761i	−0.774931	+	0.632046i	$0.782215\pi$
$258$	−0.655994	−	3.08621i	−0.0408404	−	0.192139i
$259$	1.40017	+	1.01729i	0.0870026	+	0.0632111i
$260$	−24.7672	+	17.7465i	−1.53600	+	1.10059i
$261$	13.1193	+	40.3771i	0.812065	+	2.49928i
$262$	−2.36940	+	5.32175i	−0.146382	+	0.328779i
$263$	−9.54156	+	10.5970i	−0.588358	+	0.653437i	−0.961651	−	0.274276i	$-0.911562\pi$
$263$	−9.54156	+	10.5970i	−0.588358	+	0.653437i	0.373293	+	0.927713i	$0.378228\pi$
$264$	28.0793	+	5.96844i	1.72816	+	0.367332i
$265$	−3.41357	−	4.69837i	−0.209694	−	0.288619i
$266$	−1.12507	+	5.29304i	−0.0689825	+	0.324537i
$267$	7.11958	−	6.41050i	0.435711	−	0.392316i
$268$	34.6226	−	47.6539i	2.11491	−	2.91093i
$269$	6.98873	+	7.76177i	0.426110	+	0.473243i	0.917523	−	0.397684i	$-0.130186\pi$
$269$	6.98873	+	7.76177i	0.426110	+	0.473243i	−0.491412	+	0.870927i	$0.663519\pi$
$270$	−21.8997	−	9.75037i	−1.33277	−	0.593389i
$271$	−5.68963	+	12.7791i	−0.345621	+	0.776277i	0.654181	+	0.756338i	$0.273014\pi$
$271$	−5.68963	+	12.7791i	−0.345621	+	0.776277i	−0.999801	+	0.0199383i	$0.993653\pi$
$272$	29.5451	+	21.4658i	1.79144	+	1.30155i
$273$	−4.36938	+	39.0946i	−0.264447	+	2.36611i
$274$	9.11111			0.550422
$275$	−1.84946	−	0.194386i	−0.111527	−	0.0117219i
$276$	0.139031	−	0.154409i	0.00836867	−	0.00929435i
$277$	15.1337	+	16.8077i	0.909295	+	1.00987i	0.999902	+	0.0139881i	$0.00445270\pi$
$277$	15.1337	+	16.8077i	0.909295	+	1.00987i	−0.0906068	+	0.995887i	$0.528881\pi$
$278$			6.77572i			0.406381i
$279$	4.62422	−	25.9154i	0.276845	−	1.55151i
$280$	−37.7413	−	21.7900i	−2.25547	−	1.30220i
$281$	2.26273	+	0.735205i	0.134983	+	0.0438587i	0.375729	−	0.926729i	$-0.377392\pi$
$281$	2.26273	+	0.735205i	0.134983	+	0.0438587i	−0.240746	+	0.970588i	$0.577392\pi$
$282$	−84.1610	−	17.8890i	−5.01171	−	1.06527i
$283$	2.76621	−	26.3188i	0.164434	−	1.56449i	−0.531923	−	0.846793i	$-0.678530\pi$
$283$	2.76621	−	26.3188i	0.164434	−	1.56449i	0.696357	−	0.717695i	$-0.254803\pi$
$284$	−17.2837	+	9.97878i	−1.02560	+	0.592131i
$285$	3.07251			0.182000
$286$	−15.9470	+	5.06567i	−0.942963	+	0.299539i
$287$	33.0604	−	24.0198i	1.95150	−	1.41784i
$288$	−4.56508	+	10.2533i	−0.269000	+	0.604184i
$289$	−28.0794	+	5.96846i	−1.65173	+	0.351086i
$290$	40.9347	−	18.2253i	2.40377	−	1.07023i
$291$	−34.7961	−	11.3059i	−2.03978	−	0.662765i
$292$	−1.26126	+	5.93377i	−0.0738098	+	0.347248i
$293$	−26.9360	+	2.83109i	−1.57362	+	0.165394i	−0.850743	−	0.525582i	$-0.823847\pi$
$293$	−26.9360	+	2.83109i	−1.57362	+	0.165394i	−0.722877	+	0.690977i	$0.757181\pi$
$294$	−55.4324	+	18.0111i	−3.23288	+	1.05043i
$295$	−15.8003	−	3.35846i	−0.919930	−	0.195537i
$296$	−2.23661	−	0.995802i	−0.130000	−	0.0578798i
$297$	−6.64005	−	5.97873i	−0.385295	−	0.346921i
$298$	3.87782	−	11.9347i	0.224636	−	0.691358i
$299$	−0.0136712	+	0.0622986i	−0.000790626	+	0.00360282i
$300$	3.62901	−	11.1690i	0.209521	−	0.644840i
$301$	−0.726154	+	1.63097i	−0.0418548	+	0.0940075i
$302$	−5.70181	−	2.53861i	−0.328102	−	0.146081i
$303$	−2.49873	+	1.11251i	−0.143549	+	0.0639119i
$304$		−	2.98509i		−	0.171206i
$305$	−5.38975	−	3.11178i	−0.308616	−	0.178180i
$306$	−32.4386	−	72.8582i	−1.85439	−	4.16503i
$307$	−5.19666	+	1.68850i	−0.296589	+	0.0963676i	−0.453532	−	0.891240i	$-0.649836\pi$
$307$	−5.19666	+	1.68850i	−0.296589	+	0.0963676i	0.156943	+	0.987608i	$0.449836\pi$
$308$	−20.6380	−	22.9208i	−1.17596	−	1.30603i
$309$	−15.4892	−	26.8282i	−0.881152	−	1.52620i
$310$	−27.7124	−	1.99477i	−1.57396	−	0.113296i
$311$	0.691238			0.0391965			0.0195982	−	0.999808i	$-0.493761\pi$
$311$	0.691238			0.0391965			0.0195982	+	0.999808i	$0.493761\pi$
$312$	−5.45236	−	55.3801i	−0.308679	−	3.13528i
$313$	3.88800	+	11.9660i	0.219763	+	0.676360i	0.998781	+	0.0493588i	$0.0157178\pi$
$313$	3.88800	+	11.9660i	0.219763	+	0.676360i	−0.779019	+	0.627001i	$0.784282\pi$
$314$	20.4276	+	2.14703i	1.15280	+	0.121164i
$315$	18.5566	+	32.1409i	1.04554	+	1.81094i
$316$	−13.6725	+	23.6815i	−0.769139	+	1.33219i
$317$	11.9097	−	16.3923i	0.668917	−	0.920685i	−0.330818	−	0.943695i	$-0.607325\pi$
$317$	11.9097	−	16.3923i	0.668917	−	0.920685i	0.999735	+	0.0230091i	$0.00732467\pi$
$318$	20.0298	−	2.10521i	1.12321	−	0.118055i
$319$	16.6099	−	1.74577i	0.929974	−	0.0977442i
$320$	−9.28396	−	3.01654i	−0.518989	−	0.168630i
$321$	24.5905	−	10.9484i	1.37251	−	0.611080i
$322$	−0.169436	+	0.0360147i	−0.00944230	+	0.00200702i
$323$	2.77640	+	2.49989i	0.154483	+	0.139097i
$324$	−2.83600	+	2.06047i	−0.157555	+	0.114471i
$325$	0.726281	+	3.53102i	0.0402868	+	0.195866i
$326$	8.60650	+	26.4881i	0.476670	+	1.46704i
$327$	−2.04823	+	4.60039i	−0.113267	+	0.254402i
$328$	−38.6810	+	42.9596i	−2.13580	+	2.37204i
$329$	32.5771	+	36.1805i	1.79603	+	1.99470i
$330$	−15.1661	+	20.8744i	−0.834867	+	1.14910i
$331$	−1.38515	+	1.24720i	−0.0761349	+	0.0685522i	−0.706320	−	0.707893i	$-0.749646\pi$
$331$	−1.38515	+	1.24720i	−0.0761349	+	0.0685522i	0.630185	+	0.776445i	$0.282979\pi$
$332$	36.0261	−	3.78650i	1.97719	−	0.207811i
$333$	1.22552	+	1.68678i	0.0671580	+	0.0924350i
$334$	46.5572	−	20.7286i	2.54750	−	1.13422i
$335$	13.9414	+	24.1471i	0.761697	+	1.31930i
$336$	51.0398	−	29.4679i	2.78445	−	1.60760i
$337$	11.4885	+	8.34687i	0.625818	+	0.454683i	0.854949	−	0.518712i	$-0.173588\pi$
$337$	11.4885	+	8.34687i	0.625818	+	0.454683i	−0.229131	+	0.973396i	$0.573588\pi$
$338$	18.7179	+	26.4895i	1.01812	+	1.44084i
$339$	14.4265	−	44.4001i	0.783538	−	2.41148i
$340$	−49.4772	+	28.5657i	−2.68328	+	1.54919i
$341$	−9.59383	−	3.89899i	−0.519535	−	0.211142i
$342$	−3.25947	+	5.64558i	−0.176252	+	0.305278i
$343$	5.23768	+	1.70183i	0.282808	+	0.0918900i
$344$	0.525085	−	2.47033i	0.0283107	−	0.133191i
$345$	0.0400044	+	0.0898513i	0.00215376	+	0.00483743i
$346$		−	4.01271i		−	0.215724i
$347$	−14.7861	+	25.6104i	−0.793762	+	1.37484i	0.129861	+	0.991532i	$0.458547\pi$
$347$	−14.7861	+	25.6104i	−0.793762	+	1.37484i	−0.923622	+	0.383304i	$0.874786\pi$
$348$	−11.0246	+	104.892i	−0.590978	+	5.62278i
$349$	−0.861306	+	1.93452i	−0.0461046	+	0.103553i	−0.935129	−	0.354307i	$-0.884717\pi$
$349$	−0.861306	+	1.93452i	−0.0461046	+	0.103553i	0.889025	+	0.457859i	$0.151384\pi$
$350$	−7.92073	+	5.75475i	−0.423381	+	0.307604i
$351$	−7.14895	+	15.7765i	−0.381583	+	0.842086i
$352$	3.57203	+	2.59523i	0.190390	+	0.138326i
$353$	−5.40920	−	25.4483i	−0.287903	−	1.35448i	−0.849729	−	0.527220i	$-0.823234\pi$
$353$	−5.40920	−	25.4483i	−0.287903	−	1.35448i	0.561826	−	0.827255i	$-0.310099\pi$
$354$	37.4838	−	41.6300i	1.99224	−	2.21261i
$355$	−0.987497	−	9.39541i	−0.0524109	−	0.498656i
$356$	13.8483	−	4.49960i	0.733960	−	0.238478i
$357$	−15.3359	+	72.1498i	−0.811663	+	3.81857i
$358$	10.7381	−	1.12862i	0.567527	−	0.0596495i
$359$	8.76701	−	2.84858i	0.462705	−	0.150342i	−0.0683820	−	0.997659i	$-0.521784\pi$
$359$	8.76701	−	2.84858i	0.462705	−	0.150342i	0.531087	+	0.847317i	$0.321784\pi$
$360$	−35.1297	−	39.0154i	−1.85150	−	2.05629i
$361$	−1.95412	+	18.5922i	−0.102848	+	0.978537i
$362$	−1.42920	−	6.72385i	−0.0751170	−	0.353398i
$363$	16.9588	−	12.3213i	0.890104	−	0.646699i
$364$	−30.2348	+	51.5811i	−1.58473	+	2.70358i
$365$	−2.32315	−	1.68787i	−0.121599	−	0.0883472i
$366$	18.6914	−	10.7915i	0.977013	−	0.564079i
$367$	8.51942	+	14.7561i	0.444710	+	0.770261i	0.998032	−	0.0627069i	$-0.0199733\pi$
$367$	8.51942	+	14.7561i	0.444710	+	0.770261i	−0.553322	+	0.832968i	$0.686640\pi$
$368$	0.0872946	−	0.0388661i	0.00455055	−	0.00202603i
$369$	46.8203	−	15.2128i	2.43737	−	0.791948i
$370$	1.63534	−	1.47246i	0.0850171	−	0.0765498i
$371$	−9.86932	−	5.69805i	−0.512389	−	0.295828i
$372$	36.6806	−	54.1421i	1.90180	−	2.80714i
$373$	2.87968	−	4.98775i	0.149104	−	0.258256i	−0.781792	−	0.623539i	$-0.785694\pi$
$373$	2.87968	−	4.98775i	0.149104	−	0.258256i	0.930897	+	0.365283i	$0.119028\pi$
$374$	−30.6885	+	6.52304i	−1.58686	+	0.337298i
$375$	24.7906	+	22.3215i	1.28018	+	1.15268i
$376$	−55.7178	−	40.4814i	−2.87343	−	2.08767i
$377$	−12.9734	−	29.6626i	−0.668163	−	1.52770i
$378$	−47.0408			−2.41952
$379$	13.5190	+	1.42090i	0.694424	+	0.0729869i	0.445163	−	0.895449i	$-0.353146\pi$
$379$	13.5190	+	1.42090i	0.694424	+	0.0729869i	0.249261	+	0.968436i	$0.419812\pi$
$380$	4.26613	+	1.89940i	0.218848	+	0.0974373i
$381$	−3.07120	−	29.2205i	−0.157342	−	1.49701i
$382$	34.7590	+	11.2939i	1.77842	+	0.577845i
$383$	11.4546	+	25.7275i	0.585304	+	1.31462i	0.927091	+	0.374837i	$0.122301\pi$
$383$	11.4546	+	25.7275i	0.585304	+	1.31462i	−0.341786	+	0.939778i	$0.611032\pi$
$384$	34.9660	−	31.4835i	1.78435	−	1.60664i
$385$	13.8853	−	4.51162i	0.707663	−	0.229934i
$386$	−6.29521	−	59.8949i	−0.320418	−	3.04857i
$387$	−1.43914	+	1.59833i	−0.0731556	+	0.0812475i
$388$	−41.3245	−	37.2087i	−2.09793	−	1.88899i
$389$	−17.2073	+	12.5018i	−0.872446	+	0.633869i	−0.931242	−	0.364401i	$-0.881274\pi$
$389$	−17.2073	+	12.5018i	−0.872446	+	0.633869i	0.0587964	+	0.998270i	$0.481274\pi$
$390$	47.4667	+	15.7691i	2.40357	+	0.798497i
$391$	−0.0369566	+	0.113741i	−0.00186898	+	0.00575212i
$392$	−46.3983	−	4.87665i	−2.34347	−	0.246308i
$393$	6.34874	−	1.34947i	0.320252	−	0.0680716i
$394$	6.02945	+	57.3664i	0.303759	+	2.89008i
$395$	−7.60835	−	10.4720i	−0.382818	−	0.526904i
$396$	−15.1128	−	33.9440i	−0.759449	−	1.70575i
$397$	−4.93918	−	2.85164i	−0.247890	−	0.143120i	0.370907	−	0.928670i	$-0.379047\pi$
$397$	−4.93918	−	2.85164i	−0.247890	−	0.143120i	−0.618798	+	0.785550i	$0.712380\pi$
$398$			0.298524i			0.0149636i
$399$	5.50795	−	2.45230i	0.275743	−	0.122768i
$400$	3.61389	−	4.01363i	0.180694	−	0.200681i
$401$	−6.29043	−	29.5942i	−0.314129	−	1.47786i	−0.797965	−	0.602703i	$-0.794090\pi$
$401$	−6.29043	−	29.5942i	−0.314129	−	1.47786i	0.483836	−	0.875159i	$-0.339243\pi$
$402$	−96.6956			−4.82274
$403$	−1.57306	+	20.0131i	−0.0783596	+	0.996925i
$404$	−4.15719			−0.206828
$405$	−0.345001	−	1.62310i	−0.0171433	−	0.0806527i
$406$	58.8354	−	65.3434i	2.91995	−	3.24294i
$407$	0.749297	−	0.333608i	0.0371413	−	0.0165364i
$408$		−	104.344i		−	5.16579i
$409$	−27.2208	−	15.7159i	−1.34598	−	0.777103i	−0.358304	−	0.933605i	$-0.616645\pi$
$409$	−27.2208	−	15.7159i	−1.34598	−	0.777103i	−0.987678	+	0.156502i	$0.949978\pi$
$410$	−21.1336	−	47.4669i	−1.04371	−	2.34422i
$411$	−5.96690	−	8.21274i	−0.294326	−	0.405104i
$412$	−4.92159	−	46.8258i	−0.242469	−	2.30694i
$413$	−31.0050	+	6.59032i	−1.52566	+	0.324289i
$414$	−0.207536	−	0.0218129i	−0.0101998	−	0.00107204i
$415$	−5.29882	+	16.3081i	−0.260109	+	0.800533i
$416$	2.69841	−	8.12253i	0.132300	−	0.398240i
$417$	6.10763	−	4.43745i	0.299092	−	0.217303i
$418$	1.90578	+	1.71598i	0.0932150	+	0.0839311i
$419$	12.1791	−	13.5262i	0.594986	−	0.660799i	−0.368165	−	0.929761i	$-0.620014\pi$
$419$	12.1791	−	13.5262i	0.594986	−	0.660799i	0.963151	+	0.268962i	$0.0866805\pi$
$420$	9.63740	+	91.6938i	0.470257	+	4.47420i
$421$	28.3255	−	9.20350i	1.38050	−	0.448551i	0.477666	−	0.878542i	$-0.341483\pi$
$421$	28.3255	−	9.20350i	1.38050	−	0.448551i	0.902833	+	0.429990i	$0.141483\pi$
$422$	−28.3674	+	25.5421i	−1.38090	+	1.24337i
$423$	23.8556	+	53.5807i	1.15990	+	2.60518i
$424$	15.3320	+	4.98166i	0.744587	+	0.241931i
$425$	0.706563	+	6.72249i	0.0342733	+	0.326089i
$426$	29.9298	+	13.3256i	1.45010	+	0.645627i
$427$	−12.1456	−	1.27655i	−0.587767	−	0.0617768i
$428$	40.9117			1.97754
$429$	15.0099	+	11.0570i	0.724685	+	0.533838i
$430$	1.83647	+	1.33427i	0.0885622	+	0.0643442i
$431$	15.6400	+	14.0824i	0.753355	+	0.678324i	0.953483	−	0.301446i	$-0.0974693\pi$
$431$	15.6400	+	14.0824i	0.753355	+	0.678324i	−0.200129	+	0.979770i	$0.564136\pi$
$432$	25.3825	−	5.39522i	1.22122	−	0.259578i
$433$	13.8252	−	23.9460i	0.664397	−	1.15077i	−0.315051	−	0.949075i	$-0.602022\pi$
$433$	13.8252	−	23.9460i	0.664397	−	1.15077i	0.979448	−	0.201695i	$-0.0646450\pi$
$434$	−51.2709	+	18.5425i	−2.46108	+	0.890067i
$435$	−43.2366	−	24.9626i	−2.07304	−	1.19687i
$436$	−5.68785	+	5.12137i	−0.272399	+	0.245269i
$437$	0.00929705	−	0.00302079i	0.000444738	−	0.000144504i
$438$	9.09751	−	4.05047i	0.434696	−	0.193539i
$439$	0.190369	+	0.329729i	0.00908581	+	0.0157371i	0.870533	−	0.492111i	$-0.163775\pi$
$439$	0.190369	+	0.329729i	0.00908581	+	0.0157371i	−0.861447	+	0.507848i	$0.830441\pi$
$440$	−17.8861	+	10.3266i	−0.852688	+	0.492300i
$441$	32.1430	+	23.3532i	1.53062	+	1.11206i
$442$	30.0620	+	52.8696i	1.42990	+	2.51475i
$443$	−18.9303	+	13.7537i	−0.899406	+	0.653457i	−0.938313	−	0.345786i	$-0.887612\pi$
$443$	−18.9303	+	13.7537i	−0.899406	+	0.653457i	0.0389070	+	0.999243i	$0.487612\pi$
$444$	1.07691	+	5.06644i	0.0511077	+	0.240443i
$445$	−0.720477	+	6.85488i	−0.0341539	+	0.324952i
$446$	−43.7497	−	48.5890i	−2.07161	−	2.30076i
$447$	−13.2975	+	4.32062i	−0.628950	+	0.204358i
$448$	−19.0506	+	2.00229i	−0.900054	+	0.0945995i
$449$	0.265575	−	1.24943i	0.0125332	−	0.0589643i	−0.971437	−	0.237299i	$-0.923738\pi$
$449$	0.265575	−	1.24943i	0.0125332	−	0.0589643i	0.983970	+	0.178335i	$0.0570711\pi$
$450$	−11.2174	+	3.64474i	−0.528792	+	0.171815i
$451$	−2.02435	−	19.2604i	−0.0953228	−	0.906936i
$452$	47.4787	−	52.7304i	2.23321	−	2.48023i
$453$	1.44584	+	6.80215i	0.0679316	+	0.319593i
$454$	−34.0138	−	24.7125i	−1.59635	−	1.15981i
$455$	−16.4844	−	23.0058i	−0.772801	−	1.07853i
$456$	−6.90006	+	5.01319i	−0.323125	+	0.234764i
$457$	5.89369	−	13.2374i	0.275695	−	0.619221i	−0.721633	−	0.692276i	$-0.756608\pi$
$457$	5.89369	−	13.2374i	0.275695	−	0.619221i	0.997328	+	0.0730547i	$0.0232748\pi$
$458$	2.27391	−	21.6348i	0.106253	−	1.01093i
$459$	−16.2387	+	28.1263i	−0.757960	+	1.31283i
$460$			0.149487i			0.00696988i
$461$	4.29713	+	9.65151i	0.200137	+	0.449516i	0.985534	−	0.169477i	$-0.0542078\pi$
$461$	4.29713	+	9.65151i	0.200137	+	0.449516i	−0.785397	+	0.618992i	$0.787541\pi$
$462$	−10.5269	+	49.5252i	−0.489756	+	2.30412i
$463$	−17.8728	−	5.80722i	−0.830619	−	0.269885i	−0.137313	−	0.990528i	$-0.543847\pi$
$463$	−17.8728	−	5.80722i	−0.830619	−	0.269885i	−0.693306	+	0.720643i	$0.743847\pi$
$464$	−24.2524	+	42.0063i	−1.12589	+	1.95010i
$465$	16.3509	+	26.2863i	0.758253	+	1.21900i
$466$	−29.5670	+	17.0705i	−1.36967	+	0.790778i
$467$	−4.81555	+	14.8207i	−0.222837	+	0.685822i	0.775667	+	0.631143i	$0.217414\pi$
$467$	−4.81555	+	14.8207i	−0.222837	+	0.685822i	−0.998504	+	0.0546795i	$0.982586\pi$
$468$	−53.8431	+	47.8425i	−2.48890	+	2.21152i
$469$	44.2649	+	32.1603i	2.04396	+	1.48502i
$470$	53.6094	−	30.9514i	2.47282	−	1.42768i
$471$	−11.4428	−	19.8195i	−0.527256	−	0.913235i
$472$	40.9632	−	18.2380i	1.88548	−	0.839471i
$473$	0.497317	+	0.684499i	0.0228667	+	0.0314733i
$474$	44.6435	−	4.69222i	2.05054	−	0.215521i
$475$	0.410600	−	0.369706i	0.0188396	−	0.0169633i
$476$	−65.8961	+	90.6982i	−3.02034	+	4.15715i
$477$	−9.18637	−	10.2025i	−0.420615	−	0.467140i
$478$	17.9003	−	19.8802i	0.818738	−	0.909301i
$479$	16.1992	−	36.3841i	0.740162	−	1.66243i	−0.00892542	−	0.999960i	$-0.502841\pi$
$479$	16.1992	−	36.3841i	0.740162	−	1.66243i	0.749087	−	0.662471i	$-0.230492\pi$
$480$	−4.07858	−	12.5526i	−0.186161	−	0.572945i
$481$	−1.05610	−	1.18856i	−0.0481540	−	0.0541936i
$482$	−50.3164	+	36.5570i	−2.29185	+	1.66513i
$483$	0.143428	+	0.129143i	0.00652620	+	0.00587622i
$484$	31.1639	−	6.62408i	1.41654	−	0.301095i
$485$	24.0468	−	10.7063i	1.09191	−	0.486150i
$486$	39.6706	+	12.8897i	1.79949	+	0.584691i
$487$	0.289580	−	0.0304361i	0.0131221	−	0.00137919i	−0.0979651	−	0.995190i	$-0.531233\pi$
$487$	0.289580	−	0.0304361i	0.0131221	−	0.00137919i	0.111087	+	0.993811i	$0.464567\pi$
$488$	17.1812	−	1.80582i	0.777759	−	0.0817457i
$489$	18.2399	−	25.1051i	0.824836	−	1.13529i
$490$	20.9668	−	36.3155i	0.947181	−	1.64057i
$491$	16.5390	+	28.6464i	0.746395	+	1.29279i	0.949540	+	0.313646i	$0.101550\pi$
$491$	16.5390	+	28.6464i	0.746395	+	1.29279i	−0.203145	+	0.979149i	$0.565116\pi$
$492$	121.630	+	12.7838i	5.48349	+	0.576338i
$493$	−18.7594	−	57.7355i	−0.844881	−	2.60027i
$494$	2.05185	−	4.52807i	0.0923169	−	0.203727i
$495$	17.5884			0.790541
$496$	25.5383	−	15.8856i	1.14671	−	0.713286i
$497$	−9.26911	−	16.0546i	−0.415776	−	0.720146i
$498$	−39.7905	−	44.1919i	−1.78306	−	1.98029i
$499$	−18.7104	+	6.07937i	−0.837591	+	0.272150i	−0.696239	−	0.717810i	$-0.745145\pi$
$499$	−18.7104	+	6.07937i	−0.837591	+	0.272150i	−0.141352	+	0.989959i	$0.545145\pi$
$500$	20.6223	+	46.3184i	0.922257	+	2.07142i
$501$	−49.1752	−	28.3913i	−2.19699	−	1.26843i
$502$			37.2857i			1.66414i
$503$	−12.6189	+	5.61831i	−0.562650	+	0.250508i	−0.668296	−	0.743896i	$-0.732976\pi$
$503$	−12.6189	+	5.61831i	−0.562650	+	0.250508i	0.105645	+	0.994404i	$0.466309\pi$
$504$	−94.1152	−	41.9028i	−4.19222	−	1.86650i
$505$	0.800401	−	1.79773i	0.0356174	−	0.0799979i
$506$	−0.0253678	+	0.0780741i	−0.00112774	+	0.00347082i
$507$	11.6191	−	34.2204i	0.516024	−	1.51978i
$508$	13.7996	−	42.4707i	0.612257	−	1.88433i
$509$	−23.2312	−	20.9174i	−1.02970	−	0.927149i	−0.0323220	−	0.999478i	$-0.510290\pi$
$509$	−23.2312	−	20.9174i	−1.02970	−	0.927149i	−0.997381	+	0.0723289i	$0.976957\pi$
$510$	85.6782	+	38.1464i	3.79390	+	1.68915i
$511$	−5.51177	−	1.17156i	−0.243827	−	0.0518269i
$512$	44.8493	−	14.5724i	1.98208	−	0.644016i
$513$	2.64013	−	0.277489i	0.116565	−	0.0122515i
$514$	−7.49880	+	35.2791i	−0.330758	+	1.55609i
$515$	21.1968	+	6.88726i	0.934043	+	0.303489i
$516$	−4.88113	+	2.17322i	−0.214880	+	0.0956706i
$517$	22.5686	−	4.79711i	0.992567	−	0.210977i
$518$	1.75636	−	3.94485i	0.0771700	−	0.173327i
$519$	−3.61705	+	2.62794i	−0.158771	+	0.115354i
$520$	29.5757	+	26.9847i	1.29698	+	1.18336i
$521$	−6.91366			−0.302893			−0.151447	−	0.988465i	$-0.548393\pi$
$521$	−6.91366			−0.302893			−0.151447	+	0.988465i	$0.548393\pi$
$522$	91.7351	−	52.9633i	4.01514	−	2.31814i
$523$	−0.476199	+	4.53073i	−0.0208227	+	0.198115i	−0.999988	−	0.00495111i	$-0.998424\pi$
$523$	−0.476199	+	4.53073i	−0.0208227	+	0.198115i	0.979165	+	0.203066i	$0.0650907\pi$
$524$	9.64935	+	2.05103i	0.421534	+	0.0895998i
$525$	10.3746	+	3.37093i	0.452787	+	0.147119i
$526$	30.8116	+	17.7891i	1.34345	+	0.775642i
$527$	−6.61220	+	37.0565i	−0.288032	+	1.61421i
$528$		−	27.9305i		−	1.21552i
$529$	−15.3898	−	17.0921i	−0.669122	−	0.743135i
$530$	−9.69565	+	10.7681i	−0.421152	+	0.467737i
$531$	−37.9768	−	3.99153i	−1.64805	−	0.173218i
$532$	9.16369			0.397296
$533$	−34.3960	+	15.0436i	−1.48986	+	0.651611i
$534$	−19.3381	−	14.0500i	−0.836843	−	0.608002i
$535$	−7.87689	+	17.6918i	−0.340548	+	0.764883i
$536$	−70.7078	−	31.4811i	−3.05411	−	1.35978i
$537$	−8.04978	−	8.94018i	−0.347374	−	0.385797i
$538$	15.3173	−	21.0824i	0.660375	−	0.908929i
$539$	11.6151	−	10.4583i	0.500300	−	0.450472i
$540$	−8.44026	+	39.7083i	−0.363211	+	1.70877i
$541$	−0.333172	−	0.458571i	−0.0143242	−	0.0197155i	0.801795	−	0.597599i	$-0.203879\pi$
$541$	−0.333172	−	0.458571i	−0.0143242	−	0.0197155i	−0.816119	+	0.577884i	$0.803879\pi$
$542$	34.1390	+	7.25648i	1.46640	+	0.311692i
$543$	−5.12488	+	5.69176i	−0.219930	+	0.244257i
$544$	6.52764	−	14.6613i	0.279870	−	0.628599i
$545$	−1.11957	−	3.44568i	−0.0479571	−	0.147597i
$546$	97.6774	−	9.61667i	4.18020	−	0.411555i
$547$	−1.82585	−	1.32656i	−0.0780676	−	0.0567195i	0.548067	−	0.836435i	$-0.315364\pi$
$547$	−1.82585	−	1.32656i	−0.0780676	−	0.0567195i	−0.626135	+	0.779715i	$0.715364\pi$
$548$	−3.20789	−	15.0919i	−0.137034	−	0.644696i
$549$	−13.4404	−	5.98404i	−0.573622	−	0.255393i
$550$	0.485000	+	4.61447i	0.0206805	+	0.196762i
$551$	−2.91665	+	4.01442i	−0.124253	+	0.171020i
$552$	−0.236443	−	0.136510i	−0.0100637	−	0.00581027i
$553$	−21.9973	−	12.7001i	−0.935420	−	0.540065i
$554$	33.1687	−	45.6528i	1.40920	−	1.93960i
$555$	−2.39827	−	0.509767i	−0.101801	−	0.0216384i
$556$	11.2235	−	2.38563i	0.475984	−	0.101173i
$557$	−15.2158	+	8.78487i	−0.644716	+	0.372227i	−0.786429	−	0.617681i	$-0.788072\pi$
$557$	−15.2158	+	8.78487i	−0.644716	+	0.372227i	0.141713	+	0.989908i	$0.454739\pi$
$558$	−65.6455	+	2.15804i	−2.77899	+	0.0913572i
$559$	0.972765	−	1.32053i	0.0411436	−	0.0558524i
$560$	−13.1028	+	40.3264i	−0.553696	+	1.70410i
$561$	25.9779	+	23.3906i	1.09679	+	0.987552i
$562$	0.620493	−	5.90360i	0.0261739	−	0.249028i
$563$	−1.23839	+	2.14495i	−0.0521917	+	0.0903987i	−0.890941	−	0.454119i	$-0.849954\pi$
$563$	−1.23839	+	2.14495i	−0.0521917	+	0.0903987i	0.838749	+	0.544518i	$0.183287\pi$
$564$			145.705i			6.13531i
$565$	13.6614	+	30.6840i	0.574739	+	1.29089i
$566$	−65.6661	+	6.90179i	−2.76015	+	0.290104i
$567$	−1.91393	−	2.63430i	−0.0803777	−	0.110630i
$568$	17.5475	+	19.4884i	0.736275	+	0.817716i
$569$	−2.17372	+	20.6816i	−0.0911273	+	0.867018i	0.849503	+	0.527584i	$0.176902\pi$
$569$	−2.17372	+	20.6816i	−0.0911273	+	0.867018i	−0.940630	+	0.339434i	$0.889765\pi$
$570$	−1.59385	−	7.49849i	−0.0667592	−	0.314077i
$571$	−0.416425	−	1.28162i	−0.0174268	−	0.0536343i	0.941965	−	0.335711i	$-0.108977\pi$
$571$	−0.416425	−	1.28162i	−0.0174268	−	0.0536343i	−0.959392	+	0.282077i	$0.908977\pi$
$572$	14.0056	+	24.6315i	0.585605	+	1.02989i
$573$	−12.5835	−	38.7281i	−0.525684	−	1.61789i
$574$	−75.7705	−	68.2241i	−3.16260	−	2.84762i
$575$	0.0161576	+	0.00719381i	0.000673817	+	0.000300003i
$576$	−22.5722	−	4.79787i	−0.940509	−	0.199911i
$577$	−6.98752	−	2.27038i	−0.290894	−	0.0945173i	0.159935	−	0.987128i	$-0.448872\pi$
$577$	−6.98752	−	2.27038i	−0.290894	−	0.0945173i	−0.450829	+	0.892610i	$0.648872\pi$
$578$	29.1322	+	65.4319i	1.21174	+	2.72161i
$579$	−49.8664	+	44.8999i	−2.07238	+	1.86598i
$580$	−44.6015	−	61.3887i	−1.85198	−	2.54903i
$581$	3.51721	+	33.4640i	0.145918	+	1.38832i
$582$	−9.54189	+	90.7850i	−0.395524	+	3.76316i
$583$	−4.67721	+	2.70039i	−0.193710	+	0.111839i
$584$	7.97118			0.329850
$585$	−10.3223	−	32.4951i	−0.426776	−	1.34351i
$586$	20.8823	+	64.2690i	0.862639	+	2.65493i
$587$	−1.98791	−	9.35237i	−0.0820498	−	0.386014i	0.917892	−	0.396831i	$-0.129890\pi$
$587$	−1.98791	−	9.35237i	−0.0820498	−	0.386014i	−0.999941	+	0.0108171i	$0.996557\pi$
$588$	49.3510	+	85.4785i	2.03520	+	3.52507i
$589$	2.76817	−	1.34313i	0.114060	−	0.0553426i
$590$			40.3030i			1.65925i
$591$	47.7613	−	43.0044i	1.96464	−	1.76897i
$592$	−0.495262	+	2.33003i	−0.0203552	+	0.0957635i
$593$	−3.82836	+	5.26928i	−0.157212	+	0.216383i	−0.880356	−	0.474314i	$-0.842696\pi$
$593$	−3.82836	+	5.26928i	−0.157212	+	0.216383i	0.723144	+	0.690697i	$0.242696\pi$
$594$	−11.1466	+	19.3065i	−0.457352	+	0.792157i
$595$	−26.5341	−	45.9585i	−1.08779	−	1.88411i
$596$	−21.1343	−	2.22131i	−0.865696	−	0.0909883i
$597$	0.269089	−	0.195504i	0.0110131	−	0.00800146i
$598$	0.159132	+	0.00104752i	0.00650740	+	4.28362e-5i
$599$	11.9011	−	36.6277i	0.486265	−	1.49657i	−0.343876	−	0.939015i	$-0.611740\pi$
$599$	11.9011	−	36.6277i	0.486265	−	1.49657i	0.830141	−	0.557554i	$-0.188260\pi$
$600$	−15.3468	−	1.61301i	−0.626529	−	0.0658508i
$601$	−15.3661	+	3.26616i	−0.626794	+	0.133229i	−0.510348	−	0.859968i	$-0.670484\pi$
$601$	−15.3661	+	3.26616i	−0.626794	+	0.133229i	−0.116446	+	0.993197i	$0.537150\pi$
$602$	4.35708	+	0.926127i	0.177582	+	0.0377461i
$603$	38.7433	+	53.3256i	1.57775	+	2.17159i
$604$	−2.19751	+	10.3385i	−0.0894155	+	0.420667i
$605$	−3.13559	+	14.7518i	−0.127480	+	0.599746i
$606$	4.01130	+	5.52107i	0.162948	+	0.224278i
$607$	14.0209	+	2.98023i	0.569090	+	0.120964i	0.483465	−	0.875364i	$-0.339378\pi$
$607$	14.0209	+	2.98023i	0.569090	+	0.120964i	0.0856250	+	0.996327i	$0.472711\pi$
$608$	−1.28315	+	0.272741i	−0.0520385	+	0.0110611i
$609$	−97.4320	−	10.2405i	−3.94814	−	0.414967i
$610$	−4.79840	+	14.7680i	−0.194282	+	0.597937i
$611$	−22.1079	−	38.8808i	−0.894390	−	1.57295i
$612$	−109.264	+	79.3846i	−4.41672	+	3.20893i
$613$	20.3014	+	2.13376i	0.819965	+	0.0861818i	0.505216	−	0.862993i	$-0.331413\pi$
$613$	20.3014	+	2.13376i	0.819965	+	0.0861818i	0.314749	+	0.949175i	$0.398080\pi$
$614$	6.81654	+	11.8066i	0.275093	+	0.476475i
$615$	−28.9461	+	50.1360i	−1.16722	+	2.02168i
$616$	−23.8216	+	32.7876i	−0.959800	+	1.32105i
$617$	7.19059	−	33.8291i	0.289482	−	1.36191i	−0.557452	−	0.830209i	$-0.688221\pi$
$617$	7.19059	−	33.8291i	0.289482	−	1.36191i	0.846934	−	0.531698i	$-0.178446\pi$
$618$	−57.4394	+	51.7186i	−2.31055	+	2.08043i
$619$			25.1787i			1.01202i	0.862528	+	0.506009i	$0.168880\pi$
$619$			25.1787i			1.01202i	−0.862528	+	0.506009i	$0.831120\pi$
$620$	6.45292	+	46.6060i	0.259156	+	1.87174i
$621$	0.0424896	+	0.0735941i	0.00170505	+	0.00295323i
$622$	−0.358577	−	1.68697i	−0.0143776	−	0.0676414i
$623$	4.17959	+	12.8635i	0.167452	+	0.515364i
$624$	−51.6023	+	16.3919i	−2.06575	+	0.656200i
$625$	−19.0012			−0.760048
$626$	27.1863	−	15.6960i	1.08658	−	0.627339i
$627$	0.298672	−	2.84167i	0.0119278	−	0.113485i
$628$	−3.63586	−	34.5929i	−0.145087	−	1.38041i
$629$	−1.75238	−	2.41194i	−0.0698718	−	0.0961703i
$630$	68.8140	−	61.9604i	2.74162	−	2.46856i
$631$	9.99156	+	22.4414i	0.397758	+	0.893378i	0.995769	+	0.0918906i	$0.0292910\pi$
$631$	9.99156	+	22.4414i	0.397758	+	0.893378i	−0.598012	+	0.801488i	$0.704042\pi$
$632$	34.1728	+	11.1034i	1.35932	+	0.441670i
$633$	41.6016	+	8.84269i	1.65351	+	0.351465i
$634$	−46.1838	−	20.5623i	−1.83419	−	0.816635i
$635$	15.7091	+	14.1445i	0.623396	+	0.561308i
$636$	−10.5393	−	32.4368i	−0.417912	−	1.28620i
$637$	−26.1388	−	15.3215i	−1.03566	−	0.607061i
$638$	−12.8769	−	39.6309i	−0.509800	−	1.56900i
$639$	−4.64326	−	21.8448i	−0.183685	−	0.864169i
$640$	−3.53844	+	33.6660i	−0.139869	+	1.33076i
$641$	−3.48080	−	3.86583i	−0.137484	−	0.152691i	0.670471	−	0.741936i	$-0.266092\pi$
$641$	−3.48080	−	3.86583i	−0.137484	−	0.152691i	−0.807955	+	0.589245i	$0.799425\pi$
$642$	−39.4759	−	54.3339i	−1.55799	−	2.14439i
$643$	24.0521	−	2.52798i	0.948523	−	0.0996938i	0.382384	−	0.924003i	$-0.375103\pi$
$643$	24.0521	−	2.52798i	0.948523	−	0.0996938i	0.566139	+	0.824310i	$0.308436\pi$
$644$	0.119312	+	0.267979i	0.00470155	+	0.0105599i
$645$		−	2.52921i		−	0.0995874i
$646$	4.66074	−	8.07264i	0.183374	−	0.317614i
$647$	4.66633	−	44.3972i	0.183452	−	1.74543i	−0.385180	−	0.922842i	$-0.625861\pi$
$647$	4.66633	−	44.3972i	0.183452	−	1.74543i	0.568632	−	0.822592i	$-0.307473\pi$
$648$	3.42308	+	3.08216i	0.134471	+	0.121079i
$649$	−4.64205	+	14.2868i	−0.182216	+	0.560804i
$650$	8.24072	−	3.60420i	0.323228	−	0.141368i
$651$	50.2916	+	34.0719i	1.97108	+	1.33538i
$652$	40.8455	−	23.5822i	1.59963	−	0.923549i
$653$	5.01377	−	1.06571i	0.196204	−	0.0417044i	−0.108761	−	0.994068i	$-0.534688\pi$
$653$	5.01377	−	1.06571i	0.196204	−	0.0417044i	0.304965	+	0.952363i	$0.401355\pi$
$654$	12.2898	+	2.61228i	0.480570	+	0.102148i
$655$	−2.74477	+	3.77785i	−0.107247	+	0.147613i
$656$	48.7095	+	28.1224i	1.90179	+	1.09800i
$657$	−5.87888	−	3.39417i	−0.229357	−	0.132419i
$658$	71.3996	−	98.2731i	2.78345	−	3.83109i
$659$	3.47161	+	33.0301i	0.135235	+	1.28667i	0.826032	+	0.563623i	$0.190593\pi$
$659$	3.47161	+	33.0301i	0.135235	+	1.28667i	−0.690797	+	0.723048i	$0.742740\pi$
$660$	39.9167	+	17.7721i	1.55376	+	0.691777i
$661$	−2.36362	−	11.1200i	−0.0919343	−	0.432517i	−0.999909	−	0.0134919i	$-0.995705\pi$
$661$	−2.36362	−	11.1200i	−0.0919343	−	0.432517i	0.907975	−	0.419025i	$-0.137628\pi$
$662$	3.76234	+	2.73350i	0.146227	+	0.106240i
$663$	27.9689	−	61.7224i	1.08622	−	2.39710i
$664$	−14.7089	−	45.2695i	−0.570818	−	1.75680i
$665$	−1.76432	+	3.96273i	−0.0684174	+	0.153668i
$666$	3.48087	−	3.86590i	0.134881	−	0.149801i
$667$	−0.155371	−	0.0330252i	−0.00601599	−	0.00127874i
$668$	−50.7276	−	69.8206i	−1.96271	−	2.70144i
$669$	−15.1462	+	71.2571i	−0.585584	+	2.75496i
$670$	51.6993	−	46.5502i	1.99732	−	1.79839i
$671$	−3.40191	+	4.68233i	−0.131329	+	0.180759i
$672$	−17.3302	−	19.2472i	−0.668529	−	0.742476i
$673$	24.5642	+	10.9367i	0.946881	+	0.421578i	0.821295	−	0.570504i	$-0.193252\pi$
$673$	24.5642	+	10.9367i	0.946881	+	0.421578i	0.125586	+	0.992083i	$0.459919\pi$
$674$	14.4110	−	32.3677i	0.555091	−	1.24676i
$675$	3.88576	+	2.82317i	0.149563	+	0.108664i
$676$	37.2878	−	40.3316i	1.43414	−	1.55121i
$677$	39.5675			1.52070			0.760351	−	0.649513i	$-0.225027\pi$
$677$	39.5675			1.52070			0.760351	+	0.649513i	$0.225027\pi$
$678$	−115.842	−	12.1755i	−4.44890	−	0.467599i
$679$	34.5625	−	38.3856i	1.32639	−	1.47310i
$680$	50.2321	+	55.7884i	1.92631	+	2.13939i
$681$			46.8443i			1.79508i
$682$	−4.53876	+	25.4364i	−0.173798	+	0.974011i
$683$	−4.63567	−	2.67640i	−0.177379	−	0.102410i	0.408682	−	0.912677i	$-0.365989\pi$
$683$	−4.63567	−	2.67640i	−0.177379	−	0.102410i	−0.586061	+	0.810267i	$0.699322\pi$
$684$	10.4991	+	3.41137i	0.401444	+	0.130437i
$685$	7.14396	+	1.51850i	0.272957	+	0.0580187i
$686$	1.43629	−	13.6654i	0.0548380	−	0.521749i
$687$	−20.9908	+	12.1190i	−0.800849	+	0.462370i
$688$	−2.45724			−0.0936814
$689$	7.73401	+	7.05647i	0.294642	+	0.268830i
$690$	0.198531	−	0.144241i	0.00755793	−	0.00549116i
$691$	18.4338	−	41.4029i	0.701253	−	1.57504i	−0.112382	−	0.993665i	$-0.535848\pi$
$691$	18.4338	−	41.4029i	0.701253	−	1.57504i	0.813635	−	0.581375i	$-0.197485\pi$
$692$	−6.64677	+	1.41282i	−0.252672	+	0.0537072i
$693$	31.5300	−	14.0381i	1.19772	−	0.533261i
$694$	70.1725	+	22.8004i	2.66371	+	0.865493i
$695$	−1.12927	+	5.31280i	−0.0428357	+	0.201526i
$696$	137.828	−	14.4863i	5.22435	−	0.549102i
$697$	−66.9486	+	21.7529i	−2.53586	+	0.823951i
$698$	5.16802	+	1.09850i	0.195613	+	0.0415787i
$699$	34.7509	+	15.4721i	1.31440	+	0.585209i
$700$	12.3211	+	11.0940i	0.465695	+	0.419314i
$701$	−9.34565	+	28.7630i	−0.352981	+	1.08636i	0.604191	+	0.796840i	$0.293497\pi$
$701$	−9.34565	+	28.7630i	−0.352981	+	1.08636i	−0.957171	+	0.289523i	$0.906503\pi$
$702$	42.2111	+	9.26308i	1.59316	+	0.349612i
$703$	−0.0753043	+	0.231763i	−0.00284016	+	0.00874111i
$704$	−3.69238	+	8.29321i	−0.139162	+	0.312562i
$705$	−63.0086	−	28.0532i	−2.37304	−	1.05655i
$706$	−59.3007	+	26.4024i	−2.23181	+	0.993667i
$707$		−	3.86154i		−	0.145228i
$708$	−82.1548	−	47.4321i	−3.08757	−	1.78261i
$709$	9.09786	+	20.4341i	0.341677	+	0.767419i	0.999894	+	0.0145907i	$0.00464452\pi$
$709$	9.09786	+	20.4341i	0.341677	+	0.767419i	−0.658216	+	0.752829i	$0.728689\pi$
$710$	−22.4173	+	7.28383i	−0.841307	+	0.273357i
$711$	−20.4751	−	22.7399i	−0.767877	−	0.852813i
$712$	−9.56659	−	16.5698i	−0.358523	−	0.620980i
$713$	0.0753196	+	0.0634635i	0.00282074	+	0.00237673i
$714$	184.038			6.88744
$715$	−13.3482	+	1.31417i	−0.499193	+	0.0491473i
$716$	−5.65022	−	17.3896i	−0.211159	−	0.649880i
$717$	−29.6430	−	3.11560i	−1.10704	−	0.116354i
$718$	−11.4998	−	19.9183i	−0.429170	−	0.743344i
$719$	9.51476	−	16.4800i	0.354841	−	0.614602i	−0.632250	−	0.774764i	$-0.717868\pi$
$719$	9.51476	−	16.4800i	0.354841	−	0.614602i	0.987091	+	0.160162i	$0.0512018\pi$
$720$	−30.0247	+	41.3254i	−1.11895	+	1.54011i
$721$	43.4956	−	4.57157i	1.61986	−	0.170254i
$722$	46.3881	−	4.87559i	1.72639	−	0.181451i
$723$	65.9049	+	21.4138i	2.45103	+	0.796388i
$724$	−10.6344	+	4.73474i	−0.395225	+	0.175965i
$725$	−8.78166	+	1.86660i	−0.326143	+	0.0693238i
$726$	−38.8674	−	34.9964i	−1.44251	−	1.29884i
$727$	5.53179	−	4.01908i	0.205163	−	0.149060i	−0.480460	−	0.877017i	$-0.659530\pi$
$727$	5.53179	−	4.01908i	0.205163	−	0.149060i	0.685622	+	0.727957i	$0.259530\pi$
$728$	74.5566	+	24.7687i	2.76325	+	0.917987i
$729$	−13.5925	−	41.8334i	−0.503425	−	1.54938i
$730$	−2.91414	+	6.54526i	−0.107857	+	0.242251i
$731$	2.05784	−	2.28546i	0.0761118	−	0.0845307i
$732$	−24.4563	−	27.1614i	−0.903930	−	1.00392i
$733$	20.5558	−	28.2926i	0.759246	−	1.04501i	−0.238030	−	0.971258i	$-0.576502\pi$
$733$	20.5558	−	28.2926i	0.759246	−	1.04501i	0.997276	−	0.0737549i	$-0.0234982\pi$
$734$	31.5929	−	28.4464i	1.16612	−	1.04998i
$735$	−46.4659	+	4.88377i	−1.71392	+	0.180140i
$736$	−0.0246826	−	0.0339727i	−0.000909813	−	0.00125225i
$737$	23.6881	−	10.5466i	0.872564	−	0.388491i
$738$	−61.4149	−	106.374i	−2.26071	−	3.91567i
$739$	10.0288	−	5.79014i	0.368916	−	0.212994i	−0.304069	−	0.952650i	$-0.598345\pi$
$739$	10.0288	−	5.79014i	0.368916	−	0.212994i	0.672985	+	0.739656i	$0.265012\pi$
$740$	−3.01482	−	2.19039i	−0.110827	−	0.0805204i
$741$	−5.42535	+	1.11592i	−0.199305	+	0.0409943i
$742$	−8.78648	+	27.0420i	−0.322562	+	0.992743i
$743$	−2.93346	+	1.69363i	−0.107618	+	0.0621334i	−0.552843	−	0.833285i	$-0.686457\pi$
$743$	−2.93346	+	1.69363i	−0.107618	+	0.0621334i	0.445225	+	0.895419i	$0.353124\pi$
$744$	−79.6092	−	32.3537i	−2.91862	−	1.18614i
$745$	5.02965	−	8.71161i	0.184272	−	0.319169i
$746$	−13.6665	−	4.44051i	−0.500365	−	0.162579i
$747$	−8.42790	+	39.6501i	−0.308361	+	1.45072i
$748$	21.6100	+	48.5368i	0.790138	+	1.77468i
$749$			38.0021i			1.38857i
$750$	41.6159	−	72.0808i	1.51960	−	2.63202i
$751$	3.61522	−	34.3965i	0.131921	−	1.25515i	−0.705548	−	0.708662i	$-0.749299\pi$
$751$	3.61522	−	34.3965i	0.131921	−	1.25515i	0.837469	−	0.546484i	$-0.184034\pi$
$752$	−27.2550	+	61.2158i	−0.993888	+	2.23231i
$753$	33.6092	−	24.4185i	1.22479	−	0.889861i
$754$	−65.6620	+	47.0490i	−2.39127	+	1.71342i
$755$	−4.04766	−	2.94080i	−0.147309	−	0.107026i
$756$	16.5624	+	77.9198i	0.602368	+	2.83392i
$757$	6.27452	−	6.96856i	0.228051	−	0.253277i	−0.618250	−	0.785982i	$-0.712158\pi$
$757$	6.27452	−	6.96856i	0.228051	−	0.253277i	0.846301	+	0.532705i	$0.178825\pi$
$758$	−3.54520	−	33.7303i	−0.128767	−	1.22514i
$759$	0.0869894	−	0.0282646i	0.00315751	−	0.00102594i
$760$	1.27579	−	6.00211i	0.0462777	−	0.217719i
$761$	25.6184	−	2.69260i	0.928665	−	0.0976067i	0.371897	−	0.928274i	$-0.378708\pi$
$761$	25.6184	−	2.69260i	0.928665	−	0.0976067i	0.556769	+	0.830667i	$0.312041\pi$
$762$	−69.7197	+	22.6533i	−2.52568	+	0.820642i
$763$	−4.75715	−	5.28335i	−0.172220	−	0.191270i
$764$	6.46941	−	61.5523i	0.234055	−	2.22688i
$765$	−13.2920	−	62.5340i	−0.480574	−	2.26092i
$766$	56.8462	−	41.3012i	2.05394	−	1.49227i
$767$	29.1195	+	0.191685i	1.05145	+	0.00692134i
$768$	−73.0205	−	53.0525i	−2.63490	−	1.91437i
$769$	−30.3291	+	17.5105i	−1.09369	+	0.631445i	−0.934558	−	0.355812i	$-0.884204\pi$
$769$	−30.3291	+	17.5105i	−1.09369	+	0.631445i	−0.159136	+	0.987257i	$0.550871\pi$
$770$	−18.2136	−	31.5469i	−0.656373	−	1.13687i
$771$	36.7115	−	16.3450i	1.32213	−	0.588651i
$772$	−96.9954	+	31.5157i	−3.49094	+	1.13428i
$773$	11.4745	−	10.3317i	0.412708	−	0.371604i	−0.436463	−	0.899722i	$-0.643769\pi$
$773$	11.4745	−	10.3317i	0.412708	−	0.371604i	0.849171	+	0.528118i	$0.177102\pi$
$774$	4.64728	+	2.68311i	0.167043	+	0.0964423i
$775$	5.34802	+	1.54536i	0.192106	+	0.0555109i
$776$	−36.5342	+	63.2791i	−1.31150	+	2.27159i
$777$	−4.70613	+	1.00032i	−0.168831	+	0.0358862i
$778$	39.4371	+	35.5093i	1.41389	+	1.27307i
$779$	4.65502	+	3.38207i	0.166784	+	0.121175i
$780$	9.40803	−	84.1774i	0.336861	−	3.01404i
$781$	−8.78552			−0.314370
$782$	0.296756	+	0.0311904i	0.0106120	+	0.00111536i
$783$	−39.4066	−	17.5449i	−1.40828	−	0.627005i
$784$	4.74480	+	45.1438i	0.169457	+	1.61228i
$785$	15.6593	+	5.08802i	0.558905	+	0.181599i
$786$	−6.58677	−	14.7941i	−0.234942	−	0.527689i
$787$	−23.0247	+	20.7316i	−0.820744	+	0.739001i	−0.968229	−	0.250063i	$-0.919549\pi$
$787$	−23.0247	+	20.7316i	−0.820744	+	0.739001i	0.147486	+	0.989064i	$0.452882\pi$
$788$	92.9007	−	30.1853i	3.30945	−	1.07531i
$789$	−4.14360	−	39.4237i	−0.147516	−	1.40352i
$790$	−21.6102	+	24.0006i	−0.768857	+	0.853902i
$791$	48.9803	+	44.1021i	1.74154	+	1.56809i
$792$	−39.4991	+	28.6977i	−1.40354	+	1.01973i
$793$	10.6473	+	3.53716i	0.378095	+	0.125608i
$794$	−4.39727	+	13.5334i	−0.156053	+	0.480282i
$795$	16.0561	+	1.68756i	0.569450	+	0.0598516i
$796$	0.494484	−	0.105106i	0.0175265	−	0.00372538i
$797$	3.91623	+	37.2605i	0.138720	+	1.31983i	0.813392	+	0.581716i	$0.197619\pi$
$797$	3.91623	+	37.2605i	0.138720	+	1.31983i	−0.674672	+	0.738118i	$0.735715\pi$
$798$	−8.84209	−	12.1701i	−0.313006	−	0.430816i
$799$	−34.1113	−	76.6153i	−1.20677	−	2.71046i
$800$	−2.05546	−	1.18672i	−0.0726715	−	0.0419569i
$801$			16.2940i			0.575721i
$802$	−68.9617	+	30.7037i	−2.43512	+	1.08419i
$803$	−1.78689	+	1.98454i	−0.0630579	+	0.0700329i
$804$	34.0451	+	160.170i	1.20068	+	5.64875i
$805$	−0.138856			−0.00489403
$806$	49.6582	−	6.54268i	1.74914	−	0.230456i
$807$	−29.0350			−1.02208
$808$	1.13573	+	5.34319i	0.0399548	+	0.187973i
$809$	7.61741	−	8.45999i	0.267814	−	0.297438i	−0.594205	−	0.804314i	$-0.702533\pi$
$809$	7.61741	−	8.45999i	0.267814	−	0.297438i	0.862019	+	0.506876i	$0.169200\pi$
$810$	−3.78223	+	1.68396i	−0.132894	+	0.0591682i
$811$			46.4485i			1.63103i	0.578738	+	0.815514i	$0.303545\pi$
$811$			46.4485i			1.63103i	−0.578738	+	0.815514i	$0.696455\pi$
$812$	−128.952	−	74.4505i	−4.52533	−	2.61270i
$813$	−15.8168	−	35.5252i	−0.554720	−	1.24592i
$814$	−1.20287	−	1.65561i	−0.0421605	−	0.0580290i
$815$	2.33369	+	22.2035i	0.0817454	+	0.777756i
$816$	−99.3041	+	21.1077i	−3.47634	+	0.738919i
$817$	−0.250002	−	0.0262763i	−0.00874646	−	0.000919290i
$818$	−24.2342	+	74.5852i	−0.847328	+	2.60781i
$819$	−44.4401	−	50.0139i	−1.55286	−	1.74763i
$820$	−71.1848	+	51.7188i	−2.48588	+	1.80610i
$821$	−4.18367	−	3.76699i	−0.146011	−	0.131469i	0.592888	−	0.805285i	$-0.297988\pi$
$821$	−4.18367	−	3.76699i	−0.146011	−	0.131469i	−0.738899	+	0.673816i	$0.764654\pi$
$822$	−16.9480	+	18.8226i	−0.591128	+	0.656514i
$823$	−0.625880	−	5.95485i	−0.0218168	−	0.207573i	0.978183	−	0.207744i	$-0.0666122\pi$
$823$	−0.625880	−	5.95485i	−0.0218168	−	0.207573i	−1.00000		0.000171180i	$0.999946\pi$
$824$	−58.8400	+	19.1183i	−2.04979	+	0.666017i
$825$	3.84184	−	3.45921i	0.133756	−	0.120434i
$826$	32.1675	+	72.2494i	1.11925	+	2.51388i
$827$	−23.1593	−	7.52491i	−0.805327	−	0.261667i	−0.122710	−	0.992443i	$-0.539158\pi$
$827$	−23.1593	−	7.52491i	−0.805327	−	0.261667i	−0.682618	+	0.730776i	$0.739158\pi$
$828$	0.0369387	+	0.351449i	0.00128371	+	0.0122137i
$829$	19.5834	+	8.71910i	0.680160	+	0.302827i	0.717583	−	0.696473i	$-0.245248\pi$
$829$	19.5834	+	8.71910i	0.680160	+	0.302827i	−0.0374230	+	0.999300i	$0.511915\pi$
$830$	42.5488	+	4.47206i	1.47689	+	0.155228i
$831$	−62.8737			−2.18106
$832$	17.4889	+	1.95464i	0.606320	+	0.0677649i
$833$	−45.9614	−	33.3929i	−1.59247	−	1.15700i
$834$	−13.9979	−	12.6038i	−0.484709	−	0.436434i
$835$	39.9599	−	8.49373i	1.38287	−	0.293938i
$836$	2.17140	−	3.76097i	0.0750994	−	0.130076i
$837$	16.4239	+	21.1105i	0.567693	+	0.729684i
$838$	−39.3287	−	22.7064i	−1.35859	−	0.784381i
$839$	7.87005	−	7.08623i	0.271704	−	0.244644i	−0.522003	−	0.852944i	$-0.674815\pi$
$839$	7.87005	−	7.08623i	0.271704	−	0.244644i	0.793707	+	0.608300i	$0.208148\pi$
$840$	115.220	−	37.4372i	3.97547	−	1.29171i
$841$	47.1657	−	20.9995i	1.62640	−	0.724121i
$842$	−37.1550	−	64.3543i	−1.28044	−	2.21780i
$843$	−5.72785	+	3.30698i	−0.197278	+	0.113898i
$844$	52.2966	+	37.9957i	1.80012	+	1.30787i
$845$	10.2618	+	23.8899i	0.353015	+	0.821836i
$846$	118.389	−	86.0147i	4.07030	−	2.95725i
$847$	6.15299	+	28.9475i	0.211419	+	0.994649i
$848$	1.63954	−	15.5992i	0.0563022	−	0.535679i
$849$	49.2263	+	54.6713i	1.68944	+	1.87632i
$850$	16.0398	−	5.21164i	0.550160	−	0.178758i
$851$	−0.00775805		0.000815404i	−0.000265942		2.79517e-5i
$852$	11.5351	−	54.2684i	0.395186	−	1.85920i
$853$	7.34141	−	2.38537i	0.251365	−	0.0816735i	−0.180624	−	0.983552i	$-0.557812\pi$
$853$	7.34141	−	2.38537i	0.251365	−	0.0816735i	0.431989	+	0.901879i	$0.357812\pi$
$854$	3.18504	+	30.3037i	0.108990	+	1.03697i
$855$	−3.49665	+	3.88342i	−0.119583	+	0.132810i
$856$	−11.1769	−	52.5833i	−0.382020	−	1.79726i
$857$	−28.0385	−	20.3712i	−0.957778	−	0.695866i	−0.00514404	−	0.999987i	$-0.501637\pi$
$857$	−28.0385	−	20.3712i	−0.957778	−	0.695866i	−0.952634	+	0.304121i	$0.901637\pi$
$858$	19.1984	−	42.3676i	0.655424	−	1.44641i
$859$	−30.2897	+	22.0068i	−1.03347	+	0.750862i	−0.969001	−	0.247058i	$-0.920536\pi$
$859$	−30.2897	+	22.0068i	−1.03347	+	0.750862i	−0.0644715	+	0.997920i	$0.520536\pi$
$860$	1.56354	−	3.51176i	0.0533161	−	0.119750i
$861$	−11.8746	+	112.980i	−0.404687	+	3.85034i
$862$	26.2549	−	45.4748i	0.894246	−	1.54888i
$863$		−	8.48105i		−	0.288698i	−0.989527	−	0.144349i	$-0.953891\pi$
$863$		−	8.48105i		−	0.288698i	0.989527	−	0.144349i	$-0.0461089\pi$
$864$	−4.63830	−	10.4178i	−0.157798	−	0.354420i
$865$	0.668774	−	3.14633i	0.0227390	−	0.106979i
$866$	−65.6121	−	21.3187i	−2.22959	−	0.724438i
$867$	39.9015	−	69.1114i	1.35512	−	2.34714i
$868$	48.7661	+	78.3982i	1.65523	+	2.66101i
$869$	−10.4248	+	6.01877i	−0.353638	+	0.204173i
$870$	−38.4928	+	118.469i	−1.30503	+	4.01646i
$871$	−33.3874	−	37.5749i	−1.13129	−	1.27318i
$872$	8.13633	+	5.91139i	0.275531	+	0.200185i
$873$	53.8892	−	31.1129i	1.82387	−	1.05301i
$874$	−0.0121951	−	0.0211225i	−0.000412505	−	0.000714479i
$875$	−43.0243	+	19.1557i	−1.45449	+	0.647580i
$876$	−9.91243	−	13.6433i	−0.334910	−	0.460964i
$877$	−2.27923	+	0.239557i	−0.0769642	+	0.00808926i	−0.142932	−	0.989732i	$-0.545653\pi$
$877$	−2.27923	+	0.239557i	−0.0769642	+	0.00808926i	0.0659681	+	0.997822i	$0.478986\pi$
$878$	0.705953	−	0.635643i	0.0238247	−	0.0214519i
$879$	44.2561	−	60.9133i	1.49272	−	2.05455i
$880$	13.4460	+	14.9333i	0.453265	+	0.503401i
$881$	−11.6869	+	12.9796i	−0.393742	+	0.437294i	−0.907123	−	0.420866i	$-0.861726\pi$
$881$	−11.6869	+	12.9796i	−0.393742	+	0.437294i	0.513381	+	0.858161i	$0.328393\pi$
$882$	40.3197	−	90.5596i	1.35764	−	3.04930i
$883$	−3.14207	−	9.67031i	−0.105739	−	0.325432i	0.884164	−	0.467177i	$-0.154729\pi$
$883$	−3.14207	−	9.67031i	−0.105739	−	0.325432i	−0.989903	+	0.141745i	$0.954729\pi$
$884$	76.9906	−	68.4104i	2.58947	−	2.30089i
$885$	36.3290	−	26.3946i	1.22119	−	0.887245i
$886$	43.3860	+	39.0649i	1.45758	+	1.31241i
$887$	−2.78509	+	0.591988i	−0.0935140	+	0.0198770i	−0.254431	−	0.967091i	$-0.581888\pi$
$887$	−2.78509	+	0.591988i	−0.0935140	+	0.0198770i	0.160917	+	0.986968i	$0.448555\pi$
$888$	6.21763	−	2.76827i	0.208650	−	0.0928970i
$889$	39.4503	+	12.8182i	1.32312	+	0.429908i
$890$	17.1031	−	1.79761i	0.573298	−	0.0602561i
$891$	−1.53470	+	0.161303i	−0.0514142	+	0.00540385i
$892$	−65.0807	+	89.5759i	−2.17906	+	2.99922i
$893$	−3.42756	+	5.93670i	−0.114699	+	0.198664i
$894$	17.4425	+	30.2114i	0.583366	+	1.01042i
$895$	8.60779	+	0.904715i	0.287727	+	0.0302413i
$896$	20.5270	+	63.1756i	0.685759	+	2.11055i
$897$	−0.103272	−	0.144127i	−0.00344815	−	0.00481228i
$898$	−3.18701			−0.106352
$899$	−49.8661	−	3.58942i	−1.66313	−	0.119714i
$900$	9.98674	+	17.2975i	0.332891	+	0.576585i
$901$	13.1357	+	14.5886i	0.437612	+	0.486017i
$902$	−45.9550	+	14.9317i	−1.53013	+	0.497171i
$903$	−2.01866	−	4.53399i	−0.0671769	−	0.150882i
$904$	−80.7448	−	46.6180i	−2.68553	−	1.55049i
$905$		−	5.51032i		−	0.183169i
$906$	15.8507	−	7.05718i	0.526604	−	0.234459i
$907$	−37.9960	−	16.9169i	−1.26164	−	0.561717i	−0.336619	−	0.941641i	$-0.609284\pi$
$907$	−37.9960	−	16.9169i	−1.26164	−	0.561717i	−0.925018	+	0.379924i	$0.875950\pi$
$908$	−28.9588	+	65.0424i	−0.961030	+	2.15851i
$909$	1.43754	−	4.42429i	0.0476802	−	0.146744i
$910$	−47.5946	+	52.1645i	−1.57775	+	1.72924i
$911$	2.86625	−	8.82142i	0.0949632	−	0.292267i	−0.892281	−	0.451481i	$-0.850896\pi$
$911$	2.86625	−	8.82142i	0.0949632	−	0.292267i	0.987244	+	0.159214i	$0.0508960\pi$
$912$	6.16688	+	5.55268i	0.204206	+	0.183868i
$913$	14.5678	+	6.48599i	0.482123	+	0.214655i
$914$	−35.3634	−	7.51672i	−1.16972	−	0.248631i
$915$	16.4543	−	5.34633i	0.543963	−	0.176744i
$916$	−36.6372	+	3.85073i	−1.21053	+	0.127232i
$917$	−1.90517	+	8.96311i	−0.0629142	+	0.295988i
$918$	77.0664	+	25.0404i	2.54357	+	0.826456i
$919$	−49.8194	+	22.1810i	−1.64339	+	0.731684i	−0.999443	−	0.0333850i	$-0.989371\pi$
$919$	−49.8194	+	22.1810i	−1.64339	+	0.731684i	−0.643948	+	0.765069i	$0.722705\pi$
$920$	0.192134	−	0.0408394i	0.00633448	−	0.00134643i
$921$	6.17826	−	13.8766i	0.203581	−	0.457250i
$922$	21.3255	−	15.4939i	0.702317	−	0.510263i
$923$	5.15606	+	16.2315i	0.169714	+	0.534266i
$924$	85.7416			2.82069
$925$	−0.381834	+	0.220452i	−0.0125546	+	0.00724842i
$926$	−4.90113	+	46.6312i	−0.161061	+	1.53240i
$927$	51.5362	+	10.9543i	1.69267	+	0.359788i
$928$	20.2724	+	6.58691i	0.665475	+	0.216226i
$929$	−17.3224	−	10.0011i	−0.568331	−	0.328126i	0.188152	−	0.982140i	$-0.439750\pi$
$929$	−17.3224	−	10.0011i	−0.568331	−	0.328126i	−0.756482	+	0.654014i	$0.773084\pi$
$930$	55.6700	−	53.5404i	1.82549	−	1.75566i
$931$			4.64371i			0.152191i
$932$	38.6863	+	42.9655i	1.26721	+	1.40738i
$933$	−1.28580	+	1.42803i	−0.0420952	+	0.0467515i
$934$	38.6682	+	4.06419i	1.26526	+	0.132984i
$935$	−25.1498			−0.822486
$936$	76.2012	+	56.1335i	2.49071	+	1.83478i
$937$	−2.19745	−	1.59654i	−0.0717875	−	0.0521566i	0.551313	−	0.834299i	$-0.314127\pi$
$937$	−2.19745	−	1.59654i	−0.0717875	−	0.0521566i	−0.623100	+	0.782142i	$0.714127\pi$
$938$	55.5253	−	124.712i	1.81296	−	4.07199i
$939$	−31.9528	−	14.2263i	−1.04274	−	0.464258i
$940$	−70.1440	−	77.9029i	−2.28785	−	2.54091i
$941$	0.754160	−	1.03801i	0.0245849	−	0.0338382i	−0.796548	−	0.604576i	$-0.793343\pi$
$941$	0.754160	−	1.03801i	0.0245849	−	0.0338382i	0.821133	+	0.570738i	$0.193343\pi$
$942$	−42.4338	+	38.2076i	−1.38257	+	1.24487i
$943$	−0.0382951	+	0.180164i	−0.00124706	+	0.00586696i
$944$	−25.6436	−	35.2954i	−0.834627	−	1.14877i
$945$	−36.8843	−	7.84001i	−1.19985	−	0.255035i
$946$	1.41254	−	1.56879i	0.0459258	−	0.0510057i
$947$	22.8224	−	51.2599i	0.741627	−	1.66572i	−0.00456386	−	0.999990i	$-0.501453\pi$
$947$	22.8224	−	51.2599i	0.741627	−	1.66572i	0.746191	−	0.665732i	$-0.231881\pi$
$948$	−23.4907	−	72.2969i	−0.762942	−	2.34809i
$949$	4.71519	+	2.13664i	0.153061	+	0.0693582i
$950$	−1.11527	−	0.810289i	−0.0361840	−	0.0262892i
$951$	11.7111	+	55.0963i	0.379758	+	1.78662i
$952$	134.576	+	59.9171i	4.36163	+	1.94192i
$953$	−2.44168	−	23.2310i	−0.0790937	−	0.752526i	−0.960144	−	0.279504i	$-0.909830\pi$
$953$	−2.44168	−	23.2310i	−0.0790937	−	0.752526i	0.881051	−	0.473022i	$-0.156837\pi$
$954$	−20.1339	+	27.7119i	−0.651859	+	0.897207i
$955$	25.3720	+	14.6485i	0.821018	+	0.474015i
$956$	−39.2327	−	22.6510i	−1.26888	−	0.732586i
$957$	−27.2901	+	37.5616i	−0.882164	+	1.21419i
$958$	−97.1990	−	20.6603i	−3.14036	−	0.667503i
$959$	14.0186	−	2.97975i	0.452685	−	0.0962212i
$960$	23.5013	−	13.5685i	0.758502	−	0.437921i
$961$	26.2221	+	16.5348i	0.845874	+	0.533382i
$962$	−2.35284	+	3.19398i	−0.0758586	+	0.102978i
$963$	−14.1471	+	43.5403i	−0.455884	+	1.40307i
$964$	78.2700	+	70.4746i	2.52091	+	2.26983i
$965$	5.04630	−	48.0124i	0.162446	−	1.54557i
$966$	0.240772	−	0.417030i	0.00774672	−	0.0134177i
$967$			5.45153i			0.175309i	0.996151	+	0.0876547i	$0.0279372\pi$
$967$			5.45153i			0.175309i	−0.996151	+	0.0876547i	$0.972063\pi$
$968$	−17.0277	−	38.2448i	−0.547291	−	1.22924i
$969$	−10.3290	+	1.08562i	−0.331816	+	0.0348752i
$970$	−38.6031	−	53.1327i	−1.23947	−	1.70599i
$971$	−0.295682	−	0.328388i	−0.00948889	−	0.0105385i	0.738382	−	0.674383i	$-0.235590\pi$
$971$	−0.295682	−	0.328388i	−0.00948889	−	0.0105385i	−0.747871	+	0.663845i	$0.768924\pi$
$972$	7.38356	−	70.2499i	0.236828	−	2.25327i
$973$	2.21597	+	10.4253i	0.0710408	+	0.334221i
$974$	−0.224498	−	0.690935i	−0.00719339	−	0.0221390i
$975$	−8.64570	−	5.06777i	−0.276884	−	0.162299i
$976$	−5.19421	−	15.9861i	−0.166262	−	0.511703i
$977$	25.9112	+	23.3305i	0.828971	+	0.746409i	0.969872	−	0.243615i	$-0.0783332\pi$
$977$	25.9112	+	23.3305i	0.828971	+	0.746409i	−0.140901	+	0.990024i	$0.545000\pi$
$978$	−70.7310	−	31.4915i	−2.26173	−	1.00699i
$979$	6.26983	+	1.33269i	0.200385	+	0.0425931i
$980$	−67.5362	−	21.9439i	−2.15737	−	0.700971i
$981$	−3.48358	−	7.82424i	−0.111222	−	0.249809i
$982$	61.3323	−	55.2238i	1.95719	−	1.76226i
$983$	23.7291	+	32.6604i	0.756842	+	1.04170i	0.997470	+	0.0710865i	$0.0226466\pi$
$983$	23.7291	+	32.6604i	0.756842	+	1.04170i	−0.240628	+	0.970617i	$0.577353\pi$
$984$	−16.7979	−	159.822i	−0.535499	−	5.09493i
$985$	−4.83327	+	45.9855i	−0.154001	+	1.46522i
$986$	−131.173	+	75.7325i	−4.17739	+	2.41181i
$987$	−135.343			−4.30802
$988$	−8.22286	−	1.80448i	−0.261604	−	0.0574081i
$989$	−0.00248663	−	0.00765307i	−7.90703e−5	−	0.000243353i
$990$	−9.12393	−	42.9247i	−0.289977	−	1.36424i
$991$	−8.64387	−	14.9716i	−0.274582	−	0.475589i	0.695448	−	0.718577i	$-0.255206\pi$
$991$	−8.64387	−	14.9716i	−0.274582	−	0.475589i	−0.970029	+	0.242987i	$0.921873\pi$
$992$	−9.16186	−	9.52628i	−0.290889	−	0.302460i
$993$		−	5.18155i		−	0.164431i
$994$	−34.3730	+	30.9496i	−1.09024	+	0.981661i
$995$	−0.0497532	+	0.234070i	−0.00157728	+	0.00742053i
$996$	−59.1912	+	81.4697i	−1.87554	+	2.58147i
$997$	9.97237	−	17.2726i	0.315828	−	0.547030i	−0.663785	−	0.747923i	$-0.731051\pi$
$997$	9.97237	−	17.2726i	0.315828	−	0.547030i	0.979613	+	0.200893i	$0.0643844\pi$
$998$	24.5427	+	42.5092i	0.776885	+	1.34560i
$999$	−2.10681	−	0.221435i	−0.0666565	−	0.00700588i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.bs.a.101.3	yes	288
13.4	even	6	inner	403.2.bs.a.225.34	yes	288
31.4	even	5	inner	403.2.bs.a.283.34	yes	288
403.4	even	30	inner	403.2.bs.a.4.3	✓	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.bs.a.4.3	✓	288	403.4	even	30	inner
403.2.bs.a.101.3	yes	288	1.1	even	1	trivial
403.2.bs.a.225.34	yes	288	13.4	even	6	inner
403.2.bs.a.283.34	yes	288	31.4	even	5	inner

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:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.bs (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.518746 - 2.44051i) q^{2} +(-1.86014 + 2.06590i) q^{3} +(-3.85989 + 1.71854i) q^{4} -2.00004i q^{5} +(6.00678 + 3.46802i) q^{6} +(-1.59632 - 3.58539i) q^{7} +(3.26332 + 4.49158i) q^{8} +(-0.494216 - 4.70215i) q^{9} +O(q^{10})\)	\(q+(-0.518746 - 2.44051i) q^{2} +(-1.86014 + 2.06590i) q^{3} +(-3.85989 + 1.71854i) q^{4} -2.00004i q^{5} +(6.00678 + 3.46802i) q^{6} +(-1.59632 - 3.58539i) q^{7} +(3.26332 + 4.49158i) q^{8} +(-0.494216 - 4.70215i) q^{9} +(-4.88112 + 1.03751i) q^{10} +(-1.84978 - 0.194419i) q^{11} +(3.62963 - 11.1709i) q^{12} +(0.726405 + 3.53162i) q^{13} +(-7.92208 + 5.75573i) q^{14} +(4.13188 + 3.72036i) q^{15} +(3.61450 - 4.01431i) q^{16} +(0.706683 + 6.72364i) q^{17} +(-11.2193 + 3.64536i) q^{18} +(0.410670 - 0.369769i) q^{19} +(3.43714 + 7.71995i) q^{20} +(10.3764 + 3.37150i) q^{21} +(0.485083 + 4.61525i) q^{22} +(0.0161603 + 0.00719504i) q^{23} +(-15.3494 - 1.61328i) q^{24} +0.999830 q^{25} +(8.24213 - 3.60481i) q^{26} +(3.88642 + 2.82365i) q^{27} +(12.3232 + 11.0959i) q^{28} +(-8.78316 + 1.86692i) q^{29} +(6.93618 - 12.0138i) q^{30} +(5.34893 + 1.54562i) q^{31} +(-2.05581 - 1.18692i) q^{32} +(3.84250 - 3.45980i) q^{33} +(16.0425 - 5.21253i) q^{34} +(-7.17093 + 3.19270i) q^{35} +(9.98844 + 17.3005i) q^{36} +(-0.381900 + 0.220490i) q^{37} +(-1.11546 - 0.810427i) q^{38} +(-8.64718 - 5.06863i) q^{39} +(8.98335 - 6.52678i) q^{40} +(2.16483 + 10.1847i) q^{41} +(2.84545 - 27.0727i) q^{42} +(-0.304383 - 0.338052i) q^{43} +(7.47406 - 2.42847i) q^{44} +(-9.40451 + 0.988454i) q^{45} +(0.00917645 - 0.0431718i) q^{46} +(-11.7978 + 3.83334i) q^{47} +(1.56967 + 14.9344i) q^{48} +(-5.62285 + 6.24481i) q^{49} +(-0.518658 - 2.44009i) q^{50} +(-15.2049 - 11.0470i) q^{51} +(-8.87306 - 12.3833i) q^{52} +(2.34914 - 1.70675i) q^{53} +(4.87508 - 10.9496i) q^{54} +(-0.388847 + 3.69963i) q^{55} +(10.8947 - 18.8703i) q^{56} +1.53622i q^{57} +(9.11246 + 20.4669i) q^{58} +(1.67919 - 7.89999i) q^{59} +(-22.3422 - 7.25942i) q^{60} +(1.55585 - 2.69482i) q^{61} +(0.997366 - 13.8559i) q^{62} +(-16.0701 + 9.27808i) q^{63} +(1.50824 - 4.64188i) q^{64} +(7.06339 - 1.45284i) q^{65} +(-10.4370 - 7.58289i) q^{66} +(-12.0733 + 6.97053i) q^{67} +(-14.2825 - 24.7381i) q^{68} +(-0.0449247 + 0.0200018i) q^{69} +(11.5117 + 15.8445i) q^{70} +(4.69760 - 0.493738i) q^{71} +(19.5073 - 17.5645i) q^{72} +(0.843917 - 1.16155i) q^{73} +(0.736216 + 0.817651i) q^{74} +(-1.85982 + 2.06554i) q^{75} +(-0.949681 + 2.13302i) q^{76} +(2.25576 + 6.94252i) q^{77} +(-7.88436 + 23.7328i) q^{78} +(5.23589 - 3.80410i) q^{79} +(-8.02880 - 7.22916i) q^{80} +(0.811534 - 0.172497i) q^{81} +(23.7329 - 10.5666i) q^{82} +(-8.15388 - 2.64936i) q^{83} +(-45.8459 + 4.81860i) q^{84} +(13.4476 - 1.41340i) q^{85} +(-0.667121 + 0.918213i) q^{86} +(12.4811 - 21.6178i) q^{87} +(-5.16317 - 8.94288i) q^{88} +(-3.42737 - 0.360231i) q^{89} +(7.29088 + 22.4390i) q^{90} +(11.5026 - 8.24203i) q^{91} -0.0747420 q^{92} +(-13.1429 + 8.17526i) q^{93} +(15.4754 + 26.8041i) q^{94} +(-0.739553 - 0.821357i) q^{95} +(6.27616 - 2.03925i) q^{96} +(5.35306 + 12.0232i) q^{97} +(18.1574 + 10.4832i) q^{98} +8.79403i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 9 q^{2} - q^{3} - 39 q^{4} - 42 q^{6} - 15 q^{7} + 31 q^{9}+O(q^{10}) \) 288 * q - 9 * q^2 - q^3 - 39 * q^4 - 42 * q^6 - 15 * q^7 + 31 * q^9	\( 288 q - 9 q^{2} - q^{3} - 39 q^{4} - 42 q^{6} - 15 q^{7} + 31 q^{9} + 3 q^{10} - 18 q^{11} - 46 q^{12} - q^{13} - 32 q^{14} + 18 q^{15} + 21 q^{16} - 15 q^{17} - 15 q^{19} + 51 q^{20} - 10 q^{22} - 4 q^{23} - 51 q^{24} - 296 q^{25} - 6 q^{26} - 52 q^{27} + 21 q^{28} + q^{29} + 60 q^{30} + 138 q^{32} + 69 q^{33} - 10 q^{35} + 128 q^{36} - 18 q^{37} + 32 q^{38} - 14 q^{39} + 60 q^{40} - 15 q^{41} - 49 q^{42} - 36 q^{43} + 6 q^{45} - 69 q^{46} + 21 q^{48} - 23 q^{49} + 117 q^{50} + 8 q^{51} + 26 q^{52} - 48 q^{53} + 75 q^{54} + 46 q^{55} - 98 q^{56} - 21 q^{58} - 105 q^{59} - 74 q^{61} - 3 q^{62} - 90 q^{63} + 90 q^{64} + 89 q^{65} - 8 q^{66} + 6 q^{67} - 182 q^{68} + 29 q^{69} + 3 q^{71} - 183 q^{72} - 53 q^{74} - 38 q^{75} + 144 q^{76} - 128 q^{78} - 72 q^{79} - 72 q^{80} + 11 q^{81} - 11 q^{82} - 33 q^{84} + 72 q^{85} - 18 q^{87} - 14 q^{88} + 81 q^{89} - 34 q^{90} - 48 q^{91} + 8 q^{92} + 72 q^{93} - 6 q^{94} + 141 q^{97} + 96 q^{98}+O(q^{100}) \) 288 * q - 9 * q^2 - q^3 - 39 * q^4 - 42 * q^6 - 15 * q^7 + 31 * q^9 + 3 * q^10 - 18 * q^11 - 46 * q^12 - q^13 - 32 * q^14 + 18 * q^15 + 21 * q^16 - 15 * q^17 - 15 * q^19 + 51 * q^20 - 10 * q^22 - 4 * q^23 - 51 * q^24 - 296 * q^25 - 6 * q^26 - 52 * q^27 + 21 * q^28 + q^29 + 60 * q^30 + 138 * q^32 + 69 * q^33 - 10 * q^35 + 128 * q^36 - 18 * q^37 + 32 * q^38 - 14 * q^39 + 60 * q^40 - 15 * q^41 - 49 * q^42 - 36 * q^43 + 6 * q^45 - 69 * q^46 + 21 * q^48 - 23 * q^49 + 117 * q^50 + 8 * q^51 + 26 * q^52 - 48 * q^53 + 75 * q^54 + 46 * q^55 - 98 * q^56 - 21 * q^58 - 105 * q^59 - 74 * q^61 - 3 * q^62 - 90 * q^63 + 90 * q^64 + 89 * q^65 - 8 * q^66 + 6 * q^67 - 182 * q^68 + 29 * q^69 + 3 * q^71 - 183 * q^72 - 53 * q^74 - 38 * q^75 + 144 * q^76 - 128 * q^78 - 72 * q^79 - 72 * q^80 + 11 * q^81 - 11 * q^82 - 33 * q^84 + 72 * q^85 - 18 * q^87 - 14 * q^88 + 81 * q^89 - 34 * q^90 - 48 * q^91 + 8 * q^92 + 72 * q^93 - 6 * q^94 + 141 * q^97 + 96 * q^98

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