LMFDB - Embedded newform 1089.2.e.g.727.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1089,2,Mod(364,1089)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1089, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("1089.364");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1089 = 3^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1089.e (of order $3$, degree $2$, 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:	$8.69570878012$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			727.1
Root			$-0.309017 + 0.535233i$ of defining polynomial
Character	$\chi$	$=$	1089.727
Dual form			1089.2.e.g.364.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.190983 - 0.330792i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.927051 + 1.60570i) q^{4} +(0.618034 + 1.07047i) q^{5} +0.661585i q^{6} +(0.500000 - 0.866025i) q^{7} +1.47214 q^{8} +(1.50000 - 2.59808i) q^{9} +0.472136 q^{10} +(-2.78115 - 1.60570i) q^{12} +(3.23607 + 5.60503i) q^{13} +(-0.190983 - 0.330792i) q^{14} +(-1.85410 - 1.07047i) q^{15} +(-1.57295 + 2.72443i) q^{16} +4.85410 q^{17} +(-0.572949 - 0.992377i) q^{18} +1.00000 q^{19} +(-1.14590 + 1.98475i) q^{20} +1.73205i q^{21} +(-2.30902 - 3.99933i) q^{23} +(-2.20820 + 1.27491i) q^{24} +(1.73607 - 3.00696i) q^{25} +2.47214 q^{26} +5.19615i q^{27} +1.85410 q^{28} +(2.42705 - 4.20378i) q^{29} +(-0.708204 + 0.408882i) q^{30} +(-0.309017 - 0.535233i) q^{31} +(2.07295 + 3.59045i) q^{32} +(0.927051 - 1.60570i) q^{34} +1.23607 q^{35} +5.56231 q^{36} -5.09017 q^{37} +(0.190983 - 0.330792i) q^{38} +(-9.70820 - 5.60503i) q^{39} +(0.909830 + 1.57587i) q^{40} +(1.26393 + 2.18919i) q^{41} +(0.572949 + 0.330792i) q^{42} +(-0.927051 + 1.60570i) q^{43} +3.70820 q^{45} -1.76393 q^{46} +(-5.97214 + 10.3440i) q^{47} -5.44886i q^{48} +(3.00000 + 5.19615i) q^{49} +(-0.663119 - 1.14856i) q^{50} +(-7.28115 + 4.20378i) q^{51} +(-6.00000 + 10.3923i) q^{52} +4.09017 q^{53} +(1.71885 + 0.992377i) q^{54} +(0.736068 - 1.27491i) q^{56} +(-1.50000 + 0.866025i) q^{57} +(-0.927051 - 1.60570i) q^{58} +(-0.809017 - 1.40126i) q^{59} -3.96951i q^{60} +(-5.42705 + 9.39993i) q^{61} -0.236068 q^{62} +(-1.50000 - 2.59808i) q^{63} -4.70820 q^{64} +(-4.00000 + 6.92820i) q^{65} +(-3.00000 - 5.19615i) q^{67} +(4.50000 + 7.79423i) q^{68} +(6.92705 + 3.99933i) q^{69} +(0.236068 - 0.408882i) q^{70} -2.90983 q^{71} +(2.20820 - 3.82472i) q^{72} -0.145898 q^{73} +(-0.972136 + 1.68379i) q^{74} +6.01392i q^{75} +(0.927051 + 1.60570i) q^{76} +(-3.70820 + 2.14093i) q^{78} +(-5.28115 + 9.14723i) q^{79} -3.88854 q^{80} +(-4.50000 - 7.79423i) q^{81} +0.965558 q^{82} +(4.88197 - 8.45581i) q^{83} +(-2.78115 + 1.60570i) q^{84} +(3.00000 + 5.19615i) q^{85} +(0.354102 + 0.613323i) q^{86} +8.40755i q^{87} -6.76393 q^{89} +(0.708204 - 1.22665i) q^{90} +6.47214 q^{91} +(4.28115 - 7.41517i) q^{92} +(0.927051 + 0.535233i) q^{93} +(2.28115 + 3.95107i) q^{94} +(0.618034 + 1.07047i) q^{95} +(-6.21885 - 3.59045i) q^{96} +(-3.00000 + 5.19615i) q^{97} +2.29180 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - 6 q^{3} - 3 q^{4} - 2 q^{5} + 2 q^{7} - 12 q^{8} + 6 q^{9} - 16 q^{10} + 9 q^{12} + 4 q^{13} - 3 q^{14} + 6 q^{15} - 13 q^{16} + 6 q^{17} - 9 q^{18} + 4 q^{19} - 18 q^{20} - 7 q^{23} + 18 q^{24}+ \cdots + 36 q^{98}+O(q^{100}) $ 4 * q + 3 * q^2 - 6 * q^3 - 3 * q^4 - 2 * q^5 + 2 * q^7 - 12 * q^8 + 6 * q^9 - 16 * q^10 + 9 * q^12 + 4 * q^13 - 3 * q^14 + 6 * q^15 - 13 * q^16 + 6 * q^17 - 9 * q^18 + 4 * q^19 - 18 * q^20 - 7 * q^23 + 18 * q^24 - 2 * q^25 - 8 * q^26 - 6 * q^28 + 3 * q^29 + 24 * q^30 + q^31 + 15 * q^32 - 3 * q^34 - 4 * q^35 - 18 * q^36 + 2 * q^37 + 3 * q^38 - 12 * q^39 + 26 * q^40 + 14 * q^41 + 9 * q^42 + 3 * q^43 - 12 * q^45 - 16 * q^46 - 6 * q^47 + 12 * q^49 + 13 * q^50 - 9 * q^51 - 24 * q^52 - 6 * q^53 + 27 * q^54 - 6 * q^56 - 6 * q^57 + 3 * q^58 - q^59 - 15 * q^61 + 8 * q^62 - 6 * q^63 + 8 * q^64 - 16 * q^65 - 12 * q^67 + 18 * q^68 + 21 * q^69 - 8 * q^70 - 34 * q^71 - 18 * q^72 - 14 * q^73 + 14 * q^74 - 3 * q^76 + 12 * q^78 - q^79 + 56 * q^80 - 18 * q^81 + 62 * q^82 + 24 * q^83 + 9 * q^84 + 12 * q^85 - 12 * q^86 - 36 * q^89 - 24 * q^90 + 8 * q^91 - 3 * q^92 - 3 * q^93 - 11 * q^94 - 2 * q^95 - 45 * q^96 - 12 * q^97 + 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times$.

$n$	$244$	$848$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.190983	−	0.330792i	0.135045	−	0.233905i	−0.790569	−	0.612372i	$-0.790215\pi$
$2$	0.190983	−	0.330792i	0.135045	−	0.233905i	0.925615	+	0.378467i	$0.123549\pi$
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$4$	0.927051	+	1.60570i	0.463525	+	0.802850i
$5$	0.618034	+	1.07047i	0.276393	+	0.478727i	0.970486	−	0.241159i	$-0.0775275\pi$
$5$	0.618034	+	1.07047i	0.276393	+	0.478727i	−0.694092	+	0.719886i	$0.744194\pi$
$6$			0.661585i			0.270091i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	−0.755929	−	0.654654i	$-0.772814\pi$
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i	0.944911	+	0.327327i	$0.106148\pi$
$8$	1.47214			0.520479
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	0.472136			0.149302
$11$		0			0
$11$		0			0
$12$	−2.78115	−	1.60570i	−0.802850	−	0.463525i
$13$	3.23607	+	5.60503i	0.897524	+	1.55456i	0.830650	+	0.556795i	$0.187969\pi$
$13$	3.23607	+	5.60503i	0.897524	+	1.55456i	0.0668741	+	0.997761i	$0.478697\pi$
$14$	−0.190983	−	0.330792i	−0.0510424	−	0.0884080i
$15$	−1.85410	−	1.07047i	−0.478727	−	0.276393i
$16$	−1.57295	+	2.72443i	−0.393237	+	0.681107i
$17$	4.85410			1.17729			0.588646	−	0.808391i	$-0.299661\pi$
$17$	4.85410			1.17729			0.588646	+	0.808391i	$0.299661\pi$
$18$	−0.572949	−	0.992377i	−0.135045	−	0.233905i
$19$	1.00000			0.229416			0.114708	−	0.993399i	$-0.463407\pi$
$19$	1.00000			0.229416			0.114708	+	0.993399i	$0.463407\pi$
$20$	−1.14590	+	1.98475i	−0.256231	+	0.443804i
$21$			1.73205i			0.377964i
$22$		0			0
$23$	−2.30902	−	3.99933i	−0.481463	−	0.833919i	0.518310	−	0.855193i	$-0.326561\pi$
$23$	−2.30902	−	3.99933i	−0.481463	−	0.833919i	−0.999774	+	0.0212736i	$0.993228\pi$
$24$	−2.20820	+	1.27491i	−0.450748	+	0.260239i
$25$	1.73607	−	3.00696i	0.347214	−	0.601392i
$26$	2.47214			0.484826
$27$			5.19615i			1.00000i
$28$	1.85410			0.350392
$29$	2.42705	−	4.20378i	0.450692	−	0.780622i	−0.547737	−	0.836651i	$-0.684511\pi$
$29$	2.42705	−	4.20378i	0.450692	−	0.780622i	0.998429	+	0.0560290i	$0.0178439\pi$
$30$	−0.708204	+	0.408882i	−0.129300	+	0.0746512i
$31$	−0.309017	−	0.535233i	−0.0555011	−	0.0961307i	0.836940	−	0.547295i	$-0.184342\pi$
$31$	−0.309017	−	0.535233i	−0.0555011	−	0.0961307i	−0.892441	+	0.451164i	$0.851009\pi$
$32$	2.07295	+	3.59045i	0.366449	+	0.634708i
$33$		0			0
$34$	0.927051	−	1.60570i	0.158988	−	0.275375i
$35$	1.23607			0.208934
$36$	5.56231			0.927051
$37$	−5.09017			−0.836819			−0.418409	−	0.908259i	$-0.637412\pi$
$37$	−5.09017			−0.836819			−0.418409	+	0.908259i	$0.637412\pi$
$38$	0.190983	−	0.330792i	0.0309815	−	0.0536616i
$39$	−9.70820	−	5.60503i	−1.55456	−	0.897524i
$40$	0.909830	+	1.57587i	0.143857	+	0.249167i
$41$	1.26393	+	2.18919i	0.197393	+	0.341895i	0.947682	−	0.319215i	$-0.103419\pi$
$41$	1.26393	+	2.18919i	0.197393	+	0.341895i	−0.750289	+	0.661110i	$0.770086\pi$
$42$	0.572949	+	0.330792i	0.0884080	+	0.0510424i
$43$	−0.927051	+	1.60570i	−0.141374	+	0.244867i	−0.928014	−	0.372545i	$-0.878485\pi$
$43$	−0.927051	+	1.60570i	−0.141374	+	0.244867i	0.786640	+	0.617412i	$0.211819\pi$
$44$		0			0
$45$	3.70820			0.552786
$46$	−1.76393			−0.260078
$47$	−5.97214	+	10.3440i	−0.871126	+	1.50883i	−0.0102921	+	0.999947i	$0.503276\pi$
$47$	−5.97214	+	10.3440i	−0.871126	+	1.50883i	−0.860834	+	0.508887i	$0.830057\pi$
$48$		−	5.44886i		−	0.786475i
$49$	3.00000	+	5.19615i	0.428571	+	0.742307i
$50$	−0.663119	−	1.14856i	−0.0937792	−	0.162430i
$51$	−7.28115	+	4.20378i	−1.01957	+	0.588646i
$52$	−6.00000	+	10.3923i	−0.832050	+	1.44115i
$53$	4.09017			0.561828			0.280914	−	0.959733i	$-0.409362\pi$
$53$	4.09017			0.561828			0.280914	+	0.959733i	$0.409362\pi$
$54$	1.71885	+	0.992377i	0.233905	+	0.135045i
$55$		0			0
$56$	0.736068	−	1.27491i	0.0983612	−	0.170367i
$57$	−1.50000	+	0.866025i	−0.198680	+	0.114708i
$58$	−0.927051	−	1.60570i	−0.121728	−	0.210839i
$59$	−0.809017	−	1.40126i	−0.105325	−	0.182428i	0.808546	−	0.588433i	$-0.200255\pi$
$59$	−0.809017	−	1.40126i	−0.105325	−	0.182428i	−0.913871	+	0.406005i	$0.866922\pi$
$60$		−	3.96951i		−	0.512461i
$61$	−5.42705	+	9.39993i	−0.694863	+	1.20354i	0.275364	+	0.961340i	$0.411202\pi$
$61$	−5.42705	+	9.39993i	−0.694863	+	1.20354i	−0.970227	+	0.242198i	$0.922132\pi$
$62$	−0.236068			−0.0299807
$63$	−1.50000	−	2.59808i	−0.188982	−	0.327327i
$64$	−4.70820			−0.588525
$65$	−4.00000	+	6.92820i	−0.496139	+	0.859338i
$66$		0			0
$67$	−3.00000	−	5.19615i	−0.366508	−	0.634811i	0.622509	−	0.782613i	$-0.286114\pi$
$67$	−3.00000	−	5.19615i	−0.366508	−	0.634811i	−0.989017	+	0.147802i	$0.952780\pi$
$68$	4.50000	+	7.79423i	0.545705	+	0.945189i
$69$	6.92705	+	3.99933i	0.833919	+	0.481463i
$70$	0.236068	−	0.408882i	0.0282155	−	0.0488707i
$71$	−2.90983			−0.345333			−0.172667	−	0.984980i	$-0.555238\pi$
$71$	−2.90983			−0.345333			−0.172667	+	0.984980i	$0.555238\pi$
$72$	2.20820	−	3.82472i	0.260239	−	0.450748i
$73$	−0.145898			−0.0170761			−0.00853804	−	0.999964i	$-0.502718\pi$
$73$	−0.145898			−0.0170761			−0.00853804	+	0.999964i	$0.502718\pi$
$74$	−0.972136	+	1.68379i	−0.113009	+	0.195736i
$75$			6.01392i			0.694427i
$76$	0.927051	+	1.60570i	0.106340	+	0.184186i
$77$		0			0
$78$	−3.70820	+	2.14093i	−0.419871	+	0.242413i
$79$	−5.28115	+	9.14723i	−0.594176	+	1.02914i	0.399486	+	0.916739i	$0.369188\pi$
$79$	−5.28115	+	9.14723i	−0.594176	+	1.02914i	−0.993663	+	0.112404i	$0.964145\pi$
$80$	−3.88854			−0.434752
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	0.965558			0.106628
$83$	4.88197	−	8.45581i	0.535865	−	0.928146i	−0.463256	−	0.886225i	$-0.653319\pi$
$83$	4.88197	−	8.45581i	0.535865	−	0.928146i	0.999121	−	0.0419213i	$-0.0133479\pi$
$84$	−2.78115	+	1.60570i	−0.303449	+	0.175196i
$85$	3.00000	+	5.19615i	0.325396	+	0.563602i
$86$	0.354102	+	0.613323i	0.0381838	+	0.0661363i
$87$			8.40755i			0.901384i
$88$		0			0
$89$	−6.76393			−0.716975			−0.358488	−	0.933534i	$-0.616707\pi$
$89$	−6.76393			−0.716975			−0.358488	+	0.933534i	$0.616707\pi$
$90$	0.708204	−	1.22665i	0.0746512	−	0.129300i
$91$	6.47214			0.678464
$92$	4.28115	−	7.41517i	0.446341	−	0.773085i
$93$	0.927051	+	0.535233i	0.0961307	+	0.0555011i
$94$	2.28115	+	3.95107i	0.235283	+	0.407522i
$95$	0.618034	+	1.07047i	0.0634089	+	0.109828i
$96$	−6.21885	−	3.59045i	−0.634708	−	0.366449i
$97$	−3.00000	+	5.19615i	−0.304604	+	0.527589i	−0.977173	−	0.212445i	$-0.931857\pi$
$97$	−3.00000	+	5.19615i	−0.304604	+	0.527589i	0.672569	+	0.740034i	$0.265191\pi$
$98$	2.29180			0.231506
$99$		0			0
$100$	6.43769			0.643769
$101$	4.23607	−	7.33708i	0.421505	−	0.730067i	−0.574582	−	0.818447i	$-0.694835\pi$
$101$	4.23607	−	7.33708i	0.421505	−	0.730067i	0.996087	+	0.0883795i	$0.0281688\pi$
$102$			3.21140i			0.317976i
$103$	5.11803	+	8.86469i	0.504295	+	0.873464i	0.999988	+	0.00496641i	$0.00158086\pi$
$103$	5.11803	+	8.86469i	0.504295	+	0.873464i	−0.495693	+	0.868498i	$0.665086\pi$
$104$	4.76393	+	8.25137i	0.467142	+	0.809114i
$105$	−1.85410	+	1.07047i	−0.180942	+	0.104467i
$106$	0.781153	−	1.35300i	0.0758723	−	0.131415i
$107$	14.0344			1.35676			0.678380	−	0.734711i	$-0.262682\pi$
$107$	14.0344			1.35676			0.678380	+	0.734711i	$0.262682\pi$
$108$	−8.34346	+	4.81710i	−0.802850	+	0.463525i
$109$	7.14590			0.684453			0.342226	−	0.939618i	$-0.388819\pi$
$109$	7.14590			0.684453			0.342226	+	0.939618i	$0.388819\pi$
$110$		0			0
$111$	7.63525	−	4.40822i	0.724706	−	0.418409i
$112$	1.57295	+	2.72443i	0.148630	+	0.257434i
$113$	−8.61803	−	14.9269i	−0.810716	−	1.40420i	−0.912363	−	0.409382i	$-0.865745\pi$
$113$	−8.61803	−	14.9269i	−0.810716	−	1.40420i	0.101647	−	0.994821i	$-0.467589\pi$
$114$			0.661585i			0.0619631i
$115$	2.85410	−	4.94345i	0.266146	−	0.460979i
$116$	9.00000			0.835629
$117$	19.4164			1.79505
$118$	−0.618034			−0.0568946
$119$	2.42705	−	4.20378i	0.222487	−	0.385359i
$120$	−2.72949	−	1.57587i	−0.249167	−	0.143857i
$121$		0			0
$122$	2.07295	+	3.59045i	0.187676	+	0.325064i
$123$	−3.79180	−	2.18919i	−0.341895	−	0.197393i
$124$	0.572949	−	0.992377i	0.0514523	−	0.0891181i
$125$	10.4721			0.936656
$126$	−1.14590			−0.102085
$127$	−10.5623			−0.937253			−0.468627	−	0.883396i	$-0.655251\pi$
$127$	−10.5623			−0.937253			−0.468627	+	0.883396i	$0.655251\pi$
$128$	−5.04508	+	8.73834i	−0.445927	+	0.772368i
$129$		−	3.21140i		−	0.282748i
$130$	1.52786	+	2.64634i	0.134003	+	0.232099i
$131$	−10.6180	−	18.3910i	−0.927702	−	1.60683i	−0.787157	−	0.616753i	$-0.788448\pi$
$131$	−10.6180	−	18.3910i	−0.927702	−	1.60683i	−0.140545	−	0.990074i	$-0.544885\pi$
$132$		0			0
$133$	0.500000	−	0.866025i	0.0433555	−	0.0750939i
$134$	−2.29180			−0.197981
$135$	−5.56231	+	3.21140i	−0.478727	+	0.276393i
$136$	7.14590			0.612756
$137$	4.30902	−	7.46344i	0.368144	−	0.637644i	−0.621131	−	0.783707i	$-0.713327\pi$
$137$	4.30902	−	7.46344i	0.368144	−	0.637644i	0.989275	+	0.146062i	$0.0466600\pi$
$138$	2.64590	−	1.52761i	0.225234	−	0.130039i
$139$	−4.85410	−	8.40755i	−0.411720	−	0.713119i	0.583358	−	0.812215i	$-0.301738\pi$
$139$	−4.85410	−	8.40755i	−0.411720	−	0.713119i	−0.995078	+	0.0990957i	$0.968405\pi$
$140$	1.14590	+	1.98475i	0.0968461	+	0.167742i
$141$		−	20.6881i		−	1.74225i
$142$	−0.555728	+	0.962549i	−0.0466357	+	0.0807753i
$143$		0			0
$144$	4.71885	+	8.17328i	0.393237	+	0.681107i
$145$	6.00000			0.498273
$146$	−0.0278640	+	0.0482619i	−0.00230604	+	0.00399419i
$147$	−9.00000	−	5.19615i	−0.742307	−	0.428571i
$148$	−4.71885	−	8.17328i	−0.387887	−	0.671840i
$149$	7.59017	+	13.1466i	0.621811	+	1.07701i	0.989148	+	0.146920i	$0.0469361\pi$
$149$	7.59017	+	13.1466i	0.621811	+	1.07701i	−0.367337	+	0.930088i	$0.619731\pi$
$150$	1.98936	+	1.14856i	0.162430	+	0.0937792i
$151$	−2.16312	+	3.74663i	−0.176032	+	0.304897i	−0.940518	−	0.339744i	$-0.889660\pi$
$151$	−2.16312	+	3.74663i	−0.176032	+	0.304897i	0.764486	+	0.644641i	$0.222993\pi$
$152$	1.47214			0.119406
$153$	7.28115	−	12.6113i	0.588646	−	1.01957i
$154$		0			0
$155$	0.381966	−	0.661585i	0.0306802	−	0.0531397i
$156$		−	20.7846i		−	1.66410i
$157$	−3.57295	−	6.18853i	−0.285152	−	0.493898i	0.687494	−	0.726190i	$-0.258711\pi$
$157$	−3.57295	−	6.18853i	−0.285152	−	0.493898i	−0.972646	+	0.232292i	$0.925378\pi$
$158$	2.01722	+	3.49393i	0.160481	+	0.277962i
$159$	−6.13525	+	3.54219i	−0.486557	+	0.280914i
$160$	−2.56231	+	4.43804i	−0.202568	+	0.350858i
$161$	−4.61803			−0.363952
$162$	−3.43769			−0.270091
$163$	20.7082			1.62199			0.810996	−	0.585052i	$-0.198926\pi$
$163$	20.7082			1.62199			0.810996	+	0.585052i	$0.198926\pi$
$164$	−2.34346	+	4.05899i	−0.182993	+	0.316954i
$165$		0			0
$166$	−1.86475	−	3.22983i	−0.144732	−	0.250684i
$167$	2.88197	+	4.99171i	0.223013	+	0.386270i	0.955722	−	0.294273i	$-0.0950774\pi$
$167$	2.88197	+	4.99171i	0.223013	+	0.386270i	−0.732708	+	0.680543i	$0.761744\pi$
$168$			2.54981i			0.196722i
$169$	−14.4443	+	25.0182i	−1.11110	+	1.92448i
$170$	2.29180			0.175773
$171$	1.50000	−	2.59808i	0.114708	−	0.198680i
$172$	−3.43769			−0.262122
$173$	11.5451	−	19.9967i	0.877757	−	1.52032i	0.0239595	−	0.999713i	$-0.492373\pi$
$173$	11.5451	−	19.9967i	0.877757	−	1.52032i	0.853797	−	0.520606i	$-0.174294\pi$
$174$	2.78115	+	1.60570i	0.210839	+	0.121728i
$175$	−1.73607	−	3.00696i	−0.131234	−	0.227305i
$176$		0			0
$177$	2.42705	+	1.40126i	0.182428	+	0.105325i
$178$	−1.29180	+	2.23746i	−0.0968242	+	0.167704i
$179$	−5.05573			−0.377883			−0.188941	−	0.981988i	$-0.560506\pi$
$179$	−5.05573			−0.377883			−0.188941	+	0.981988i	$0.560506\pi$
$180$	3.43769	+	5.95426i	0.256231	+	0.443804i
$181$	−9.90983			−0.736592			−0.368296	−	0.929709i	$-0.620059\pi$
$181$	−9.90983			−0.736592			−0.368296	+	0.929709i	$0.620059\pi$
$182$	1.23607	−	2.14093i	0.0916235	−	0.158696i
$183$		−	18.7999i		−	1.38973i
$184$	−3.39919	−	5.88756i	−0.250591	−	0.434037i
$185$	−3.14590	−	5.44886i	−0.231291	−	0.400608i
$186$	0.354102	−	0.204441i	0.0259640	−	0.0149903i
$187$		0			0
$188$	−22.1459			−1.61516
$189$	4.50000	+	2.59808i	0.327327	+	0.188982i
$190$	0.472136			0.0342523
$191$	−2.97214	+	5.14789i	−0.215056	+	0.372488i	−0.953290	−	0.302057i	$-0.902327\pi$
$191$	−2.97214	+	5.14789i	−0.215056	+	0.372488i	0.738234	+	0.674545i	$0.235660\pi$
$192$	7.06231	−	4.07742i	0.509678	−	0.294263i
$193$	5.50000	+	9.52628i	0.395899	+	0.685717i	0.993215	−	0.116289i	$-0.0370998\pi$
$193$	5.50000	+	9.52628i	0.395899	+	0.685717i	−0.597317	+	0.802005i	$0.703766\pi$
$194$	1.14590	+	1.98475i	0.0822707	+	0.142497i
$195$		−	13.8564i		−	0.992278i
$196$	−5.56231	+	9.63420i	−0.397308	+	0.688157i
$197$	8.23607			0.586796			0.293398	−	0.955990i	$-0.405214\pi$
$197$	8.23607			0.586796			0.293398	+	0.955990i	$0.405214\pi$
$198$		0			0
$199$	−7.14590			−0.506559			−0.253280	−	0.967393i	$-0.581509\pi$
$199$	−7.14590			−0.506559			−0.253280	+	0.967393i	$0.581509\pi$
$200$	2.55573	−	4.42665i	0.180717	−	0.313011i
$201$	9.00000	+	5.19615i	0.634811	+	0.366508i
$202$	−1.61803	−	2.80252i	−0.113844	−	0.197184i
$203$	−2.42705	−	4.20378i	−0.170346	−	0.295047i
$204$	−13.5000	−	7.79423i	−0.945189	−	0.545705i
$205$	−1.56231	+	2.70599i	−0.109116	+	0.188995i
$206$	3.90983			0.272411
$207$	−13.8541			−0.962927
$208$	−20.3607			−1.41176
$209$		0			0
$210$			0.817763i			0.0564310i
$211$	−10.2361	−	17.7294i	−0.704680	−	1.22054i	−0.966807	−	0.255508i	$-0.917757\pi$
$211$	−10.2361	−	17.7294i	−0.704680	−	1.22054i	0.262127	−	0.965033i	$-0.415576\pi$
$212$	3.79180	+	6.56758i	0.260422	+	0.451063i
$213$	4.36475	−	2.51999i	0.299067	−	0.172667i
$214$	2.68034	−	4.64248i	0.183224	−	0.317354i
$215$	−2.29180			−0.156299
$216$			7.64944i			0.520479i
$217$	−0.618034			−0.0419549
$218$	1.36475	−	2.36381i	0.0924322	−	0.160097i
$219$	0.218847	−	0.126351i	0.0147883	−	0.00853804i
$220$		0			0
$221$	15.7082	+	27.2074i	1.05665	+	1.83017i
$222$		−	3.36758i		−	0.226017i
$223$	7.75329	−	13.4291i	0.519199	−	0.899278i	−0.480552	−	0.876966i	$-0.659564\pi$
$223$	7.75329	−	13.4291i	0.519199	−	0.899278i	0.999751	−	0.0223124i	$-0.00710285\pi$
$224$	4.14590			0.277009
$225$	−5.20820	−	9.02087i	−0.347214	−	0.601392i
$226$	−6.58359			−0.437934
$227$	8.30902	−	14.3916i	0.551489	−	0.955207i	−0.446679	−	0.894694i	$-0.647393\pi$
$227$	8.30902	−	14.3916i	0.551489	−	0.955207i	0.998167	−	0.0605122i	$-0.0192734\pi$
$228$	−2.78115	−	1.60570i	−0.184186	−	0.106340i
$229$	−5.09017	−	8.81643i	−0.336368	−	0.582606i	0.647379	−	0.762168i	$-0.275865\pi$
$229$	−5.09017	−	8.81643i	−0.336368	−	0.582606i	−0.983747	+	0.179562i	$0.942532\pi$
$230$	−1.09017	−	1.88823i	−0.0718837	−	0.124506i
$231$		0			0
$232$	3.57295	−	6.18853i	0.234576	−	0.406297i
$233$	−11.1246			−0.728798			−0.364399	−	0.931243i	$-0.618725\pi$
$233$	−11.1246			−0.728798			−0.364399	+	0.931243i	$0.618725\pi$
$234$	3.70820	−	6.42280i	0.242413	−	0.419871i
$235$	−14.7639			−0.963093
$236$	1.50000	−	2.59808i	0.0976417	−	0.169120i
$237$		−	18.2945i		−	1.18835i
$238$	−0.927051	−	1.60570i	−0.0600918	−	0.104082i
$239$	−5.23607	−	9.06914i	−0.338693	−	0.586634i	0.645494	−	0.763765i	$-0.276651\pi$
$239$	−5.23607	−	9.06914i	−0.338693	−	0.586634i	−0.984187	+	0.177132i	$0.943318\pi$
$240$	5.83282	−	3.36758i	0.376507	−	0.217376i
$241$	13.4164	−	23.2379i	0.864227	−	1.49688i	−0.00358606	−	0.999994i	$-0.501141\pi$
$241$	13.4164	−	23.2379i	0.864227	−	1.49688i	0.867813	−	0.496891i	$-0.165525\pi$
$242$		0			0
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$	−20.1246			−1.28835
$245$	−3.70820	+	6.42280i	−0.236908	+	0.410337i
$246$	−1.44834	+	0.836198i	−0.0923426	+	0.0533140i
$247$	3.23607	+	5.60503i	0.205906	+	0.356640i
$248$	−0.454915	−	0.787936i	−0.0288871	−	0.0500340i
$249$			16.9116i			1.07173i
$250$	2.00000	−	3.46410i	0.126491	−	0.219089i
$251$	20.5623			1.29788			0.648941	−	0.760839i	$-0.275212\pi$
$251$	20.5623			1.29788			0.648941	+	0.760839i	$0.275212\pi$
$252$	2.78115	−	4.81710i	0.175196	−	0.303449i
$253$		0			0
$254$	−2.01722	+	3.49393i	−0.126572	+	0.219229i
$255$	−9.00000	−	5.19615i	−0.563602	−	0.325396i
$256$	−2.78115	−	4.81710i	−0.173822	−	0.301069i
$257$	7.45492	+	12.9123i	0.465025	+	0.805447i	0.999203	−	0.0399255i	$-0.0127121\pi$
$257$	7.45492	+	12.9123i	0.465025	+	0.805447i	−0.534178	+	0.845372i	$0.679379\pi$
$258$	−1.06231	−	0.613323i	−0.0661363	−	0.0381838i
$259$	−2.54508	+	4.40822i	−0.158144	+	0.273913i
$260$	−14.8328			−0.919892
$261$	−7.28115	−	12.6113i	−0.450692	−	0.780622i
$262$	−8.11146			−0.501127
$263$	6.35410	−	11.0056i	0.391811	−	0.678636i	−0.600878	−	0.799341i	$-0.705182\pi$
$263$	6.35410	−	11.0056i	0.391811	−	0.678636i	0.992688	+	0.120705i	$0.0385155\pi$
$264$		0			0
$265$	2.52786	+	4.37839i	0.155285	+	0.268962i
$266$	−0.190983	−	0.330792i	−0.0117099	−	0.0202822i
$267$	10.1459	−	5.85774i	0.620919	−	0.358488i
$268$	5.56231	−	9.63420i	0.339772	−	0.588502i
$269$	−21.2705			−1.29689			−0.648443	−	0.761263i	$-0.724579\pi$
$269$	−21.2705			−1.29689			−0.648443	+	0.761263i	$0.724579\pi$
$270$			2.45329i			0.149302i
$271$	10.7639			0.653862			0.326931	−	0.945048i	$-0.393985\pi$
$271$	10.7639			0.653862			0.326931	+	0.945048i	$0.393985\pi$
$272$	−7.63525	+	13.2246i	−0.462955	+	0.801862i
$273$	−9.70820	+	5.60503i	−0.587567	+	0.339232i
$274$	−1.64590	−	2.85078i	−0.0994323	−	0.172222i
$275$		0			0
$276$			14.8303i			0.892682i
$277$	9.61803	−	16.6589i	0.577892	−	1.00094i	−0.417829	−	0.908526i	$-0.637209\pi$
$277$	9.61803	−	16.6589i	0.577892	−	1.00094i	0.995721	−	0.0924121i	$-0.0294577\pi$
$278$	−3.70820			−0.222403
$279$	−1.85410			−0.111002
$280$	1.81966			0.108745
$281$	4.66312	−	8.07676i	0.278178	−	0.481819i	−0.692754	−	0.721174i	$-0.743603\pi$
$281$	4.66312	−	8.07676i	0.278178	−	0.481819i	0.970932	+	0.239355i	$0.0769360\pi$
$282$	−6.84346	−	3.95107i	−0.407522	−	0.235283i
$283$	8.50000	+	14.7224i	0.505273	+	0.875158i	0.999981	+	0.00609896i	$0.00194137\pi$
$283$	8.50000	+	14.7224i	0.505273	+	0.875158i	−0.494709	+	0.869059i	$0.664725\pi$
$284$	−2.69756	−	4.67231i	−0.160071	−	0.277251i
$285$	−1.85410	−	1.07047i	−0.109828	−	0.0634089i
$286$		0			0
$287$	2.52786			0.149215
$288$	12.4377			0.732898
$289$	6.56231			0.386018
$290$	1.14590	−	1.98475i	0.0672894	−	0.116549i
$291$		−	10.3923i		−	0.609208i
$292$	−0.135255	−	0.234268i	−0.00791520	−	0.0137095i
$293$	14.5902	+	25.2709i	0.852367	+	1.47634i	0.879067	+	0.476699i	$0.158167\pi$
$293$	14.5902	+	25.2709i	0.852367	+	1.47634i	−0.0266997	+	0.999644i	$0.508500\pi$
$294$	−3.43769	+	1.98475i	−0.200490	+	0.115753i
$295$	1.00000	−	1.73205i	0.0582223	−	0.100844i
$296$	−7.49342			−0.435546
$297$		0			0
$298$	5.79837			0.335891
$299$	14.9443	−	25.8842i	0.864250	−	1.49692i
$300$	−9.65654	+	5.57521i	−0.557521	+	0.321885i
$301$	0.927051	+	1.60570i	0.0534343	+	0.0925510i
$302$	0.826238	+	1.43109i	0.0475446	+	0.0823497i
$303$			14.6742i			0.843009i
$304$	−1.57295	+	2.72443i	−0.0902148	+	0.156257i
$305$	−13.4164			−0.768221
$306$	−2.78115	−	4.81710i	−0.158988	−	0.275375i
$307$	7.85410			0.448257			0.224129	−	0.974560i	$-0.428046\pi$
$307$	7.85410			0.448257			0.224129	+	0.974560i	$0.428046\pi$
$308$		0			0
$309$	−15.3541	−	8.86469i	−0.873464	−	0.504295i
$310$	−0.145898	−	0.252703i	−0.00828645	−	0.0143526i
$311$	−7.59017	−	13.1466i	−0.430399	−	0.745473i	0.566509	−	0.824056i	$-0.308294\pi$
$311$	−7.59017	−	13.1466i	−0.430399	−	0.745473i	−0.996908	+	0.0785828i	$0.974960\pi$
$312$	−14.2918	−	8.25137i	−0.809114	−	0.467142i
$313$	−1.73607	+	3.00696i	−0.0981284	+	0.169963i	−0.910910	−	0.412605i	$-0.864619\pi$
$313$	−1.73607	+	3.00696i	−0.0981284	+	0.169963i	0.812782	+	0.582569i	$0.197952\pi$
$314$	−2.72949			−0.154034
$315$	1.85410	−	3.21140i	0.104467	−	0.180942i
$316$	−19.5836			−1.10166
$317$	−10.4721	+	18.1383i	−0.588174	+	1.01875i	0.406298	+	0.913741i	$0.366820\pi$
$317$	−10.4721	+	18.1383i	−0.588174	+	1.01875i	−0.994472	+	0.105006i	$0.966514\pi$
$318$			2.70599i			0.151745i
$319$		0			0
$320$	−2.90983	−	5.03997i	−0.162664	−	0.281743i
$321$	−21.0517	+	12.1542i	−1.17499	+	0.678380i
$322$	−0.881966	+	1.52761i	−0.0491500	+	0.0851304i
$323$	4.85410			0.270089
$324$	8.34346	−	14.4513i	0.463525	−	0.802850i
$325$	22.4721			1.24653
$326$	3.95492	−	6.85011i	0.219042	−	0.379393i
$327$	−10.7188	+	6.18853i	−0.592754	+	0.342226i
$328$	1.86068	+	3.22279i	0.102739	+	0.177949i
$329$	5.97214	+	10.3440i	0.329255	+	0.570286i
$330$		0			0
$331$	−7.20820	+	12.4850i	−0.396199	+	0.686236i	−0.993253	−	0.115964i	$-0.963004\pi$
$331$	−7.20820	+	12.4850i	−0.396199	+	0.686236i	0.597055	+	0.802201i	$0.296338\pi$
$332$	18.1033			0.993549
$333$	−7.63525	+	13.2246i	−0.418409	+	0.724706i
$334$	2.20163			0.120468
$335$	3.70820	−	6.42280i	0.202601	−	0.350915i
$336$	−4.71885	−	2.72443i	−0.257434	−	0.148630i
$337$	5.73607	+	9.93516i	0.312464	+	0.541203i	0.978895	−	0.204364i	$-0.0655125\pi$
$337$	5.73607	+	9.93516i	0.312464	+	0.541203i	−0.666432	+	0.745566i	$0.732179\pi$
$338$	5.51722	+	9.55611i	0.300097	+	0.519784i
$339$	25.8541	+	14.9269i	1.40420	+	0.810716i
$340$	−5.56231	+	9.63420i	−0.301658	+	0.522488i
$341$		0			0
$342$	−0.572949	−	0.992377i	−0.0309815	−	0.0536616i
$343$	13.0000			0.701934
$344$	−1.36475	+	2.36381i	−0.0735821	+	0.127448i
$345$			9.88690i			0.532293i
$346$	−4.40983	−	7.63805i	−0.237074	−	0.410624i
$347$	4.44427	+	7.69770i	0.238581	+	0.413234i	0.960307	−	0.278944i	$-0.0899844\pi$
$347$	4.44427	+	7.69770i	0.238581	+	0.413234i	−0.721726	+	0.692179i	$0.756651\pi$
$348$	−13.5000	+	7.79423i	−0.723676	+	0.417815i
$349$	2.07295	−	3.59045i	0.110962	−	0.192193i	−0.805196	−	0.593009i	$-0.797940\pi$
$349$	2.07295	−	3.59045i	0.110962	−	0.192193i	0.916159	+	0.400816i	$0.131273\pi$
$350$	−1.32624			−0.0708904
$351$	−29.1246	+	16.8151i	−1.55456	+	0.897524i
$352$		0			0
$353$	8.20820	−	14.2170i	0.436879	−	0.756696i	−0.560568	−	0.828108i	$-0.689417\pi$
$353$	8.20820	−	14.2170i	0.436879	−	0.756696i	0.997447	+	0.0714123i	$0.0227506\pi$
$354$	0.927051	−	0.535233i	0.0492722	−	0.0284473i
$355$	−1.79837	−	3.11487i	−0.0954478	−	0.165320i
$356$	−6.27051	−	10.8608i	−0.332336	−	0.575623i
$357$			8.40755i			0.444975i
$358$	−0.965558	+	1.67240i	−0.0510313	+	0.0883889i
$359$	−22.8541			−1.20619			−0.603097	−	0.797668i	$-0.706067\pi$
$359$	−22.8541			−1.20619			−0.603097	+	0.797668i	$0.706067\pi$
$360$	5.45898			0.287714
$361$	−18.0000			−0.947368
$362$	−1.89261	+	3.27810i	−0.0994733	+	0.172293i
$363$		0			0
$364$	6.00000	+	10.3923i	0.314485	+	0.544705i
$365$	−0.0901699	−	0.156179i	−0.00471971	−	0.00817478i
$366$	−6.21885	−	3.59045i	−0.325064	−	0.187676i
$367$	6.35410	−	11.0056i	0.331681	−	0.574489i	−0.651160	−	0.758940i	$-0.725717\pi$
$367$	6.35410	−	11.0056i	0.331681	−	0.574489i	0.982842	+	0.184451i	$0.0590508\pi$
$368$	14.5279			0.757317
$369$	7.58359			0.394786
$370$	−2.40325			−0.124939
$371$	2.04508	−	3.54219i	0.106176	−	0.183901i
$372$			1.98475i			0.102905i
$373$	2.82624	+	4.89519i	0.146337	+	0.253463i	0.929871	−	0.367886i	$-0.119918\pi$
$373$	2.82624	+	4.89519i	0.146337	+	0.253463i	−0.783534	+	0.621349i	$0.786585\pi$
$374$		0			0
$375$	−15.7082	+	9.06914i	−0.811168	+	0.468328i
$376$	−8.79180	+	15.2278i	−0.453402	+	0.785316i
$377$	31.4164			1.61803
$378$	1.71885	−	0.992377i	0.0884080	−	0.0510424i
$379$	15.7984			0.811508			0.405754	−	0.913982i	$-0.367009\pi$
$379$	15.7984			0.811508			0.405754	+	0.913982i	$0.367009\pi$
$380$	−1.14590	+	1.98475i	−0.0587833	+	0.101816i
$381$	15.8435	−	9.14723i	0.811685	−	0.468627i
$382$	1.13525	+	1.96632i	0.0580847	+	0.100606i
$383$	−9.92705	−	17.1942i	−0.507249	−	0.878580i	−0.999965	−	0.00839030i	$-0.997329\pi$
$383$	−9.92705	−	17.1942i	−0.507249	−	0.878580i	0.492716	−	0.870190i	$-0.336004\pi$
$384$		−	17.4767i		−	0.891853i
$385$		0			0
$386$	4.20163			0.213857
$387$	2.78115	+	4.81710i	0.141374	+	0.244867i
$388$	−11.1246			−0.564767
$389$	11.3262	−	19.6176i	0.574263	−	0.994653i	−0.421858	−	0.906662i	$-0.638622\pi$
$389$	11.3262	−	19.6176i	0.574263	−	0.994653i	0.996121	−	0.0879910i	$-0.0280447\pi$
$390$	−4.58359	−	2.64634i	−0.232099	−	0.134003i
$391$	−11.2082	−	19.4132i	−0.566823	−	0.981767i
$392$	4.41641	+	7.64944i	0.223062	+	0.386355i
$393$	31.8541	+	18.3910i	1.60683	+	0.927702i
$394$	1.57295	−	2.72443i	0.0792440	−	0.137255i
$395$	−13.0557			−0.656905
$396$		0			0
$397$	−2.12461			−0.106631			−0.0533156	−	0.998578i	$-0.516979\pi$
$397$	−2.12461			−0.106631			−0.0533156	+	0.998578i	$0.516979\pi$
$398$	−1.36475	+	2.36381i	−0.0684085	+	0.118487i
$399$			1.73205i			0.0867110i
$400$	5.46149	+	9.45958i	0.273075	+	0.472979i
$401$	−7.28115	−	12.6113i	−0.363603	−	0.629780i	0.624948	−	0.780667i	$-0.285120\pi$
$401$	−7.28115	−	12.6113i	−0.363603	−	0.629780i	−0.988551	+	0.150887i	$0.951787\pi$
$402$	3.43769	−	1.98475i	0.171457	−	0.0989905i
$403$	2.00000	−	3.46410i	0.0996271	−	0.172559i
$404$	15.7082			0.781512
$405$	5.56231	−	9.63420i	0.276393	−	0.478727i
$406$	−1.85410			−0.0920175
$407$		0			0
$408$	−10.7188	+	6.18853i	−0.530662	+	0.306378i
$409$	16.8713	+	29.2220i	0.834233	+	1.44493i	0.894653	+	0.446761i	$0.147423\pi$
$409$	16.8713	+	29.2220i	0.834233	+	1.44493i	−0.0604200	+	0.998173i	$0.519244\pi$
$410$	0.596748	+	1.03360i	0.0294713	+	0.0510457i
$411$			14.9269i			0.736288i
$412$	−9.48936	+	16.4360i	−0.467507	+	0.809746i
$413$	−1.61803			−0.0796182
$414$	−2.64590	+	4.58283i	−0.130039	+	0.225234i
$415$	12.0689			0.592438
$416$	−13.4164	+	23.2379i	−0.657794	+	1.13933i
$417$	14.5623	+	8.40755i	0.713119	+	0.411720i
$418$		0			0
$419$	−4.04508	−	7.00629i	−0.197615	−	0.342280i	0.750139	−	0.661280i	$-0.229986\pi$
$419$	−4.04508	−	7.00629i	−0.197615	−	0.342280i	−0.947755	+	0.319000i	$0.896653\pi$
$420$	−3.43769	−	1.98475i	−0.167742	−	0.0968461i
$421$	−5.11803	+	8.86469i	−0.249438	+	0.432039i	−0.963370	−	0.268176i	$-0.913579\pi$
$421$	−5.11803	+	8.86469i	−0.249438	+	0.432039i	0.713932	+	0.700215i	$0.246912\pi$
$422$	−7.81966			−0.380655
$423$	17.9164	+	31.0321i	0.871126	+	1.50883i
$424$	6.02129			0.292420
$425$	8.42705	−	14.5961i	0.408772	−	0.708014i
$426$		−	1.92510i		−	0.0932713i
$427$	5.42705	+	9.39993i	0.262633	+	0.454894i
$428$	13.0106	+	22.5351i	0.628893	+	1.08927i
$429$		0			0
$430$	−0.437694	+	0.758108i	−0.0211075	+	0.0365592i
$431$	−34.0689			−1.64104			−0.820520	−	0.571618i	$-0.806316\pi$
$431$	−34.0689			−1.64104			−0.820520	+	0.571618i	$0.806316\pi$
$432$	−14.1565	−	8.17328i	−0.681107	−	0.393237i
$433$	14.7426			0.708486			0.354243	−	0.935153i	$-0.384739\pi$
$433$	14.7426			0.708486			0.354243	+	0.935153i	$0.384739\pi$
$434$	−0.118034	+	0.204441i	−0.00566581	+	0.00981348i
$435$	−9.00000	+	5.19615i	−0.431517	+	0.249136i
$436$	6.62461	+	11.4742i	0.317261	+	0.549513i
$437$	−2.30902	−	3.99933i	−0.110455	−	0.191314i
$438$		−	0.0965239i		−	0.00461209i
$439$	0.354102	−	0.613323i	0.0169004	−	0.0292723i	−0.857452	−	0.514565i	$-0.827954\pi$
$439$	0.354102	−	0.613323i	0.0169004	−	0.0292723i	0.874352	+	0.485292i	$0.161287\pi$
$440$		0			0
$441$	18.0000			0.857143
$442$	12.0000			0.570782
$443$	0.618034	−	1.07047i	0.0293637	−	0.0508594i	−0.850970	−	0.525214i	$-0.823985\pi$
$443$	0.618034	−	1.07047i	0.0293637	−	0.0508594i	0.880334	+	0.474355i	$0.157319\pi$
$444$	14.1565	+	8.17328i	0.671840	+	0.387887i
$445$	−4.18034	−	7.24056i	−0.198167	−	0.343236i
$446$	−2.96149	−	5.12946i	−0.140231	−	0.242887i
$447$	−22.7705	−	13.1466i	−1.07701	−	0.621811i
$448$	−2.35410	+	4.07742i	−0.111221	+	0.192640i
$449$	7.47214			0.352632			0.176316	−	0.984334i	$-0.443582\pi$
$449$	7.47214			0.352632			0.176316	+	0.984334i	$0.443582\pi$
$450$	−3.97871			−0.187558
$451$		0			0
$452$	15.9787	−	27.6759i	0.751575	−	1.30177i
$453$		−	7.49326i		−	0.352064i
$454$	−3.17376	−	5.49712i	−0.148952	−	0.257992i
$455$	4.00000	+	6.92820i	0.187523	+	0.324799i
$456$	−2.20820	+	1.27491i	−0.103409	+	0.0597030i
$457$	0.500000	−	0.866025i	0.0233890	−	0.0405110i	−0.854094	−	0.520119i	$-0.825888\pi$
$457$	0.500000	−	0.866025i	0.0233890	−	0.0405110i	0.877483	+	0.479608i	$0.159221\pi$
$458$	−3.88854			−0.181700
$459$			25.2227i			1.17729i
$460$	10.5836			0.493463
$461$	8.07295	−	13.9828i	0.375995	−	0.651242i	−0.614481	−	0.788932i	$-0.710634\pi$
$461$	8.07295	−	13.9828i	0.375995	−	0.651242i	0.990475	+	0.137690i	$0.0439677\pi$
$462$		0			0
$463$	−8.50000	−	14.7224i	−0.395029	−	0.684209i	0.598076	−	0.801439i	$-0.295932\pi$
$463$	−8.50000	−	14.7224i	−0.395029	−	0.684209i	−0.993105	+	0.117230i	$0.962599\pi$
$464$	7.63525	+	13.2246i	0.354458	+	0.613939i
$465$			1.32317i			0.0613605i
$466$	−2.12461	+	3.67994i	−0.0984207	+	0.170470i
$467$	−0.763932			−0.0353506			−0.0176753	−	0.999844i	$-0.505627\pi$
$467$	−0.763932			−0.0353506			−0.0176753	+	0.999844i	$0.505627\pi$
$468$	18.0000	+	31.1769i	0.832050	+	1.44115i
$469$	−6.00000			−0.277054
$470$	−2.81966	+	4.88379i	−0.130061	+	0.225273i
$471$	10.7188	+	6.18853i	0.493898	+	0.285152i
$472$	−1.19098	−	2.06284i	−0.0548194	−	0.0949500i
$473$		0			0
$474$	−6.05166	−	3.49393i	−0.277962	−	0.160481i
$475$	1.73607	−	3.00696i	0.0796563	−	0.137969i
$476$	9.00000			0.412514
$477$	6.13525	−	10.6266i	0.280914	−	0.486557i
$478$	−4.00000			−0.182956
$479$	5.88197	−	10.1879i	0.268754	−	0.465495i	−0.699786	−	0.714352i	$-0.746722\pi$
$479$	5.88197	−	10.1879i	0.268754	−	0.465495i	0.968540	+	0.248857i	$0.0800548\pi$
$480$		−	8.87609i		−	0.405136i
$481$	−16.4721	−	28.5306i	−0.751065	−	1.30088i
$482$	−5.12461	−	8.87609i	−0.233420	−	0.404295i
$483$	6.92705	−	3.99933i	0.315192	−	0.181976i
$484$		0			0
$485$	−7.41641			−0.336762
$486$	5.15654	−	2.97713i	0.233905	−	0.135045i
$487$	−12.9787			−0.588122			−0.294061	−	0.955787i	$-0.595007\pi$
$487$	−12.9787			−0.588122			−0.294061	+	0.955787i	$0.595007\pi$
$488$	−7.98936	+	13.8380i	−0.361661	+	0.626416i
$489$	−31.0623	+	17.9338i	−1.40469	+	0.810996i
$490$	1.41641	+	2.45329i	0.0639868	+	0.110828i
$491$	−3.66312	−	6.34471i	−0.165314	−	0.286333i	0.771453	−	0.636287i	$-0.219531\pi$
$491$	−3.66312	−	6.34471i	−0.165314	−	0.286333i	−0.936767	+	0.349954i	$0.886197\pi$
$492$		−	8.11798i		−	0.365987i
$493$	11.7812	−	20.4056i	0.530596	−	0.919020i
$494$	2.47214			0.111227
$495$		0			0
$496$	1.94427			0.0873004
$497$	−1.45492	+	2.51999i	−0.0652619	+	0.113037i
$498$	5.59424	+	3.22983i	0.250684	+	0.144732i
$499$	−19.2082	−	33.2696i	−0.859877	−	1.48935i	−0.872045	−	0.489425i	$-0.837207\pi$
$499$	−19.2082	−	33.2696i	−0.859877	−	1.48935i	0.0121680	−	0.999926i	$-0.496127\pi$
$500$	9.70820	+	16.8151i	0.434164	+	0.751994i
$501$	−8.64590	−	4.99171i	−0.386270	−	0.223013i
$502$	3.92705	−	6.80185i	0.175273	−	0.303582i
$503$	−9.52786			−0.424826			−0.212413	−	0.977180i	$-0.568132\pi$
$503$	−9.52786			−0.424826			−0.212413	+	0.977180i	$0.568132\pi$
$504$	−2.20820	−	3.82472i	−0.0983612	−	0.170367i
$505$	10.4721			0.466004
$506$		0			0
$507$		−	50.0364i		−	2.22220i
$508$	−9.79180	−	16.9599i	−0.434441	−	0.752473i
$509$	13.5902	+	23.5389i	0.602374	+	1.04334i	0.992461	+	0.122564i	$0.0391116\pi$
$509$	13.5902	+	23.5389i	0.602374	+	1.04334i	−0.390087	+	0.920778i	$0.627555\pi$
$510$	−3.43769	+	1.98475i	−0.152224	+	0.0878864i
$511$	−0.0729490	+	0.126351i	−0.00322707	+	0.00558946i
$512$	−22.3050			−0.985749
$513$			5.19615i			0.229416i
$514$	5.69505			0.251198
$515$	−6.32624	+	10.9574i	−0.278767	+	0.482839i
$516$	5.15654	−	2.97713i	0.227004	−	0.131061i
$517$		0			0
$518$	0.972136	+	1.68379i	0.0427132	+	0.0739814i
$519$			39.9933i			1.75551i
$520$	−5.88854	+	10.1993i	−0.258230	+	0.447267i
$521$	−40.3607			−1.76823			−0.884117	−	0.467266i	$-0.845239\pi$
$521$	−40.3607			−1.76823			−0.884117	+	0.467266i	$0.845239\pi$
$522$	−5.56231			−0.243456
$523$		0			0			−	1.00000i	$-0.5\pi$
$523$		0			0				1.00000i	$0.5\pi$
$524$	19.6869	−	34.0987i	0.860027	−	1.48961i
$525$	5.20820	+	3.00696i	0.227305	+	0.131234i
$526$	−2.42705	−	4.20378i	−0.105824	−	0.183293i
$527$	−1.50000	−	2.59808i	−0.0653410	−	0.113174i
$528$		0			0
$529$	0.836881	−	1.44952i	0.0363861	−	0.0630226i
$530$	1.93112			0.0838823
$531$	−4.85410			−0.210650
$532$	1.85410			0.0803855
$533$	−8.18034	+	14.1688i	−0.354330	+	0.613717i
$534$		−	4.47491i		−	0.193648i
$535$	8.67376	+	15.0234i	0.374999	+	0.649518i
$536$	−4.41641	−	7.64944i	−0.190760	−	0.330406i
$537$	7.58359	−	4.37839i	0.327256	−	0.188941i
$538$	−4.06231	+	7.03612i	−0.175138	+	0.303349i
$539$		0			0
$540$	−10.3131	−	5.95426i	−0.443804	−	0.256231i
$541$	−11.9098			−0.512044			−0.256022	−	0.966671i	$-0.582412\pi$
$541$	−11.9098			−0.512044			−0.256022	+	0.966671i	$0.582412\pi$
$542$	2.05573	−	3.56063i	0.0883011	−	0.152942i
$543$	14.8647	−	8.58216i	0.637907	−	0.368296i
$544$	10.0623	+	17.4284i	0.431418	+	0.747238i
$545$	4.41641	+	7.64944i	0.189178	+	0.327666i
$546$			4.28187i			0.183247i
$547$	16.1631	−	27.9953i	0.691085	−	1.19699i	−0.280398	−	0.959884i	$-0.590466\pi$
$547$	16.1631	−	27.9953i	0.691085	−	1.19699i	0.971483	−	0.237111i	$-0.0762003\pi$
$548$	15.9787			0.682577
$549$	16.2812	+	28.1998i	0.694863	+	1.20354i
$550$		0			0
$551$	2.42705	−	4.20378i	0.103396	−	0.179087i
$552$	10.1976	+	5.88756i	0.434037	+	0.250591i
$553$	5.28115	+	9.14723i	0.224577	+	0.388980i
$554$	−3.67376	−	6.36314i	−0.156083	−	0.270344i
$555$	9.43769	+	5.44886i	0.400608	+	0.231291i
$556$	9.00000	−	15.5885i	0.381685	−	0.661098i
$557$	−0.652476			−0.0276463			−0.0138231	−	0.999904i	$-0.504400\pi$
$557$	−0.652476			−0.0276463			−0.0138231	+	0.999904i	$0.504400\pi$
$558$	−0.354102	+	0.613323i	−0.0149903	+	0.0259640i
$559$	−12.0000			−0.507546
$560$	−1.94427	+	3.36758i	−0.0821605	+	0.142306i
$561$		0			0
$562$	−1.78115	−	3.08505i	−0.0751334	−	0.130135i
$563$	10.1525	+	17.5846i	0.427876	+	0.741103i	0.996684	−	0.0813674i	$-0.0259287\pi$
$563$	10.1525	+	17.5846i	0.427876	+	0.741103i	−0.568808	+	0.822470i	$0.692595\pi$
$564$	33.2188	−	19.1789i	1.39877	−	0.807578i
$565$	10.6525	−	18.4506i	0.448153	−	0.776224i
$566$	6.49342			0.272939
$567$	−9.00000			−0.377964
$568$	−4.28367			−0.179739
$569$	−19.3992	+	33.6004i	−0.813256	+	1.40860i	0.0973171	+	0.995253i	$0.468974\pi$
$569$	−19.3992	+	33.6004i	−0.813256	+	1.40860i	−0.910573	+	0.413348i	$0.864359\pi$
$570$	−0.708204	+	0.408882i	−0.0296634	+	0.0171262i
$571$	9.26393	+	16.0456i	0.387683	+	0.671488i	0.992138	−	0.125153i	$-0.0399420\pi$
$571$	9.26393	+	16.0456i	0.387683	+	0.671488i	−0.604454	+	0.796640i	$0.706609\pi$
$572$		0			0
$573$		−	10.2958i		−	0.430112i
$574$	0.482779	−	0.836198i	0.0201508	−	0.0349022i
$575$	−16.0344			−0.668682
$576$	−7.06231	+	12.2323i	−0.294263	+	0.509678i
$577$	35.4164			1.47440			0.737202	−	0.675672i	$-0.236147\pi$
$577$	35.4164			1.47440			0.737202	+	0.675672i	$0.236147\pi$
$578$	1.25329	−	2.17076i	0.0521299	−	0.0902917i
$579$	−16.5000	−	9.52628i	−0.685717	−	0.395899i
$580$	5.56231	+	9.63420i	0.230962	+	0.400038i
$581$	−4.88197	−	8.45581i	−0.202538	−	0.350806i
$582$	−3.43769	−	1.98475i	−0.142497	−	0.0822707i
$583$		0			0
$584$	−0.214782			−0.00888773
$585$	12.0000	+	20.7846i	0.496139	+	0.859338i
$586$	11.1459			0.460433
$587$	−6.70820	+	11.6190i	−0.276877	+	0.479565i	−0.970607	−	0.240670i	$-0.922633\pi$
$587$	−6.70820	+	11.6190i	−0.276877	+	0.479565i	0.693730	+	0.720235i	$0.255966\pi$
$588$		−	19.2684i		−	0.794615i
$589$	−0.309017	−	0.535233i	−0.0127328	−	0.0220539i
$590$	−0.381966	−	0.661585i	−0.0157253	−	0.0272370i
$591$	−12.3541	+	7.13264i	−0.508180	+	0.293398i
$592$	8.00658	−	13.8678i	0.329068	−	0.569963i
$593$	−10.9443			−0.449427			−0.224714	−	0.974425i	$-0.572145\pi$
$593$	−10.9443			−0.449427			−0.224714	+	0.974425i	$0.572145\pi$
$594$		0			0
$595$	6.00000			0.245976
$596$	−14.0729	+	24.3751i	−0.576450	+	0.998441i
$597$	10.7188	−	6.18853i	0.438693	−	0.253280i
$598$	−5.70820	−	9.88690i	−0.233426	−	0.404305i
$599$	6.68034	+	11.5707i	0.272951	+	0.472765i	0.969616	−	0.244631i	$-0.0786669\pi$
$599$	6.68034	+	11.5707i	0.272951	+	0.472765i	−0.696665	+	0.717397i	$0.745334\pi$
$600$			8.85330i			0.361435i
$601$	8.73607	−	15.1313i	0.356352	−	0.617219i	−0.630997	−	0.775786i	$-0.717354\pi$
$601$	8.73607	−	15.1313i	0.356352	−	0.617219i	0.987348	+	0.158566i	$0.0506872\pi$
$602$	0.708204			0.0288642
$603$	−18.0000			−0.733017
$604$	−8.02129			−0.326382
$605$		0			0
$606$	4.85410	+	2.80252i	0.197184	+	0.113844i
$607$	1.79180	+	3.10348i	0.0727268	+	0.125966i	0.900095	−	0.435693i	$-0.143497\pi$
$607$	1.79180	+	3.10348i	0.0727268	+	0.125966i	−0.827369	+	0.561659i	$0.810163\pi$
$608$	2.07295	+	3.59045i	0.0840692	+	0.145612i
$609$	7.28115	+	4.20378i	0.295047	+	0.170346i
$610$	−2.56231	+	4.43804i	−0.103745	+	0.179691i
$611$	−77.3050			−3.12742
$612$	27.0000			1.09141
$613$	19.8541			0.801900			0.400950	−	0.916100i	$-0.368680\pi$
$613$	19.8541			0.801900			0.400950	+	0.916100i	$0.368680\pi$
$614$	1.50000	−	2.59808i	0.0605351	−	0.104850i
$615$		−	5.41199i		−	0.218232i
$616$		0			0
$617$	13.5795	+	23.5204i	0.546691	+	0.946897i	0.998498	+	0.0547813i	$0.0174462\pi$
$617$	13.5795	+	23.5204i	0.546691	+	0.946897i	−0.451807	+	0.892116i	$0.649221\pi$
$618$	−5.86475	+	3.38601i	−0.235915	+	0.136205i
$619$	−13.7812	+	23.8697i	−0.553911	+	0.959403i	0.444076	+	0.895989i	$0.353532\pi$
$619$	−13.7812	+	23.8697i	−0.553911	+	0.959403i	−0.997987	+	0.0634134i	$0.979801\pi$
$620$	1.41641			0.0568843
$621$	20.7812	−	11.9980i	0.833919	−	0.481463i
$622$	−5.79837			−0.232494
$623$	−3.38197	+	5.85774i	−0.135496	+	0.234685i
$624$	30.5410	−	17.6329i	1.22262	−	0.705880i
$625$	−2.20820	−	3.82472i	−0.0883282	−	0.152989i
$626$	0.663119	+	1.14856i	0.0265036	+	0.0459055i
$627$		0			0
$628$	6.62461	−	11.4742i	0.264351	−	0.457869i
$629$	−24.7082			−0.985181
$630$	−0.708204	−	1.22665i	−0.0282155	−	0.0488707i
$631$	−10.8885			−0.433466			−0.216733	−	0.976231i	$-0.569540\pi$
$631$	−10.8885			−0.433466			−0.216733	+	0.976231i	$0.569540\pi$
$632$	−7.77458	+	13.4660i	−0.309256	+	0.535647i
$633$	30.7082	+	17.7294i	1.22054	+	0.704680i
$634$	4.00000	+	6.92820i	0.158860	+	0.275154i
$635$	−6.52786	−	11.3066i	−0.259050	−	0.448688i
$636$	−11.3754	−	6.56758i	−0.451063	−	0.260422i
$637$	−19.4164	+	33.6302i	−0.769306	+	1.33248i
$638$		0			0
$639$	−4.36475	+	7.55996i	−0.172667	+	0.299067i
$640$	−12.4721			−0.493004
$641$	10.2254	−	17.7110i	0.403880	−	0.699541i	−0.590310	−	0.807176i	$-0.700995\pi$
$641$	10.2254	−	17.7110i	0.403880	−	0.699541i	0.994190	+	0.107636i	$0.0343280\pi$
$642$			9.28497i			0.366449i
$643$	3.42705	+	5.93583i	0.135150	+	0.234086i	0.925655	−	0.378370i	$-0.123515\pi$
$643$	3.42705	+	5.93583i	0.135150	+	0.234086i	−0.790505	+	0.612456i	$0.790182\pi$
$644$	−4.28115	−	7.41517i	−0.168701	−	0.292199i
$645$	3.43769	−	1.98475i	0.135359	−	0.0781496i
$646$	0.927051	−	1.60570i	0.0364743	−	0.0631754i
$647$	−4.18034			−0.164346			−0.0821731	−	0.996618i	$-0.526186\pi$
$647$	−4.18034			−0.164346			−0.0821731	+	0.996618i	$0.526186\pi$
$648$	−6.62461	−	11.4742i	−0.260239	−	0.450748i
$649$		0			0
$650$	4.29180	−	7.43361i	0.168338	−	0.291570i
$651$	0.927051	−	0.535233i	0.0363340	−	0.0209774i
$652$	19.1976	+	33.2512i	0.751835	+	1.30222i
$653$	0.680340	+	1.17838i	0.0266238	+	0.0461137i	0.879030	−	0.476766i	$-0.158191\pi$
$653$	0.680340	+	1.17838i	0.0266238	+	0.0461137i	−0.852407	+	0.522880i	$0.824858\pi$
$654$			4.72762i			0.184864i
$655$	13.1246	−	22.7325i	0.512821	−	0.888232i
$656$	−7.95240			−0.310489
$657$	−0.218847	+	0.379054i	−0.00853804	+	0.0147883i
$658$	4.56231			0.177857
$659$	−4.98936	+	8.64182i	−0.194358	+	0.336637i	−0.946690	−	0.322147i	$-0.895596\pi$
$659$	−4.98936	+	8.64182i	−0.194358	+	0.336637i	0.752332	+	0.658784i	$0.228929\pi$
$660$		0			0
$661$	2.14590	+	3.71680i	0.0834658	+	0.144567i	0.904736	−	0.425972i	$-0.140068\pi$
$661$	2.14590	+	3.71680i	0.0834658	+	0.144567i	−0.821271	+	0.570539i	$0.806734\pi$
$662$	2.75329	+	4.76884i	0.107010	+	0.185346i
$663$	−47.1246	−	27.2074i	−1.83017	−	1.05665i
$664$	7.18692	−	12.4481i	0.278906	−	0.483080i
$665$	1.23607			0.0479327
$666$	2.91641	+	5.05137i	0.113009	+	0.195736i
$667$	−22.4164			−0.867967
$668$	−5.34346	+	9.25514i	−0.206745	+	0.358092i
$669$			26.8582i			1.03840i
$670$	−1.41641	−	2.45329i	−0.0547206	−	0.0947789i
$671$		0			0
$672$	−6.21885	+	3.59045i	−0.239897	+	0.138505i
$673$	14.7812	−	25.6017i	0.569772	−	0.986873i	−0.426817	−	0.904338i	$-0.640365\pi$
$673$	14.7812	−	25.6017i	0.569772	−	0.986873i	0.996588	−	0.0825351i	$-0.0263017\pi$
$674$	4.38197			0.168787
$675$	15.6246	+	9.02087i	0.601392	+	0.347214i
$676$	−53.5623			−2.06009
$677$	−3.02786	+	5.24441i	−0.116370	+	0.201559i	−0.918327	−	0.395823i	$-0.870459\pi$
$677$	−3.02786	+	5.24441i	−0.116370	+	0.201559i	0.801956	+	0.597383i	$0.203793\pi$
$678$	9.87539	−	5.70156i	0.379262	−	0.218967i
$679$	3.00000	+	5.19615i	0.115129	+	0.199410i
$680$	4.41641	+	7.64944i	0.169362	+	0.293343i
$681$			28.7833i			1.10298i
$682$		0			0
$683$	−5.52786			−0.211518			−0.105759	−	0.994392i	$-0.533727\pi$
$683$	−5.52786			−0.211518			−0.105759	+	0.994392i	$0.533727\pi$
$684$	5.56231			0.212680
$685$	10.6525			0.407010
$686$	2.48278	−	4.30030i	0.0947929	−	0.164186i
$687$	15.2705	+	8.81643i	0.582606	+	0.336368i
$688$	−2.91641	−	5.05137i	−0.111187	−	0.192582i
$689$	13.2361	+	22.9255i	0.504254	+	0.873394i
$690$	3.27051	+	1.88823i	0.124506	+	0.0718837i
$691$	−7.29837	+	12.6412i	−0.277643	+	0.480892i	−0.970799	−	0.239896i	$-0.922887\pi$
$691$	−7.29837	+	12.6412i	−0.277643	+	0.480892i	0.693155	+	0.720788i	$0.256220\pi$
$692$	42.8115			1.62745
$693$		0			0
$694$	3.39512			0.128877
$695$	6.00000	−	10.3923i	0.227593	−	0.394203i
$696$			12.3771i			0.469151i
$697$	6.13525	+	10.6266i	0.232389	+	0.402510i
$698$	−0.791796	−	1.37143i	−0.0299699	−	0.0519094i
$699$	16.6869	−	9.63420i	0.631157	−	0.364399i
$700$	3.21885	−	5.57521i	0.121661	−	0.210723i
$701$	−47.7214			−1.80241			−0.901205	−	0.433392i	$-0.857317\pi$
$701$	−47.7214			−1.80241			−0.901205	+	0.433392i	$0.857317\pi$
$702$			12.8456i			0.484826i
$703$	−5.09017			−0.191979
$704$		0			0
$705$	22.1459	−	12.7859i	0.834063	−	0.481546i
$706$	−3.13525	−	5.43042i	−0.117997	−	0.204377i
$707$	−4.23607	−	7.33708i	−0.159314	−	0.275939i
$708$			5.19615i			0.195283i
$709$	12.8820	−	22.3122i	0.483792	−	0.837953i	−0.516034	−	0.856568i	$-0.672592\pi$
$709$	12.8820	−	22.3122i	0.483792	−	0.837953i	0.999827	+	0.0186149i	$0.00592565\pi$
$710$	−1.37384			−0.0515591
$711$	15.8435	+	27.4417i	0.594176	+	1.02914i
$712$	−9.95743			−0.373170
$713$	−1.42705	+	2.47172i	−0.0534435	+	0.0925668i
$714$	2.78115	+	1.60570i	0.104082	+	0.0600918i
$715$		0			0
$716$	−4.68692	−	8.11798i	−0.175158	−	0.303383i
$717$	15.7082	+	9.06914i	0.586634	+	0.338693i
$718$	−4.36475	+	7.55996i	−0.162891	+	0.282135i
$719$	−19.5967			−0.730835			−0.365418	−	0.930844i	$-0.619074\pi$
$719$	−19.5967			−0.730835			−0.365418	+	0.930844i	$0.619074\pi$
$720$	−5.83282	+	10.1027i	−0.217376	+	0.376507i
$721$	10.2361			0.381211
$722$	−3.43769	+	5.95426i	−0.127938	+	0.221595i
$723$			46.4758i			1.72845i
$724$	−9.18692	−	15.9122i	−0.341429	−	0.591373i
$725$	−8.42705	−	14.5961i	−0.312973	−	0.542085i
$726$		0			0
$727$	−9.41641	+	16.3097i	−0.349235	+	0.604893i	−0.986114	−	0.166071i	$-0.946892\pi$
$727$	−9.41641	+	16.3097i	−0.349235	+	0.604893i	0.636879	+	0.770964i	$0.280225\pi$
$728$	9.52786			0.353126
$729$	−27.0000			−1.00000
$730$	−0.0688837			−0.00254950
$731$	−4.50000	+	7.79423i	−0.166439	+	0.288280i
$732$	30.1869	−	17.4284i	1.11574	−	0.644173i
$733$	−24.2361	−	41.9781i	−0.895180	−	1.55050i	−0.833582	−	0.552395i	$-0.813714\pi$
$733$	−24.2361	−	41.9781i	−0.895180	−	1.55050i	−0.0615974	−	0.998101i	$-0.519619\pi$
$734$	−2.42705	−	4.20378i	−0.0895841	−	0.155164i
$735$		−	12.8456i		−	0.473817i
$736$	9.57295	−	16.5808i	0.352864	−	0.611178i
$737$		0			0
$738$	1.44834	−	2.50859i	0.0533140	−	0.0923426i
$739$	42.5410			1.56490			0.782448	−	0.622715i	$-0.213971\pi$
$739$	42.5410			1.56490			0.782448	+	0.622715i	$0.213971\pi$
$740$	5.83282	−	10.1027i	0.214419	−	0.371384i
$741$	−9.70820	−	5.60503i	−0.356640	−	0.205906i
$742$	−0.781153	−	1.35300i	−0.0286770	−	0.0496701i
$743$	21.1803	+	36.6854i	0.777031	+	1.34586i	0.933646	+	0.358198i	$0.116609\pi$
$743$	21.1803	+	36.6854i	0.777031	+	1.34586i	−0.156614	+	0.987660i	$0.550058\pi$
$744$	1.36475	+	0.787936i	0.0500340	+	0.0288871i
$745$	−9.38197	+	16.2500i	−0.343729	+	0.595355i
$746$	2.15905			0.0790486
$747$	−14.6459	−	25.3674i	−0.535865	−	0.928146i
$748$		0			0
$749$	7.01722	−	12.1542i	0.256404	−	0.444104i
$750$			6.92820i			0.252982i
$751$	15.6246	+	27.0626i	0.570150	+	0.987529i	0.996550	+	0.0829943i	$0.0264483\pi$
$751$	15.6246	+	27.0626i	0.570150	+	0.987529i	−0.426400	+	0.904535i	$0.640218\pi$
$752$	−18.7877	−	32.5413i	−0.685118	−	1.18666i
$753$	−30.8435	+	17.8075i	−1.12400	+	0.648941i
$754$	6.00000	−	10.3923i	0.218507	−	0.378465i
$755$	−5.34752			−0.194616
$756$			9.63420i			0.350392i
$757$	11.0000			0.399802			0.199901	−	0.979816i	$-0.435938\pi$
$757$	11.0000			0.399802			0.199901	+	0.979816i	$0.435938\pi$
$758$	3.01722	−	5.22598i	0.109590	−	0.189816i
$759$		0			0
$760$	0.909830	+	1.57587i	0.0330030	+	0.0571629i
$761$	−3.48936	−	6.04374i	−0.126489	−	0.219086i	0.795825	−	0.605527i	$-0.207038\pi$
$761$	−3.48936	−	6.04374i	−0.126489	−	0.219086i	−0.922314	+	0.386441i	$0.873704\pi$
$762$		−	6.98786i		−	0.253143i
$763$	3.57295	−	6.18853i	0.129349	−	0.224040i
$764$	−11.0213			−0.398736
$765$	18.0000			0.650791
$766$	−7.58359			−0.274006
$767$	5.23607	−	9.06914i	0.189063	−	0.327468i
$768$	8.34346	+	4.81710i	0.301069	+	0.173822i
$769$	7.89919	+	13.6818i	0.284852	+	0.493378i	0.972573	−	0.232597i	$-0.0747222\pi$
$769$	7.89919	+	13.6818i	0.284852	+	0.493378i	−0.687721	+	0.725975i	$0.741389\pi$
$770$		0			0
$771$	−22.3647	−	12.9123i	−0.805447	−	0.465025i
$772$	−10.1976	+	17.6627i	−0.367018	+	0.635694i
$773$	23.6525			0.850720			0.425360	−	0.905024i	$-0.360147\pi$
$773$	23.6525			0.850720			0.425360	+	0.905024i	$0.360147\pi$
$774$	2.12461			0.0763676
$775$	−2.14590			−0.0770829
$776$	−4.41641	+	7.64944i	−0.158540	+	0.274599i
$777$		−	8.81643i		−	0.316288i
$778$	−4.32624	−	7.49326i	−0.155103	−	0.268647i
$779$	1.26393	+	2.18919i	0.0452851	+	0.0784360i
$780$	22.2492	−	12.8456i	0.796650	−	0.459946i
$781$		0			0
$782$	−8.56231			−0.306187
$783$	21.8435	+	12.6113i	0.780622	+	0.450692i
$784$	−18.8754			−0.674121
$785$	4.41641	−	7.64944i	0.157628	−	0.273020i
$786$	12.1672	−	7.02473i	0.433989	−	0.250564i
$787$	−18.0000	−	31.1769i	−0.641631	−	1.11134i	−0.985069	−	0.172162i	$-0.944925\pi$
$787$	−18.0000	−	31.1769i	−0.641631	−	1.11134i	0.343438	−	0.939175i	$-0.388408\pi$
$788$	7.63525	+	13.2246i	0.271995	+	0.471109i
$789$			22.0113i			0.783621i
$790$	−2.49342	+	4.31873i	−0.0887120	+	0.153654i
$791$	−17.2361			−0.612844
$792$		0			0
$793$	−70.2492			−2.49462
$794$	−0.405765	+	0.702805i	−0.0144001	+	0.0249416i
$795$	−7.58359	−	4.37839i	−0.268962	−	0.155285i
$796$	−6.62461	−	11.4742i	−0.234803	−	0.406691i
$797$	−12.1353	−	21.0189i	−0.429853	−	0.744527i	0.567007	−	0.823713i	$-0.308101\pi$
$797$	−12.1353	−	21.0189i	−0.429853	−	0.744527i	−0.996860	+	0.0791861i	$0.974768\pi$
$798$	0.572949	+	0.330792i	0.0202822	+	0.0117099i
$799$	−28.9894	+	50.2110i	−1.02557	+	1.77634i
$800$	14.3951			0.508944
$801$	−10.1459	+	17.5732i	−0.358488	+	0.620919i
$802$	−5.56231			−0.196412
$803$		0			0
$804$			19.2684i			0.679544i
$805$	−2.85410	−	4.94345i	−0.100594	−	0.174234i
$806$	−0.763932	−	1.32317i	−0.0269084	−	0.0466066i
$807$	31.9058	−	18.4208i	1.12314	−	0.648443i
$808$	6.23607	−	10.8012i	0.219384	−	0.379984i
$809$	−18.0902			−0.636017			−0.318008	−	0.948088i	$-0.603014\pi$
$809$	−18.0902			−0.636017			−0.318008	+	0.948088i	$0.603014\pi$
$810$	−2.12461	−	3.67994i	−0.0746512	−	0.129300i
$811$	8.68692			0.305039			0.152519	−	0.988300i	$-0.451261\pi$
$811$	8.68692			0.305039			0.152519	+	0.988300i	$0.451261\pi$
$812$	4.50000	−	7.79423i	0.157919	−	0.273524i
$813$	−16.1459	+	9.32184i	−0.566261	+	0.326931i
$814$		0			0
$815$	12.7984	+	22.1674i	0.448307	+	0.776491i
$816$		−	26.4493i		−	0.925911i
$817$	−0.927051	+	1.60570i	−0.0324334	+	0.0561763i
$818$	12.8885			0.450637
$819$	9.70820	−	16.8151i	0.339232	−	0.587567i
$820$	−5.79335			−0.202313
$821$	−19.1074	+	33.0950i	−0.666853	+	1.15502i	0.311927	+	0.950106i	$0.399026\pi$
$821$	−19.1074	+	33.0950i	−0.666853	+	1.15502i	−0.978779	+	0.204916i	$0.934308\pi$
$822$	4.93769	+	2.85078i	0.172222	+	0.0994323i
$823$	21.1459	+	36.6258i	0.737100	+	1.27669i	0.953796	+	0.300455i	$0.0971385\pi$
$823$	21.1459	+	36.6258i	0.737100	+	1.27669i	−0.216696	+	0.976239i	$0.569528\pi$
$824$	7.53444	+	13.0500i	0.262475	+	0.454620i
$825$		0			0
$826$	−0.309017	+	0.535233i	−0.0107521	+	0.0186231i
$827$	−57.0344			−1.98328			−0.991641	−	0.129028i	$-0.958814\pi$
$827$	−57.0344			−1.98328			−0.991641	+	0.129028i	$0.958814\pi$
$828$	−12.8435	−	22.2455i	−0.446341	−	0.773085i
$829$	43.5410			1.51224			0.756121	−	0.654432i	$-0.227092\pi$
$829$	43.5410			1.51224			0.756121	+	0.654432i	$0.227092\pi$
$830$	2.30495	−	3.99229i	0.0800060	−	0.138575i
$831$			33.3178i			1.15578i
$832$	−15.2361	−	26.3896i	−0.528216	−	0.914896i
$833$	14.5623	+	25.2227i	0.504554	+	0.873913i
$834$	5.56231	−	3.21140i	0.192607	−	0.111202i
$835$	−3.56231	+	6.17009i	−0.123279	+	0.213525i
$836$		0			0
$837$	2.78115	−	1.60570i	0.0961307	−	0.0555011i
$838$	−3.09017			−0.106748
$839$	8.64590	−	14.9751i	0.298490	−	0.516999i	−0.677301	−	0.735706i	$-0.736851\pi$
$839$	8.64590	−	14.9751i	0.298490	−	0.516999i	0.975791	+	0.218707i	$0.0701839\pi$
$840$	−2.72949	+	1.57587i	−0.0941764	+	0.0543727i
$841$	2.71885	+	4.70918i	0.0937533	+	0.162386i
$842$	1.95492	+	3.38601i	0.0673708	+	0.116690i
$843$			16.1535i			0.556357i
$844$	18.9787	−	32.8721i	0.653274	−	1.13150i
$845$	−35.7082			−1.22840
$846$	13.6869			0.470566
$847$		0			0
$848$	−6.43363	+	11.1434i	−0.220932	+	0.382665i
$849$	−25.5000	−	14.7224i	−0.875158	−	0.505273i
$850$	−3.21885	−	5.57521i	−0.110406	−	0.191228i
$851$	11.7533	+	20.3573i	0.402898	+	0.697839i
$852$	8.09268	+	4.67231i	0.277251	+	0.160071i
$853$	17.7188	−	30.6899i	0.606682	−	1.05080i	−0.385102	−	0.922874i	$-0.625834\pi$
$853$	17.7188	−	30.6899i	0.606682	−	1.05080i	0.991783	−	0.127929i	$-0.0408331\pi$
$854$	4.14590			0.141870
$855$	3.70820			0.126818
$856$	20.6606			0.706165
$857$	−12.6803	+	21.9630i	−0.433152	+	0.750242i	−0.997143	−	0.0755396i	$-0.975932\pi$
$857$	−12.6803	+	21.9630i	−0.433152	+	0.750242i	0.563991	+	0.825781i	$0.309265\pi$
$858$		0			0
$859$	16.2812	+	28.1998i	0.555506	+	0.962164i	0.997864	+	0.0653258i	$0.0208087\pi$
$859$	16.2812	+	28.1998i	0.555506	+	0.962164i	−0.442358	+	0.896838i	$0.645858\pi$
$860$	−2.12461	−	3.67994i	−0.0724487	−	0.125485i
$861$	−3.79180	+	2.18919i	−0.129224	+	0.0746075i
$862$	−6.50658	+	11.2697i	−0.221615	+	0.383848i
$863$	14.4508			0.491913			0.245956	−	0.969281i	$-0.420898\pi$
$863$	14.4508			0.491913			0.245956	+	0.969281i	$0.420898\pi$
$864$	−18.6565	+	10.7714i	−0.634708	+	0.366449i
$865$	28.5410			0.970424
$866$	2.81559	−	4.87675i	0.0956778	−	0.165719i
$867$	−9.84346	+	5.68312i	−0.334301	+	0.193009i
$868$	−0.572949	−	0.992377i	−0.0194472	−	0.0336835i
$869$		0			0
$870$			3.96951i			0.134579i
$871$	19.4164	−	33.6302i	0.657900	−	1.13952i
$872$	10.5197			0.356243
$873$	9.00000	+	15.5885i	0.304604	+	0.527589i
$874$	−1.76393			−0.0596659
$875$	5.23607	−	9.06914i	0.177011	−	0.306593i
$876$	0.405765	+	0.234268i	0.0137095	+	0.00791520i
$877$	−5.79837	−	10.0431i	−0.195797	−	0.339131i	0.751364	−	0.659888i	$-0.229396\pi$
$877$	−5.79837	−	10.0431i	−0.195797	−	0.339131i	−0.947162	+	0.320757i	$0.896063\pi$
$878$	−0.135255	−	0.234268i	−0.00456463	−	0.00790618i
$879$	−43.7705	−	25.2709i	−1.47634	−	0.852367i
$880$		0			0
$881$	1.81966			0.0613059			0.0306530	−	0.999530i	$-0.490241\pi$
$881$	1.81966			0.0613059			0.0306530	+	0.999530i	$0.490241\pi$
$882$	3.43769	−	5.95426i	0.115753	−	0.200490i
$883$	−35.6525			−1.19980			−0.599901	−	0.800074i	$-0.704793\pi$
$883$	−35.6525			−1.19980			−0.599901	+	0.800074i	$0.704793\pi$
$884$	−29.1246	+	50.4453i	−0.979567	+	1.69666i
$885$			3.46410i			0.116445i
$886$	−0.236068	−	0.408882i	−0.00793086	−	0.0137367i
$887$	2.01722	+	3.49393i	0.0677316	+	0.117315i	0.897902	−	0.440194i	$-0.145090\pi$
$887$	2.01722	+	3.49393i	0.0677316	+	0.117315i	−0.830171	+	0.557509i	$0.811757\pi$
$888$	11.2401	−	6.48949i	0.377194	−	0.217773i
$889$	−5.28115	+	9.14723i	−0.177124	+	0.306788i
$890$	−3.19350			−0.107046
$891$		0			0
$892$	28.7508			0.962647
$893$	−5.97214	+	10.3440i	−0.199850	+	0.346150i
$894$	−8.69756	+	5.02154i	−0.290890	+	0.167945i
$895$	−3.12461	−	5.41199i	−0.104444	−	0.180903i
$896$	5.04508	+	8.73834i	0.168544	+	0.291928i
$897$			51.7685i			1.72850i
$898$	1.42705	−	2.47172i	0.0476213	−	0.0824825i
$899$	−3.00000			−0.100056
$900$	9.65654	−	16.7256i	0.321885	−	0.557521i
$901$	19.8541			0.661436
$902$		0			0
$903$	−2.78115	−	1.60570i	−0.0925510	−	0.0534343i
$904$	−12.6869	−	21.9744i	−0.421961	−	0.730857i
$905$	−6.12461	−	10.6081i	−0.203589	−	0.352626i
$906$	−2.47871	−	1.43109i	−0.0823497	−	0.0475446i
$907$	7.29180	−	12.6298i	0.242120	−	0.419364i	−0.719198	−	0.694805i	$-0.755491\pi$
$907$	7.29180	−	12.6298i	0.242120	−	0.419364i	0.961318	+	0.275441i	$0.0888239\pi$
$908$	30.8115			1.02252
$909$	−12.7082	−	22.0113i	−0.421505	−	0.730067i
$910$	3.05573			0.101296
$911$	9.59017	−	16.6107i	0.317737	−	0.550336i	−0.662279	−	0.749257i	$-0.730411\pi$
$911$	9.59017	−	16.6107i	0.317737	−	0.550336i	0.980015	+	0.198922i	$0.0637439\pi$
$912$		−	5.44886i		−	0.180430i
$913$		0			0
$914$	−0.190983	−	0.330792i	−0.00631716	−	0.0109416i
$915$	20.1246	−	11.6190i	0.665299	−	0.384111i
$916$	9.43769	−	16.3466i	0.311830	−	0.540106i
$917$	−21.2361			−0.701277
$918$	8.34346	+	4.81710i	0.275375	+	0.158988i
$919$	−26.8673			−0.886269			−0.443135	−	0.896455i	$-0.646134\pi$
$919$	−26.8673			−0.886269			−0.443135	+	0.896455i	$0.646134\pi$
$920$	4.20163	−	7.27743i	0.138524	−	0.239930i
$921$	−11.7812	+	6.80185i	−0.388202	+	0.224129i
$922$	−3.08359	−	5.34094i	−0.101553	−	0.175894i
$923$	−9.41641	−	16.3097i	−0.309945	−	0.536840i
$924$		0			0
$925$	−8.83688	+	15.3059i	−0.290555	+	0.503256i
$926$	−6.49342			−0.213387
$927$	30.7082			1.00859
$928$	20.1246			0.660623
$929$	24.1353	−	41.8035i	0.791852	−	1.37153i	−0.132967	−	0.991120i	$-0.542450\pi$
$929$	24.1353	−	41.8035i	0.791852	−	1.37153i	0.924819	−	0.380407i	$-0.124216\pi$
$930$	0.437694	+	0.252703i	0.0143526	+	0.00828645i
$931$	3.00000	+	5.19615i	0.0983210	+	0.170297i
$932$	−10.3131	−	17.8628i	−0.337816	−	0.585115i
$933$	22.7705	+	13.1466i	0.745473	+	0.430399i
$934$	−0.145898	+	0.252703i	−0.00477393	+	0.00826869i
$935$		0			0
$936$	28.5836			0.934284
$937$	−23.0344			−0.752502			−0.376251	−	0.926518i	$-0.622787\pi$
$937$	−23.0344			−0.752502			−0.376251	+	0.926518i	$0.622787\pi$
$938$	−1.14590	+	1.98475i	−0.0374149	+	0.0648045i
$939$		−	6.01392i		−	0.196257i
$940$	−13.6869	−	23.7064i	−0.446418	−	0.773219i
$941$	−13.5795	−	23.5204i	−0.442680	−	0.766744i	0.555207	−	0.831712i	$-0.312639\pi$
$941$	−13.5795	−	23.5204i	−0.442680	−	0.766744i	−0.997887	+	0.0649678i	$0.979306\pi$
$942$	4.09424	−	2.36381i	0.133397	−	0.0770170i
$943$	5.83688	−	10.1098i	0.190075	−	0.329220i
$944$	5.09017			0.165671
$945$			6.42280i			0.208934i
$946$		0			0
$947$	−18.3541	+	31.7902i	−0.596428	+	1.03304i	0.396915	+	0.917855i	$0.370081\pi$
$947$	−18.3541	+	31.7902i	−0.596428	+	1.03304i	−0.993344	+	0.115189i	$0.963253\pi$
$948$	29.3754	−	16.9599i	0.954068	−	0.550832i
$949$	−0.472136	−	0.817763i	−0.0153262	−	0.0265457i
$950$	−0.663119	−	1.14856i	−0.0215144	−	0.0372641i
$951$		−	36.2765i		−	1.17635i
$952$	3.57295	−	6.18853i	0.115800	−	0.200571i
$953$	−9.49342			−0.307522			−0.153761	−	0.988108i	$-0.549139\pi$
$953$	−9.49342			−0.307522			−0.153761	+	0.988108i	$0.549139\pi$
$954$	−2.34346	−	4.05899i	−0.0758723	−	0.131415i
$955$	−7.34752			−0.237760
$956$	9.70820	−	16.8151i	0.313986	−	0.543839i
$957$		0			0
$958$	−2.24671	−	3.89142i	−0.0725879	−	0.125726i
$959$	−4.30902	−	7.46344i	−0.139145	−	0.241007i
$960$	8.72949	+	5.03997i	0.281743	+	0.162664i
$961$	15.3090	−	26.5160i	0.493839	−	0.855355i
$962$	−12.5836			−0.405711
$963$	21.0517	−	36.4625i	0.678380	−	1.17499i
$964$	49.7508			1.60236
$965$	−6.79837	+	11.7751i	−0.218847	+	0.379055i
$966$		−	3.05522i		−	0.0983001i
$967$	−26.2426	−	45.4536i	−0.843907	−	1.46169i	−0.886567	−	0.462599i	$-0.846917\pi$
$967$	−26.2426	−	45.4536i	−0.843907	−	1.46169i	0.0426608	−	0.999090i	$-0.486417\pi$
$968$		0			0
$969$	−7.28115	+	4.20378i	−0.233904	+	0.135045i
$970$	−1.41641	+	2.45329i	−0.0454781	+	0.0787704i
$971$	9.27051			0.297505			0.148752	−	0.988874i	$-0.452474\pi$
$971$	9.27051			0.297505			0.148752	+	0.988874i	$0.452474\pi$
$972$			28.9026i			0.927051i
$973$	−9.70820			−0.311231
$974$	−2.47871	+	4.29326i	−0.0794231	+	0.137565i
$975$	−33.7082	+	19.4614i	−1.07953	+	0.623265i
$976$	−17.0729	−	29.5712i	−0.546492	−	0.946552i
$977$	−7.88197	−	13.6520i	−0.252166	−	0.436765i	0.711956	−	0.702224i	$-0.247810\pi$
$977$	−7.88197	−	13.6520i	−0.252166	−	0.436765i	−0.964122	+	0.265459i	$0.914476\pi$
$978$			13.7002i			0.438085i
$979$		0			0
$980$	−13.7508			−0.439252
$981$	10.7188	−	18.5656i	0.342226	−	0.592754i
$982$	−2.79837			−0.0892997
$983$	−4.62868	+	8.01710i	−0.147632	+	0.255706i	−0.930352	−	0.366668i	$-0.880498\pi$
$983$	−4.62868	+	8.01710i	−0.147632	+	0.255706i	0.782720	+	0.622374i	$0.213832\pi$
$984$	−5.58204	−	3.22279i	−0.177949	−	0.102739i
$985$	5.09017	+	8.81643i	0.162186	+	0.280915i
$986$	−4.50000	−	7.79423i	−0.143309	−	0.248219i
$987$	−17.9164	−	10.3440i	−0.570286	−	0.329255i
$988$	−6.00000	+	10.3923i	−0.190885	+	0.330623i
$989$	8.56231			0.272265
$990$		0			0
$991$	20.5967			0.654277			0.327139	−	0.944976i	$-0.393916\pi$
$991$	20.5967			0.654277			0.327139	+	0.944976i	$0.393916\pi$
$992$	1.28115	−	2.21902i	0.0406766	−	0.0704540i
$993$		−	24.9700i		−	0.792397i
$994$	0.555728	+	0.962549i	0.0176266	+	0.0305302i
$995$	−4.41641	−	7.64944i	−0.140010	−	0.242504i
$996$	−27.1550	+	15.6779i	−0.860439	+	0.496775i
$997$	−3.69098	+	6.39297i	−0.116895	+	0.202467i	−0.918536	−	0.395338i	$-0.870627\pi$
$997$	−3.69098	+	6.39297i	−0.116895	+	0.202467i	0.801641	+	0.597806i	$0.203961\pi$
$998$	−14.6738			−0.464490
$999$		−	26.4493i		−	0.836819i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1089.2.e.g.727.1		4
9.2	odd	6		9801.2.a.bb.1.1		2
9.4	even	3	inner	1089.2.e.g.364.1		4
9.7	even	3		9801.2.a.n.1.2		2
11.3	even	5		99.2.m.a.97.1	yes	8
11.4	even	5		99.2.m.a.16.1	✓	8
11.10	odd	2		1089.2.e.d.727.2		4
33.14	odd	10		297.2.n.a.262.1		8
33.26	odd	10		297.2.n.a.181.1		8
99.4	even	15		99.2.m.a.49.1	yes	8
99.14	odd	30		297.2.n.a.64.1		8
99.25	even	15		891.2.f.b.163.1		4
99.43	odd	6		9801.2.a.bc.1.1		2
99.47	odd	30		891.2.f.a.163.1		4
99.58	even	15		99.2.m.a.31.1	yes	8
99.59	odd	30		297.2.n.a.280.1		8
99.65	even	6		9801.2.a.m.1.2		2
99.70	even	15		891.2.f.b.82.1		4
99.76	odd	6		1089.2.e.d.364.2		4
99.92	odd	30		891.2.f.a.82.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.a.16.1	✓	8	11.4	even	5
99.2.m.a.31.1	yes	8	99.58	even	15
99.2.m.a.49.1	yes	8	99.4	even	15
99.2.m.a.97.1	yes	8	11.3	even	5
297.2.n.a.64.1		8	99.14	odd	30
297.2.n.a.181.1		8	33.26	odd	10
297.2.n.a.262.1		8	33.14	odd	10
297.2.n.a.280.1		8	99.59	odd	30
891.2.f.a.82.1		4	99.92	odd	30
891.2.f.a.163.1		4	99.47	odd	30
891.2.f.b.82.1		4	99.70	even	15
891.2.f.b.163.1		4	99.25	even	15
1089.2.e.d.364.2		4	99.76	odd	6
1089.2.e.d.727.2		4	11.10	odd	2
1089.2.e.g.364.1		4	9.4	even	3	inner
1089.2.e.g.727.1		4	1.1	even	1	trivial
9801.2.a.m.1.2		2	99.65	even	6
9801.2.a.n.1.2		2	9.7	even	3
9801.2.a.bb.1.1		2	9.2	odd	6
9801.2.a.bc.1.1		2	99.43	odd	6

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:	\( N \)	\(=\)	\( 1089 = 3^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1089.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.190983 - 0.330792i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(0.927051 + 1.60570i) q^{4} +(0.618034 + 1.07047i) q^{5} +0.661585i q^{6} +(0.500000 - 0.866025i) q^{7} +1.47214 q^{8} +(1.50000 - 2.59808i) q^{9} +0.472136 q^{10} +(-2.78115 - 1.60570i) q^{12} +(3.23607 + 5.60503i) q^{13} +(-0.190983 - 0.330792i) q^{14} +(-1.85410 - 1.07047i) q^{15} +(-1.57295 + 2.72443i) q^{16} +4.85410 q^{17} +(-0.572949 - 0.992377i) q^{18} +1.00000 q^{19} +(-1.14590 + 1.98475i) q^{20} +1.73205i q^{21} +(-2.30902 - 3.99933i) q^{23} +(-2.20820 + 1.27491i) q^{24} +(1.73607 - 3.00696i) q^{25} +2.47214 q^{26} +5.19615i q^{27} +1.85410 q^{28} +(2.42705 - 4.20378i) q^{29} +(-0.708204 + 0.408882i) q^{30} +(-0.309017 - 0.535233i) q^{31} +(2.07295 + 3.59045i) q^{32} +(0.927051 - 1.60570i) q^{34} +1.23607 q^{35} +5.56231 q^{36} -5.09017 q^{37} +(0.190983 - 0.330792i) q^{38} +(-9.70820 - 5.60503i) q^{39} +(0.909830 + 1.57587i) q^{40} +(1.26393 + 2.18919i) q^{41} +(0.572949 + 0.330792i) q^{42} +(-0.927051 + 1.60570i) q^{43} +3.70820 q^{45} -1.76393 q^{46} +(-5.97214 + 10.3440i) q^{47} -5.44886i q^{48} +(3.00000 + 5.19615i) q^{49} +(-0.663119 - 1.14856i) q^{50} +(-7.28115 + 4.20378i) q^{51} +(-6.00000 + 10.3923i) q^{52} +4.09017 q^{53} +(1.71885 + 0.992377i) q^{54} +(0.736068 - 1.27491i) q^{56} +(-1.50000 + 0.866025i) q^{57} +(-0.927051 - 1.60570i) q^{58} +(-0.809017 - 1.40126i) q^{59} -3.96951i q^{60} +(-5.42705 + 9.39993i) q^{61} -0.236068 q^{62} +(-1.50000 - 2.59808i) q^{63} -4.70820 q^{64} +(-4.00000 + 6.92820i) q^{65} +(-3.00000 - 5.19615i) q^{67} +(4.50000 + 7.79423i) q^{68} +(6.92705 + 3.99933i) q^{69} +(0.236068 - 0.408882i) q^{70} -2.90983 q^{71} +(2.20820 - 3.82472i) q^{72} -0.145898 q^{73} +(-0.972136 + 1.68379i) q^{74} +6.01392i q^{75} +(0.927051 + 1.60570i) q^{76} +(-3.70820 + 2.14093i) q^{78} +(-5.28115 + 9.14723i) q^{79} -3.88854 q^{80} +(-4.50000 - 7.79423i) q^{81} +0.965558 q^{82} +(4.88197 - 8.45581i) q^{83} +(-2.78115 + 1.60570i) q^{84} +(3.00000 + 5.19615i) q^{85} +(0.354102 + 0.613323i) q^{86} +8.40755i q^{87} -6.76393 q^{89} +(0.708204 - 1.22665i) q^{90} +6.47214 q^{91} +(4.28115 - 7.41517i) q^{92} +(0.927051 + 0.535233i) q^{93} +(2.28115 + 3.95107i) q^{94} +(0.618034 + 1.07047i) q^{95} +(-6.21885 - 3.59045i) q^{96} +(-3.00000 + 5.19615i) q^{97} +2.29180 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - 6 q^{3} - 3 q^{4} - 2 q^{5} + 2 q^{7} - 12 q^{8} + 6 q^{9} - 16 q^{10} + 9 q^{12} + 4 q^{13} - 3 q^{14} + 6 q^{15} - 13 q^{16} + 6 q^{17} - 9 q^{18} + 4 q^{19} - 18 q^{20} - 7 q^{23} + 18 q^{24}+ \cdots + 36 q^{98}+O(q^{100}) \) 4 * q + 3 * q^2 - 6 * q^3 - 3 * q^4 - 2 * q^5 + 2 * q^7 - 12 * q^8 + 6 * q^9 - 16 * q^10 + 9 * q^12 + 4 * q^13 - 3 * q^14 + 6 * q^15 - 13 * q^16 + 6 * q^17 - 9 * q^18 + 4 * q^19 - 18 * q^20 - 7 * q^23 + 18 * q^24 - 2 * q^25 - 8 * q^26 - 6 * q^28 + 3 * q^29 + 24 * q^30 + q^31 + 15 * q^32 - 3 * q^34 - 4 * q^35 - 18 * q^36 + 2 * q^37 + 3 * q^38 - 12 * q^39 + 26 * q^40 + 14 * q^41 + 9 * q^42 + 3 * q^43 - 12 * q^45 - 16 * q^46 - 6 * q^47 + 12 * q^49 + 13 * q^50 - 9 * q^51 - 24 * q^52 - 6 * q^53 + 27 * q^54 - 6 * q^56 - 6 * q^57 + 3 * q^58 - q^59 - 15 * q^61 + 8 * q^62 - 6 * q^63 + 8 * q^64 - 16 * q^65 - 12 * q^67 + 18 * q^68 + 21 * q^69 - 8 * q^70 - 34 * q^71 - 18 * q^72 - 14 * q^73 + 14 * q^74 - 3 * q^76 + 12 * q^78 - q^79 + 56 * q^80 - 18 * q^81 + 62 * q^82 + 24 * q^83 + 9 * q^84 + 12 * q^85 - 12 * q^86 - 36 * q^89 - 24 * q^90 + 8 * q^91 - 3 * q^92 - 3 * q^93 - 11 * q^94 - 2 * q^95 - 45 * q^96 - 12 * q^97 + 36 * q^98

Introduction

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