LMFDB - Embedded newform 207.2.i.d.154.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [207,2,Mod(55,207)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(207, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("207.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 207 = 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	207.i (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.65290332184$
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} - 7 x^{19} + 24 x^{18} - 70 x^{17} + 209 x^{16} - 527 x^{15} + 1115 x^{14} - 2187 x^{13} + \cdots + 529 $ x^20 - 7x^19 + 24x^18 - 70x^17 + 209x^16 - 527x^15 + 1115x^14 - 2187x^13 + 4165x^12 - 7040x^11 + 10649x^10 - 13519x^9 + 15111x^8 - 12101x^7 + 8244x^6 - 2837x^5 + 1859x^4 - 1730x^3 + 1957x^2 - 1656*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 69)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			154.2
Root			$-0.591994 - 0.380451i$ of defining polynomial
Character	$\chi$	$=$	207.154
Dual form			207.2.i.d.82.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37624 - 1.58827i) q^{2} +(-0.343924 - 2.39205i) q^{4} +(-1.43308 - 3.13801i) q^{5} +(-1.51768 + 0.445631i) q^{7} +(-0.736612 - 0.473392i) q^{8} +O(q^{10})$	\(q+(1.37624 - 1.58827i) q^{2} +(-0.343924 - 2.39205i) q^{4} +(-1.43308 - 3.13801i) q^{5} +(-1.51768 + 0.445631i) q^{7} +(-0.736612 - 0.473392i) q^{8} +(-6.95628 - 2.04255i) q^{10} +(0.903570 + 1.04278i) q^{11} +(4.36913 + 1.28289i) q^{13} +(-1.38092 + 3.02378i) q^{14} +(2.87188 - 0.843259i) q^{16} +(-0.575735 + 4.00433i) q^{17} +(-0.869183 - 6.04530i) q^{19} +(-7.01340 + 4.50724i) q^{20} +2.89974 q^{22} +(3.84094 - 2.87179i) q^{23} +(-4.51910 + 5.21532i) q^{25} +(8.05057 - 5.17378i) q^{26} +(1.58794 + 3.47710i) q^{28} +(-1.43619 + 9.98890i) q^{29} +(0.956733 + 0.614855i) q^{31} +(3.34056 - 7.31481i) q^{32} +(5.56760 + 6.42535i) q^{34} +(3.57336 + 4.12388i) q^{35} +(-3.43311 + 7.51746i) q^{37} +(-10.7978 - 6.93931i) q^{38} +(-0.429884 + 2.98991i) q^{40} +(-2.03647 - 4.45925i) q^{41} +(-2.41809 + 1.55401i) q^{43} +(2.18361 - 2.52002i) q^{44} +(0.724889 - 10.0527i) q^{46} -4.66656 q^{47} +(-3.78401 + 2.43183i) q^{49} +(2.06395 + 14.3551i) q^{50} +(1.56609 - 10.8924i) q^{52} +(6.27174 - 1.84155i) q^{53} +(1.97735 - 4.32980i) q^{55} +(1.32890 + 0.390200i) q^{56} +(13.8885 + 16.0282i) q^{58} +(0.908902 + 0.266878i) q^{59} +(0.641360 + 0.412177i) q^{61} +(2.29325 - 0.673360i) q^{62} +(-4.53369 - 9.92740i) q^{64} +(-2.23559 - 15.5489i) q^{65} +(1.82896 - 2.11073i) q^{67} +9.77655 q^{68} +11.4676 q^{70} +(-3.71613 + 4.28865i) q^{71} +(-0.129513 - 0.900780i) q^{73} +(7.21496 + 15.7986i) q^{74} +(-14.1617 + 4.15825i) q^{76} +(-1.83602 - 1.17994i) q^{77} +(-9.35234 - 2.74609i) q^{79} +(-6.76179 - 7.80352i) q^{80} +(-9.88516 - 2.90255i) q^{82} +(2.01659 - 4.41571i) q^{83} +(13.3907 - 3.93187i) q^{85} +(-0.859691 + 5.97928i) q^{86} +(-0.171939 - 1.19586i) q^{88} +(3.08440 - 1.98222i) q^{89} -7.20264 q^{91} +(-8.19045 - 8.20003i) q^{92} +(-6.42232 + 7.41176i) q^{94} +(-17.7246 + 11.3909i) q^{95} +(-0.708736 - 1.55192i) q^{97} +(-1.34531 + 9.35682i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} - 10 q^{8}+O(q^{10}) $ 20 * q + 4 * q^2 - 6 * q^4 + 6 * q^5 - 6 * q^7 - 10 * q^8	$ 20 q + 4 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} - 10 q^{8} - 18 q^{10} + 16 q^{11} + 14 q^{13} + 22 q^{14} - 8 q^{16} - 11 q^{17} - 11 q^{19} - 57 q^{20} + 26 q^{22} - 4 q^{25} + 14 q^{26} - 14 q^{28} - 12 q^{29} + 41 q^{31} + 46 q^{32} - 3 q^{34} + 26 q^{35} - 18 q^{37} - 70 q^{38} - 13 q^{40} - 10 q^{43} + 3 q^{44} - 24 q^{46} - 18 q^{47} - 10 q^{49} - 33 q^{50} + 61 q^{52} + 20 q^{53} - 17 q^{55} - 6 q^{56} - 37 q^{58} - 40 q^{59} - 12 q^{61} + 89 q^{62} - 2 q^{64} + 51 q^{65} - 47 q^{67} + 12 q^{68} + 32 q^{70} + 47 q^{71} + 39 q^{73} + 50 q^{74} - 39 q^{76} - 22 q^{77} - 2 q^{79} - 12 q^{80} + 26 q^{82} + 52 q^{83} + 35 q^{85} - 34 q^{86} + 30 q^{88} - 36 q^{89} + 8 q^{91} + 19 q^{92} + 21 q^{94} - 89 q^{95} - 85 q^{98}+O(q^{100}) $ 20 * q + 4 * q^2 - 6 * q^4 + 6 * q^5 - 6 * q^7 - 10 * q^8 - 18 * q^10 + 16 * q^11 + 14 * q^13 + 22 * q^14 - 8 * q^16 - 11 * q^17 - 11 * q^19 - 57 * q^20 + 26 * q^22 - 4 * q^25 + 14 * q^26 - 14 * q^28 - 12 * q^29 + 41 * q^31 + 46 * q^32 - 3 * q^34 + 26 * q^35 - 18 * q^37 - 70 * q^38 - 13 * q^40 - 10 * q^43 + 3 * q^44 - 24 * q^46 - 18 * q^47 - 10 * q^49 - 33 * q^50 + 61 * q^52 + 20 * q^53 - 17 * q^55 - 6 * q^56 - 37 * q^58 - 40 * q^59 - 12 * q^61 + 89 * q^62 - 2 * q^64 + 51 * q^65 - 47 * q^67 + 12 * q^68 + 32 * q^70 + 47 * q^71 + 39 * q^73 + 50 * q^74 - 39 * q^76 - 22 * q^77 - 2 * q^79 - 12 * q^80 + 26 * q^82 + 52 * q^83 + 35 * q^85 - 34 * q^86 + 30 * q^88 - 36 * q^89 + 8 * q^91 + 19 * q^92 + 21 * q^94 - 89 * q^95 - 85 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{4}{11}\right)$	$1$

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 $

$2$	1.37624	−	1.58827i	0.973151	−	1.12308i	−0.0192234	−	0.999815i	$-0.506119\pi$
$2$	1.37624	−	1.58827i	0.973151	−	1.12308i	0.992374	−	0.123261i	$-0.0393352\pi$
$3$		0			0
$3$		0			0
$4$	−0.343924	−	2.39205i	−0.171962	−	1.19602i
$5$	−1.43308	−	3.13801i	−0.640894	−	1.40336i	−0.899303	−	0.437326i	$-0.855925\pi$
$5$	−1.43308	−	3.13801i	−0.640894	−	1.40336i	0.258409	−	0.966036i	$-0.416802\pi$
$6$		0			0
$7$	−1.51768	+	0.445631i	−0.573629	+	0.168433i	−0.555666	−	0.831406i	$-0.687537\pi$
$7$	−1.51768	+	0.445631i	−0.573629	+	0.168433i	−0.0179637	+	0.999839i	$0.505718\pi$
$8$	−0.736612	−	0.473392i	−0.260432	−	0.167369i
$9$		0			0
$10$	−6.95628	−	2.04255i	−2.19977	−	0.645910i
$11$	0.903570	+	1.04278i	0.272437	+	0.314409i	0.875437	−	0.483332i	$-0.160574\pi$
$11$	0.903570	+	1.04278i	0.272437	+	0.314409i	−0.603000	+	0.797741i	$0.706028\pi$
$12$		0			0
$13$	4.36913	+	1.28289i	1.21178	+	0.355810i	0.824345	−	0.566087i	$-0.191543\pi$
$13$	4.36913	+	1.28289i	1.21178	+	0.355810i	0.387434	+	0.921898i	$0.373362\pi$
$14$	−1.38092	+	3.02378i	−0.369065	+	0.808140i
$15$		0			0
$16$	2.87188	−	0.843259i	0.717969	−	0.210815i
$17$	−0.575735	+	4.00433i	−0.139636	+	0.971192i	0.792703	+	0.609608i	$0.208673\pi$
$17$	−0.575735	+	4.00433i	−0.139636	+	0.971192i	−0.932340	+	0.361584i	$0.882236\pi$
$18$		0			0
$19$	−0.869183	−	6.04530i	−0.199404	−	1.38689i	−0.806018	−	0.591891i	$-0.798382\pi$
$19$	−0.869183	−	6.04530i	−0.199404	−	1.38689i	0.606614	−	0.794996i	$-0.292527\pi$
$20$	−7.01340	+	4.50724i	−1.56824	+	1.00785i
$21$		0			0
$22$	2.89974			0.618227
$23$	3.84094	−	2.87179i	0.800891	−	0.598810i
$23$	3.84094	−	2.87179i	0.800891	−	0.598810i
$24$		0			0
$25$	−4.51910	+	5.21532i	−0.903819	+	1.04306i
$26$	8.05057	−	5.17378i	1.57885	−	1.01466i
$27$		0			0
$28$	1.58794	+	3.47710i	0.300092	+	0.657110i
$29$	−1.43619	+	9.98890i	−0.266693	+	1.85489i	0.212471	+	0.977167i	$0.431849\pi$
$29$	−1.43619	+	9.98890i	−0.266693	+	1.85489i	−0.479164	+	0.877725i	$0.659060\pi$
$30$		0			0
$31$	0.956733	+	0.614855i	0.171834	+	0.110431i	0.623731	−	0.781639i	$-0.285616\pi$
$31$	0.956733	+	0.614855i	0.171834	+	0.110431i	−0.451897	+	0.892070i	$0.649252\pi$
$32$	3.34056	−	7.31481i	0.590534	−	1.29309i
$33$		0			0
$34$	5.56760	+	6.42535i	0.954835	+	1.10194i
$35$	3.57336	+	4.12388i	0.604008	+	0.697062i
$36$		0			0
$37$	−3.43311	+	7.51746i	−0.564400	+	1.23586i	0.385326	+	0.922780i	$0.374089\pi$
$37$	−3.43311	+	7.51746i	−0.564400	+	1.23586i	−0.949726	+	0.313082i	$0.898638\pi$
$38$	−10.7978	−	6.93931i	−1.75163	−	1.12570i
$39$		0			0
$40$	−0.429884	+	2.98991i	−0.0679706	+	0.472746i
$41$	−2.03647	−	4.45925i	−0.318043	−	0.696417i	0.681324	−	0.731982i	$-0.261404\pi$
$41$	−2.03647	−	4.45925i	−0.318043	−	0.696417i	−0.999367	+	0.0355645i	$0.988677\pi$
$42$		0			0
$43$	−2.41809	+	1.55401i	−0.368755	+	0.236985i	−0.711874	−	0.702307i	$-0.752153\pi$
$43$	−2.41809	+	1.55401i	−0.368755	+	0.236985i	0.343118	+	0.939292i	$0.388517\pi$
$44$	2.18361	−	2.52002i	0.329191	−	0.379907i
$45$		0			0
$46$	0.724889	−	10.0527i	0.106879	−	1.48219i
$47$	−4.66656			−0.680688			−0.340344	−	0.940301i	$-0.610544\pi$
$47$	−4.66656			−0.680688			−0.340344	+	0.940301i	$0.610544\pi$
$48$		0			0
$49$	−3.78401	+	2.43183i	−0.540573	+	0.347405i
$50$	2.06395	+	14.3551i	0.291887	+	2.03012i
$51$		0			0
$52$	1.56609	−	10.8924i	0.217177	−	1.51050i
$53$	6.27174	−	1.84155i	0.861490	−	0.252956i	0.178998	−	0.983849i	$-0.442714\pi$
$53$	6.27174	−	1.84155i	0.861490	−	0.252956i	0.682492	+	0.730893i	$0.260896\pi$
$54$		0			0
$55$	1.97735	−	4.32980i	0.266626	−	0.583830i
$56$	1.32890	+	0.390200i	0.177582	+	0.0521427i
$57$		0			0
$58$	13.8885	+	16.0282i	1.82365	+	2.10461i
$59$	0.908902	+	0.266878i	0.118329	+	0.0347445i	0.340361	−	0.940295i	$-0.389451\pi$
$59$	0.908902	+	0.266878i	0.118329	+	0.0347445i	−0.222032	+	0.975039i	$0.571269\pi$
$60$		0			0
$61$	0.641360	+	0.412177i	0.0821177	+	0.0527739i	0.581055	−	0.813864i	$-0.302640\pi$
$61$	0.641360	+	0.412177i	0.0821177	+	0.0527739i	−0.498938	+	0.866638i	$0.666276\pi$
$62$	2.29325	−	0.673360i	0.291243	−	0.0855168i
$63$		0			0
$64$	−4.53369	−	9.92740i	−0.566712	−	1.24093i
$65$	−2.23559	−	15.5489i	−0.277291	−	1.92860i
$66$		0			0
$67$	1.82896	−	2.11073i	0.223443	−	0.257867i	−0.632949	−	0.774194i	$-0.718156\pi$
$67$	1.82896	−	2.11073i	0.223443	−	0.257867i	0.856392	+	0.516327i	$0.172701\pi$
$68$	9.77655			1.18558
$69$		0			0
$70$	11.4676			1.37064
$71$	−3.71613	+	4.28865i	−0.441024	+	0.508969i	−0.932126	−	0.362133i	$-0.882049\pi$
$71$	−3.71613	+	4.28865i	−0.441024	+	0.508969i	0.491103	+	0.871102i	$0.336594\pi$
$72$		0			0
$73$	−0.129513	−	0.900780i	−0.0151583	−	0.105428i	0.980838	−	0.194827i	$-0.0624145\pi$
$73$	−0.129513	−	0.900780i	−0.0151583	−	0.105428i	−0.995996	+	0.0893987i	$0.971505\pi$
$74$	7.21496	+	15.7986i	0.838722	+	1.83654i
$75$		0			0
$76$	−14.1617	+	4.15825i	−1.62446	+	0.476984i
$77$	−1.83602	−	1.17994i	−0.209234	−	0.134467i
$78$		0			0
$79$	−9.35234	−	2.74609i	−1.05222	−	0.308960i	−0.290506	−	0.956873i	$-0.593824\pi$
$79$	−9.35234	−	2.74609i	−1.05222	−	0.308960i	−0.761714	+	0.647913i	$0.775642\pi$
$80$	−6.76179	−	7.80352i	−0.755991	−	0.872460i
$81$		0			0
$82$	−9.88516	−	2.90255i	−1.09163	−	0.320532i
$83$	2.01659	−	4.41571i	0.221349	−	0.484687i	−0.766081	−	0.642744i	$-0.777796\pi$
$83$	2.01659	−	4.41571i	0.221349	−	0.484687i	0.987430	+	0.158057i	$0.0505231\pi$
$84$		0			0
$85$	13.3907	−	3.93187i	1.45243	−	0.426471i
$86$	−0.859691	+	5.97928i	−0.0927028	+	0.644762i
$87$		0			0
$88$	−0.171939	−	1.19586i	−0.0183288	−	0.127479i
$89$	3.08440	−	1.98222i	0.326946	−	0.210115i	−0.366862	−	0.930275i	$-0.619568\pi$
$89$	3.08440	−	1.98222i	0.326946	−	0.210115i	0.693808	+	0.720160i	$0.255932\pi$
$90$		0			0
$91$	−7.20264			−0.755042
$92$	−8.19045	−	8.20003i	−0.853914	−	0.854912i
$93$		0			0
$94$	−6.42232	+	7.41176i	−0.662412	+	0.764464i
$95$	−17.7246	+	11.3909i	−1.81851	+	1.16868i
$96$		0			0
$97$	−0.708736	−	1.55192i	−0.0719613	−	0.157573i	0.870233	−	0.492640i	$-0.163968\pi$
$97$	−0.708736	−	1.55192i	−0.0719613	−	0.157573i	−0.942194	+	0.335067i	$0.891241\pi$
$98$	−1.34531	+	9.35682i	−0.135897	+	0.945181i
$99$		0			0
$100$	14.0295	+	9.01622i	1.40295	+	0.901622i
$101$	−2.86027	+	6.26312i	−0.284608	+	0.623204i	−0.996900	−	0.0786790i	$-0.974930\pi$
$101$	−2.86027	+	6.26312i	−0.284608	+	0.623204i	0.712292	+	0.701883i	$0.247657\pi$
$102$		0			0
$103$	−0.188331	−	0.217346i	−0.0185569	−	0.0214158i	0.746395	−	0.665503i	$-0.231783\pi$
$103$	−0.188331	−	0.217346i	−0.0185569	−	0.0214158i	−0.764952	+	0.644087i	$0.777237\pi$
$104$	−2.61104	−	3.01331i	−0.256034	−	0.295479i
$105$		0			0
$106$	5.70656	−	12.4956i	0.554271	−	1.21368i
$107$	−6.97450	−	4.48224i	−0.674250	−	0.433314i	0.158205	−	0.987406i	$-0.449429\pi$
$107$	−6.97450	−	4.48224i	−0.674250	−	0.433314i	−0.832455	+	0.554092i	$0.813066\pi$
$108$		0			0
$109$	−2.92433	+	20.3392i	−0.280100	+	1.94814i	0.0358379	+	0.999358i	$0.488590\pi$
$109$	−2.92433	+	20.3392i	−0.280100	+	1.94814i	−0.315938	+	0.948780i	$0.602319\pi$
$110$	−4.15557	−	9.09942i	−0.396218	−	0.867596i
$111$		0			0
$112$	−3.98281	+	2.55959i	−0.376340	+	0.241859i
$113$	−1.06272	+	1.22644i	−0.0999719	+	0.115374i	−0.803531	−	0.595263i	$-0.797048\pi$
$113$	−1.06272	+	1.22644i	−0.0999719	+	0.115374i	0.703559	+	0.710637i	$0.251593\pi$
$114$		0			0
$115$	−14.5161	−	7.93740i	−1.35363	−	0.740167i
$116$	24.3879			2.26436
$117$		0			0
$118$	1.67474	−	1.07629i	0.154173	−	0.0990807i
$119$	−0.910671	−	6.33385i	−0.0834810	−	0.580623i
$120$		0			0
$121$	1.29452	−	9.00360i	0.117684	−	0.818509i
$122$	1.53732	−	0.451397i	0.139182	−	0.0408675i
$123$		0			0
$124$	1.14172	−	2.50001i	0.102529	−	0.224508i
$125$	6.29186	+	1.84746i	0.562761	+	0.165242i
$126$		0			0
$127$	−6.34610	−	7.32379i	−0.563126	−	0.649882i	0.400765	−	0.916181i	$-0.368744\pi$
$127$	−6.34610	−	7.32379i	−0.563126	−	0.649882i	−0.963890	+	0.266299i	$0.914199\pi$
$128$	−6.57531	−	1.93069i	−0.581181	−	0.170650i
$129$		0			0
$130$	−27.7725	−	17.8483i	−2.43581	−	1.56540i
$131$	10.9926	−	3.22771i	0.960425	−	0.282006i	0.236304	−	0.971679i	$-0.424064\pi$
$131$	10.9926	−	3.22771i	0.960425	−	0.282006i	0.724121	+	0.689673i	$0.242246\pi$
$132$		0			0
$133$	4.01312	+	8.78750i	0.347981	+	0.761973i
$134$	−0.835317	−	5.80976i	−0.0721604	−	0.501886i
$135$		0			0
$136$	2.31971	−	2.67709i	0.198913	−	0.229558i
$137$	−1.64372			−0.140433			−0.0702163	−	0.997532i	$-0.522369\pi$
$137$	−1.64372			−0.140433			−0.0702163	+	0.997532i	$0.522369\pi$
$138$		0			0
$139$	−5.57603			−0.472952			−0.236476	−	0.971637i	$-0.575993\pi$
$139$	−5.57603			−0.472952			−0.236476	+	0.971637i	$0.575993\pi$
$140$	8.63554	−	9.96594i	0.729836	−	0.842276i
$141$		0			0
$142$	1.69722	+	11.8044i	0.142428	+	0.990607i
$143$	2.61005	+	5.71520i	0.218263	+	0.477929i
$144$		0			0
$145$	33.4035	−	9.80815i	2.77401	−	0.814522i
$146$	−1.60892	−	1.03399i	−0.133155	−	0.0855737i
$147$		0			0
$148$	19.1628	+	5.62672i	1.57518	+	0.462513i
$149$	3.98279	+	4.59639i	0.326283	+	0.376551i	0.895063	−	0.445939i	$-0.147130\pi$
$149$	3.98279	+	4.59639i	0.326283	+	0.376551i	−0.568781	+	0.822489i	$0.692585\pi$
$150$		0			0
$151$	22.7086	+	6.66784i	1.84800	+	0.542621i	0.999919	+	0.0127498i	$0.00405850\pi$
$151$	22.7086	+	6.66784i	1.84800	+	0.542621i	0.848078	+	0.529871i	$0.177760\pi$
$152$	−2.22155	+	4.86451i	−0.180191	+	0.394564i
$153$		0			0
$154$	−4.40088	+	1.29221i	−0.354633	+	0.104130i
$155$	0.558345	−	3.88338i	0.0448474	−	0.311920i
$156$		0			0
$157$	−2.21713	−	15.4205i	−0.176946	−	1.23069i	−0.863778	−	0.503872i	$-0.831908\pi$
$157$	−2.21713	−	15.4205i	−0.176946	−	1.23069i	0.686832	−	0.726816i	$-0.259001\pi$
$158$	−17.2326	+	11.0747i	−1.37095	+	0.881059i
$159$		0			0
$160$	−27.7413			−2.19314
$161$	−4.54956	+	6.07010i	−0.358555	+	0.478391i
$162$		0			0
$163$	4.03515	−	4.65682i	0.316058	−	0.364750i	−0.575386	−	0.817882i	$-0.695148\pi$
$163$	4.03515	−	4.65682i	0.316058	−	0.364750i	0.891443	+	0.453132i	$0.149693\pi$
$164$	−9.96633	+	6.40497i	−0.778240	+	0.500144i
$165$		0			0
$166$	−4.23802	−	9.27997i	−0.328934	−	0.720265i
$167$	1.34398	−	9.34759i	0.104000	−	0.723338i	−0.869380	−	0.494144i	$-0.835482\pi$
$167$	1.34398	−	9.34759i	0.104000	−	0.723338i	0.973381	−	0.229195i	$-0.0736093\pi$
$168$		0			0
$169$	6.50719	+	4.18192i	0.500553	+	0.321686i
$170$	12.1840	−	26.6792i	0.934470	−	2.04620i
$171$		0			0
$172$	4.54891	+	5.24972i	0.346851	+	0.400288i
$173$	4.64554	+	5.36123i	0.353194	+	0.407607i	0.904348	−	0.426796i	$-0.140358\pi$
$173$	4.64554	+	5.36123i	0.353194	+	0.407607i	−0.551154	+	0.834403i	$0.685812\pi$
$174$		0			0
$175$	4.53444	−	9.92903i	0.342771	−	0.750564i
$176$	3.47427	+	2.23278i	0.261883	+	0.168302i
$177$		0			0
$178$	1.09658	−	7.62688i	0.0821921	−	0.571659i
$179$	−3.33449	−	7.30152i	−0.249232	−	0.545741i	0.743124	−	0.669154i	$-0.233343\pi$
$179$	−3.33449	−	7.30152i	−0.249232	−	0.545741i	−0.992355	+	0.123413i	$0.960616\pi$
$180$		0			0
$181$	−9.91759	+	6.37365i	−0.737169	+	0.473750i	−0.854571	−	0.519335i	$-0.826180\pi$
$181$	−9.91759	+	6.37365i	−0.737169	+	0.473750i	0.117402	+	0.993084i	$0.462543\pi$
$182$	−9.91259	+	11.4397i	−0.734770	+	0.847970i
$183$		0			0
$184$	−4.18877	+	0.297127i	−0.308800	+	0.0219045i
$185$	28.5098			2.09608
$186$		0			0
$187$	−4.69583	+	3.01783i	−0.343393	+	0.220685i
$188$	1.60494	+	11.1626i	0.117053	+	0.814119i
$189$		0			0
$190$	−6.30154	+	43.8282i	−0.457162	+	3.17963i
$191$	−25.3783	+	7.45175i	−1.83631	+	0.539190i	−0.999959	−	0.00900195i	$-0.997135\pi$
$191$	−25.3783	+	7.45175i	−1.83631	+	0.539190i	−0.836353	+	0.548192i	$0.815316\pi$
$192$		0			0
$193$	7.83014	−	17.1456i	0.563626	−	1.23417i	−0.386497	−	0.922291i	$-0.626315\pi$
$193$	7.83014	−	17.1456i	0.563626	−	1.23417i	0.950122	−	0.311877i	$-0.100958\pi$
$194$	−3.44025	−	1.01015i	−0.246996	−	0.0725245i
$195$		0			0
$196$	7.11847	+	8.21516i	0.508462	+	0.586797i
$197$	8.46097	+	2.48436i	0.602819	+	0.177004i	0.568880	−	0.822420i	$-0.307377\pi$
$197$	8.46097	+	2.48436i	0.602819	+	0.177004i	0.0339386	+	0.999424i	$0.489195\pi$
$198$		0			0
$199$	12.6239	+	8.11290i	0.894885	+	0.575108i	0.905269	−	0.424838i	$-0.139669\pi$
$199$	12.6239	+	8.11290i	0.894885	+	0.575108i	−0.0103839	+	0.999946i	$0.503305\pi$
$200$	5.79771	−	1.70236i	0.409960	−	0.120375i
$201$		0			0
$202$	6.01110	+	13.1625i	0.422939	+	0.926108i
$203$	−2.27169	−	15.8000i	−0.159442	−	1.10894i
$204$		0			0
$205$	−11.0747	+	12.7809i	−0.773494	+	0.892659i
$206$	−0.604394			−0.0421101
$207$		0			0
$208$	13.6294			0.945030
$209$	5.51852	−	6.36871i	0.381724	−	0.440533i
$210$		0			0
$211$	3.80345	+	26.4536i	0.261840	+	1.82114i	0.519005	+	0.854771i	$0.326303\pi$
$211$	3.80345	+	26.4536i	0.261840	+	1.82114i	−0.257164	+	0.966368i	$0.582788\pi$
$212$	−6.56208	−	14.3689i	−0.450685	−	0.986863i
$213$		0			0
$214$	−16.7176	+	4.90873i	−1.14279	+	0.335554i
$215$	8.34184	+	5.36097i	0.568908	+	0.365615i
$216$		0			0
$217$	−1.72601	−	0.506803i	−0.117169	−	0.0344040i
$218$	28.2795	+	32.6362i	1.91533	+	2.21041i
$219$		0			0
$220$	−11.0371	−	3.24080i	−0.744123	−	0.218494i
$221$	−7.65258	+	16.7568i	−0.514768	+	1.12719i
$222$		0			0
$223$	−11.7966	+	3.46380i	−0.789960	+	0.231953i	−0.651734	−	0.758447i	$-0.725958\pi$
$223$	−11.7966	+	3.46380i	−0.789960	+	0.231953i	−0.138226	+	0.990401i	$0.544140\pi$
$224$	−1.81020	+	12.5902i	−0.120949	+	0.841219i
$225$		0			0
$226$	0.485361	+	3.37576i	0.0322857	+	0.224552i
$227$	13.8661	−	8.91123i	0.920328	−	0.591459i	0.00757515	−	0.999971i	$-0.497589\pi$
$227$	13.8661	−	8.91123i	0.920328	−	0.591459i	0.912753	+	0.408512i	$0.133952\pi$
$228$		0			0
$229$	−0.636413			−0.0420554			−0.0210277	−	0.999779i	$-0.506694\pi$
$229$	−0.636413			−0.0420554			−0.0210277	+	0.999779i	$0.506694\pi$
$230$	−32.5844	+	12.1317i	−2.14855	+	0.799939i
$231$		0			0
$232$	5.78658	−	6.67807i	0.379908	−	0.438437i
$233$	−0.541416	+	0.347947i	−0.0354693	+	0.0227947i	−0.558255	−	0.829669i	$-0.688529\pi$
$233$	−0.541416	+	0.347947i	−0.0354693	+	0.0227947i	0.522786	+	0.852464i	$0.324893\pi$
$234$		0			0
$235$	6.68757	+	14.6437i	0.436249	+	0.955252i
$236$	0.325790	−	2.26592i	0.0212071	−	0.147499i
$237$		0			0
$238$	−11.3132	−	7.27053i	−0.733324	−	0.471279i
$239$	4.00001	−	8.75880i	0.258739	−	0.566560i	−0.735028	−	0.678037i	$-0.762831\pi$
$239$	4.00001	−	8.75880i	0.258739	−	0.566560i	0.993767	+	0.111477i	$0.0355582\pi$
$240$		0			0
$241$	3.90622	+	4.50802i	0.251622	+	0.290387i	0.867482	−	0.497468i	$-0.165737\pi$
$241$	3.90622	+	4.50802i	0.251622	+	0.290387i	−0.615860	+	0.787855i	$0.711191\pi$
$242$	−12.5186	−	14.4472i	−0.804723	−	0.928700i
$243$		0			0
$244$	0.765367	−	1.67592i	0.0489976	−	0.107290i
$245$	13.0539	+	8.38925i	0.833984	+	0.535969i
$246$		0			0
$247$	3.95790	−	27.5278i	0.251835	−	1.75155i
$248$	−0.413674	−	0.905819i	−0.0262683	−	0.0575196i
$249$		0			0
$250$	11.5934	−	7.45062i	0.733230	−	0.471218i
$251$	−2.52430	+	2.91320i	−0.159332	+	0.183879i	−0.829803	−	0.558057i	$-0.811547\pi$
$251$	−2.52430	+	2.91320i	−0.159332	+	0.183879i	0.670470	+	0.741936i	$0.266092\pi$
$252$		0			0
$253$	6.46519	+	1.41037i	0.406463	+	0.0886693i
$254$	−20.3659			−1.27787
$255$		0			0
$256$	6.24661	−	4.01445i	0.390413	−	0.250903i
$257$	−1.68086	−	11.6906i	−0.104849	−	0.729242i	−0.972641	−	0.232314i	$-0.925370\pi$
$257$	−1.68086	−	11.6906i	−0.104849	−	0.729242i	0.867792	−	0.496928i	$-0.165539\pi$
$258$		0			0
$259$	1.86035	−	12.9390i	0.115596	−	0.803990i
$260$	−36.4248	+	10.6953i	−2.25897	+	0.663293i
$261$		0			0
$262$	10.0020	−	21.9013i	0.617924	−	1.35307i
$263$	14.0599	+	4.12835i	0.866968	+	0.254565i	0.684825	−	0.728707i	$-0.259879\pi$
$263$	14.0599	+	4.12835i	0.866968	+	0.254565i	0.182143	+	0.983272i	$0.441697\pi$
$264$		0			0
$265$	−14.7667	−	17.0417i	−0.907113	−	1.04686i
$266$	19.4799	+	5.71983i	1.19439	+	0.350705i
$267$		0			0
$268$	−5.67799	−	3.64902i	−0.346838	−	0.222899i
$269$	−26.1145	+	7.66790i	−1.59223	+	0.467520i	−0.953370	−	0.301804i	$-0.902411\pi$
$269$	−26.1145	+	7.66790i	−1.59223	+	0.467520i	−0.638858	+	0.769324i	$0.720593\pi$
$270$		0			0
$271$	−1.77962	−	3.89682i	−0.108104	−	0.236715i	0.847847	−	0.530241i	$-0.177899\pi$
$271$	−1.77962	−	3.89682i	−0.108104	−	0.236715i	−0.955951	+	0.293526i	$0.905171\pi$
$272$	1.72324	+	11.9854i	0.104487	+	0.726723i
$273$		0			0
$274$	−2.26216	+	2.61067i	−0.136662	+	0.157717i
$275$	−9.52172			−0.574181
$276$		0			0
$277$	6.86176			0.412283			0.206142	−	0.978522i	$-0.433909\pi$
$277$	6.86176			0.412283			0.206142	+	0.978522i	$0.433909\pi$
$278$	−7.67397	+	8.85623i	−0.460254	+	0.531161i
$279$		0			0
$280$	−0.679970	−	4.72930i	−0.0406360	−	0.282629i
$281$	5.52742	+	12.1034i	0.329738	+	0.722025i	0.999794	−	0.0202849i	$-0.00645733\pi$
$281$	5.52742	+	12.1034i	0.329738	+	0.722025i	−0.670056	+	0.742310i	$0.733730\pi$
$282$		0			0
$283$	−18.4431	+	5.41539i	−1.09633	+	0.321912i	−0.779393	−	0.626535i	$-0.784473\pi$
$283$	−18.4431	+	5.41539i	−1.09633	+	0.321912i	−0.316937	+	0.948447i	$0.602654\pi$
$284$	11.5367	+	7.41419i	0.684578	+	0.439951i
$285$		0			0
$286$	12.6693	+	3.72005i	0.749154	+	0.219971i
$287$	5.07789	+	5.86020i	0.299738	+	0.345916i
$288$		0			0
$289$	0.608222	+	0.178590i	0.0357778	+	0.0105053i
$290$	30.3933	−	66.5521i	1.78476	−	3.90807i
$291$		0			0
$292$	−2.11016	+	0.619600i	−0.123488	+	0.0362594i
$293$	1.94185	−	13.5058i	0.113444	−	0.789019i	−0.851082	−	0.525032i	$-0.824053\pi$
$293$	1.94185	−	13.5058i	0.113444	−	0.789019i	0.964526	−	0.263987i	$-0.0850376\pi$
$294$		0			0
$295$	−0.465066	−	3.23460i	−0.0270772	−	0.188326i
$296$	6.08757	−	3.91225i	0.353833	−	0.227395i
$297$		0			0
$298$	12.7816			0.740417
$299$	20.4658	−	7.61972i	1.18357	−	0.440660i
$300$		0			0
$301$	2.97737	−	3.43607i	0.171613	−	0.198052i
$302$	41.8428	−	26.8908i	2.40778	−	1.54739i
$303$		0			0
$304$	−7.59394	−	16.6284i	−0.435542	−	0.953704i
$305$	0.374295	−	2.60328i	0.0214321	−	0.149063i
$306$		0			0
$307$	−21.3942	−	13.7492i	−1.22103	−	0.784709i	−0.238561	−	0.971128i	$-0.576676\pi$
$307$	−21.3942	−	13.7492i	−1.22103	−	0.784709i	−0.982470	+	0.186418i	$0.940312\pi$
$308$	−2.19102	+	4.79766i	−0.124845	+	0.273372i
$309$		0			0
$310$	−5.39943	−	6.23128i	−0.306667	−	0.353913i
$311$	−20.6138	−	23.7896i	−1.16890	−	1.34898i	−0.925358	−	0.379095i	$-0.876236\pi$
$311$	−20.6138	−	23.7896i	−1.16890	−	1.34898i	−0.243544	−	0.969890i	$-0.578310\pi$
$312$		0			0
$313$	5.59541	−	12.2522i	0.316271	−	0.692537i	−0.683011	−	0.730408i	$-0.739330\pi$
$313$	5.59541	−	12.2522i	0.316271	−	0.692537i	0.999283	+	0.0378702i	$0.0120574\pi$
$314$	−27.5432	−	17.7009i	−1.55435	−	0.998921i
$315$		0			0
$316$	−3.35229	+	23.3157i	−0.188581	+	1.31161i
$317$	1.59881	+	3.50090i	0.0897980	+	0.196630i	0.949202	−	0.314666i	$-0.101893\pi$
$317$	1.59881	+	3.50090i	0.0897980	+	0.196630i	−0.859404	+	0.511297i	$0.829165\pi$
$318$		0			0
$319$	−11.7139	+	7.52805i	−0.655851	+	0.421490i
$320$	−24.6552	+	28.4536i	−1.37827	+	1.59060i
$321$		0			0
$322$	3.37966	+	15.5799i	0.188341	+	0.868232i
$323$	24.7078			1.37478
$324$		0			0
$325$	−26.4352	+	16.9889i	−1.46636	+	0.942374i
$326$	−1.84292	−	12.8178i	−0.102070	−	0.709914i
$327$		0			0
$328$	−0.610883	+	4.24878i	−0.0337304	+	0.234600i
$329$	7.08235	−	2.07957i	0.390463	−	0.114650i
$330$		0			0
$331$	−8.39492	+	18.3823i	−0.461427	+	1.01038i	0.525733	+	0.850649i	$0.323791\pi$
$331$	−8.39492	+	18.3823i	−0.461427	+	1.01038i	−0.987160	+	0.159734i	$0.948936\pi$
$332$	−11.2561	−	3.30510i	−0.617760	−	0.181391i
$333$		0			0
$334$	−12.9969	−	14.9992i	−0.711156	−	0.820718i
$335$	−9.24455	−	2.71444i	−0.505084	−	0.148306i
$336$		0			0
$337$	9.26412	+	5.95369i	0.504649	+	0.324318i	0.768073	−	0.640362i	$-0.221216\pi$
$337$	9.26412	+	5.95369i	0.504649	+	0.324318i	−0.263425	+	0.964680i	$0.584852\pi$
$338$	15.5975	−	4.57984i	0.848392	−	0.249110i
$339$		0			0
$340$	−14.0106	−	30.6789i	−0.759831	−	1.66380i
$341$	0.223320	+	1.55322i	0.0120934	+	0.0841117i
$342$		0			0
$343$	11.9100	−	13.7449i	0.643080	−	0.742154i
$344$	2.51685			0.135700
$345$		0			0
$346$	14.9085			0.801484
$347$	−17.2640	+	19.9238i	−0.926782	+	1.06956i	0.0706185	+	0.997503i	$0.477503\pi$
$347$	−17.2640	+	19.9238i	−0.926782	+	1.06956i	−0.997400	+	0.0720598i	$0.977043\pi$
$348$		0			0
$349$	−2.66076	−	18.5060i	−0.142427	−	0.990602i	−0.928199	−	0.372085i	$-0.878643\pi$
$349$	−2.66076	−	18.5060i	−0.142427	−	0.990602i	0.785772	−	0.618517i	$-0.212266\pi$
$350$	−9.52949	−	20.8667i	−0.509373	−	1.11537i
$351$		0			0
$352$	10.6461	−	3.12599i	0.567441	−	0.166616i
$353$	−19.8432	−	12.7524i	−1.05615	−	0.678744i	−0.107218	−	0.994236i	$-0.534194\pi$
$353$	−19.8432	−	12.7524i	−1.05615	−	0.678744i	−0.948928	+	0.315491i	$0.897831\pi$
$354$		0			0
$355$	18.7834	+	5.51529i	0.996917	+	0.292721i
$356$	−5.80237	−	6.69630i	−0.307525	−	0.354903i
$357$		0			0
$358$	−16.1859	−	4.75259i	−0.855449	−	0.251182i
$359$	6.25424	−	13.6949i	0.330086	−	0.722788i	−0.669717	−	0.742616i	$-0.733585\pi$
$359$	6.25424	−	13.6949i	0.330086	−	0.722788i	0.999803	+	0.0198281i	$0.00631188\pi$
$360$		0			0
$361$	−17.5598	+	5.15603i	−0.924201	+	0.271370i
$362$	−3.52595	+	24.5235i	−0.185320	+	1.28893i
$363$		0			0
$364$	2.47716	+	17.2291i	0.129839	+	0.903048i
$365$	−2.64106	+	1.69730i	−0.138239	+	0.0888409i
$366$		0			0
$367$	33.1504			1.73043			0.865217	−	0.501397i	$-0.167180\pi$
$367$	33.1504			1.73043			0.865217	+	0.501397i	$0.167180\pi$
$368$	8.60904	−	11.4863i	0.448777	−	0.598766i
$369$		0			0
$370$	39.2364	−	45.2813i	2.03981	−	2.35406i
$371$	−8.69785	+	5.58977i	−0.451570	+	0.290206i
$372$		0			0
$373$	13.6829	+	29.9614i	0.708475	+	1.55134i	0.829383	+	0.558680i	$0.188692\pi$
$373$	13.6829	+	29.9614i	0.708475	+	1.55134i	−0.120908	+	0.992664i	$0.538581\pi$
$374$	−1.66948	+	11.6115i	−0.0863269	+	0.600417i
$375$		0			0
$376$	3.43745	+	2.20911i	0.177273	+	0.113926i
$377$	−19.0896	+	41.8003i	−0.983163	+	2.15283i
$378$		0			0
$379$	−14.4104	−	16.6305i	−0.740213	−	0.854252i	0.253368	−	0.967370i	$-0.418462\pi$
$379$	−14.4104	−	16.6305i	−0.740213	−	0.854252i	−0.993582	+	0.113118i	$0.963916\pi$
$380$	33.3435	+	38.4805i	1.71049	+	1.97401i
$381$		0			0
$382$	−23.0914	+	50.5631i	−1.18146	+	2.58703i
$383$	−3.93919	−	2.53156i	−0.201283	−	0.129357i	0.436116	−	0.899890i	$-0.356354\pi$
$383$	−3.93919	−	2.53156i	−0.201283	−	0.129357i	−0.637400	+	0.770533i	$0.719990\pi$
$384$		0			0
$385$	−1.07150	+	7.45242i	−0.0546085	+	0.379810i
$386$	−16.4557	−	36.0329i	−0.837572	−	1.83403i
$387$		0			0
$388$	−3.46850	+	2.22907i	−0.176087	+	0.113164i
$389$	−9.18800	+	10.6035i	−0.465850	+	0.537620i	−0.939253	−	0.343226i	$-0.888480\pi$
$389$	−9.18800	+	10.6035i	−0.465850	+	0.537620i	0.473402	+	0.880846i	$0.343026\pi$
$390$		0			0
$391$	9.28823	+	17.0338i	0.469726	+	0.861435i
$392$	3.93856			0.198927
$393$		0			0
$394$	15.5902	−	10.0192i	0.785422	−	0.504760i
$395$	4.78539	+	33.2831i	0.240779	+	1.67466i
$396$		0			0
$397$	−1.60265	+	11.1467i	−0.0804348	+	0.559437i	0.909258	+	0.416232i	$0.136650\pi$
$397$	−1.60265	+	11.1467i	−0.0804348	+	0.559437i	−0.989693	+	0.143204i	$0.954259\pi$
$398$	30.2590	−	8.88486i	1.51675	−	0.445358i
$399$		0			0
$400$	−8.58042	+	18.7885i	−0.429021	+	0.939425i
$401$	−16.4297	−	4.82419i	−0.820459	−	0.240909i	−0.155546	−	0.987829i	$-0.549714\pi$
$401$	−16.4297	−	4.82419i	−0.820459	−	0.240909i	−0.664914	+	0.746920i	$0.731532\pi$
$402$		0			0
$403$	3.39130	+	3.91377i	0.168933	+	0.194959i
$404$	15.9654	+	4.68786i	0.794308	+	0.233230i
$405$		0			0
$406$	−28.2210	−	18.1365i	−1.40059	−	0.900102i
$407$	−10.9411	+	3.21259i	−0.542329	+	0.159242i
$408$		0			0
$409$	−3.73112	−	8.17001i	−0.184492	−	0.403981i	0.794676	−	0.607034i	$-0.207641\pi$
$409$	−3.73112	−	8.17001i	−0.184492	−	0.403981i	−0.979168	+	0.203053i	$0.934914\pi$
$410$	5.05803	+	35.1793i	0.249798	+	1.73738i
$411$		0			0
$412$	−0.455130	+	0.525248i	−0.0224227	+	0.0258771i
$413$	−1.49835			−0.0737290
$414$		0			0
$415$	−16.7465			−0.822052
$416$	23.9795	−	27.6738i	1.17569	−	1.35682i
$417$		0			0
$418$	−2.52040	−	17.5298i	−0.123277	−	0.857410i
$419$	2.92531	+	6.40554i	0.142911	+	0.312931i	0.967530	−	0.252758i	$-0.0813376\pi$
$419$	2.92531	+	6.40554i	0.142911	+	0.312931i	−0.824619	+	0.565689i	$0.808610\pi$
$420$		0			0
$421$	−11.7991	+	3.46454i	−0.575055	+	0.168851i	−0.556313	−	0.830973i	$-0.687784\pi$
$421$	−11.7991	+	3.46454i	−0.575055	+	0.168851i	−0.0187420	+	0.999824i	$0.505966\pi$
$422$	47.2499	+	30.3656i	2.30009	+	1.47818i
$423$		0			0
$424$	−5.49162	−	1.61248i	−0.266696	−	0.0783091i
$425$	−18.2820	−	21.0986i	−0.886808	−	1.02343i
$426$		0			0
$427$	−1.15706	−	0.339743i	−0.0559940	−	0.0164413i
$428$	−8.32302	+	18.2249i	−0.402309	+	0.880933i
$429$		0			0
$430$	19.9951	−	5.87108i	0.964248	−	0.283129i
$431$	0.717708	−	4.99177i	0.0345708	−	0.240445i	−0.965208	−	0.261484i	$-0.915788\pi$
$431$	0.717708	−	4.99177i	0.0345708	−	0.240445i	0.999779	+	0.0210388i	$0.00669734\pi$
$432$		0			0
$433$	0.126595	+	0.880491i	0.00608379	+	0.0423137i	0.992637	−	0.121125i	$-0.0386503\pi$
$433$	0.126595	+	0.880491i	0.00608379	+	0.0423137i	−0.986553	+	0.163439i	$0.947741\pi$
$434$	−3.18035	+	2.04389i	−0.152662	+	0.0981098i
$435$		0			0
$436$	49.6580			2.37818
$437$	−20.6993	−	20.7235i	−0.990183	−	0.991340i
$438$		0			0
$439$	−26.1182	+	30.1421i	−1.24656	+	1.43860i	−0.391409	+	0.920217i	$0.628012\pi$
$439$	−26.1182	+	30.1421i	−1.24656	+	1.43860i	−0.855147	+	0.518385i	$0.826533\pi$
$440$	−3.50623	+	2.25332i	−0.167153	+	0.107423i
$441$		0			0
$442$	16.0825	+	35.2158i	0.764968	+	1.67505i
$443$	1.82310	−	12.6799i	0.0866180	−	0.602441i	−0.899566	−	0.436785i	$-0.856117\pi$
$443$	1.82310	−	12.6799i	0.0866180	−	0.602441i	0.986184	−	0.165656i	$-0.0529740\pi$
$444$		0			0
$445$	−10.6404	−	6.83820i	−0.504405	−	0.324162i
$446$	−10.7336	+	23.5032i	−0.508249	+	1.11291i
$447$		0			0
$448$	11.3047	+	13.0463i	0.534095	+	0.616378i
$449$	−8.73849	−	10.0848i	−0.412395	−	0.475929i	0.511110	−	0.859515i	$-0.329234\pi$
$449$	−8.73849	−	10.0848i	−0.412395	−	0.475929i	−0.923505	+	0.383586i	$0.874689\pi$
$450$		0			0
$451$	2.80990	−	6.15282i	0.132313	−	0.289725i
$452$	3.29920	+	2.12026i	0.155181	+	0.0997288i
$453$		0			0
$454$	4.92975	−	34.2872i	0.231365	−	1.60918i
$455$	10.3220	+	22.6020i	0.483902	+	1.05960i
$456$		0			0
$457$	19.4014	−	12.4685i	0.907559	−	0.583253i	−0.00146402	−	0.999999i	$-0.500466\pi$
$457$	19.4014	−	12.4685i	0.907559	−	0.583253i	0.909023	+	0.416746i	$0.136830\pi$
$458$	−0.875860	+	1.01080i	−0.0409262	+	0.0472314i
$459$		0			0
$460$	−13.9942	+	37.4531i	−0.652483	+	1.74626i
$461$	7.59985			0.353960			0.176980	−	0.984214i	$-0.443367\pi$
$461$	7.59985			0.353960			0.176980	+	0.984214i	$0.443367\pi$
$462$		0			0
$463$	8.55341	−	5.49694i	0.397511	−	0.255465i	−0.326580	−	0.945170i	$-0.605896\pi$
$463$	8.55341	−	5.49694i	0.397511	−	0.255465i	0.724090	+	0.689705i	$0.242260\pi$
$464$	4.29868	+	29.8980i	0.199561	+	1.38798i
$465$		0			0
$466$	−0.192487	+	1.33877i	−0.00891677	+	0.0620175i
$467$	−9.91443	+	2.91114i	−0.458785	+	0.134711i	−0.502955	−	0.864313i	$-0.667754\pi$
$467$	−9.91443	+	2.91114i	−0.458785	+	0.134711i	0.0441700	+	0.999024i	$0.485936\pi$
$468$		0			0
$469$	−1.83517	+	4.01846i	−0.0847401	+	0.185555i
$470$	32.4619	+	9.53168i	1.49736	+	0.439664i
$471$		0			0
$472$	−0.543170	−	0.626852i	−0.0250014	−	0.0288532i
$473$	−3.80540	−	1.11737i	−0.174972	−	0.0513765i
$474$		0			0
$475$	35.4561	+	22.7862i	1.62684	+	1.04550i
$476$	−14.8377	+	4.35673i	−0.680084	+	0.199691i
$477$		0			0
$478$	−8.40634	−	18.4073i	−0.384497	−	0.841932i
$479$	−1.23975	−	8.62266i	−0.0566457	−	0.393980i	−0.998344	−	0.0575217i	$-0.981680\pi$
$479$	−1.23975	−	8.62266i	−0.0566457	−	0.393980i	0.941699	−	0.336458i	$-0.109229\pi$
$480$		0			0
$481$	−24.6438	+	28.4405i	−1.12366	+	1.29677i
$482$	12.5359			0.570993
$483$		0			0
$484$	−21.9822			−0.999193
$485$	−3.85426	+	4.44805i	−0.175013	+	0.201975i
$486$		0			0
$487$	−3.24014	−	22.5356i	−0.146825	−	1.02119i	−0.921375	−	0.388675i	$-0.872933\pi$
$487$	−3.24014	−	22.5356i	−0.146825	−	1.02119i	0.774550	−	0.632512i	$-0.217976\pi$
$488$	−0.277312	−	0.607229i	−0.0125533	−	0.0274880i
$489$		0			0
$490$	31.2898	−	9.18750i	1.41353	−	0.415049i
$491$	−23.5914	−	15.1613i	−1.06466	−	0.684219i	−0.113699	−	0.993515i	$-0.536270\pi$
$491$	−23.5914	−	15.1613i	−1.06466	−	0.684219i	−0.950966	+	0.309297i	$0.899906\pi$
$492$		0			0
$493$	−39.1720	−	11.5019i	−1.76422	−	0.518021i
$494$	−38.2745	−	44.1711i	−1.72205	−	1.98735i
$495$		0			0
$496$	3.26610	+	0.959013i	0.146652	+	0.0430610i
$497$	3.72875	−	8.16482i	0.167257	−	0.366242i
$498$		0			0
$499$	14.0554	−	4.12705i	0.629207	−	0.184752i	0.0484460	−	0.998826i	$-0.484573\pi$
$499$	14.0554	−	4.12705i	0.629207	−	0.184752i	0.580761	+	0.814074i	$0.302755\pi$
$500$	2.25528	−	15.6858i	0.100859	−	0.701491i
$501$		0			0
$502$	1.15289	+	8.01853i	0.0514560	+	0.357885i
$503$	1.35700	−	0.872088i	0.0605055	−	0.0388845i	−0.510038	−	0.860152i	$-0.670369\pi$
$503$	1.35700	−	0.872088i	0.0605055	−	0.0388845i	0.570544	+	0.821267i	$0.306732\pi$
$504$		0			0
$505$	23.7528			1.05698
$506$	11.1377	−	8.32745i	0.495132	−	0.370200i
$507$		0			0
$508$	−15.3363	+	17.6990i	−0.680437	+	0.785266i
$509$	20.5963	−	13.2364i	0.912914	−	0.586694i	0.00232071	−	0.999997i	$-0.499261\pi$
$509$	20.5963	−	13.2364i	0.912914	−	0.586694i	0.910594	+	0.413303i	$0.135625\pi$
$510$		0			0
$511$	0.597974	+	1.30938i	0.0264528	+	0.0579236i
$512$	4.17136	−	29.0125i	0.184350	−	1.28218i
$513$		0			0
$514$	−20.8812	−	13.4195i	−0.921029	−	0.591909i
$515$	−0.412140	+	0.902462i	−0.0181611	+	0.0397672i
$516$		0			0
$517$	−4.21656	−	4.86617i	−0.185444	−	0.214014i
$518$	−17.9903	−	20.7619i	−0.790450	−	0.912228i
$519$		0			0
$520$	−5.71395	+	12.5118i	−0.250573	+	0.548679i
$521$	30.5797	+	19.6524i	1.33972	+	0.860986i	0.996920	−	0.0784221i	$-0.0249882\pi$
$521$	30.5797	+	19.6524i	1.33972	+	0.860986i	0.342800	+	0.939408i	$0.388625\pi$
$522$		0			0
$523$	2.57768	−	17.9282i	0.112714	−	0.783943i	−0.852546	−	0.522652i	$-0.824943\pi$
$523$	2.57768	−	17.9282i	0.112714	−	0.783943i	0.965260	−	0.261291i	$-0.0841483\pi$
$524$	−11.5014	−	25.1847i	−0.502443	−	1.10020i
$525$		0			0
$526$	25.9067	−	16.6492i	1.12959	−	0.725941i
$527$	−3.01290	+	3.47708i	−0.131244	+	0.151464i
$528$		0			0
$529$	6.50563	−	22.0608i	0.282854	−	0.959163i
$530$	−47.3894			−2.05847
$531$		0			0
$532$	19.6399	−	12.6218i	0.851498	−	0.547224i
$533$	−3.17687	−	22.0956i	−0.137605	−	0.957067i
$534$		0			0
$535$	−4.07029	+	28.3095i	−0.175974	+	1.22393i
$536$	−2.34644	+	0.688976i	−0.101351	+	0.0297592i
$537$		0			0
$538$	−23.7612	+	52.0297i	−1.02442	+	2.24316i
$539$	−5.95497	−	1.74854i	−0.256499	−	0.0753148i
$540$		0			0
$541$	−23.7651	−	27.4264i	−1.02174	−	1.17915i	−0.983689	−	0.179879i	$-0.942429\pi$
$541$	−23.7651	−	27.4264i	−1.02174	−	1.17915i	−0.0380547	−	0.999276i	$-0.512116\pi$
$542$	−8.63840	−	2.53646i	−0.371051	−	0.108950i
$543$		0			0
$544$	27.3676	+	17.5881i	1.17338	+	0.754083i
$545$	68.0153	−	19.9711i	2.91346	−	0.855468i
$546$		0			0
$547$	−4.79518	−	10.5000i	−0.205027	−	0.448947i	0.778986	−	0.627041i	$-0.215734\pi$
$547$	−4.79518	−	10.5000i	−0.205027	−	0.448947i	−0.984013	+	0.178094i	$0.943007\pi$
$548$	0.565316	+	3.93186i	0.0241491	+	0.167961i
$549$		0			0
$550$	−13.1042	+	15.1231i	−0.558765	+	0.644849i
$551$	61.6342			2.62571
$552$		0			0
$553$	15.4176			0.655623
$554$	9.44345	−	10.8983i	0.401214	−	0.463025i
$555$		0			0
$556$	1.91773	+	13.3381i	0.0813299	+	0.565662i
$557$	−7.05495	−	15.4482i	−0.298928	−	0.654560i	0.699252	−	0.714876i	$-0.253517\pi$
$557$	−7.05495	−	15.4482i	−0.298928	−	0.654560i	−0.998179	+	0.0603152i	$0.980789\pi$
$558$		0			0
$559$	−12.5586	+	3.68753i	−0.531172	+	0.155966i
$560$	13.7397	+	8.82999i	0.580610	+	0.373135i
$561$		0			0
$562$	26.8304	+	7.87813i	1.13177	+	0.332319i
$563$	10.7487	+	12.4046i	0.453002	+	0.522792i	0.935606	−	0.353047i	$-0.114854\pi$
$563$	10.7487	+	12.4046i	0.453002	+	0.522792i	−0.482604	+	0.875839i	$0.660309\pi$
$564$		0			0
$565$	5.37154	+	1.57723i	0.225983	+	0.0663545i
$566$	−16.7811	+	36.7455i	−0.705363	+	1.54453i
$567$		0			0
$568$	4.76756	−	1.39988i	0.200042	−	0.0587377i
$569$	−0.107529	+	0.747877i	−0.00450783	+	0.0313526i	−0.991951	−	0.126621i	$-0.959587\pi$
$569$	−0.107529	+	0.747877i	−0.00450783	+	0.0313526i	0.987443	+	0.157973i	$0.0504960\pi$
$570$		0			0
$571$	−3.85667	−	26.8237i	−0.161397	−	1.12254i	−0.896004	−	0.444046i	$-0.853543\pi$
$571$	−3.85667	−	26.8237i	−0.161397	−	1.12254i	0.734608	−	0.678492i	$-0.237366\pi$
$572$	12.7734	−	8.20895i	0.534082	−	0.343233i
$573$		0			0
$574$	16.2960			0.680181
$575$	−2.38028	+	33.0096i	−0.0992645	+	1.37660i
$576$		0			0
$577$	−6.23334	+	7.19365i	−0.259497	+	0.299476i	−0.870516	−	0.492141i	$-0.836215\pi$
$577$	−6.23334	+	7.19365i	−0.259497	+	0.299476i	0.611019	+	0.791616i	$0.290760\pi$
$578$	1.12071	−	0.720237i	0.0466154	−	0.0299579i
$579$		0			0
$580$	−34.9498	−	76.5294i	−1.45121	−	3.17771i
$581$	−1.09276	+	7.60028i	−0.0453352	+	0.315313i
$582$		0			0
$583$	7.58728	+	4.87605i	0.314233	+	0.201945i
$584$	−0.331021	+	0.724835i	−0.0136978	+	0.0299939i
$585$		0			0
$586$	−18.7784	−	21.6715i	−0.775731	−	0.895241i
$587$	27.9888	+	32.3008i	1.15522	+	1.33320i	0.933706	+	0.358040i	$0.116555\pi$
$587$	27.9888	+	32.3008i	1.15522	+	1.33320i	0.221515	+	0.975157i	$0.428900\pi$
$588$		0			0
$589$	2.88541	−	6.31816i	0.118891	−	0.260335i
$590$	−5.77746	−	3.71295i	−0.237854	−	0.152860i
$591$		0			0
$592$	−3.52030	+	24.4842i	−0.144683	+	1.00629i
$593$	5.31366	+	11.6353i	0.218206	+	0.477805i	0.986802	−	0.161930i	$-0.0517717\pi$
$593$	5.31366	+	11.6353i	0.218206	+	0.477805i	−0.768596	+	0.639734i	$0.779044\pi$
$594$		0			0
$595$	−18.5706	+	11.9346i	−0.761322	+	0.489272i
$596$	9.62499	−	11.1078i	0.394255	−	0.454994i
$597$		0			0
$598$	16.0637	−	42.9917i	0.656894	−	1.75806i
$599$	−27.4971			−1.12350			−0.561751	−	0.827306i	$-0.689872\pi$
$599$	−27.4971			−1.12350			−0.561751	+	0.827306i	$0.689872\pi$
$600$		0			0
$601$	28.7319	−	18.4649i	1.17200	−	0.753198i	0.198100	−	0.980182i	$-0.436523\pi$
$601$	28.7319	−	18.4649i	1.17200	−	0.753198i	0.973899	+	0.226984i	$0.0728864\pi$
$602$	−1.35982	−	9.45774i	−0.0554220	−	0.385469i
$603$		0			0
$604$	8.13975	−	56.6132i	0.331202	−	2.30356i
$605$	−30.1086	+	8.84067i	−1.22409	+	0.359424i
$606$		0			0
$607$	−12.4592	+	27.2819i	−0.505704	+	1.10734i	0.468869	+	0.883267i	$0.344661\pi$
$607$	−12.4592	+	27.2819i	−0.505704	+	1.10734i	−0.974573	+	0.224069i	$0.928066\pi$
$608$	−47.1238	−	13.8368i	−1.91112	−	0.561156i
$609$		0			0
$610$	−3.61959	−	4.17723i	−0.146553	−	0.169131i
$611$	−20.3888	−	5.98670i	−0.824843	−	0.242196i
$612$		0			0
$613$	5.60513	+	3.60220i	0.226389	+	0.145491i	0.648919	−	0.760858i	$-0.275221\pi$
$613$	5.60513	+	3.60220i	0.226389	+	0.145491i	−0.422530	+	0.906349i	$0.638858\pi$
$614$	−51.2811	+	15.0575i	−2.06954	+	0.607671i
$615$		0			0
$616$	0.793863	+	1.73832i	0.0319857	+	0.0700388i
$617$	4.06924	+	28.3022i	0.163822	+	1.13940i	0.891346	+	0.453323i	$0.149761\pi$
$617$	4.06924	+	28.3022i	0.163822	+	1.13940i	−0.727525	+	0.686081i	$0.759329\pi$
$618$		0			0
$619$	1.97493	−	2.27919i	0.0793791	−	0.0916084i	−0.714671	−	0.699461i	$-0.753423\pi$
$619$	1.97493	−	2.27919i	0.0793791	−	0.0916084i	0.794050	+	0.607853i	$0.207969\pi$
$620$	−9.48125			−0.380776
$621$		0			0
$622$	−66.1539			−2.65253
$623$	−3.79779	+	4.38289i	−0.152155	+	0.175597i
$624$		0			0
$625$	1.69106	+	11.7616i	0.0676423	+	0.470462i
$626$	−11.7592	−	25.7491i	−0.469993	−	1.02914i
$627$		0			0
$628$	−36.1240	+	10.6070i	−1.44150	+	0.423264i
$629$	−28.1258	−	18.0754i	−1.12145	−	0.720711i
$630$		0			0
$631$	25.2937	+	7.42689i	1.00692	+	0.295660i	0.743295	−	0.668964i	$-0.233262\pi$
$631$	25.2937	+	7.42689i	1.00692	+	0.295660i	0.263630	+	0.964624i	$0.415080\pi$
$632$	5.58907	+	6.45013i	0.222321	+	0.256572i
$633$		0			0
$634$	7.76073	+	2.27875i	0.308218	+	0.0905009i
$635$	−13.8877	+	30.4098i	−0.551115	+	1.20677i
$636$		0			0
$637$	−19.6526	+	5.77053i	−0.778665	+	0.228637i
$638$	−4.16457	+	28.9652i	−0.164877	+	1.14674i
$639$		0			0
$640$	3.36445	+	23.4002i	0.132991	+	0.924976i
$641$	−13.0722	+	8.40101i	−0.516322	+	0.331820i	−0.772716	−	0.634752i	$-0.781102\pi$
$641$	−13.0722	+	8.40101i	−0.516322	+	0.331820i	0.256394	+	0.966572i	$0.417466\pi$
$642$		0			0
$643$	−40.0898			−1.58099			−0.790493	−	0.612471i	$-0.790176\pi$
$643$	−40.0898			−1.58099			−0.790493	+	0.612471i	$0.790176\pi$
$644$	16.0847	+	8.79510i	0.633825	+	0.346576i
$645$		0			0
$646$	34.0039	−	39.2426i	1.33787	−	1.54398i
$647$	15.6948	−	10.0864i	0.617025	−	0.396538i	−0.194460	−	0.980910i	$-0.562296\pi$
$647$	15.6948	−	10.0864i	0.617025	−	0.396538i	0.811486	+	0.584372i	$0.198659\pi$
$648$		0			0
$649$	0.542963	+	1.18892i	0.0213131	+	0.0466693i
$650$	−9.39837	+	65.3671i	−0.368634	+	2.56391i
$651$		0			0
$652$	−12.5271	−	8.05068i	−0.490599	−	0.315289i
$653$	19.3948	−	42.4686i	0.758976	−	1.66193i	0.00944723	−	0.999955i	$-0.496993\pi$
$653$	19.3948	−	42.4686i	0.758976	−	1.66193i	0.749529	−	0.661971i	$-0.230280\pi$
$654$		0			0
$655$	−25.8819	−	29.8693i	−1.01129	−	1.16709i
$656$	−9.60879	−	11.0891i	−0.375160	−	0.432958i
$657$		0			0
$658$	6.44413	−	14.1107i	0.251218	−	0.550091i
$659$	10.3563	+	6.65560i	0.403425	+	0.259266i	0.726582	−	0.687080i	$-0.241108\pi$
$659$	10.3563	+	6.65560i	0.403425	+	0.259266i	−0.323157	+	0.946345i	$0.604744\pi$
$660$		0			0
$661$	−5.03323	+	35.0069i	−0.195770	+	1.36161i	0.620622	+	0.784110i	$0.286880\pi$
$661$	−5.03323	+	35.0069i	−0.195770	+	1.36161i	−0.816391	+	0.577499i	$0.804029\pi$
$662$	17.6426	+	38.6319i	0.685700	+	1.50147i
$663$		0			0
$664$	−3.57580	+	2.29803i	−0.138768	+	0.0891808i
$665$	21.8242	−	25.1864i	0.846305	−	0.976688i
$666$		0			0
$667$	23.1697	+	42.4912i	0.897136	+	1.64527i
$668$	−22.8221			−0.883014
$669$		0			0
$670$	−17.0340	+	10.9471i	−0.658081	+	0.422923i
$671$	0.149706	+	1.04122i	0.00577932	+	0.0401960i
$672$		0			0
$673$	0.0996232	−	0.692895i	0.00384019	−	0.0267091i	−0.987811	−	0.155656i	$-0.950251\pi$
$673$	0.0996232	−	0.692895i	0.00384019	−	0.0267091i	0.991651	+	0.128947i	$0.0411598\pi$
$674$	22.2057	−	6.52019i	0.855333	−	0.251148i
$675$		0			0
$676$	7.76536	−	17.0038i	0.298668	−	0.653991i
$677$	−10.9530	−	3.21609i	−0.420958	−	0.123604i	0.0643912	−	0.997925i	$-0.479489\pi$
$677$	−10.9530	−	3.21609i	−0.420958	−	0.123604i	−0.485349	+	0.874320i	$0.661308\pi$
$678$		0			0
$679$	1.76722	+	2.03948i	0.0678196	+	0.0782680i
$680$	−11.7251	−	3.44279i	−0.449636	−	0.132025i
$681$		0			0
$682$	2.77428	+	1.78292i	0.106233	+	0.0682715i
$683$	23.6595	−	6.94705i	0.905305	−	0.265821i	0.204241	−	0.978921i	$-0.434527\pi$
$683$	23.6595	−	6.94705i	0.905305	−	0.265821i	0.701063	+	0.713099i	$0.252709\pi$
$684$		0			0
$685$	2.35559	+	5.15802i	0.0900024	+	0.197078i
$686$	−5.43951	−	37.8326i	−0.207681	−	1.44446i
$687$		0			0
$688$	−5.63402	+	6.50201i	−0.214795	+	0.247887i
$689$	29.7646			1.13394
$690$		0			0
$691$	16.2668			0.618819			0.309410	−	0.950929i	$-0.399869\pi$
$691$	16.2668			0.618819			0.309410	+	0.950929i	$0.399869\pi$
$692$	11.2266	−	12.9562i	0.426772	−	0.492521i
$693$		0			0
$694$	7.88478	+	54.8399i	0.299302	+	2.08169i
$695$	7.99091	+	17.4976i	0.303112	+	0.663723i
$696$		0			0
$697$	19.0287	−	5.58734i	0.720765	−	0.211636i
$698$	−33.0543	−	21.2427i	−1.25112	−	0.804048i
$699$		0			0
$700$	−25.3102	−	7.43175i	−0.956636	−	0.280894i
$701$	15.8662	+	18.3105i	0.599256	+	0.691579i	0.971631	−	0.236504i	$-0.0760016\pi$
$701$	15.8662	+	18.3105i	0.599256	+	0.691579i	−0.372374	+	0.928083i	$0.621456\pi$
$702$		0			0
$703$	48.4293	+	14.2201i	1.82655	+	0.536322i
$704$	6.25554	−	13.6977i	0.235765	−	0.516252i
$705$		0			0
$706$	−47.5634	+	13.9659i	−1.79007	+	0.525612i
$707$	1.54994	−	10.7800i	0.0582914	−	0.405425i
$708$		0			0
$709$	2.90120	+	20.1783i	0.108957	+	0.757811i	0.968906	+	0.247431i	$0.0795863\pi$
$709$	2.90120	+	20.1783i	0.108957	+	0.757811i	−0.859949	+	0.510381i	$0.829505\pi$
$710$	34.6102	−	22.2426i	1.29890	−	0.834752i
$711$		0			0
$712$	−3.21038			−0.120314
$713$	5.44049	−	0.385917i	0.203748	−	0.0144527i
$714$		0			0
$715$	14.1940	−	16.3807i	0.530824	−	0.612604i
$716$	−16.3188	+	10.4874i	−0.609861	+	0.391934i
$717$		0			0
$718$	−13.1438	−	28.7809i	−0.490522	−	1.07409i
$719$	−3.34111	+	23.2379i	−0.124602	+	0.866628i	0.827634	+	0.561268i	$0.189686\pi$
$719$	−3.34111	+	23.2379i	−0.124602	+	0.866628i	−0.952237	+	0.305361i	$0.901223\pi$
$720$		0			0
$721$	0.382683	+	0.245936i	0.0142519	+	0.00915912i
$722$	−15.9774	+	34.9857i	−0.594618	+	1.30203i
$723$		0			0
$724$	18.6570	+	21.5313i	0.693381	+	0.800204i
$725$	−45.6050	−	52.6310i	−1.69373	−	1.95467i
$726$		0			0
$727$	9.01408	−	19.7381i	0.334314	−	0.732045i	−0.665584	−	0.746323i	$-0.731818\pi$
$727$	9.01408	−	19.7381i	0.334314	−	0.732045i	0.999898	+	0.0142776i	$0.00454485\pi$
$728$	5.30555	+	3.40967i	0.196637	+	0.126371i
$729$		0			0
$730$	−0.938960	+	6.53061i	−0.0347525	+	0.241709i
$731$	−4.83059	−	10.5775i	−0.178666	−	0.391224i
$732$		0			0
$733$	27.2542	−	17.5152i	1.00666	−	0.646939i	0.0701305	−	0.997538i	$-0.477658\pi$
$733$	27.2542	−	17.5152i	1.00666	−	0.646939i	0.936526	+	0.350599i	$0.114022\pi$
$734$	45.6229	−	52.6517i	1.68397	−	1.94341i
$735$		0			0
$736$	−8.17571	−	37.6891i	−0.301361	−	1.38924i
$737$	3.85361			0.141949
$738$		0			0
$739$	30.7673	−	19.7730i	1.13179	−	0.727360i	0.165860	−	0.986149i	$-0.446960\pi$
$739$	30.7673	−	19.7730i	1.13179	−	0.727360i	0.965934	+	0.258789i	$0.0833236\pi$
$740$	−9.80522	−	68.1968i	−0.360447	−	2.50696i
$741$		0			0
$742$	−3.09230	+	21.5074i	−0.113522	+	0.789562i
$743$	26.6770	−	7.83308i	0.978685	−	0.287368i	0.247003	−	0.969015i	$-0.420554\pi$
$743$	26.6770	−	7.83308i	0.978685	−	0.287368i	0.731681	+	0.681647i	$0.238736\pi$
$744$		0			0
$745$	8.71585	−	19.0850i	0.319324	−	0.699222i
$746$	66.4179	+	19.5020i	2.43173	+	0.714021i
$747$		0			0
$748$	8.83379	+	10.1947i	0.322995	+	0.372757i
$749$	12.5825	+	3.69455i	0.459754	+	0.134996i
$750$		0			0
$751$	−20.6293	−	13.2576i	−0.752774	−	0.483778i	0.107123	−	0.994246i	$-0.465836\pi$
$751$	−20.6293	−	13.2576i	−0.752774	−	0.483778i	−0.859897	+	0.510467i	$0.829472\pi$
$752$	−13.4018	+	3.93512i	−0.488713	+	0.143499i
$753$		0			0
$754$	40.1183	+	87.8468i	1.46102	+	3.19919i
$755$	−11.6195	−	80.8153i	−0.422877	−	2.94117i
$756$		0			0
$757$	32.7294	−	37.7717i	1.18957	−	1.37284i	0.278578	−	0.960414i	$-0.410137\pi$
$757$	32.7294	−	37.7717i	1.18957	−	1.37284i	0.910992	−	0.412424i	$-0.135318\pi$
$758$	−46.2460			−1.67973
$759$		0			0
$760$	18.4485			0.669199
$761$	−0.591990	+	0.683192i	−0.0214596	+	0.0247657i	−0.766378	−	0.642390i	$-0.777943\pi$
$761$	−0.591990	+	0.683192i	−0.0214596	+	0.0247657i	0.744918	+	0.667156i	$0.232488\pi$
$762$		0			0
$763$	−4.62556	−	32.1715i	−0.167457	−	1.16469i
$764$	26.5532	+	58.1433i	0.960660	+	2.10355i
$765$		0			0
$766$	−9.44209	+	2.77245i	−0.341156	+	0.100173i
$767$	3.62873	+	2.33205i	0.131026	+	0.0842053i
$768$		0			0
$769$	−45.0748	−	13.2351i	−1.62544	−	0.477272i	−0.662965	−	0.748650i	$-0.730702\pi$
$769$	−45.0748	−	13.2351i	−1.62544	−	0.477272i	−0.962473	+	0.271379i	$0.912520\pi$
$770$	10.3618	+	11.9582i	0.373414	+	0.430942i
$771$		0			0
$772$	−43.7061	−	12.8333i	−1.57302	−	0.461879i
$773$	−17.5403	+	38.4080i	−0.630882	+	1.38144i	0.276451	+	0.961028i	$0.410842\pi$
$773$	−17.5403	+	38.4080i	−0.630882	+	1.38144i	−0.907333	+	0.420412i	$0.861886\pi$
$774$		0			0
$775$	−7.53023	+	2.21108i	−0.270494	+	0.0794242i
$776$	−0.212601	+	1.47867i	−0.00763192	+	0.0530812i
$777$		0			0
$778$	4.19632	+	29.1860i	0.150445	+	1.04637i
$779$	−25.1874	+	16.1870i	−0.902433	+	0.579958i
$780$		0			0
$781$	−7.82988			−0.280175
$782$	39.8371	+	8.69040i	1.42457	+	0.310768i
$783$		0			0
$784$	−8.81653	+	10.1748i	−0.314876	+	0.363387i
$785$	−45.2123	+	29.0562i	−1.61370	+	1.03706i
$786$		0			0
$787$	7.78645	+	17.0499i	0.277557	+	0.607765i	0.996150	−	0.0876659i	$-0.0279408\pi$
$787$	7.78645	+	17.0499i	0.277557	+	0.607765i	−0.718593	+	0.695431i	$0.755214\pi$
$788$	3.03278	−	21.0935i	0.108038	−	0.751423i
$789$		0			0
$790$	59.4485	+	38.2052i	2.11508	+	1.35928i
$791$	1.06632	−	2.33492i	0.0379141	−	0.0830203i
$792$		0			0
$793$	2.27341	+	2.62365i	0.0807310	+	0.0931686i
$794$	15.4983	+	17.8860i	0.550015	+	0.634751i
$795$		0			0
$796$	15.0648	−	32.9872i	0.533956	−	1.16920i
$797$	40.5721	+	26.0741i	1.43714	+	0.923593i	0.999704	+	0.0243425i	$0.00774923\pi$
$797$	40.5721	+	26.0741i	1.43714	+	0.923593i	0.437435	+	0.899250i	$0.355887\pi$
$798$		0			0
$799$	2.68670	−	18.6864i	0.0950488	−	0.661079i
$800$	23.0527	+	50.4784i	0.815037	+	1.78468i
$801$		0			0
$802$	−30.2734	+	19.4555i	−1.06899	+	0.686998i
$803$	0.822287	−	0.948970i	0.0290179	−	0.0334884i
$804$		0			0
$805$	25.5680	+	5.57762i	0.901152	+	0.196585i
$806$	10.8834			0.383350
$807$		0			0
$808$	5.07182	−	3.25946i	0.178426	−	0.114668i
$809$	−7.57169	−	52.6623i	−0.266206	−	1.85151i	−0.483428	−	0.875384i	$-0.660609\pi$
$809$	−7.57169	−	52.6623i	−0.266206	−	1.85151i	0.217222	−	0.976122i	$-0.430300\pi$
$810$		0			0
$811$	−0.523752	+	3.64278i	−0.0183914	+	0.127915i	−0.996949	−	0.0780599i	$-0.975127\pi$
$811$	−0.523752	+	3.64278i	−0.0183914	+	0.127915i	0.978557	+	0.205975i	$0.0660366\pi$
$812$	−37.0130	+	10.8680i	−1.29890	+	0.381392i
$813$		0			0
$814$	−9.95512	+	21.7987i	−0.348927	+	0.764043i
$815$	−20.3959	−	5.98876i	−0.714436	−	0.209777i
$816$		0			0
$817$	11.4962	+	13.2674i	0.402202	+	0.464166i
$818$	−18.1111	−	5.31790i	−0.633240	−	0.185936i
$819$		0			0
$820$	34.3815	+	22.0956i	1.20065	+	0.771613i
$821$	2.34866	−	0.689628i	0.0819686	−	0.0240682i	−0.240491	−	0.970651i	$-0.577308\pi$
$821$	2.34866	−	0.689628i	0.0819686	−	0.0240682i	0.322460	+	0.946583i	$0.395490\pi$
$822$		0			0
$823$	0.368876	+	0.807725i	0.0128582	+	0.0281555i	0.915952	−	0.401287i	$-0.131437\pi$
$823$	0.368876	+	0.807725i	0.0128582	+	0.0281555i	−0.903094	+	0.429443i	$0.858710\pi$
$824$	0.0358374	+	0.249254i	0.00124845	+	0.00868319i
$825$		0			0
$826$	−2.06210	+	2.37979i	−0.0717495	+	0.0828033i
$827$	−25.9780			−0.903343			−0.451671	−	0.892184i	$-0.649172\pi$
$827$	−25.9780			−0.903343			−0.451671	+	0.892184i	$0.649172\pi$
$828$		0			0
$829$	−18.5613			−0.644662			−0.322331	−	0.946627i	$-0.604466\pi$
$829$	−18.5613			−0.644662			−0.322331	+	0.946627i	$0.604466\pi$
$830$	−23.0472	+	26.5979i	−0.799981	+	0.923227i
$831$		0			0
$832$	−7.07250	−	49.1904i	−0.245195	−	1.70537i
$833$	−7.55927	−	16.5525i	−0.261913	−	0.573510i
$834$		0			0
$835$	−31.2589	+	9.17844i	−1.08176	+	0.317633i
$836$	−17.1322	−	11.0102i	−0.592530	−	0.380796i
$837$		0			0
$838$	14.1997	+	4.16940i	0.490519	+	0.144029i
$839$	−11.1414	−	12.8578i	−0.384643	−	0.443902i	0.530102	−	0.847934i	$-0.322154\pi$
$839$	−11.1414	−	12.8578i	−0.384643	−	0.443902i	−0.914745	+	0.404032i	$0.867608\pi$
$840$		0			0
$841$	−69.8902	−	20.5216i	−2.41001	−	0.707642i
$842$	−10.7359	+	23.5083i	−0.369982	+	0.810148i
$843$		0			0
$844$	61.9701	−	18.1961i	2.13310	−	0.626334i
$845$	3.79757	−	26.4127i	0.130640	−	0.908624i
$846$		0			0
$847$	2.04761	+	14.2415i	0.0703568	+	0.489342i
$848$	16.4588	−	10.5774i	0.565196	−	0.363229i
$849$		0			0
$850$	−58.6707			−2.01239
$851$	8.40221	+	38.7333i	0.288024	+	1.32776i
$852$		0			0
$853$	−21.6663	+	25.0043i	−0.741841	+	0.856130i	−0.993751	−	0.111621i	$-0.964396\pi$
$853$	−21.6663	+	25.0043i	−0.741841	+	0.856130i	0.251910	+	0.967751i	$0.418941\pi$
$854$	−2.13200	+	1.37015i	−0.0729555	+	0.0468856i
$855$		0			0
$856$	3.01565	+	6.60334i	0.103073	+	0.225698i
$857$	−1.42530	+	9.91317i	−0.0486873	+	0.338628i	0.950889	+	0.309531i	$0.100172\pi$
$857$	−1.42530	+	9.91317i	−0.0486873	+	0.338628i	−0.999577	+	0.0290964i	$0.990737\pi$
$858$		0			0
$859$	31.7908	+	20.4307i	1.08469	+	0.697087i	0.955636	−	0.294551i	$-0.0951699\pi$
$859$	31.7908	+	20.4307i	1.08469	+	0.697087i	0.129053	+	0.991638i	$0.458806\pi$
$860$	9.95474	−	21.7978i	0.339454	−	0.743300i
$861$		0			0
$862$	−6.94053	−	8.00980i	−0.236395	−	0.272815i
$863$	25.4019	+	29.3154i	0.864691	+	0.997906i	0.999975	+	0.00709937i	$0.00225982\pi$
$863$	25.4019	+	29.3154i	0.864691	+	0.997906i	−0.135284	+	0.990807i	$0.543195\pi$
$864$		0			0
$865$	10.1662	−	22.2608i	0.345661	−	0.756891i
$866$	1.57268	+	1.01070i	0.0534419	+	0.0343450i
$867$		0			0
$868$	−0.618679	+	4.30301i	−0.0209993	+	0.146054i
$869$	−5.58693	−	12.2337i	−0.189524	−	0.414999i
$870$		0			0
$871$	10.6988	−	6.87570i	0.362515	−	0.232974i
$872$	11.7825	−	13.5977i	0.399005	−	0.460477i
$873$		0			0
$874$	−61.4018	+	4.35549i	−2.07695	+	0.147327i
$875$	−10.3723			−0.350648
$876$		0			0
$877$	−19.9423	+	12.8161i	−0.673404	+	0.432770i	−0.832151	−	0.554549i	$-0.812891\pi$
$877$	−19.9423	+	12.8161i	−0.673404	+	0.432770i	0.158747	+	0.987319i	$0.449255\pi$
$878$	11.9287	+	82.9656i	0.402573	+	2.79995i
$879$		0			0
$880$	2.02757	−	14.1021i	0.0683494	−	0.475380i
$881$	18.9632	−	5.56809i	0.638885	−	0.187594i	0.0537823	−	0.998553i	$-0.482872\pi$
$881$	18.9632	−	5.56809i	0.638885	−	0.187594i	0.585103	+	0.810959i	$0.301054\pi$
$882$		0			0
$883$	11.0250	−	24.1413i	0.371020	−	0.812420i	−0.628385	−	0.777903i	$-0.716284\pi$
$883$	11.0250	−	24.1413i	0.371020	−	0.812420i	0.999404	−	0.0345167i	$-0.0109892\pi$
$884$	42.7150	+	12.5423i	1.43666	+	0.421842i
$885$		0			0
$886$	−17.6301	−	20.3462i	−0.592295	−	0.683545i
$887$	−12.3340	−	3.62160i	−0.414136	−	0.121601i	0.0680256	−	0.997684i	$-0.478330\pi$
$887$	−12.3340	−	3.62160i	−0.414136	−	0.121601i	−0.482162	+	0.876082i	$0.660148\pi$
$888$		0			0
$889$	12.8951	+	8.28716i	0.432487	+	0.277942i
$890$	−25.5047	+	7.48887i	−0.854921	+	0.251027i
$891$		0			0
$892$	12.3427	+	27.0268i	0.413265	+	0.904924i
$893$	4.05610	+	28.2108i	0.135732	+	0.944037i
$894$		0			0
$895$	−18.1337	+	20.9274i	−0.606141	+	0.699524i
$896$	10.8396			0.362125
$897$		0			0
$898$	−28.0436			−0.935827
$899$	−7.51577	+	8.67366i	−0.250665	+	0.289283i
$900$		0			0
$901$	3.76330	+	26.1743i	0.125374	+	0.871994i
$902$	−5.90523	−	12.9307i	−0.196623	−	0.430544i
$903$		0			0
$904$	1.36340	−	0.400329i	0.0453459	−	0.0133148i
$905$	34.2133	+	21.9876i	1.13729	+	0.730891i
$906$		0			0
$907$	38.4349	+	11.2855i	1.27621	+	0.374729i	0.848504	−	0.529189i	$-0.177504\pi$
$907$	38.4349	+	11.2855i	1.27621	+	0.374729i	0.427706	+	0.903918i	$0.359322\pi$
$908$	−26.0850	−	30.1037i	−0.865660	−	0.999025i
$909$		0			0
$910$	50.1036	+	14.7117i	1.66092	+	0.487690i
$911$	18.9746	−	41.5487i	0.628658	−	1.37657i	−0.280393	−	0.959885i	$-0.590465\pi$
$911$	18.9746	−	41.5487i	0.628658	−	1.37657i	0.909051	−	0.416684i	$-0.136808\pi$
$912$		0			0
$913$	6.42671	−	1.88705i	0.212693	−	0.0624523i
$914$	6.89767	−	47.9743i	0.228155	−	1.58685i
$915$		0			0
$916$	0.218878	+	1.52233i	0.00723194	+	0.0502992i
$917$	−15.2448	+	9.79726i	−0.503429	+	0.323534i
$918$		0			0
$919$	9.12733			0.301083			0.150541	−	0.988604i	$-0.451898\pi$
$919$	9.12733			0.301083			0.150541	+	0.988604i	$0.451898\pi$
$920$	6.93524	+	12.7186i	0.228648	+	0.419320i
$921$		0			0
$922$	10.4592	−	12.0706i	0.344457	−	0.397524i
$923$	−21.7381	+	13.9703i	−0.715520	+	0.459837i
$924$		0			0
$925$	−23.6914	−	51.8769i	−0.778967	−	1.70570i
$926$	3.04095	−	21.1502i	0.0999317	−	0.695040i
$927$		0			0
$928$	68.2693	+	43.8740i	2.24105	+	1.44023i
$929$	−0.242509	+	0.531021i	−0.00795647	+	0.0174222i	−0.913569	−	0.406685i	$-0.866685\pi$
$929$	−0.242509	+	0.531021i	−0.00795647	+	0.0174222i	0.905612	+	0.424107i	$0.139412\pi$
$930$		0			0
$931$	17.9902	+	20.7618i	0.589604	+	0.680439i
$932$	1.01851	+	1.17542i	0.0333624	+	0.0385023i
$933$		0			0
$934$	−9.02099	+	19.7532i	−0.295176	+	0.646345i
$935$	16.1995	+	10.4108i	0.529780	+	0.340469i
$936$		0			0
$937$	7.47312	−	51.9767i	0.244136	−	1.69800i	−0.386795	−	0.922166i	$-0.626418\pi$
$937$	7.47312	−	51.9767i	0.244136	−	1.69800i	0.630931	−	0.775839i	$-0.282673\pi$
$938$	3.85675	+	8.44511i	0.125927	+	0.275743i
$939$		0			0
$940$	32.7285	−	21.0333i	1.06749	−	0.686031i
$941$	−34.9319	+	40.3135i	−1.13875	+	1.31418i	−0.196025	+	0.980599i	$0.562803\pi$
$941$	−34.9319	+	40.3135i	−1.13875	+	1.31418i	−0.942720	+	0.333584i	$0.891742\pi$
$942$		0			0
$943$	−20.6280	−	11.2794i	−0.671739	−	0.367307i
$944$	2.83530			0.0922811
$945$		0			0
$946$	−7.01183	+	4.50623i	−0.227974	+	0.146510i
$947$	−1.81889	−	12.6507i	−0.0591060	−	0.411091i	−0.997798	−	0.0663332i	$-0.978870\pi$
$947$	−1.81889	−	12.6507i	−0.0591060	−	0.411091i	0.938692	−	0.344758i	$-0.112039\pi$
$948$		0			0
$949$	0.589746	−	4.10177i	0.0191440	−	0.133149i
$950$	84.9869	−	24.9544i	2.75734	−	0.809627i
$951$		0			0
$952$	−2.32758	+	5.09670i	−0.0754374	+	0.165185i
$953$	−25.7813	−	7.57006i	−0.835137	−	0.245218i	−0.163915	−	0.986474i	$-0.552412\pi$
$953$	−25.7813	−	7.57006i	−0.835137	−	0.245218i	−0.671222	+	0.741256i	$0.734230\pi$
$954$		0			0
$955$	59.7529	+	68.9586i	1.93356	+	2.23145i
$956$	−22.3272	−	6.55584i	−0.722112	−	0.212031i
$957$		0			0
$958$	−15.4013	−	9.89782i	−0.497594	−	0.319784i
$959$	2.49464	−	0.732494i	0.0805563	−	0.0236535i
$960$		0			0
$961$	−12.3406	−	27.0221i	−0.398083	−	0.871680i
$962$	11.2552	+	78.2820i	0.362884	+	2.52391i
$963$		0			0
$964$	9.43995	−	10.8943i	0.304040	−	0.350881i
$965$	−65.0244			−2.09321
$966$		0			0
$967$	12.5704			0.404236			0.202118	−	0.979361i	$-0.435218\pi$
$967$	12.5704			0.404236			0.202118	+	0.979361i	$0.435218\pi$
$968$	−5.21579	+	6.01934i	−0.167642	+	0.193469i
$969$		0			0
$970$	1.76031	+	12.2432i	0.0565200	+	0.393105i
$971$	8.30513	+	18.1857i	0.266524	+	0.583607i	0.994820	−	0.101657i	$-0.0324144\pi$
$971$	8.30513	+	18.1857i	0.266524	+	0.583607i	−0.728295	+	0.685263i	$0.759687\pi$
$972$		0			0
$973$	8.46263	−	2.48485i	0.271299	−	0.0796607i
$974$	−40.2519	−	25.8683i	−1.28975	−	0.828874i
$975$		0			0
$976$	2.18948	+	0.642889i	0.0700835	+	0.0205784i
$977$	−18.0952	−	20.8830i	−0.578917	−	0.668106i	0.388454	−	0.921468i	$-0.373009\pi$
$977$	−18.0952	−	20.8830i	−0.578917	−	0.668106i	−0.967372	+	0.253362i	$0.918464\pi$
$978$		0			0
$979$	4.85399	+	1.42526i	0.155134	+	0.0455515i
$980$	15.5779	−	34.1109i	0.497618	−	1.08963i
$981$		0			0
$982$	−56.5477	+	16.6039i	−1.80451	+	0.529852i
$983$	3.34878	−	23.2913i	0.106809	−	0.742876i	−0.864081	−	0.503353i	$-0.832100\pi$
$983$	3.34878	−	23.2913i	0.106809	−	0.742876i	0.970891	−	0.239523i	$-0.0769912\pi$
$984$		0			0
$985$	−4.32930	−	30.1109i	−0.137943	−	0.959414i
$986$	−72.1783	+	46.3862i	−2.29863	+	1.47724i
$987$		0			0
$988$	−67.2089			−2.13820
$989$	−4.82494	+	12.9131i	−0.153424	+	0.410613i
$990$		0			0
$991$	−28.0874	+	32.4146i	−0.892226	+	1.02968i	0.107146	+	0.994243i	$0.465829\pi$
$991$	−28.0874	+	32.4146i	−0.892226	+	1.02968i	−0.999372	+	0.0354405i	$0.988717\pi$
$992$	7.69357	−	4.94436i	0.244271	−	0.156984i
$993$		0			0
$994$	−7.83627	−	17.1590i	−0.248551	−	0.544252i
$995$	7.36726	−	51.2405i	0.233558	−	1.62443i
$996$		0			0
$997$	−32.7183	−	21.0268i	−1.03620	−	0.665925i	−0.0921555	−	0.995745i	$-0.529376\pi$
$997$	−32.7183	−	21.0268i	−1.03620	−	0.665925i	−0.944044	+	0.329820i	$0.893012\pi$
$998$	12.7888	−	28.0036i	0.404823	−	0.886439i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.i.d.154.2		20
3.2	odd	2		69.2.e.c.16.1	yes	20
23.6	even	11		4761.2.a.bt.1.1		10
23.13	even	11	inner	207.2.i.d.82.2		20
23.17	odd	22		4761.2.a.bu.1.1		10
69.17	even	22		1587.2.a.t.1.10		10
69.29	odd	22		1587.2.a.u.1.10		10
69.59	odd	22		69.2.e.c.13.1	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.c.13.1	✓	20	69.59	odd	22
69.2.e.c.16.1	yes	20	3.2	odd	2
207.2.i.d.82.2		20	23.13	even	11	inner
207.2.i.d.154.2		20	1.1	even	1	trivial
1587.2.a.t.1.10		10	69.17	even	22
1587.2.a.u.1.10		10	69.29	odd	22
4761.2.a.bt.1.1		10	23.6	even	11
4761.2.a.bu.1.1		10	23.17	odd	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 207 = 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	207.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37624 - 1.58827i) q^{2} +(-0.343924 - 2.39205i) q^{4} +(-1.43308 - 3.13801i) q^{5} +(-1.51768 + 0.445631i) q^{7} +(-0.736612 - 0.473392i) q^{8} +O(q^{10})\)	\(q+(1.37624 - 1.58827i) q^{2} +(-0.343924 - 2.39205i) q^{4} +(-1.43308 - 3.13801i) q^{5} +(-1.51768 + 0.445631i) q^{7} +(-0.736612 - 0.473392i) q^{8} +(-6.95628 - 2.04255i) q^{10} +(0.903570 + 1.04278i) q^{11} +(4.36913 + 1.28289i) q^{13} +(-1.38092 + 3.02378i) q^{14} +(2.87188 - 0.843259i) q^{16} +(-0.575735 + 4.00433i) q^{17} +(-0.869183 - 6.04530i) q^{19} +(-7.01340 + 4.50724i) q^{20} +2.89974 q^{22} +(3.84094 - 2.87179i) q^{23} +(-4.51910 + 5.21532i) q^{25} +(8.05057 - 5.17378i) q^{26} +(1.58794 + 3.47710i) q^{28} +(-1.43619 + 9.98890i) q^{29} +(0.956733 + 0.614855i) q^{31} +(3.34056 - 7.31481i) q^{32} +(5.56760 + 6.42535i) q^{34} +(3.57336 + 4.12388i) q^{35} +(-3.43311 + 7.51746i) q^{37} +(-10.7978 - 6.93931i) q^{38} +(-0.429884 + 2.98991i) q^{40} +(-2.03647 - 4.45925i) q^{41} +(-2.41809 + 1.55401i) q^{43} +(2.18361 - 2.52002i) q^{44} +(0.724889 - 10.0527i) q^{46} -4.66656 q^{47} +(-3.78401 + 2.43183i) q^{49} +(2.06395 + 14.3551i) q^{50} +(1.56609 - 10.8924i) q^{52} +(6.27174 - 1.84155i) q^{53} +(1.97735 - 4.32980i) q^{55} +(1.32890 + 0.390200i) q^{56} +(13.8885 + 16.0282i) q^{58} +(0.908902 + 0.266878i) q^{59} +(0.641360 + 0.412177i) q^{61} +(2.29325 - 0.673360i) q^{62} +(-4.53369 - 9.92740i) q^{64} +(-2.23559 - 15.5489i) q^{65} +(1.82896 - 2.11073i) q^{67} +9.77655 q^{68} +11.4676 q^{70} +(-3.71613 + 4.28865i) q^{71} +(-0.129513 - 0.900780i) q^{73} +(7.21496 + 15.7986i) q^{74} +(-14.1617 + 4.15825i) q^{76} +(-1.83602 - 1.17994i) q^{77} +(-9.35234 - 2.74609i) q^{79} +(-6.76179 - 7.80352i) q^{80} +(-9.88516 - 2.90255i) q^{82} +(2.01659 - 4.41571i) q^{83} +(13.3907 - 3.93187i) q^{85} +(-0.859691 + 5.97928i) q^{86} +(-0.171939 - 1.19586i) q^{88} +(3.08440 - 1.98222i) q^{89} -7.20264 q^{91} +(-8.19045 - 8.20003i) q^{92} +(-6.42232 + 7.41176i) q^{94} +(-17.7246 + 11.3909i) q^{95} +(-0.708736 - 1.55192i) q^{97} +(-1.34531 + 9.35682i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} - 10 q^{8}+O(q^{10}) \) 20 * q + 4 * q^2 - 6 * q^4 + 6 * q^5 - 6 * q^7 - 10 * q^8	\( 20 q + 4 q^{2} - 6 q^{4} + 6 q^{5} - 6 q^{7} - 10 q^{8} - 18 q^{10} + 16 q^{11} + 14 q^{13} + 22 q^{14} - 8 q^{16} - 11 q^{17} - 11 q^{19} - 57 q^{20} + 26 q^{22} - 4 q^{25} + 14 q^{26} - 14 q^{28} - 12 q^{29} + 41 q^{31} + 46 q^{32} - 3 q^{34} + 26 q^{35} - 18 q^{37} - 70 q^{38} - 13 q^{40} - 10 q^{43} + 3 q^{44} - 24 q^{46} - 18 q^{47} - 10 q^{49} - 33 q^{50} + 61 q^{52} + 20 q^{53} - 17 q^{55} - 6 q^{56} - 37 q^{58} - 40 q^{59} - 12 q^{61} + 89 q^{62} - 2 q^{64} + 51 q^{65} - 47 q^{67} + 12 q^{68} + 32 q^{70} + 47 q^{71} + 39 q^{73} + 50 q^{74} - 39 q^{76} - 22 q^{77} - 2 q^{79} - 12 q^{80} + 26 q^{82} + 52 q^{83} + 35 q^{85} - 34 q^{86} + 30 q^{88} - 36 q^{89} + 8 q^{91} + 19 q^{92} + 21 q^{94} - 89 q^{95} - 85 q^{98}+O(q^{100}) \) 20 * q + 4 * q^2 - 6 * q^4 + 6 * q^5 - 6 * q^7 - 10 * q^8 - 18 * q^10 + 16 * q^11 + 14 * q^13 + 22 * q^14 - 8 * q^16 - 11 * q^17 - 11 * q^19 - 57 * q^20 + 26 * q^22 - 4 * q^25 + 14 * q^26 - 14 * q^28 - 12 * q^29 + 41 * q^31 + 46 * q^32 - 3 * q^34 + 26 * q^35 - 18 * q^37 - 70 * q^38 - 13 * q^40 - 10 * q^43 + 3 * q^44 - 24 * q^46 - 18 * q^47 - 10 * q^49 - 33 * q^50 + 61 * q^52 + 20 * q^53 - 17 * q^55 - 6 * q^56 - 37 * q^58 - 40 * q^59 - 12 * q^61 + 89 * q^62 - 2 * q^64 + 51 * q^65 - 47 * q^67 + 12 * q^68 + 32 * q^70 + 47 * q^71 + 39 * q^73 + 50 * q^74 - 39 * q^76 - 22 * q^77 - 2 * q^79 - 12 * q^80 + 26 * q^82 + 52 * q^83 + 35 * q^85 - 34 * q^86 + 30 * q^88 - 36 * q^89 + 8 * q^91 + 19 * q^92 + 21 * q^94 - 89 * q^95 - 85 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more