LMFDB - Embedded newform 1148.2.k.b.337.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1148,2,Mod(337,1148)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1148, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 3]))

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

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

chi := DirichletCharacter("1148.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1148 = 2^{2} \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1148.k (of order $4$, 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:	$9.16682615204$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			337.8
Character	$\chi$	$=$	1148.337
Dual form			1148.2.k.b.729.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.350714 - 0.350714i) q^{3} +3.08423i q^{5} +(-0.707107 - 0.707107i) q^{7} -2.75400i q^{9} +O(q^{10})$	\(q+(-0.350714 - 0.350714i) q^{3} +3.08423i q^{5} +(-0.707107 - 0.707107i) q^{7} -2.75400i q^{9} +(1.14202 + 1.14202i) q^{11} +(-2.88280 - 2.88280i) q^{13} +(1.08168 - 1.08168i) q^{15} +(3.58376 - 3.58376i) q^{17} +(2.29327 - 2.29327i) q^{19} +0.495985i q^{21} +3.46961 q^{23} -4.51245 q^{25} +(-2.01801 + 2.01801i) q^{27} +(4.60631 + 4.60631i) q^{29} +2.08732 q^{31} -0.801046i q^{33} +(2.18088 - 2.18088i) q^{35} +6.46508 q^{37} +2.02208i q^{39} +(6.11172 - 1.90968i) q^{41} +6.95000i q^{43} +8.49395 q^{45} +(-3.66137 + 3.66137i) q^{47} +1.00000i q^{49} -2.51375 q^{51} +(5.69357 + 5.69357i) q^{53} +(-3.52225 + 3.52225i) q^{55} -1.60857 q^{57} +2.42066 q^{59} -8.24899i q^{61} +(-1.94737 + 1.94737i) q^{63} +(8.89122 - 8.89122i) q^{65} +(-5.59189 + 5.59189i) q^{67} +(-1.21684 - 1.21684i) q^{69} +(-3.14338 - 3.14338i) q^{71} -8.57857i q^{73} +(1.58258 + 1.58258i) q^{75} -1.61506i q^{77} +(5.97983 + 5.97983i) q^{79} -6.84651 q^{81} +13.2534 q^{83} +(11.0531 + 11.0531i) q^{85} -3.23100i q^{87} +(-3.25227 - 3.25227i) q^{89} +4.07690i q^{91} +(-0.732052 - 0.732052i) q^{93} +(7.07296 + 7.07296i) q^{95} +(-3.75610 + 3.75610i) q^{97} +(3.14513 - 3.14513i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q+O(q^{10}) $ 36 * q	$ 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) $ 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1148\mathbb{Z}\right)^\times$.

$n$	$493$	$575$	$785$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{4}\right)$

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			0
$2$		0			0
$3$	−0.350714	−	0.350714i	−0.202485	−	0.202485i	0.598579	−	0.801064i	$-0.295732\pi$
$3$	−0.350714	−	0.350714i	−0.202485	−	0.202485i	−0.801064	+	0.598579i	$0.795732\pi$
$4$		0			0
$5$			3.08423i			1.37931i	0.724139	+	0.689654i	$0.242237\pi$
$5$			3.08423i			1.37931i	−0.724139	+	0.689654i	$0.757763\pi$
$6$		0			0
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$7$	−0.707107	−	0.707107i	−0.267261	−	0.267261i
$8$		0			0
$9$		−	2.75400i		−	0.918000i
$10$		0			0
$11$	1.14202	+	1.14202i	0.344332	+	0.344332i	0.857993	−	0.513661i	$-0.171711\pi$
$11$	1.14202	+	1.14202i	0.344332	+	0.344332i	−0.513661	+	0.857993i	$0.671711\pi$
$12$		0			0
$13$	−2.88280	−	2.88280i	−0.799546	−	0.799546i	0.183478	−	0.983024i	$-0.441264\pi$
$13$	−2.88280	−	2.88280i	−0.799546	−	0.799546i	−0.983024	+	0.183478i	$0.941264\pi$
$14$		0			0
$15$	1.08168	−	1.08168i	0.279289	−	0.279289i
$16$		0			0
$17$	3.58376	−	3.58376i	0.869188	−	0.869188i	−0.123194	−	0.992383i	$-0.539314\pi$
$17$	3.58376	−	3.58376i	0.869188	−	0.869188i	0.992383	+	0.123194i	$0.0393138\pi$
$18$		0			0
$19$	2.29327	−	2.29327i	0.526112	−	0.526112i	−0.393298	−	0.919411i	$-0.628666\pi$
$19$	2.29327	−	2.29327i	0.526112	−	0.526112i	0.919411	+	0.393298i	$0.128666\pi$
$20$		0			0
$21$			0.495985i			0.108233i
$22$		0			0
$23$	3.46961			0.723464			0.361732	−	0.932282i	$-0.382186\pi$
$23$	3.46961			0.723464			0.361732	+	0.932282i	$0.382186\pi$
$24$		0			0
$25$	−4.51245			−0.902489
$26$		0			0
$27$	−2.01801	+	2.01801i	−0.388366	+	0.388366i
$28$		0			0
$29$	4.60631	+	4.60631i	0.855371	+	0.855371i	0.990789	−	0.135418i	$-0.0432377\pi$
$29$	4.60631	+	4.60631i	0.855371	+	0.855371i	−0.135418	+	0.990789i	$0.543238\pi$
$30$		0			0
$31$	2.08732			0.374893			0.187447	−	0.982275i	$-0.439979\pi$
$31$	2.08732			0.374893			0.187447	+	0.982275i	$0.439979\pi$
$32$		0			0
$33$		−	0.801046i		−	0.139444i
$34$		0			0
$35$	2.18088	−	2.18088i	0.368635	−	0.368635i
$36$		0			0
$37$	6.46508			1.06285			0.531427	−	0.847104i	$-0.321656\pi$
$37$	6.46508			1.06285			0.531427	+	0.847104i	$0.321656\pi$
$38$		0			0
$39$			2.02208i			0.323792i
$40$		0			0
$41$	6.11172	−	1.90968i	0.954490	−	0.298242i
$41$	6.11172	−	1.90968i	0.954490	−	0.298242i
$42$		0			0
$43$			6.95000i			1.05987i	0.848040	+	0.529933i	$0.177783\pi$
$43$			6.95000i			1.05987i	−0.848040	+	0.529933i	$0.822217\pi$
$44$		0			0
$45$	8.49395			1.26620
$46$		0			0
$47$	−3.66137	+	3.66137i	−0.534066	+	0.534066i	−0.921780	−	0.387714i	$-0.873265\pi$
$47$	−3.66137	+	3.66137i	−0.534066	+	0.534066i	0.387714	+	0.921780i	$0.373265\pi$
$48$		0			0
$49$			1.00000i			0.142857i
$50$		0			0
$51$	−2.51375			−0.351995
$52$		0			0
$53$	5.69357	+	5.69357i	0.782072	+	0.782072i	0.980180	−	0.198108i	$-0.0634797\pi$
$53$	5.69357	+	5.69357i	0.782072	+	0.782072i	−0.198108	+	0.980180i	$0.563480\pi$
$54$		0			0
$55$	−3.52225	+	3.52225i	−0.474940	+	0.474940i
$56$		0			0
$57$	−1.60857			−0.213060
$58$		0			0
$59$	2.42066			0.315143			0.157572	−	0.987508i	$-0.449633\pi$
$59$	2.42066			0.315143			0.157572	+	0.987508i	$0.449633\pi$
$60$		0			0
$61$		−	8.24899i		−	1.05618i	−0.849190	−	0.528088i	$-0.822909\pi$
$61$		−	8.24899i		−	1.05618i	0.849190	−	0.528088i	$-0.177091\pi$
$62$		0			0
$63$	−1.94737	+	1.94737i	−0.245346	+	0.245346i
$64$		0			0
$65$	8.89122	−	8.89122i	1.10282	−	1.10282i
$66$		0			0
$67$	−5.59189	+	5.59189i	−0.683157	+	0.683157i	−0.960710	−	0.277553i	$-0.910477\pi$
$67$	−5.59189	+	5.59189i	−0.683157	+	0.683157i	0.277553	+	0.960710i	$0.410477\pi$
$68$		0			0
$69$	−1.21684	−	1.21684i	−0.146491	−	0.146491i
$70$		0			0
$71$	−3.14338	−	3.14338i	−0.373051	−	0.373051i	0.495536	−	0.868587i	$-0.334972\pi$
$71$	−3.14338	−	3.14338i	−0.373051	−	0.373051i	−0.868587	+	0.495536i	$0.834972\pi$
$72$		0			0
$73$		−	8.57857i		−	1.00405i	−0.864855	−	0.502023i	$-0.832589\pi$
$73$		−	8.57857i		−	1.00405i	0.864855	−	0.502023i	$-0.167411\pi$
$74$		0			0
$75$	1.58258	+	1.58258i	0.182740	+	0.182740i
$76$		0			0
$77$		−	1.61506i		−	0.184053i
$78$		0			0
$79$	5.97983	+	5.97983i	0.672783	+	0.672783i	0.958357	−	0.285574i	$-0.0921841\pi$
$79$	5.97983	+	5.97983i	0.672783	+	0.672783i	−0.285574	+	0.958357i	$0.592184\pi$
$80$		0			0
$81$	−6.84651			−0.760723
$82$		0			0
$83$	13.2534			1.45474			0.727372	−	0.686243i	$-0.240741\pi$
$83$	13.2534			1.45474			0.727372	+	0.686243i	$0.240741\pi$
$84$		0			0
$85$	11.0531	+	11.0531i	1.19888	+	1.19888i
$86$		0			0
$87$		−	3.23100i		−	0.346399i
$88$		0			0
$89$	−3.25227	−	3.25227i	−0.344740	−	0.344740i	0.513406	−	0.858146i	$-0.328384\pi$
$89$	−3.25227	−	3.25227i	−0.344740	−	0.344740i	−0.858146	+	0.513406i	$0.828384\pi$
$90$		0			0
$91$			4.07690i			0.427375i
$92$		0			0
$93$	−0.732052	−	0.732052i	−0.0759102	−	0.0759102i
$94$		0			0
$95$	7.07296	+	7.07296i	0.725671	+	0.725671i
$96$		0			0
$97$	−3.75610	+	3.75610i	−0.381375	+	0.381375i	−0.871597	−	0.490223i	$-0.836915\pi$
$97$	−3.75610	+	3.75610i	−0.381375	+	0.381375i	0.490223	+	0.871597i	$0.336915\pi$
$98$		0			0
$99$	3.14513	−	3.14513i	0.316097	−	0.316097i
$100$		0			0
$101$	12.9714	−	12.9714i	1.29071	−	1.29071i	0.356356	−	0.934350i	$-0.384019\pi$
$101$	12.9714	−	12.9714i	1.29071	−	1.29071i	0.934350	−	0.356356i	$-0.115981\pi$
$102$		0			0
$103$		−	15.3568i		−	1.51316i	−0.653904	−	0.756578i	$-0.726870\pi$
$103$		−	15.3568i		−	1.51316i	0.653904	−	0.756578i	$-0.273130\pi$
$104$		0			0
$105$	−1.52973			−0.149286
$106$		0			0
$107$	−17.0156			−1.64496			−0.822482	−	0.568791i	$-0.807411\pi$
$107$	−17.0156			−1.64496			−0.822482	+	0.568791i	$0.807411\pi$
$108$		0			0
$109$	7.54205	−	7.54205i	0.722398	−	0.722398i	−0.246695	−	0.969093i	$-0.579345\pi$
$109$	7.54205	−	7.54205i	0.722398	−	0.722398i	0.969093	+	0.246695i	$0.0793447\pi$
$110$		0			0
$111$	−2.26740	−	2.26740i	−0.215212	−	0.215212i
$112$		0			0
$113$	−1.18116			−0.111114			−0.0555569	−	0.998456i	$-0.517693\pi$
$113$	−1.18116			−0.111114			−0.0555569	+	0.998456i	$0.517693\pi$
$114$		0			0
$115$			10.7011i			0.997880i
$116$		0			0
$117$	−7.93924	+	7.93924i	−0.733983	+	0.733983i
$118$		0			0
$119$	−5.06820			−0.464601
$120$		0			0
$121$		−	8.39157i		−	0.762870i
$122$		0			0
$123$	−2.81322	−	1.47372i	−0.253659	−	0.132880i
$124$		0			0
$125$			1.50373i			0.134497i
$126$		0			0
$127$	−4.49326			−0.398713			−0.199356	−	0.979927i	$-0.563885\pi$
$127$	−4.49326			−0.398713			−0.199356	+	0.979927i	$0.563885\pi$
$128$		0			0
$129$	2.43746	−	2.43746i	0.214607	−	0.214607i
$130$		0			0
$131$		−	21.3610i		−	1.86632i	−0.359457	−	0.933162i	$-0.617038\pi$
$131$		−	21.3610i		−	1.86632i	0.359457	−	0.933162i	$-0.382962\pi$
$132$		0			0
$133$	−3.24317			−0.281219
$134$		0			0
$135$	−6.22399	−	6.22399i	−0.535676	−	0.535676i
$136$		0			0
$137$	9.76621	−	9.76621i	0.834384	−	0.834384i	−0.153729	−	0.988113i	$-0.549128\pi$
$137$	9.76621	−	9.76621i	0.834384	−	0.834384i	0.988113	+	0.153729i	$0.0491283\pi$
$138$		0			0
$139$	−14.2159			−1.20577			−0.602887	−	0.797826i	$-0.705983\pi$
$139$	−14.2159			−1.20577			−0.602887	+	0.797826i	$0.705983\pi$
$140$		0			0
$141$	2.56819			0.216281
$142$		0			0
$143$		−	6.58445i		−	0.550619i
$144$		0			0
$145$	−14.2069	+	14.2069i	−1.17982	+	1.17982i
$146$		0			0
$147$	0.350714	−	0.350714i	0.0289264	−	0.0289264i
$148$		0			0
$149$	−1.36730	+	1.36730i	−0.112013	+	0.112013i	−0.760892	−	0.648879i	$-0.775238\pi$
$149$	−1.36730	+	1.36730i	−0.112013	+	0.112013i	0.648879	+	0.760892i	$0.275238\pi$
$150$		0			0
$151$	13.6530	+	13.6530i	1.11106	+	1.11106i	0.993007	+	0.118057i	$0.0376667\pi$
$151$	13.6530	+	13.6530i	1.11106	+	1.11106i	0.118057	+	0.993007i	$0.462333\pi$
$152$		0			0
$153$	−9.86966	−	9.86966i	−0.797915	−	0.797915i
$154$		0			0
$155$			6.43776i			0.517093i
$156$		0			0
$157$	16.6525	+	16.6525i	1.32901	+	1.32901i	0.906234	+	0.422777i	$0.138945\pi$
$157$	16.6525	+	16.6525i	1.32901	+	1.32901i	0.422777	+	0.906234i	$0.361055\pi$
$158$		0			0
$159$		−	3.99363i		−	0.316716i
$160$		0			0
$161$	−2.45339	−	2.45339i	−0.193354	−	0.193354i
$162$		0			0
$163$	−12.6265			−0.988984			−0.494492	−	0.869182i	$-0.664646\pi$
$163$	−12.6265			−0.988984			−0.494492	+	0.869182i	$0.664646\pi$
$164$		0			0
$165$	2.47061			0.192336
$166$		0			0
$167$	−8.16594	−	8.16594i	−0.631900	−	0.631900i	0.316645	−	0.948544i	$-0.397444\pi$
$167$	−8.16594	−	8.16594i	−0.631900	−	0.631900i	−0.948544	+	0.316645i	$0.897444\pi$
$168$		0			0
$169$			3.62112i			0.278547i
$170$		0			0
$171$	−6.31567	−	6.31567i	−0.482971	−	0.482971i
$172$		0			0
$173$			7.35324i			0.559056i	0.960138	+	0.279528i	$0.0901780\pi$
$173$			7.35324i			0.559056i	−0.960138	+	0.279528i	$0.909822\pi$
$174$		0			0
$175$	3.19078	+	3.19078i	0.241200	+	0.241200i
$176$		0			0
$177$	−0.848961	−	0.848961i	−0.0638118	−	0.0638118i
$178$		0			0
$179$	3.78388	−	3.78388i	0.282820	−	0.282820i	−0.551413	−	0.834233i	$-0.685911\pi$
$179$	3.78388	−	3.78388i	0.282820	−	0.282820i	0.834233	+	0.551413i	$0.185911\pi$
$180$		0			0
$181$	1.72775	−	1.72775i	0.128423	−	0.128423i	−0.639974	−	0.768397i	$-0.721055\pi$
$181$	1.72775	−	1.72775i	0.128423	−	0.128423i	0.768397	+	0.639974i	$0.221055\pi$
$182$		0			0
$183$	−2.89304	+	2.89304i	−0.213860	+	0.213860i
$184$		0			0
$185$			19.9398i			1.46600i
$186$		0			0
$187$	8.18545			0.598579
$188$		0			0
$189$	2.85390			0.207590
$190$		0			0
$191$	−2.38197	+	2.38197i	−0.172353	+	0.172353i	−0.788012	−	0.615659i	$-0.788890\pi$
$191$	−2.38197	+	2.38197i	−0.172353	+	0.172353i	0.615659	+	0.788012i	$0.288890\pi$
$192$		0			0
$193$	4.79415	+	4.79415i	0.345091	+	0.345091i	0.858277	−	0.513187i	$-0.171535\pi$
$193$	4.79415	+	4.79415i	0.345091	+	0.345091i	−0.513187	+	0.858277i	$0.671535\pi$
$194$		0			0
$195$	−6.23655			−0.446609
$196$		0			0
$197$			13.5041i			0.962126i	0.876686	+	0.481063i	$0.159749\pi$
$197$			13.5041i			0.962126i	−0.876686	+	0.481063i	$0.840251\pi$
$198$		0			0
$199$	−6.97853	+	6.97853i	−0.494695	+	0.494695i	−0.909782	−	0.415087i	$-0.863751\pi$
$199$	−6.97853	+	6.97853i	−0.494695	+	0.494695i	0.415087	+	0.909782i	$0.363751\pi$
$200$		0			0
$201$	3.92231			0.276658
$202$		0			0
$203$		−	6.51431i		−	0.457215i
$204$		0			0
$205$	5.88988	+	18.8499i	0.411367	+	1.31654i
$206$		0			0
$207$		−	9.55531i		−	0.664140i
$208$		0			0
$209$	5.23793			0.362315
$210$		0			0
$211$	3.62001	−	3.62001i	0.249212	−	0.249212i	−0.571435	−	0.820647i	$-0.693613\pi$
$211$	3.62001	−	3.62001i	0.249212	−	0.249212i	0.820647	+	0.571435i	$0.193613\pi$
$212$		0			0
$213$			2.20486i			0.151074i
$214$		0			0
$215$	−21.4354			−1.46188
$216$		0			0
$217$	−1.47596	−	1.47596i	−0.100194	−	0.100194i
$218$		0			0
$219$	−3.00862	+	3.00862i	−0.203304	+	0.203304i
$220$		0			0
$221$	−20.6625			−1.38991
$222$		0			0
$223$	−7.04165			−0.471544			−0.235772	−	0.971808i	$-0.575762\pi$
$223$	−7.04165			−0.471544			−0.235772	+	0.971808i	$0.575762\pi$
$224$		0			0
$225$			12.4273i			0.828485i
$226$		0			0
$227$	−14.6416	+	14.6416i	−0.971798	+	0.971798i	−0.999613	−	0.0278151i	$-0.991145\pi$
$227$	−14.6416	+	14.6416i	−0.971798	+	0.971798i	0.0278151	+	0.999613i	$0.491145\pi$
$228$		0			0
$229$	−8.53015	+	8.53015i	−0.563688	+	0.563688i	−0.930353	−	0.366665i	$-0.880500\pi$
$229$	−8.53015	+	8.53015i	−0.563688	+	0.563688i	0.366665	+	0.930353i	$0.380500\pi$
$230$		0			0
$231$	−0.566425	+	0.566425i	−0.0372680	+	0.0372680i
$232$		0			0
$233$	−6.94405	−	6.94405i	−0.454920	−	0.454920i	0.442064	−	0.896984i	$-0.354246\pi$
$233$	−6.94405	−	6.94405i	−0.454920	−	0.454920i	−0.896984	+	0.442064i	$0.854246\pi$
$234$		0			0
$235$	−11.2925	−	11.2925i	−0.736641	−	0.736641i
$236$		0			0
$237$		−	4.19442i		−	0.272457i
$238$		0			0
$239$	17.5762	+	17.5762i	1.13691	+	1.13691i	0.989001	+	0.147910i	$0.0472545\pi$
$239$	17.5762	+	17.5762i	1.13691	+	1.13691i	0.147910	+	0.989001i	$0.452745\pi$
$240$		0			0
$241$			16.6390i			1.07181i	0.844277	+	0.535906i	$0.180030\pi$
$241$			16.6390i			1.07181i	−0.844277	+	0.535906i	$0.819970\pi$
$242$		0			0
$243$	8.45519	+	8.45519i	0.542401	+	0.542401i
$244$		0			0
$245$	−3.08423			−0.197044
$246$		0			0
$247$	−13.2221			−0.841302
$248$		0			0
$249$	−4.64814	−	4.64814i	−0.294564	−	0.294564i
$250$		0			0
$251$			15.1077i			0.953591i	0.879014	+	0.476796i	$0.158202\pi$
$251$			15.1077i			0.953591i	−0.879014	+	0.476796i	$0.841798\pi$
$252$		0			0
$253$	3.96237	+	3.96237i	0.249112	+	0.249112i
$254$		0			0
$255$		−	7.75296i		−	0.485509i
$256$		0			0
$257$	−9.96474	−	9.96474i	−0.621583	−	0.621583i	0.324353	−	0.945936i	$-0.394854\pi$
$257$	−9.96474	−	9.96474i	−0.621583	−	0.621583i	−0.945936	+	0.324353i	$0.894854\pi$
$258$		0			0
$259$	−4.57150	−	4.57150i	−0.284059	−	0.284059i
$260$		0			0
$261$	12.6858	−	12.6858i	0.785230	−	0.785230i
$262$		0			0
$263$	7.19183	−	7.19183i	0.443467	−	0.443467i	−0.449708	−	0.893175i	$-0.648472\pi$
$263$	7.19183	−	7.19183i	0.443467	−	0.443467i	0.893175	+	0.449708i	$0.148472\pi$
$264$		0			0
$265$	−17.5603	+	17.5603i	−1.07872	+	1.07872i
$266$		0			0
$267$			2.28124i			0.139609i
$268$		0			0
$269$	−24.3989			−1.48763			−0.743815	−	0.668386i	$-0.766986\pi$
$269$	−24.3989			−1.48763			−0.743815	+	0.668386i	$0.766986\pi$
$270$		0			0
$271$	−14.4777			−0.879455			−0.439727	−	0.898131i	$-0.644925\pi$
$271$	−14.4777			−0.879455			−0.439727	+	0.898131i	$0.644925\pi$
$272$		0			0
$273$	1.42983	−	1.42983i	0.0865370	−	0.0865370i
$274$		0			0
$275$	−5.15331	−	5.15331i	−0.310756	−	0.310756i
$276$		0			0
$277$	−0.579517			−0.0348198			−0.0174099	−	0.999848i	$-0.505542\pi$
$277$	−0.579517			−0.0348198			−0.0174099	+	0.999848i	$0.505542\pi$
$278$		0			0
$279$		−	5.74847i		−	0.344152i
$280$		0			0
$281$	21.1972	−	21.1972i	1.26452	−	1.26452i	0.315639	−	0.948879i	$-0.397781\pi$
$281$	21.1972	−	21.1972i	1.26452	−	1.26452i	0.948879	−	0.315639i	$-0.102219\pi$
$282$		0			0
$283$	6.92684			0.411758			0.205879	−	0.978577i	$-0.433995\pi$
$283$	6.92684			0.411758			0.205879	+	0.978577i	$0.433995\pi$
$284$		0			0
$285$		−	4.96118i		−	0.293875i
$286$		0			0
$287$	−5.67199	−	2.97129i	−0.334807	−	0.175390i
$288$		0			0
$289$		−	8.68660i		−	0.510977i
$290$		0			0
$291$	2.63464			0.154445
$292$		0			0
$293$	−8.37536	+	8.37536i	−0.489294	+	0.489294i	−0.908083	−	0.418790i	$-0.862455\pi$
$293$	−8.37536	+	8.37536i	−0.489294	+	0.489294i	0.418790	+	0.908083i	$0.362455\pi$
$294$		0			0
$295$			7.46587i			0.434680i
$296$		0			0
$297$	−4.60922			−0.267454
$298$		0			0
$299$	−10.0022	−	10.0022i	−0.578443	−	0.578443i
$300$		0			0
$301$	4.91439	−	4.91439i	0.283261	−	0.283261i
$302$		0			0
$303$	−9.09853			−0.522697
$304$		0			0
$305$	25.4418			1.45679
$306$		0			0
$307$		−	33.0329i		−	1.88529i	−0.333803	−	0.942643i	$-0.608332\pi$
$307$		−	33.0329i		−	1.88529i	0.333803	−	0.942643i	$-0.391668\pi$
$308$		0			0
$309$	−5.38586	+	5.38586i	−0.306391	+	0.306391i
$310$		0			0
$311$	−1.21706	+	1.21706i	−0.0690130	+	0.0690130i	−0.740771	−	0.671758i	$-0.765540\pi$
$311$	−1.21706	+	1.21706i	−0.0690130	+	0.0690130i	0.671758	+	0.740771i	$0.265540\pi$
$312$		0			0
$313$	4.53381	−	4.53381i	0.256266	−	0.256266i	−0.567267	−	0.823534i	$-0.691999\pi$
$313$	4.53381	−	4.53381i	0.256266	−	0.256266i	0.823534	+	0.567267i	$0.191999\pi$
$314$		0			0
$315$	−6.00613	−	6.00613i	−0.338407	−	0.338407i
$316$		0			0
$317$	−11.9738	−	11.9738i	−0.672515	−	0.672515i	0.285780	−	0.958295i	$-0.407747\pi$
$317$	−11.9738	−	11.9738i	−0.672515	−	0.672515i	−0.958295	+	0.285780i	$0.907747\pi$
$318$		0			0
$319$			10.5210i			0.589064i
$320$		0			0
$321$	5.96763	+	5.96763i	0.333080	+	0.333080i
$322$		0			0
$323$		−	16.4370i		−	0.914582i
$324$		0			0
$325$	13.0085	+	13.0085i	0.721582	+	0.721582i
$326$		0			0
$327$	−5.29021			−0.292549
$328$		0			0
$329$	5.17796			0.285470
$330$		0			0
$331$	18.8893	+	18.8893i	1.03825	+	1.03825i	0.999239	+	0.0390120i	$0.0124211\pi$
$331$	18.8893	+	18.8893i	1.03825	+	1.03825i	0.0390120	+	0.999239i	$0.487579\pi$
$332$		0			0
$333$		−	17.8048i		−	0.975699i
$334$		0			0
$335$	−17.2466	−	17.2466i	−0.942284	−	0.942284i
$336$		0			0
$337$		−	10.4913i		−	0.571495i	−0.958305	−	0.285748i	$-0.907758\pi$
$337$		−	10.4913i		−	0.571495i	0.958305	−	0.285748i	$-0.0922419\pi$
$338$		0			0
$339$	0.414248	+	0.414248i	0.0224989	+	0.0224989i
$340$		0			0
$341$	2.38376	+	2.38376i	0.129088	+	0.129088i
$342$		0			0
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$		0			0
$345$	3.75302	−	3.75302i	0.202056	−	0.202056i
$346$		0			0
$347$	−24.3424	+	24.3424i	−1.30677	+	1.30677i	−0.383035	+	0.923734i	$0.625121\pi$
$347$	−24.3424	+	24.3424i	−1.30677	+	1.30677i	−0.923734	+	0.383035i	$0.874879\pi$
$348$		0			0
$349$			9.46542i			0.506672i	0.967378	+	0.253336i	$0.0815279\pi$
$349$			9.46542i			0.506672i	−0.967378	+	0.253336i	$0.918472\pi$
$350$		0			0
$351$	11.6350			0.621033
$352$		0			0
$353$	−7.45234			−0.396648			−0.198324	−	0.980137i	$-0.563550\pi$
$353$	−7.45234			−0.396648			−0.198324	+	0.980137i	$0.563550\pi$
$354$		0			0
$355$	9.69490	−	9.69490i	0.514552	−	0.514552i
$356$		0			0
$357$	1.77749	+	1.77749i	0.0940746	+	0.0940746i
$358$		0			0
$359$	−22.9714			−1.21238			−0.606192	−	0.795319i	$-0.707304\pi$
$359$	−22.9714			−1.21238			−0.606192	+	0.795319i	$0.707304\pi$
$360$		0			0
$361$			8.48182i			0.446411i
$362$		0			0
$363$	−2.94304	+	2.94304i	−0.154470	+	0.154470i
$364$		0			0
$365$	26.4582			1.38489
$366$		0			0
$367$			3.19066i			0.166551i	0.996527	+	0.0832756i	$0.0265382\pi$
$367$			3.19066i			0.166551i	−0.996527	+	0.0832756i	$0.973462\pi$
$368$		0			0
$369$	−5.25925	−	16.8317i	−0.273786	−	0.876222i
$370$		0			0
$371$		−	8.05192i		−	0.418035i
$372$		0			0
$373$	3.74084			0.193693			0.0968467	−	0.995299i	$-0.469124\pi$
$373$	3.74084			0.193693			0.0968467	+	0.995299i	$0.469124\pi$
$374$		0			0
$375$	0.527378	−	0.527378i	0.0272337	−	0.0272337i
$376$		0			0
$377$		−	26.5582i		−	1.36782i
$378$		0			0
$379$	32.2983			1.65905			0.829525	−	0.558470i	$-0.188611\pi$
$379$	32.2983			1.65905			0.829525	+	0.558470i	$0.188611\pi$
$380$		0			0
$381$	1.57585	+	1.57585i	0.0807333	+	0.0807333i
$382$		0			0
$383$	−11.6140	+	11.6140i	−0.593449	+	0.593449i	−0.938561	−	0.345112i	$-0.887841\pi$
$383$	−11.6140	+	11.6140i	−0.593449	+	0.593449i	0.345112	+	0.938561i	$0.387841\pi$
$384$		0			0
$385$	4.98122			0.253866
$386$		0			0
$387$	19.1403			0.972956
$388$		0			0
$389$		−	16.1631i		−	0.819504i	−0.912197	−	0.409752i	$-0.865615\pi$
$389$		−	16.1631i		−	0.819504i	0.912197	−	0.409752i	$-0.134385\pi$
$390$		0			0
$391$	12.4342	−	12.4342i	0.628827	−	0.628827i
$392$		0			0
$393$	−7.49162	+	7.49162i	−0.377902	+	0.377902i
$394$		0			0
$395$	−18.4431	+	18.4431i	−0.927975	+	0.927975i
$396$		0			0
$397$	−5.34629	−	5.34629i	−0.268323	−	0.268323i	0.560101	−	0.828424i	$-0.310762\pi$
$397$	−5.34629	−	5.34629i	−0.268323	−	0.268323i	−0.828424	+	0.560101i	$0.810762\pi$
$398$		0			0
$399$	1.13743	+	1.13743i	0.0569426	+	0.0569426i
$400$		0			0
$401$		−	15.7388i		−	0.785960i	−0.919547	−	0.392980i	$-0.871444\pi$
$401$		−	15.7388i		−	0.785960i	0.919547	−	0.392980i	$-0.128556\pi$
$402$		0			0
$403$	−6.01733	−	6.01733i	−0.299744	−	0.299744i
$404$		0			0
$405$		−	21.1162i		−	1.04927i
$406$		0			0
$407$	7.38326	+	7.38326i	0.365975	+	0.365975i
$408$		0			0
$409$	−16.5501			−0.818351			−0.409175	−	0.912456i	$-0.634184\pi$
$409$	−16.5501			−0.818351			−0.409175	+	0.912456i	$0.634184\pi$
$410$		0			0
$411$	−6.85030			−0.337900
$412$		0			0
$413$	−1.71167	−	1.71167i	−0.0842256	−	0.0842256i
$414$		0			0
$415$			40.8763i			2.00654i
$416$		0			0
$417$	4.98571	+	4.98571i	0.244151	+	0.244151i
$418$		0			0
$419$		−	10.1682i		−	0.496747i	−0.968664	−	0.248374i	$-0.920104\pi$
$419$		−	10.1682i		−	0.496747i	0.968664	−	0.248374i	$-0.0798960\pi$
$420$		0			0
$421$	23.6838	+	23.6838i	1.15428	+	1.15428i	0.985686	+	0.168594i	$0.0539228\pi$
$421$	23.6838	+	23.6838i	1.15428	+	1.15428i	0.168594	+	0.985686i	$0.446077\pi$
$422$		0			0
$423$	10.0834	+	10.0834i	0.490272	+	0.490272i
$424$		0			0
$425$	−16.1715	+	16.1715i	−0.784433	+	0.784433i
$426$		0			0
$427$	−5.83292	+	5.83292i	−0.282275	+	0.282275i
$428$		0			0
$429$	−2.30926	+	2.30926i	−0.111492	+	0.111492i
$430$		0			0
$431$			13.0393i			0.628080i	0.949410	+	0.314040i	$0.101683\pi$
$431$			13.0393i			0.628080i	−0.949410	+	0.314040i	$0.898317\pi$
$432$		0			0
$433$	−24.1559			−1.16086			−0.580430	−	0.814310i	$-0.697115\pi$
$433$	−24.1559			−1.16086			−0.580430	+	0.814310i	$0.697115\pi$
$434$		0			0
$435$	9.96513			0.477791
$436$		0			0
$437$	7.95676	−	7.95676i	0.380623	−	0.380623i
$438$		0			0
$439$	−3.76046	−	3.76046i	−0.179477	−	0.179477i	0.611651	−	0.791128i	$-0.290506\pi$
$439$	−3.76046	−	3.76046i	−0.179477	−	0.179477i	−0.791128	+	0.611651i	$0.790506\pi$
$440$		0			0
$441$	2.75400			0.131143
$442$		0			0
$443$			2.59993i			0.123526i	0.998091	+	0.0617632i	$0.0196723\pi$
$443$			2.59993i			0.123526i	−0.998091	+	0.0617632i	$0.980328\pi$
$444$		0			0
$445$	10.0307	−	10.0307i	0.475503	−	0.475503i
$446$		0			0
$447$	0.959060			0.0453620
$448$		0			0
$449$		−	19.5739i		−	0.923751i	−0.886945	−	0.461876i	$-0.847177\pi$
$449$		−	19.5739i		−	0.923751i	0.886945	−	0.461876i	$-0.152823\pi$
$450$		0			0
$451$	9.16061	+	4.79882i	0.431356	+	0.225968i
$452$		0			0
$453$		−	9.57659i		−	0.449947i
$454$		0			0
$455$	−12.5741			−0.589482
$456$		0			0
$457$	−28.8002	+	28.8002i	−1.34721	+	1.34721i	−0.458542	+	0.888672i	$0.651628\pi$
$457$	−28.8002	+	28.8002i	−1.34721	+	1.34721i	−0.888672	+	0.458542i	$0.848372\pi$
$458$		0			0
$459$			14.4641i			0.675126i
$460$		0			0
$461$	36.7491			1.71157			0.855787	−	0.517328i	$-0.173073\pi$
$461$	36.7491			1.71157			0.855787	+	0.517328i	$0.173073\pi$
$462$		0			0
$463$	1.01334	+	1.01334i	0.0470941	+	0.0470941i	0.730262	−	0.683168i	$-0.239398\pi$
$463$	1.01334	+	1.01334i	0.0470941	+	0.0470941i	−0.683168	+	0.730262i	$0.739398\pi$
$464$		0			0
$465$	2.25781	−	2.25781i	0.104704	−	0.104704i
$466$		0			0
$467$	2.72582			0.126136			0.0630679	−	0.998009i	$-0.479912\pi$
$467$	2.72582			0.126136			0.0630679	+	0.998009i	$0.479912\pi$
$468$		0			0
$469$	7.90812			0.365163
$470$		0			0
$471$		−	11.6805i		−	0.538209i
$472$		0			0
$473$	−7.93705	+	7.93705i	−0.364946	+	0.364946i
$474$		0			0
$475$	−10.3483	+	10.3483i	−0.474811	+	0.474811i
$476$		0			0
$477$	15.6801	−	15.6801i	0.717942	−	0.717942i
$478$		0			0
$479$	12.2164	+	12.2164i	0.558183	+	0.558183i	0.928790	−	0.370607i	$-0.120850\pi$
$479$	12.2164	+	12.2164i	0.558183	+	0.558183i	−0.370607	+	0.928790i	$0.620850\pi$
$480$		0			0
$481$	−18.6376	−	18.6376i	−0.849800	−	0.849800i
$482$		0			0
$483$			1.72087i			0.0783025i
$484$		0			0
$485$	−11.5847	−	11.5847i	−0.526033	−	0.526033i
$486$		0			0
$487$			18.8554i			0.854420i	0.904152	+	0.427210i	$0.140504\pi$
$487$			18.8554i			0.854420i	−0.904152	+	0.427210i	$0.859496\pi$
$488$		0			0
$489$	4.42829	+	4.42829i	0.200254	+	0.200254i
$490$		0			0
$491$	−23.8689			−1.07719			−0.538594	−	0.842565i	$-0.681044\pi$
$491$	−23.8689			−1.07719			−0.538594	+	0.842565i	$0.681044\pi$
$492$		0			0
$493$	33.0158			1.48696
$494$		0			0
$495$	9.70028	+	9.70028i	0.435995	+	0.435995i
$496$		0			0
$497$			4.44542i			0.199404i
$498$		0			0
$499$	−11.8815	−	11.8815i	−0.531887	−	0.531887i	0.389246	−	0.921134i	$-0.372735\pi$
$499$	−11.8815	−	11.8815i	−0.531887	−	0.531887i	−0.921134	+	0.389246i	$0.872735\pi$
$500$		0			0
$501$			5.72782i			0.255900i
$502$		0			0
$503$	4.58613	+	4.58613i	0.204485	+	0.204485i	0.801919	−	0.597433i	$-0.203813\pi$
$503$	4.58613	+	4.58613i	0.204485	+	0.204485i	−0.597433	+	0.801919i	$0.703813\pi$
$504$		0			0
$505$	40.0068	+	40.0068i	1.78028	+	1.78028i
$506$		0			0
$507$	1.26998	−	1.26998i	0.0564016	−	0.0564016i
$508$		0			0
$509$	2.65834	−	2.65834i	0.117829	−	0.117829i	−0.645734	−	0.763563i	$-0.723448\pi$
$509$	2.65834	−	2.65834i	0.117829	−	0.117829i	0.763563	+	0.645734i	$0.223448\pi$
$510$		0			0
$511$	−6.06596	+	6.06596i	−0.268342	+	0.268342i
$512$		0			0
$513$			9.25568i			0.408648i
$514$		0			0
$515$	47.3640			2.08711
$516$		0			0
$517$	−8.36273			−0.367792
$518$		0			0
$519$	2.57888	−	2.57888i	0.113200	−	0.113200i
$520$		0			0
$521$	16.0084	+	16.0084i	0.701341	+	0.701341i	0.964698	−	0.263358i	$-0.0848299\pi$
$521$	16.0084	+	16.0084i	0.701341	+	0.701341i	−0.263358	+	0.964698i	$0.584830\pi$
$522$		0			0
$523$	35.7387			1.56274			0.781371	−	0.624067i	$-0.214521\pi$
$523$	35.7387			1.56274			0.781371	+	0.624067i	$0.214521\pi$
$524$		0			0
$525$		−	2.23810i		−	0.0976789i
$526$		0			0
$527$	7.48044	−	7.48044i	0.325853	−	0.325853i
$528$		0			0
$529$	−10.9618			−0.476600
$530$		0			0
$531$		−	6.66650i		−	0.289302i
$532$		0			0
$533$	−23.1241	−	12.1137i	−1.00162	−	0.524701i
$534$		0			0
$535$		−	52.4801i		−	2.26891i
$536$		0			0
$537$	−2.65412			−0.114534
$538$		0			0
$539$	−1.14202	+	1.14202i	−0.0491903	+	0.0491903i
$540$		0			0
$541$		−	16.3733i		−	0.703945i	−0.936010	−	0.351973i	$-0.885511\pi$
$541$		−	16.3733i		−	0.703945i	0.936010	−	0.351973i	$-0.114489\pi$
$542$		0			0
$543$	−1.21189			−0.0520074
$544$		0			0
$545$	23.2614	+	23.2614i	0.996409	+	0.996409i
$546$		0			0
$547$	6.15079	−	6.15079i	0.262989	−	0.262989i	−0.563278	−	0.826267i	$-0.690460\pi$
$547$	6.15079	−	6.15079i	0.262989	−	0.262989i	0.826267	+	0.563278i	$0.190460\pi$
$548$		0			0
$549$	−22.7177			−0.969569
$550$		0			0
$551$	21.1270			0.900042
$552$		0			0
$553$		−	8.45675i		−	0.359618i
$554$		0			0
$555$	6.99316	−	6.99316i	0.296843	−	0.296843i
$556$		0			0
$557$	0.278382	−	0.278382i	0.0117954	−	0.0117954i	−0.701184	−	0.712980i	$-0.747345\pi$
$557$	0.278382	−	0.278382i	0.0117954	−	0.0117954i	0.712980	+	0.701184i	$0.247345\pi$
$558$		0			0
$559$	20.0355	−	20.0355i	0.847411	−	0.847411i
$560$		0			0
$561$	−2.87075	−	2.87075i	−0.121203	−	0.121203i
$562$		0			0
$563$	9.87314	+	9.87314i	0.416103	+	0.416103i	0.883858	−	0.467755i	$-0.154937\pi$
$563$	9.87314	+	9.87314i	0.416103	+	0.416103i	−0.467755	+	0.883858i	$0.654937\pi$
$564$		0			0
$565$		−	3.64295i		−	0.153260i
$566$		0			0
$567$	4.84121	+	4.84121i	0.203312	+	0.203312i
$568$		0			0
$569$			0.289569i			0.0121394i	0.999982	+	0.00606968i	$0.00193205\pi$
$569$			0.289569i			0.0121394i	−0.999982	+	0.00606968i	$0.998068\pi$
$570$		0			0
$571$	13.2936	+	13.2936i	0.556320	+	0.556320i	0.928258	−	0.371938i	$-0.121307\pi$
$571$	13.2936	+	13.2936i	0.556320	+	0.556320i	−0.371938	+	0.928258i	$0.621307\pi$
$572$		0			0
$573$	1.67078			0.0697978
$574$		0			0
$575$	−15.6564			−0.652919
$576$		0			0
$577$	10.2346	+	10.2346i	0.426073	+	0.426073i	0.887288	−	0.461215i	$-0.152586\pi$
$577$	10.2346	+	10.2346i	0.426073	+	0.426073i	−0.461215	+	0.887288i	$0.652586\pi$
$578$		0			0
$579$		−	3.36275i		−	0.139751i
$580$		0			0
$581$	−9.37154	−	9.37154i	−0.388797	−	0.388797i
$582$		0			0
$583$			13.0044i			0.538585i
$584$		0			0
$585$	−24.4864	−	24.4864i	−1.01239	−	1.01239i
$586$		0			0
$587$	−1.81926	−	1.81926i	−0.0750888	−	0.0750888i	0.668565	−	0.743654i	$-0.266909\pi$
$587$	−1.81926	−	1.81926i	−0.0750888	−	0.0750888i	−0.743654	+	0.668565i	$0.766909\pi$
$588$		0			0
$589$	4.78678	−	4.78678i	0.197236	−	0.197236i
$590$		0			0
$591$	4.73607	−	4.73607i	0.194816	−	0.194816i
$592$		0			0
$593$	−6.36714	+	6.36714i	−0.261467	+	0.261467i	−0.825650	−	0.564183i	$-0.809191\pi$
$593$	−6.36714	+	6.36714i	−0.261467	+	0.261467i	0.564183	+	0.825650i	$0.309191\pi$
$594$		0			0
$595$		−	15.6315i		−	0.640827i
$596$		0			0
$597$	4.89494			0.200337
$598$		0			0
$599$	15.0843			0.616329			0.308165	−	0.951333i	$-0.400285\pi$
$599$	15.0843			0.616329			0.308165	+	0.951333i	$0.400285\pi$
$600$		0			0
$601$	−14.4682	+	14.4682i	−0.590172	+	0.590172i	−0.937678	−	0.347506i	$-0.887029\pi$
$601$	−14.4682	+	14.4682i	−0.590172	+	0.590172i	0.347506	+	0.937678i	$0.387029\pi$
$602$		0			0
$603$	15.4000	+	15.4000i	0.627138	+	0.627138i
$604$		0			0
$605$	25.8815			1.05223
$606$		0			0
$607$			41.4685i			1.68315i	0.540137	+	0.841577i	$0.318372\pi$
$607$			41.4685i			1.68315i	−0.540137	+	0.841577i	$0.681628\pi$
$608$		0			0
$609$	−2.28466	+	2.28466i	−0.0925791	+	0.0925791i
$610$		0			0
$611$	21.1100			0.854020
$612$		0			0
$613$			3.69825i			0.149371i	0.997207	+	0.0746854i	$0.0237953\pi$
$613$			3.69825i			0.149371i	−0.997207	+	0.0746854i	$0.976205\pi$
$614$		0			0
$615$	4.54527	−	8.67660i	0.183283	−	0.349874i
$616$		0			0
$617$		−	3.24686i		−	0.130714i	−0.997862	−	0.0653569i	$-0.979181\pi$
$617$		−	3.24686i		−	0.130714i	0.997862	−	0.0653569i	$-0.0208186\pi$
$618$		0			0
$619$	−25.9486			−1.04296			−0.521481	−	0.853263i	$-0.674620\pi$
$619$	−25.9486			−1.04296			−0.521481	+	0.853263i	$0.674620\pi$
$620$		0			0
$621$	−7.00171	+	7.00171i	−0.280969	+	0.280969i
$622$		0			0
$623$			4.59941i			0.184271i
$624$		0			0
$625$	−27.2001			−1.08800
$626$		0			0
$627$	−1.83702	−	1.83702i	−0.0733633	−	0.0733633i
$628$		0			0
$629$	23.1693	−	23.1693i	0.923820	−	0.923820i
$630$		0			0
$631$	−18.0145			−0.717145			−0.358572	−	0.933502i	$-0.616736\pi$
$631$	−18.0145			−0.717145			−0.358572	+	0.933502i	$0.616736\pi$
$632$		0			0
$633$	−2.53918			−0.100923
$634$		0			0
$635$		−	13.8582i		−	0.549947i
$636$		0			0
$637$	2.88280	−	2.88280i	0.114221	−	0.114221i
$638$		0			0
$639$	−8.65688	+	8.65688i	−0.342461	+	0.342461i
$640$		0			0
$641$	−28.6846	+	28.6846i	−1.13297	+	1.13297i	−0.143294	+	0.989680i	$0.545770\pi$
$641$	−28.6846	+	28.6846i	−1.13297	+	1.13297i	−0.989680	+	0.143294i	$0.954230\pi$
$642$		0			0
$643$	−8.96702	−	8.96702i	−0.353625	−	0.353625i	0.507832	−	0.861456i	$-0.330447\pi$
$643$	−8.96702	−	8.96702i	−0.353625	−	0.353625i	−0.861456	+	0.507832i	$0.830447\pi$
$644$		0			0
$645$	7.51769	+	7.51769i	0.296009	+	0.296009i
$646$		0			0
$647$			21.6818i			0.852399i	0.904629	+	0.426199i	$0.140148\pi$
$647$			21.6818i			0.852399i	−0.904629	+	0.426199i	$0.859852\pi$
$648$		0			0
$649$	2.76445	+	2.76445i	0.108514	+	0.108514i
$650$		0			0
$651$			1.03528i			0.0405757i
$652$		0			0
$653$	−20.3145	−	20.3145i	−0.794969	−	0.794969i	0.187328	−	0.982297i	$-0.440017\pi$
$653$	−20.3145	−	20.3145i	−0.794969	−	0.794969i	−0.982297	+	0.187328i	$0.940017\pi$
$654$		0			0
$655$	65.8823			2.57423
$656$		0			0
$657$	−23.6254			−0.921713
$658$		0			0
$659$	−23.9096	−	23.9096i	−0.931385	−	0.931385i	0.0664074	−	0.997793i	$-0.478846\pi$
$659$	−23.9096	−	23.9096i	−0.931385	−	0.931385i	−0.997793	+	0.0664074i	$0.978846\pi$
$660$		0			0
$661$			12.1735i			0.473494i	0.971571	+	0.236747i	$0.0760813\pi$
$661$			12.1735i			0.473494i	−0.971571	+	0.236747i	$0.923919\pi$
$662$		0			0
$663$	7.24664	+	7.24664i	0.281436	+	0.281436i
$664$		0			0
$665$		−	10.0027i		−	0.387887i
$666$		0			0
$667$	15.9821	+	15.9821i	0.618830	+	0.618830i
$668$		0			0
$669$	2.46961	+	2.46961i	0.0954805	+	0.0954805i
$670$		0			0
$671$	9.42053	−	9.42053i	0.363675	−	0.363675i
$672$		0			0
$673$	−22.0905	+	22.0905i	−0.851525	+	0.851525i	−0.990321	−	0.138796i	$-0.955677\pi$
$673$	−22.0905	+	22.0905i	−0.851525	+	0.851525i	0.138796	+	0.990321i	$0.455677\pi$
$674$		0			0
$675$	9.10616	−	9.10616i	0.350496	−	0.350496i
$676$		0			0
$677$		−	28.0742i		−	1.07898i	−0.841992	−	0.539490i	$-0.818617\pi$
$677$		−	28.0742i		−	1.07898i	0.841992	−	0.539490i	$-0.181383\pi$
$678$		0			0
$679$	5.31193			0.203853
$680$		0			0
$681$	10.2700			0.393549
$682$		0			0
$683$	−7.78438	+	7.78438i	−0.297861	+	0.297861i	−0.840176	−	0.542315i	$-0.817548\pi$
$683$	−7.78438	+	7.78438i	−0.297861	+	0.297861i	0.542315	+	0.840176i	$0.317548\pi$
$684$		0			0
$685$	30.1212	+	30.1212i	1.15087	+	1.15087i
$686$		0			0
$687$	5.98329			0.228277
$688$		0			0
$689$		−	32.8269i		−	1.25061i
$690$		0			0
$691$	16.1447	−	16.1447i	0.614173	−	0.614173i	−0.329857	−	0.944031i	$-0.607001\pi$
$691$	16.1447	−	16.1447i	0.614173	−	0.614173i	0.944031	+	0.329857i	$0.107001\pi$
$692$		0			0
$693$	−4.44788			−0.168961
$694$		0			0
$695$		−	43.8449i		−	1.66313i
$696$		0			0
$697$	15.0591	−	28.7467i	0.570404	−	1.08886i
$698$		0			0
$699$			4.87075i			0.184229i
$700$		0			0
$701$	43.5009			1.64300			0.821502	−	0.570205i	$-0.193136\pi$
$701$	43.5009			1.64300			0.821502	+	0.570205i	$0.193136\pi$
$702$		0			0
$703$	14.8262	−	14.8262i	0.559180	−	0.559180i
$704$		0			0
$705$			7.92088i			0.298317i
$706$		0			0
$707$	−18.3444			−0.689912
$708$		0			0
$709$	28.7431	+	28.7431i	1.07947	+	1.07947i	0.996557	+	0.0829115i	$0.0264219\pi$
$709$	28.7431	+	28.7431i	1.07947	+	1.07947i	0.0829115	+	0.996557i	$0.473578\pi$
$710$		0			0
$711$	16.4684	−	16.4684i	0.617615	−	0.617615i
$712$		0			0
$713$	7.24218			0.271222
$714$		0			0
$715$	20.3079			0.759473
$716$		0			0
$717$		−	12.3285i		−	0.460415i
$718$		0			0
$719$	5.06655	−	5.06655i	0.188951	−	0.188951i	−0.606292	−	0.795242i	$-0.707344\pi$
$719$	5.06655	−	5.06655i	0.188951	−	0.188951i	0.795242	+	0.606292i	$0.207344\pi$
$720$		0			0
$721$	−10.8589	+	10.8589i	−0.404408	+	0.404408i
$722$		0			0
$723$	5.83554	−	5.83554i	0.217026	−	0.217026i
$724$		0			0
$725$	−20.7857	−	20.7857i	−0.771963	−	0.771963i
$726$		0			0
$727$	−20.0991	−	20.0991i	−0.745435	−	0.745435i	0.228183	−	0.973618i	$-0.426722\pi$
$727$	−20.0991	−	20.0991i	−0.745435	−	0.745435i	−0.973618	+	0.228183i	$0.926722\pi$
$728$		0			0
$729$			14.6088i			0.541067i
$730$		0			0
$731$	24.9071	+	24.9071i	0.921223	+	0.921223i
$732$		0			0
$733$		−	21.8279i		−	0.806231i	−0.915149	−	0.403116i	$-0.867927\pi$
$733$		−	21.8279i		−	0.806231i	0.915149	−	0.403116i	$-0.132073\pi$
$734$		0			0
$735$	1.08168	+	1.08168i	0.0398984	+	0.0398984i
$736$		0			0
$737$	−12.7721			−0.470466
$738$		0			0
$739$	−52.4937			−1.93101			−0.965507	−	0.260378i	$-0.916153\pi$
$739$	−52.4937			−1.93101			−0.965507	+	0.260378i	$0.916153\pi$
$740$		0			0
$741$	4.63718	+	4.63718i	0.170351	+	0.170351i
$742$		0			0
$743$			8.77031i			0.321751i	0.986975	+	0.160876i	$0.0514318\pi$
$743$			8.77031i			0.321751i	−0.986975	+	0.160876i	$0.948568\pi$
$744$		0			0
$745$	−4.21705	−	4.21705i	−0.154501	−	0.154501i
$746$		0			0
$747$		−	36.4997i		−	1.33546i
$748$		0			0
$749$	12.0319	+	12.0319i	0.439635	+	0.439635i
$750$		0			0
$751$	−18.3382	−	18.3382i	−0.669170	−	0.669170i	0.288354	−	0.957524i	$-0.406892\pi$
$751$	−18.3382	−	18.3382i	−0.669170	−	0.669170i	−0.957524	+	0.288354i	$0.906892\pi$
$752$		0			0
$753$	5.29849	−	5.29849i	0.193088	−	0.193088i
$754$		0			0
$755$	−42.1089	+	42.1089i	−1.53250	+	1.53250i
$756$		0			0
$757$	7.70846	−	7.70846i	0.280169	−	0.280169i	−0.553007	−	0.833176i	$-0.686520\pi$
$757$	7.70846	−	7.70846i	0.280169	−	0.280169i	0.833176	+	0.553007i	$0.186520\pi$
$758$		0			0
$759$		−	2.77932i		−	0.100883i
$760$		0			0
$761$	2.73457			0.0991282			0.0495641	−	0.998771i	$-0.484217\pi$
$761$	2.73457			0.0991282			0.0495641	+	0.998771i	$0.484217\pi$
$762$		0			0
$763$	−10.6661			−0.386138
$764$		0			0
$765$	30.4403	−	30.4403i	1.10057	−	1.10057i
$766$		0			0
$767$	−6.97829	−	6.97829i	−0.251972	−	0.251972i
$768$		0			0
$769$	27.1439			0.978834			0.489417	−	0.872050i	$-0.337210\pi$
$769$	27.1439			0.978834			0.489417	+	0.872050i	$0.337210\pi$
$770$		0			0
$771$			6.98955i			0.251723i
$772$		0			0
$773$	29.7365	−	29.7365i	1.06955	−	1.06955i	0.0721522	−	0.997394i	$-0.477013\pi$
$773$	29.7365	−	29.7365i	1.06955	−	1.06955i	0.997394	−	0.0721522i	$-0.0229867\pi$
$774$		0			0
$775$	−9.41891			−0.338337
$776$		0			0
$777$			3.20658i			0.115036i
$778$		0			0
$779$	9.63642	−	18.3952i	0.345261	−	0.659078i
$780$		0			0
$781$		−	7.17962i		−	0.256907i
$782$		0			0
$783$	−18.5912			−0.664394
$784$		0			0
$785$	−51.3599	+	51.3599i	−1.83311	+	1.83311i
$786$		0			0
$787$		−	24.9010i		−	0.887626i	−0.896119	−	0.443813i	$-0.853625\pi$
$787$		−	24.9010i		−	0.887626i	0.896119	−	0.443813i	$-0.146375\pi$
$788$		0			0
$789$	−5.04455			−0.179591
$790$		0			0
$791$	0.835203	+	0.835203i	0.0296964	+	0.0296964i
$792$		0			0
$793$	−23.7802	+	23.7802i	−0.844461	+	0.844461i
$794$		0			0
$795$	12.3173			0.436848
$796$		0			0
$797$	−23.9782			−0.849352			−0.424676	−	0.905345i	$-0.639612\pi$
$797$	−23.9782			−0.849352			−0.424676	+	0.905345i	$0.639612\pi$
$798$		0			0
$799$			26.2429i			0.928408i
$800$		0			0
$801$	−8.95675	+	8.95675i	−0.316471	+	0.316471i
$802$		0			0
$803$	9.79690	−	9.79690i	0.345725	−	0.345725i
$804$		0			0
$805$	7.56680	−	7.56680i	0.266695	−	0.266695i
$806$		0			0
$807$	8.55705	+	8.55705i	0.301223	+	0.301223i
$808$		0			0
$809$	−13.1746	−	13.1746i	−0.463194	−	0.463194i	0.436507	−	0.899701i	$-0.356215\pi$
$809$	−13.1746	−	13.1746i	−0.463194	−	0.463194i	−0.899701	+	0.436507i	$0.856215\pi$
$810$		0			0
$811$		−	10.2488i		−	0.359883i	−0.983677	−	0.179941i	$-0.942409\pi$
$811$		−	10.2488i		−	0.359883i	0.983677	−	0.179941i	$-0.0575908\pi$
$812$		0			0
$813$	5.07752	+	5.07752i	0.178076	+	0.178076i
$814$		0			0
$815$		−	38.9430i		−	1.36411i
$816$		0			0
$817$	15.9382	+	15.9382i	0.557608	+	0.557608i
$818$		0			0
$819$	11.2278			0.392330
$820$		0			0
$821$	2.09256			0.0730307			0.0365153	−	0.999333i	$-0.488374\pi$
$821$	2.09256			0.0730307			0.0365153	+	0.999333i	$0.488374\pi$
$822$		0			0
$823$	−27.2308	−	27.2308i	−0.949205	−	0.949205i	0.0495656	−	0.998771i	$-0.484216\pi$
$823$	−27.2308	−	27.2308i	−0.949205	−	0.949205i	−0.998771	+	0.0495656i	$0.984216\pi$
$824$		0			0
$825$			3.61468i			0.125847i
$826$		0			0
$827$	19.0921	+	19.0921i	0.663897	+	0.663897i	0.956296	−	0.292399i	$-0.0944536\pi$
$827$	19.0921	+	19.0921i	0.663897	+	0.663897i	−0.292399	+	0.956296i	$0.594454\pi$
$828$		0			0
$829$			23.3840i			0.812160i	0.913838	+	0.406080i	$0.133105\pi$
$829$			23.3840i			0.812160i	−0.913838	+	0.406080i	$0.866895\pi$
$830$		0			0
$831$	0.203245	+	0.203245i	0.00705049	+	0.00705049i
$832$		0			0
$833$	3.58376	+	3.58376i	0.124170	+	0.124170i
$834$		0			0
$835$	25.1856	−	25.1856i	0.871584	−	0.871584i
$836$		0			0
$837$	−4.21223	+	4.21223i	−0.145596	+	0.145596i
$838$		0			0
$839$	−12.2610	+	12.2610i	−0.423298	+	0.423298i	−0.886338	−	0.463040i	$-0.846759\pi$
$839$	−12.2610	+	12.2610i	−0.423298	+	0.423298i	0.463040	+	0.886338i	$0.346759\pi$
$840$		0			0
$841$			13.4362i			0.463318i
$842$		0			0
$843$	−14.8683			−0.512092
$844$		0			0
$845$	−11.1683			−0.384202
$846$		0			0
$847$	−5.93374	+	5.93374i	−0.203886	+	0.203886i
$848$		0			0
$849$	−2.42934	−	2.42934i	−0.0833748	−	0.0833748i
$850$		0			0
$851$	22.4313			0.768936
$852$		0			0
$853$			22.1493i			0.758377i	0.925319	+	0.379189i	$0.123797\pi$
$853$			22.1493i			0.758377i	−0.925319	+	0.379189i	$0.876203\pi$
$854$		0			0
$855$	19.4789	−	19.4789i	0.666166	−	0.666166i
$856$		0			0
$857$	−15.5160			−0.530015			−0.265008	−	0.964246i	$-0.585375\pi$
$857$	−15.5160			−0.530015			−0.265008	+	0.964246i	$0.585375\pi$
$858$		0			0
$859$			37.2939i			1.27245i	0.771503	+	0.636226i	$0.219505\pi$
$859$			37.2939i			1.27245i	−0.771503	+	0.636226i	$0.780495\pi$
$860$		0			0
$861$	0.947171	+	3.03132i	0.0322795	+	0.103307i
$862$		0			0
$863$		−	2.44574i		−	0.0832541i	−0.999133	−	0.0416270i	$-0.986746\pi$
$863$		−	2.44574i		−	0.0832541i	0.999133	−	0.0416270i	$-0.0132541\pi$
$864$		0			0
$865$	−22.6790			−0.771111
$866$		0			0
$867$	−3.04651	+	3.04651i	−0.103465	+	0.103465i
$868$		0			0
$869$			13.6582i			0.463322i
$870$		0			0
$871$	32.2406			1.09243
$872$		0			0
$873$	10.3443	+	10.3443i	0.350102	+	0.350102i
$874$		0			0
$875$	1.06329	−	1.06329i	0.0359459	−	0.0359459i
$876$		0			0
$877$	−5.88683			−0.198784			−0.0993921	−	0.995048i	$-0.531690\pi$
$877$	−5.88683			−0.198784			−0.0993921	+	0.995048i	$0.531690\pi$
$878$		0			0
$879$	5.87472			0.198149
$880$		0			0
$881$			0.576792i			0.0194326i	0.999953	+	0.00971631i	$0.00309284\pi$
$881$			0.576792i			0.0194326i	−0.999953	+	0.00971631i	$0.996907\pi$
$882$		0			0
$883$	−12.5405	+	12.5405i	−0.422020	+	0.422020i	−0.885899	−	0.463879i	$-0.846457\pi$
$883$	−12.5405	+	12.5405i	−0.422020	+	0.422020i	0.463879	+	0.885899i	$0.346457\pi$
$884$		0			0
$885$	2.61839	−	2.61839i	0.0880161	−	0.0880161i
$886$		0			0
$887$	−29.9454	+	29.9454i	−1.00547	+	1.00547i	−0.00548171	+	0.999985i	$0.501745\pi$
$887$	−29.9454	+	29.9454i	−1.00547	+	1.00547i	−0.999985	+	0.00548171i	$0.998255\pi$
$888$		0			0
$889$	3.17722	+	3.17722i	0.106560	+	0.106560i
$890$		0			0
$891$	−7.81886	−	7.81886i	−0.261942	−	0.261942i
$892$		0			0
$893$			16.7930i			0.561957i
$894$		0			0
$895$	11.6703	+	11.6703i	0.390096	+	0.390096i
$896$		0			0
$897$			7.01583i			0.234252i
$898$		0			0
$899$	9.61484	+	9.61484i	0.320673	+	0.320673i
$900$		0			0
$901$	40.8087			1.35954
$902$		0			0
$903$	−3.44709			−0.114712
$904$		0			0
$905$	5.32878	+	5.32878i	0.177135	+	0.177135i
$906$		0			0
$907$			50.3443i			1.67166i	0.548992	+	0.835828i	$0.315012\pi$
$907$			50.3443i			1.67166i	−0.548992	+	0.835828i	$0.684988\pi$
$908$		0			0
$909$	−35.7233	−	35.7233i	−1.18487	−	1.18487i
$910$		0			0
$911$		−	52.2112i		−	1.72983i	−0.501915	−	0.864917i	$-0.667371\pi$
$911$		−	52.2112i		−	1.72983i	0.501915	−	0.864917i	$-0.332629\pi$
$912$		0			0
$913$	15.1356	+	15.1356i	0.500916	+	0.500916i
$914$		0			0
$915$	−8.92278	−	8.92278i	−0.294978	−	0.294978i
$916$		0			0
$917$	−15.1045	+	15.1045i	−0.498796	+	0.498796i
$918$		0			0
$919$	−13.0544	+	13.0544i	−0.430624	+	0.430624i	−0.888840	−	0.458217i	$-0.848488\pi$
$919$	−13.0544	+	13.0544i	−0.430624	+	0.430624i	0.458217	+	0.888840i	$0.348488\pi$
$920$		0			0
$921$	−11.5851	+	11.5851i	−0.381742	+	0.381742i
$922$		0			0
$923$			18.1235i			0.596543i
$924$		0			0
$925$	−29.1733			−0.959214
$926$		0			0
$927$	−42.2927			−1.38908
$928$		0			0
$929$	29.8188	−	29.8188i	0.978323	−	0.978323i	−0.0214469	−	0.999770i	$-0.506827\pi$
$929$	29.8188	−	29.8188i	0.978323	−	0.978323i	0.999770	+	0.0214469i	$0.00682728\pi$
$930$		0			0
$931$	2.29327	+	2.29327i	0.0751589	+	0.0751589i
$932$		0			0
$933$	0.853678			0.0279482
$934$		0			0
$935$			25.2458i			0.825625i
$936$		0			0
$937$	−40.6306	+	40.6306i	−1.32734	+	1.32734i	−0.419665	+	0.907679i	$0.637852\pi$
$937$	−40.6306	+	40.6306i	−1.32734	+	1.32734i	−0.907679	+	0.419665i	$0.862148\pi$
$938$		0			0
$939$	−3.18014			−0.103780
$940$		0			0
$941$		−	21.7805i		−	0.710025i	−0.934862	−	0.355012i	$-0.884477\pi$
$941$		−	21.7805i		−	0.710025i	0.934862	−	0.355012i	$-0.115523\pi$
$942$		0			0
$943$	21.2053	−	6.62584i	0.690540	−	0.215767i
$944$		0			0
$945$			8.80206i			0.286331i
$946$		0			0
$947$	5.10582			0.165917			0.0829584	−	0.996553i	$-0.473563\pi$
$947$	5.10582			0.165917			0.0829584	+	0.996553i	$0.473563\pi$
$948$		0			0
$949$	−24.7303	+	24.7303i	−0.802780	+	0.802780i
$950$		0			0
$951$			8.39876i			0.272348i
$952$		0			0
$953$	50.8224			1.64630			0.823149	−	0.567825i	$-0.192215\pi$
$953$	50.8224			1.64630			0.823149	+	0.567825i	$0.192215\pi$
$954$		0			0
$955$	−7.34652	−	7.34652i	−0.237728	−	0.237728i
$956$		0			0
$957$	3.68987	−	3.68987i	0.119277	−	0.119277i
$958$		0			0
$959$	−13.8115			−0.445997
$960$		0			0
$961$	−26.6431			−0.859455
$962$		0			0
$963$			46.8611i			1.51008i
$964$		0			0
$965$	−14.7862	+	14.7862i	−0.475986	+	0.475986i
$966$		0			0
$967$	−18.3758	+	18.3758i	−0.590925	+	0.590925i	−0.937881	−	0.346957i	$-0.887215\pi$
$967$	−18.3758	+	18.3758i	−0.590925	+	0.590925i	0.346957	+	0.937881i	$0.387215\pi$
$968$		0			0
$969$	−5.76470	+	5.76470i	−0.185189	+	0.185189i
$970$		0			0
$971$	−11.4163	−	11.4163i	−0.366367	−	0.366367i	0.499784	−	0.866150i	$-0.333413\pi$
$971$	−11.4163	−	11.4163i	−0.366367	−	0.366367i	−0.866150	+	0.499784i	$0.833413\pi$
$972$		0			0
$973$	10.0521	+	10.0521i	0.322257	+	0.322257i
$974$		0			0
$975$		−	9.12453i		−	0.292219i
$976$		0			0
$977$	13.2760	+	13.2760i	0.424736	+	0.424736i	0.886830	−	0.462095i	$-0.152902\pi$
$977$	13.2760	+	13.2760i	0.424736	+	0.424736i	−0.462095	+	0.886830i	$0.652902\pi$
$978$		0			0
$979$		−	7.42833i		−	0.237410i
$980$		0			0
$981$	−20.7708	−	20.7708i	−0.663161	−	0.663161i
$982$		0			0
$983$	34.0979			1.08755			0.543777	−	0.839230i	$-0.316994\pi$
$983$	34.0979			1.08755			0.543777	+	0.839230i	$0.316994\pi$
$984$		0			0
$985$	−41.6496			−1.32707
$986$		0			0
$987$	−1.81598	−	1.81598i	−0.0578034	−	0.0578034i
$988$		0			0
$989$			24.1138i			0.766775i
$990$		0			0
$991$	15.6965	+	15.6965i	0.498615	+	0.498615i	0.911007	−	0.412392i	$-0.135306\pi$
$991$	15.6965	+	15.6965i	0.498615	+	0.498615i	−0.412392	+	0.911007i	$0.635306\pi$
$992$		0			0
$993$		−	13.2495i		−	0.420460i
$994$		0			0
$995$	−21.5234	−	21.5234i	−0.682337	−	0.682337i
$996$		0			0
$997$	−36.0012	−	36.0012i	−1.14017	−	1.14017i	−0.988419	−	0.151752i	$-0.951508\pi$
$997$	−36.0012	−	36.0012i	−1.14017	−	1.14017i	−0.151752	−	0.988419i	$-0.548492\pi$
$998$		0			0
$999$	−13.0466	+	13.0466i	−0.412776	+	0.412776i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1148.2.k.b.337.8	✓	36
41.32	even	4	inner	1148.2.k.b.729.8	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1148.2.k.b.337.8	✓	36	1.1	even	1	trivial
1148.2.k.b.729.8	yes	36	41.32	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1148 = 2^{2} \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1148.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.350714 - 0.350714i) q^{3} +3.08423i q^{5} +(-0.707107 - 0.707107i) q^{7} -2.75400i q^{9} +O(q^{10})\)	\(q+(-0.350714 - 0.350714i) q^{3} +3.08423i q^{5} +(-0.707107 - 0.707107i) q^{7} -2.75400i q^{9} +(1.14202 + 1.14202i) q^{11} +(-2.88280 - 2.88280i) q^{13} +(1.08168 - 1.08168i) q^{15} +(3.58376 - 3.58376i) q^{17} +(2.29327 - 2.29327i) q^{19} +0.495985i q^{21} +3.46961 q^{23} -4.51245 q^{25} +(-2.01801 + 2.01801i) q^{27} +(4.60631 + 4.60631i) q^{29} +2.08732 q^{31} -0.801046i q^{33} +(2.18088 - 2.18088i) q^{35} +6.46508 q^{37} +2.02208i q^{39} +(6.11172 - 1.90968i) q^{41} +6.95000i q^{43} +8.49395 q^{45} +(-3.66137 + 3.66137i) q^{47} +1.00000i q^{49} -2.51375 q^{51} +(5.69357 + 5.69357i) q^{53} +(-3.52225 + 3.52225i) q^{55} -1.60857 q^{57} +2.42066 q^{59} -8.24899i q^{61} +(-1.94737 + 1.94737i) q^{63} +(8.89122 - 8.89122i) q^{65} +(-5.59189 + 5.59189i) q^{67} +(-1.21684 - 1.21684i) q^{69} +(-3.14338 - 3.14338i) q^{71} -8.57857i q^{73} +(1.58258 + 1.58258i) q^{75} -1.61506i q^{77} +(5.97983 + 5.97983i) q^{79} -6.84651 q^{81} +13.2534 q^{83} +(11.0531 + 11.0531i) q^{85} -3.23100i q^{87} +(-3.25227 - 3.25227i) q^{89} +4.07690i q^{91} +(-0.732052 - 0.732052i) q^{93} +(7.07296 + 7.07296i) q^{95} +(-3.75610 + 3.75610i) q^{97} +(3.14513 - 3.14513i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q+O(q^{10}) \) 36 * q	\( 36 q - 12 q^{11} - 16 q^{17} - 4 q^{19} - 36 q^{23} - 64 q^{25} + 12 q^{27} + 16 q^{29} - 28 q^{31} + 12 q^{35} + 48 q^{37} + 4 q^{41} + 36 q^{45} + 12 q^{47} - 12 q^{51} - 12 q^{53} + 12 q^{55} + 76 q^{57} + 20 q^{59} - 4 q^{65} - 44 q^{67} + 72 q^{69} - 20 q^{71} + 72 q^{75} - 8 q^{79} - 100 q^{81} - 40 q^{83} - 8 q^{85} - 16 q^{89} + 20 q^{93} + 76 q^{95} - 16 q^{97} + 56 q^{99}+O(q^{100}) \) 36 * q - 12 * q^11 - 16 * q^17 - 4 * q^19 - 36 * q^23 - 64 * q^25 + 12 * q^27 + 16 * q^29 - 28 * q^31 + 12 * q^35 + 48 * q^37 + 4 * q^41 + 36 * q^45 + 12 * q^47 - 12 * q^51 - 12 * q^53 + 12 * q^55 + 76 * q^57 + 20 * q^59 - 4 * q^65 - 44 * q^67 + 72 * q^69 - 20 * q^71 + 72 * q^75 - 8 * q^79 - 100 * q^81 - 40 * q^83 - 8 * q^85 - 16 * q^89 + 20 * q^93 + 76 * q^95 - 16 * q^97 + 56 * q^99

Introduction

L-functions

Modular forms

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Database

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