LMFDB - Embedded newform 841.2.b.c.840.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [841,2,Mod(840,841)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(841, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("841.840"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 841 = 29^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	841.b (of order $2$, degree $1$, not minimal)

Newform invariants

comment:select newform

sage:traces = [6,0,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)

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

Self dual:	no
Analytic conductor:	$6.71541880999$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.153664.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 5x^{4} + 6x^{2} + 1 $ x^6 + 5x^4 + 6x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 29)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			840.1
Root			$-1.80194i$ of defining polynomial
Character	$\chi$	$=$	841.840
Dual form			841.2.b.c.840.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.80194i q^{2} +0.445042i q^{3} -1.24698 q^{4} -0.356896 q^{5} +0.801938 q^{6} -4.04892 q^{7} -1.35690i q^{8} +2.80194 q^{9} +0.643104i q^{10} +2.91185i q^{11} -0.554958i q^{12} -5.18598 q^{13} +7.29590i q^{14} -0.158834i q^{15} -4.93900 q^{16} +1.10992i q^{17} -5.04892i q^{18} +2.04892i q^{19} +0.445042 q^{20} -1.80194i q^{21} +5.24698 q^{22} -4.13706 q^{23} +0.603875 q^{24} -4.87263 q^{25} +9.34481i q^{26} +2.58211i q^{27} +5.04892 q^{28} -0.286208 q^{30} -6.35690i q^{31} +6.18598i q^{32} -1.29590 q^{33} +2.00000 q^{34} +1.44504 q^{35} -3.49396 q^{36} +2.91185i q^{37} +3.69202 q^{38} -2.30798i q^{39} +0.484271i q^{40} -0.396125i q^{41} -3.24698 q^{42} +5.74094i q^{43} -3.63102i q^{44} -1.00000 q^{45} +7.45473i q^{46} +7.80194i q^{47} -2.19806i q^{48} +9.39373 q^{49} +8.78017i q^{50} -0.493959 q^{51} +6.46681 q^{52} -4.35690 q^{53} +4.65279 q^{54} -1.03923i q^{55} +5.49396i q^{56} -0.911854 q^{57} -9.10992 q^{59} +0.198062i q^{60} -6.04892i q^{61} -11.4547 q^{62} -11.3448 q^{63} +1.26875 q^{64} +1.85086 q^{65} +2.33513i q^{66} -0.374354 q^{67} -1.38404i q^{68} -1.84117i q^{69} -2.60388i q^{70} +11.4058 q^{71} -3.80194i q^{72} +8.94869i q^{73} +5.24698 q^{74} -2.16852i q^{75} -2.55496i q^{76} -11.7899i q^{77} -4.15883 q^{78} -0.594187i q^{79} +1.76271 q^{80} +7.25667 q^{81} -0.713792 q^{82} -9.43296 q^{83} +2.24698i q^{84} -0.396125i q^{85} +10.3448 q^{86} +3.95108 q^{88} +1.42327i q^{89} +1.80194i q^{90} +20.9976 q^{91} +5.15883 q^{92} +2.82908 q^{93} +14.0586 q^{94} -0.731250i q^{95} -2.75302 q^{96} -15.7506i q^{97} -16.9269i q^{98} +8.15883i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{4} + 6 q^{5} - 4 q^{6} - 6 q^{7} + 8 q^{9} - 2 q^{13} - 10 q^{16} + 2 q^{20} + 22 q^{22} - 14 q^{23} - 14 q^{24} + 4 q^{25} + 12 q^{28} - 18 q^{30} + 20 q^{33} + 12 q^{34} + 8 q^{35} - 2 q^{36}+ \cdots - 26 q^{96}+O(q^{100}) $ 6 * q + 2 * q^4 + 6 * q^5 - 4 * q^6 - 6 * q^7 + 8 * q^9 - 2 * q^13 - 10 * q^16 + 2 * q^20 + 22 * q^22 - 14 * q^23 - 14 * q^24 + 4 * q^25 + 12 * q^28 - 18 * q^30 + 20 * q^33 + 12 * q^34 + 8 * q^35 - 2 * q^36 + 12 * q^38 - 10 * q^42 - 6 * q^45 - 8 * q^49 + 16 * q^51 + 32 * q^52 - 18 * q^53 - 8 * q^54 + 2 * q^57 - 56 * q^59 - 24 * q^62 - 22 * q^63 - 8 * q^64 - 16 * q^65 - 26 * q^67 + 42 * q^71 + 22 * q^74 - 8 * q^78 - 24 * q^80 - 10 * q^81 + 12 * q^82 - 18 * q^83 + 16 * q^86 + 42 * q^88 + 44 * q^91 + 14 * q^92 - 4 * q^93 + 22 * q^94 - 26 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/841\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	− 1.80194i	− 1.27416i	−0.770797	−	0.637081i	$-0.780142\pi$
$2$	− 1.80194i	− 1.27416i	0.770797	−	0.637081i	$-0.219858\pi$
$3$	0.445042i	0.256945i	0.991713	+	0.128473i	$0.0410074\pi$
$3$	0.445042i	0.256945i	−0.991713	+	0.128473i	$0.958993\pi$
$4$	−1.24698	−0.623490
$5$	−0.356896	−0.159609	−0.0798043	−	0.996811i	$-0.525430\pi$
$5$	−0.356896	−0.159609	−0.0798043	+	0.996811i	$0.525430\pi$
$6$	0.801938	0.327390
$7$	−4.04892	−1.53035	−0.765173	−	0.643824i	$-0.777347\pi$
$7$	−4.04892	−1.53035	−0.765173	+	0.643824i	$0.777347\pi$
$8$	− 1.35690i	− 0.479735i
$9$	2.80194	0.933979
$10$	0.643104i	0.203367i
$11$	2.91185i	0.877957i	0.898498	+	0.438979i	$0.144660\pi$
$11$	2.91185i	0.877957i	−0.898498	+	0.438979i	$0.855340\pi$
$12$	− 0.554958i	− 0.160203i
$13$	−5.18598	−1.43833	−0.719166	−	0.694838i	$-0.755476\pi$
$13$	−5.18598	−1.43833	−0.719166	+	0.694838i	$0.755476\pi$
$14$	7.29590i	1.94991i
$15$	− 0.158834i	− 0.0410107i
$16$	−4.93900	−1.23475
$17$	1.10992i	0.269194i	0.990900	+	0.134597i	$0.0429740\pi$
$17$	1.10992i	0.269194i	−0.990900	+	0.134597i	$0.957026\pi$
$18$	− 5.04892i	− 1.19004i
$19$	2.04892i	0.470054i	0.971989	+	0.235027i	$0.0755178\pi$
$19$	2.04892i	0.470054i	−0.971989	+	0.235027i	$0.924482\pi$
$20$	0.445042	0.0995144
$21$	− 1.80194i	− 0.393215i
$22$	5.24698	1.11866
$23$	−4.13706	−0.862637	−0.431319	−	0.902200i	$-0.641952\pi$
$23$	−4.13706	−0.862637	−0.431319	+	0.902200i	$0.641952\pi$
$24$	0.603875	0.123266
$25$	−4.87263	−0.974525
$26$	9.34481i	1.83267i
$27$	2.58211i	0.496926i
$28$	5.04892	0.954156
$29$	0	0
$29$	0	0
$30$	−0.286208	−0.0522542
$31$	− 6.35690i	− 1.14173i	−0.821043	−	0.570866i	$-0.806608\pi$
$31$	− 6.35690i	− 1.14173i	0.821043	−	0.570866i	$-0.193392\pi$
$32$	6.18598i	1.09354i
$33$	−1.29590	−0.225587
$34$	2.00000	0.342997
$35$	1.44504	0.244257
$36$	−3.49396	−0.582327
$37$	2.91185i	0.478706i	0.970933	+	0.239353i	$0.0769353\pi$
$37$	2.91185i	0.478706i	−0.970933	+	0.239353i	$0.923065\pi$
$38$	3.69202	0.598925
$39$	− 2.30798i	− 0.369572i
$40$	0.484271i	0.0765699i
$41$	− 0.396125i	− 0.0618643i	−0.999521	−	0.0309321i	$-0.990152\pi$
$41$	− 0.396125i	− 0.0618643i	0.999521	−	0.0309321i	$-0.00984757\pi$
$42$	−3.24698	−0.501020
$43$	5.74094i	0.875485i	0.899100	+	0.437742i	$0.144222\pi$
$43$	5.74094i	0.875485i	−0.899100	+	0.437742i	$0.855778\pi$
$44$	− 3.63102i	− 0.547397i
$45$	−1.00000	−0.149071
$46$	7.45473i	1.09914i
$47$	7.80194i	1.13803i	0.822327	+	0.569015i	$0.192675\pi$
$47$	7.80194i	1.13803i	−0.822327	+	0.569015i	$0.807325\pi$
$48$	− 2.19806i	− 0.317263i
$49$	9.39373	1.34196
$50$	8.78017i	1.24170i
$51$	−0.493959	−0.0691681
$52$	6.46681	0.896785
$53$	−4.35690	−0.598466	−0.299233	−	0.954180i	$-0.596731\pi$
$53$	−4.35690	−0.598466	−0.299233	+	0.954180i	$0.596731\pi$
$54$	4.65279	0.633165
$55$	− 1.03923i	− 0.140130i
$56$	5.49396i	0.734161i
$57$	−0.911854	−0.120778
$58$	0	0
$59$	−9.10992	−1.18601	−0.593005	−	0.805199i	$-0.702059\pi$
$59$	−9.10992	−1.18601	−0.593005	+	0.805199i	$0.702059\pi$
$60$	0.198062i	0.0255697i
$61$	− 6.04892i	− 0.774485i	−0.921978	−	0.387242i	$-0.873428\pi$
$61$	− 6.04892i	− 0.774485i	0.921978	−	0.387242i	$-0.126572\pi$
$62$	−11.4547	−1.45475
$63$	−11.3448	−1.42931
$64$	1.26875	0.158594
$65$	1.85086	0.229570
$66$	2.33513i	0.287434i
$67$	−0.374354	−0.0457347	−0.0228673	−	0.999739i	$-0.507280\pi$
$67$	−0.374354	−0.0457347	−0.0228673	+	0.999739i	$0.507280\pi$
$68$	− 1.38404i	− 0.167840i
$69$	− 1.84117i	− 0.221650i
$70$	− 2.60388i	− 0.311223i
$71$	11.4058	1.35362	0.676810	−	0.736157i	$-0.263362\pi$
$71$	11.4058	1.35362	0.676810	+	0.736157i	$0.263362\pi$
$72$	− 3.80194i	− 0.448063i
$73$	8.94869i	1.04736i	0.851914	+	0.523682i	$0.175442\pi$
$73$	8.94869i	1.04736i	−0.851914	+	0.523682i	$0.824558\pi$
$74$	5.24698	0.609949
$75$	− 2.16852i	− 0.250399i
$76$	− 2.55496i	− 0.293074i
$77$	− 11.7899i	− 1.34358i
$78$	−4.15883	−0.470895
$79$	− 0.594187i	− 0.0668512i	−0.999441	−	0.0334256i	$-0.989358\pi$
$79$	− 0.594187i	− 0.0668512i	0.999441	−	0.0334256i	$-0.0106417\pi$
$80$	1.76271	0.197077
$81$	7.25667	0.806296
$82$	−0.713792	−0.0788251
$83$	−9.43296	−1.03540	−0.517701	−	0.855562i	$-0.673212\pi$
$83$	−9.43296	−1.03540	−0.517701	+	0.855562i	$0.673212\pi$
$84$	2.24698i	0.245166i
$85$	− 0.396125i	− 0.0429657i
$86$	10.3448	1.11551
$87$	0	0
$88$	3.95108	0.421187
$89$	1.42327i	0.150866i	0.997151	+	0.0754332i	$0.0240340\pi$
$89$	1.42327i	0.150866i	−0.997151	+	0.0754332i	$0.975966\pi$
$90$	1.80194i	0.189941i
$91$	20.9976	2.20115
$92$	5.15883	0.537846
$93$	2.82908	0.293362
$94$	14.0586	1.45003
$95$	− 0.731250i	− 0.0750247i
$96$	−2.75302	−0.280979
$97$	− 15.7506i	− 1.59923i	−0.600510	−	0.799617i	$-0.705036\pi$
$97$	− 15.7506i	− 1.59923i	0.600510	−	0.799617i	$-0.294964\pi$
$98$	− 16.9269i	− 1.70988i
$99$	8.15883i	0.819994i
$100$	6.07606	0.607606
$101$	− 17.4426i	− 1.73561i	−0.496906	−	0.867804i	$-0.665531\pi$
$101$	− 17.4426i	− 1.73561i	0.496906	−	0.867804i	$-0.334469\pi$
$102$	0.890084i	0.0881314i
$103$	−2.81402	−0.277274	−0.138637	−	0.990343i	$-0.544272\pi$
$103$	−2.81402	−0.277274	−0.138637	+	0.990343i	$0.544272\pi$
$104$	7.03684i	0.690019i
$105$	0.643104i	0.0627605i
$106$	7.85086i	0.762542i
$107$	−7.46011	−0.721196	−0.360598	−	0.932721i	$-0.617427\pi$
$107$	−7.46011	−0.721196	−0.360598	+	0.932721i	$0.617427\pi$
$108$	− 3.21983i	− 0.309829i
$109$	1.65279	0.158309	0.0791544	−	0.996862i	$-0.474778\pi$
$109$	1.65279	0.158309	0.0791544	+	0.996862i	$0.474778\pi$
$110$	−1.87263	−0.178548
$111$	−1.29590	−0.123001
$112$	19.9976	1.88960
$113$	− 8.64071i	− 0.812850i	−0.913684	−	0.406425i	$-0.866775\pi$
$113$	− 8.64071i	− 0.812850i	0.913684	−	0.406425i	$-0.133225\pi$
$114$	1.64310i	0.153891i
$115$	1.47650	0.137684
$116$	0	0
$117$	−14.5308	−1.34337
$118$	16.4155i	1.51117i
$119$	− 4.49396i	− 0.411961i
$120$	−0.215521	−0.0196743
$121$	2.52111	0.229191
$122$	−10.8998	−0.986819
$123$	0.176292	0.0158957
$124$	7.92692i	0.711858i
$125$	3.52350	0.315151
$126$	20.4426i	1.82118i
$127$	10.4722i	0.929257i	0.885506	+	0.464628i	$0.153812\pi$
$127$	10.4722i	0.929257i	−0.885506	+	0.464628i	$0.846188\pi$
$128$	10.0858i	0.891463i
$129$	−2.55496	−0.224952
$130$	− 3.33513i	− 0.292510i
$131$	0.454731i	0.0397300i	0.999803	+	0.0198650i	$0.00632364\pi$
$131$	0.454731i	0.0397300i	−0.999803	+	0.0198650i	$0.993676\pi$
$132$	1.61596	0.140651
$133$	− 8.29590i	− 0.719345i
$134$	0.674563i	0.0582734i
$135$	− 0.921543i	− 0.0793138i
$136$	1.50604	0.129142
$137$	− 13.2403i	− 1.13119i	−0.824682	−	0.565597i	$-0.808646\pi$
$137$	− 13.2403i	− 1.13119i	0.824682	−	0.565597i	$-0.191354\pi$
$138$	−3.31767	−0.282419
$139$	−2.79656	−0.237201	−0.118601	−	0.992942i	$-0.537841\pi$
$139$	−2.79656	−0.237201	−0.118601	+	0.992942i	$0.537841\pi$
$140$	−1.80194	−0.152292
$141$	−3.47219	−0.292411
$142$	− 20.5526i	− 1.72473i
$143$	− 15.1008i	− 1.26279i
$144$	−13.8388	−1.15323
$145$	0	0
$146$	16.1250	1.33451
$147$	4.18060i	0.344810i
$148$	− 3.63102i	− 0.298468i
$149$	−2.70841	−0.221882	−0.110941	−	0.993827i	$-0.535386\pi$
$149$	−2.70841	−0.221882	−0.110941	+	0.993827i	$0.535386\pi$
$150$	−3.90754	−0.319049
$151$	2.43535	0.198186	0.0990931	−	0.995078i	$-0.468406\pi$
$151$	2.43535	0.198186	0.0990931	+	0.995078i	$0.468406\pi$
$152$	2.78017	0.225501
$153$	3.10992i	0.251422i
$154$	−21.2446	−1.71194
$155$	2.26875i	0.182230i
$156$	2.87800i	0.230425i
$157$	− 17.6775i	− 1.41082i	−0.708799	−	0.705411i	$-0.750762\pi$
$157$	− 17.6775i	− 1.41082i	0.708799	−	0.705411i	$-0.249238\pi$
$158$	−1.07069	−0.0851793
$159$	− 1.93900i	− 0.153773i
$160$	− 2.20775i	− 0.174538i
$161$	16.7506	1.32013
$162$	− 13.0761i	− 1.02735i
$163$	4.96615i	0.388979i	0.980905	+	0.194489i	$0.0623050\pi$
$163$	4.96615i	0.388979i	−0.980905	+	0.194489i	$0.937695\pi$
$164$	0.493959i	0.0385717i
$165$	0.462500	0.0360056
$166$	16.9976i	1.31927i
$167$	−14.4644	−1.11929	−0.559645	−	0.828732i	$-0.689063\pi$
$167$	−14.4644	−1.11929	−0.559645	+	0.828732i	$0.689063\pi$
$168$	−2.44504	−0.188639
$169$	13.8944	1.06880
$170$	−0.713792	−0.0547453
$171$	5.74094i	0.439021i
$172$	− 7.15883i	− 0.545856i
$173$	−10.5133	−0.799314	−0.399657	−	0.916665i	$-0.630871\pi$
$173$	−10.5133	−0.799314	−0.399657	+	0.916665i	$0.630871\pi$
$174$	0	0
$175$	19.7289	1.49136
$176$	− 14.3817i	− 1.08406i
$177$	− 4.05429i	− 0.304739i
$178$	2.56465	0.192228
$179$	5.74094	0.429098	0.214549	−	0.976713i	$-0.431172\pi$
$179$	5.74094	0.429098	0.214549	+	0.976713i	$0.431172\pi$
$180$	1.24698	0.0929444
$181$	−6.64071	−0.493600	−0.246800	−	0.969066i	$-0.579379\pi$
$181$	−6.64071	−0.493600	−0.246800	+	0.969066i	$0.579379\pi$
$182$	− 37.8364i	− 2.80462i
$183$	2.69202	0.199000
$184$	5.61356i	0.413837i
$185$	− 1.03923i	− 0.0764056i
$186$	− 5.09783i	− 0.373791i
$187$	−3.23191	−0.236341
$188$	− 9.72886i	− 0.709550i
$189$	− 10.4547i	− 0.760470i
$190$	−1.31767	−0.0955936
$191$	− 18.8116i	− 1.36116i	−0.732673	−	0.680581i	$-0.761728\pi$
$191$	− 18.8116i	− 1.36116i	0.732673	−	0.680581i	$-0.238272\pi$
$192$	0.564647i	0.0407499i
$193$	10.8847i	0.783498i	0.920072	+	0.391749i	$0.128130\pi$
$193$	10.8847i	0.783498i	−0.920072	+	0.391749i	$0.871870\pi$
$194$	−28.3817	−2.03768
$195$	0.823708i	0.0589870i
$196$	−11.7138	−0.836699
$197$	−8.40044	−0.598506	−0.299253	−	0.954174i	$-0.596738\pi$
$197$	−8.40044	−0.598506	−0.299253	+	0.954174i	$0.596738\pi$
$198$	14.7017	1.04481
$199$	−6.62133	−0.469374	−0.234687	−	0.972071i	$-0.575407\pi$
$199$	−6.62133	−0.469374	−0.234687	+	0.972071i	$0.575407\pi$
$200$	6.61165i	0.467514i
$201$	− 0.166603i	− 0.0117513i
$202$	−31.4306	−2.21145
$203$	0	0
$204$	0.615957	0.0431256
$205$	0.141375i	0.00987407i
$206$	5.07069i	0.353292i
$207$	−11.5918	−0.805685
$208$	25.6136	1.77598
$209$	−5.96615	−0.412687
$210$	1.15883	0.0799671
$211$	8.10023i	0.557643i	0.960343	+	0.278821i	$0.0899437\pi$
$211$	8.10023i	0.557643i	−0.960343	+	0.278821i	$0.910056\pi$
$212$	5.43296	0.373137
$213$	5.07606i	0.347806i
$214$	13.4426i	0.918921i
$215$	− 2.04892i	− 0.139735i
$216$	3.50365	0.238393
$217$	25.7385i	1.74725i
$218$	− 2.97823i	− 0.201711i
$219$	−3.98254	−0.269115
$220$	1.29590i	0.0873694i
$221$	− 5.75600i	− 0.387191i
$222$	2.33513i	0.156723i
$223$	21.9191	1.46781	0.733907	−	0.679250i	$-0.237695\pi$
$223$	21.9191	1.46781	0.733907	+	0.679250i	$0.237695\pi$
$224$	− 25.0465i	− 1.67349i
$225$	−13.6528	−0.910186
$226$	−15.5700	−1.03570
$227$	−18.2784	−1.21318	−0.606591	−	0.795014i	$-0.707464\pi$
$227$	−18.2784	−1.21318	−0.606591	+	0.795014i	$0.707464\pi$
$228$	1.13706	0.0753039
$229$	− 16.0248i	− 1.05895i	−0.848327	−	0.529473i	$-0.822390\pi$
$229$	− 16.0248i	− 1.05895i	0.848327	−	0.529473i	$-0.177610\pi$
$230$	− 2.66056i	− 0.175432i
$231$	5.24698	0.345226
$232$	0	0
$233$	1.95646	0.128172	0.0640860	−	0.997944i	$-0.479587\pi$
$233$	1.95646	0.128172	0.0640860	+	0.997944i	$0.479587\pi$
$234$	26.1836i	1.71167i
$235$	− 2.78448i	− 0.181639i
$236$	11.3599	0.739465
$237$	0.264438	0.0171771
$238$	−8.09783	−0.524905
$239$	−8.96316	−0.579779	−0.289889	−	0.957060i	$-0.593619\pi$
$239$	−8.96316	−0.579779	−0.289889	+	0.957060i	$0.593619\pi$
$240$	0.784479i	0.0506379i
$241$	−19.8998	−1.28186	−0.640929	−	0.767601i	$-0.721451\pi$
$241$	−19.8998	−1.28186	−0.640929	+	0.767601i	$0.721451\pi$
$242$	− 4.54288i	− 0.292027i
$243$	10.9758i	0.704100i
$244$	7.54288i	0.482883i
$245$	−3.35258	−0.214189
$246$	− 0.317667i	− 0.0202537i
$247$	− 10.6256i	− 0.676094i
$248$	−8.62565	−0.547729
$249$	− 4.19806i	− 0.266041i
$250$	− 6.34913i	− 0.401554i
$251$	25.8049i	1.62879i	0.580309	+	0.814396i	$0.302932\pi$
$251$	25.8049i	1.62879i	−0.580309	+	0.814396i	$0.697068\pi$
$252$	14.1468	0.891162
$253$	− 12.0465i	− 0.757359i
$254$	18.8702	1.18402
$255$	0.176292	0.0110398
$256$	20.7114	1.29446
$257$	11.9511	0.745488	0.372744	−	0.927934i	$-0.378417\pi$
$257$	11.9511	0.745488	0.372744	+	0.927934i	$0.378417\pi$
$258$	4.60388i	0.286625i
$259$	− 11.7899i	− 0.732586i
$260$	−2.30798	−0.143135
$261$	0	0
$262$	0.819396	0.0506225
$263$	− 0.332733i	− 0.0205172i	−0.999947	−	0.0102586i	$-0.996735\pi$
$263$	− 0.332733i	− 0.0205172i	0.999947	−	0.0102586i	$-0.00326547\pi$
$264$	1.75840i	0.108222i
$265$	1.55496	0.0955203
$266$	−14.9487	−0.916563
$267$	−0.633415	−0.0387644
$268$	0.466812	0.0285151
$269$	1.06398i	0.0648722i	0.999474	+	0.0324361i	$0.0103265\pi$
$269$	1.06398i	0.0648722i	−0.999474	+	0.0324361i	$0.989673\pi$
$270$	−1.66056	−0.101059
$271$	16.4644i	1.00014i	0.865984	+	0.500071i	$0.166693\pi$
$271$	16.4644i	1.00014i	−0.865984	+	0.500071i	$0.833307\pi$
$272$	− 5.48188i	− 0.332388i
$273$	9.34481i	0.565574i
$274$	−23.8582	−1.44132
$275$	− 14.1884i	− 0.855591i
$276$	2.29590i	0.138197i
$277$	6.59419	0.396206	0.198103	−	0.980181i	$-0.436522\pi$
$277$	6.59419	0.396206	0.198103	+	0.980181i	$0.436522\pi$
$278$	5.03923i	0.302233i
$279$	− 17.8116i	− 1.06635i
$280$	− 1.96077i	− 0.117179i
$281$	−30.5351	−1.82157	−0.910786	−	0.412879i	$-0.864523\pi$
$281$	−30.5351	−1.82157	−0.910786	+	0.412879i	$0.864523\pi$
$282$	6.25667i	0.372579i
$283$	3.55496	0.211320	0.105660	−	0.994402i	$-0.466304\pi$
$283$	3.55496	0.211320	0.105660	+	0.994402i	$0.466304\pi$
$284$	−14.2228	−0.843969
$285$	0.325437	0.0192772
$286$	−27.2107	−1.60900
$287$	1.60388i	0.0946738i
$288$	17.3327i	1.02134i
$289$	15.7681	0.927534
$290$	0	0
$291$	7.00969	0.410915
$292$	− 11.1588i	− 0.653021i
$293$	32.8799i	1.92087i	0.278512	+	0.960433i	$0.410159\pi$
$293$	32.8799i	1.92087i	−0.278512	+	0.960433i	$0.589841\pi$
$294$	7.53319	0.439344
$295$	3.25129	0.189298
$296$	3.95108	0.229652
$297$	−7.51871	−0.436280
$298$	4.88040i	0.282714i
$299$	21.4547	1.24076
$300$	2.70410i	0.156121i
$301$	− 23.2446i	− 1.33980i
$302$	− 4.38835i	− 0.252521i
$303$	7.76271	0.445956
$304$	− 10.1196i	− 0.580399i
$305$	2.15883i	0.123614i
$306$	5.60388	0.320352
$307$	14.6703i	0.837275i	0.908153	+	0.418638i	$0.137492\pi$
$307$	14.6703i	0.837275i	−0.908153	+	0.418638i	$0.862508\pi$
$308$	14.7017i	0.837708i
$309$	− 1.25236i	− 0.0712441i
$310$	4.08815	0.232191
$311$	18.5265i	1.05054i	0.850935	+	0.525270i	$0.176036\pi$
$311$	18.5265i	1.05054i	−0.850935	+	0.525270i	$0.823964\pi$
$312$	−3.13169	−0.177297
$313$	22.9922	1.29960	0.649799	−	0.760106i	$-0.274853\pi$
$313$	22.9922	1.29960	0.649799	+	0.760106i	$0.274853\pi$
$314$	−31.8538	−1.79762
$315$	4.04892	0.228131
$316$	0.740939i	0.0416811i
$317$	− 14.0586i	− 0.789610i	−0.918765	−	0.394805i	$-0.870812\pi$
$317$	− 14.0586i	− 0.789610i	0.918765	−	0.394805i	$-0.129188\pi$
$318$	−3.49396	−0.195932
$319$	0	0
$320$	−0.452812	−0.0253129
$321$	− 3.32006i	− 0.185308i
$322$	− 30.1836i	− 1.68207i
$323$	−2.27413	−0.126536
$324$	−9.04892	−0.502718
$325$	25.2693	1.40169
$326$	8.94869	0.495622
$327$	0.735562i	0.0406767i
$328$	−0.537500	−0.0296785
$329$	− 31.5894i	− 1.74158i
$330$	− 0.833397i	− 0.0458770i
$331$	− 13.9565i	− 0.767116i	−0.923517	−	0.383558i	$-0.874699\pi$
$331$	− 13.9565i	− 0.767116i	0.923517	−	0.383558i	$-0.125301\pi$
$332$	11.7627	0.645563
$333$	8.15883i	0.447101i
$334$	26.0640i	1.42616i
$335$	0.133605	0.00729965
$336$	8.89977i	0.485522i
$337$	13.9976i	0.762498i	0.924472	+	0.381249i	$0.124506\pi$
$337$	13.9976i	0.762498i	−0.924472	+	0.381249i	$0.875494\pi$
$338$	− 25.0368i	− 1.36182i
$339$	3.84548	0.208858
$340$	0.493959i	0.0267887i
$341$	18.5104	1.00239
$342$	10.3448	0.559383
$343$	−9.69202	−0.523320
$344$	7.78986	0.420001
$345$	0.657105i	0.0353773i
$346$	18.9444i	1.01846i
$347$	19.8538	1.06581	0.532905	−	0.846175i	$-0.321100\pi$
$347$	19.8538	1.06581	0.532905	+	0.846175i	$0.321100\pi$
$348$	0	0
$349$	−26.9202	−1.44101	−0.720503	−	0.693452i	$-0.756089\pi$
$349$	−26.9202	−1.44101	−0.720503	+	0.693452i	$0.756089\pi$
$350$	− 35.5502i	− 1.90024i
$351$	− 13.3907i	− 0.714745i
$352$	−18.0127	−0.960079
$353$	4.01507	0.213700	0.106850	−	0.994275i	$-0.465923\pi$
$353$	4.01507	0.213700	0.106850	+	0.994275i	$0.465923\pi$
$354$	−7.30559	−0.388287
$355$	−4.07069	−0.216050
$356$	− 1.77479i	− 0.0940637i
$357$	2.00000	0.105851
$358$	− 10.3448i	− 0.546740i
$359$	− 0.746316i	− 0.0393890i	−0.999806	−	0.0196945i	$-0.993731\pi$
$359$	− 0.746316i	− 0.0393890i	0.999806	−	0.0196945i	$-0.00626936\pi$
$360$	1.35690i	0.0715147i
$361$	14.8019	0.779049
$362$	11.9661i	0.628927i
$363$	1.12200i	0.0588896i
$364$	−26.1836	−1.37239
$365$	− 3.19375i	− 0.167169i
$366$	− 4.85086i	− 0.253558i
$367$	− 34.0489i	− 1.77734i	−0.458548	−	0.888670i	$-0.651630\pi$
$367$	− 34.0489i	− 1.77734i	0.458548	−	0.888670i	$-0.348370\pi$
$368$	20.4330	1.06514
$369$	− 1.10992i	− 0.0577799i
$370$	−1.87263	−0.0973532
$371$	17.6407	0.915860
$372$	−3.52781	−0.182908
$373$	28.0006	1.44982	0.724908	−	0.688846i	$-0.241882\pi$
$373$	28.0006	1.44982	0.724908	+	0.688846i	$0.241882\pi$
$374$	5.82371i	0.301137i
$375$	1.56810i	0.0809766i
$376$	10.5864	0.545953
$377$	0	0
$378$	−18.8388	−0.968962
$379$	22.8810i	1.17532i	0.809109	+	0.587659i	$0.199950\pi$
$379$	22.8810i	1.17532i	−0.809109	+	0.587659i	$0.800050\pi$
$380$	0.911854i	0.0467771i
$381$	−4.66056	−0.238768
$382$	−33.8974	−1.73434
$383$	−11.8582	−0.605923	−0.302962	−	0.953003i	$-0.597975\pi$
$383$	−11.8582	−0.605923	−0.302962	+	0.953003i	$0.597975\pi$
$384$	−4.48858	−0.229057
$385$	4.20775i	0.214447i
$386$	19.6136	0.998304
$387$	16.0858i	0.817685i
$388$	19.6407i	0.997106i
$389$	10.3913i	0.526862i	0.964678	+	0.263431i	$0.0848541\pi$
$389$	10.3913i	0.526862i	−0.964678	+	0.263431i	$0.915146\pi$
$390$	1.48427	0.0751590
$391$	− 4.59179i	− 0.232217i
$392$	− 12.7463i	− 0.643786i
$393$	−0.202374	−0.0102084
$394$	15.1371i	0.762594i
$395$	0.212063i	0.0106700i
$396$	− 10.1739i	− 0.511258i
$397$	8.21744	0.412421	0.206211	−	0.978508i	$-0.433887\pi$
$397$	8.21744	0.412421	0.206211	+	0.978508i	$0.433887\pi$
$398$	11.9312i	0.598059i
$399$	3.69202	0.184832
$400$	24.0659	1.20330
$401$	24.8810	1.24250	0.621249	−	0.783614i	$-0.286626\pi$
$401$	24.8810	1.24250	0.621249	+	0.783614i	$0.286626\pi$
$402$	−0.300209	−0.0149731
$403$	32.9667i	1.64219i
$404$	21.7506i	1.08213i
$405$	−2.58987	−0.128692
$406$	0	0
$407$	−8.47889	−0.420283
$408$	0.670251i	0.0331824i
$409$	18.8955i	0.934320i	0.884173	+	0.467160i	$0.154723\pi$
$409$	18.8955i	0.934320i	−0.884173	+	0.467160i	$0.845277\pi$
$410$	0.254749	0.0125812
$411$	5.89248	0.290654
$412$	3.50902	0.172877
$413$	36.8853	1.81501
$414$	20.8877i	1.02657i
$415$	3.36658	0.165259
$416$	− 32.0804i	− 1.57287i
$417$	− 1.24459i	− 0.0609477i
$418$	10.7506i	0.525830i
$419$	10.8925	0.532132	0.266066	−	0.963955i	$-0.414276\pi$
$419$	10.8925	0.532132	0.266066	+	0.963955i	$0.414276\pi$
$420$	− 0.801938i	− 0.0391306i
$421$	19.9608i	0.972828i	0.873728	+	0.486414i	$0.161695\pi$
$421$	19.9608i	0.972828i	−0.873728	+	0.486414i	$0.838305\pi$
$422$	14.5961	0.710527
$423$	21.8605i	1.06290i
$424$	5.91185i	0.287105i
$425$	− 5.40821i	− 0.262337i
$426$	9.14675	0.443162
$427$	24.4916i	1.18523i
$428$	9.30260	0.449658
$429$	6.72050	0.324469
$430$	−3.69202	−0.178045
$431$	−30.1903	−1.45422	−0.727108	−	0.686524i	$-0.759136\pi$
$431$	−30.1903	−1.45422	−0.727108	+	0.686524i	$0.759136\pi$
$432$	− 12.7530i	− 0.613580i
$433$	20.1914i	0.970335i	0.874421	+	0.485167i	$0.161241\pi$
$433$	20.1914i	0.970335i	−0.874421	+	0.485167i	$0.838759\pi$
$434$	46.3793	2.22628
$435$	0	0
$436$	−2.06100	−0.0987039
$437$	− 8.47650i	− 0.405486i
$438$	7.17629i	0.342896i
$439$	10.6649	0.509007	0.254503	−	0.967072i	$-0.418088\pi$
$439$	10.6649	0.509007	0.254503	+	0.967072i	$0.418088\pi$
$440$	−1.41013	−0.0672251
$441$	26.3207	1.25336
$442$	−10.3720	−0.493344
$443$	20.3502i	0.966867i	0.875381	+	0.483433i	$0.160610\pi$
$443$	20.3502i	0.966867i	−0.875381	+	0.483433i	$0.839390\pi$
$444$	1.61596	0.0766899
$445$	− 0.507960i	− 0.0240796i
$446$	− 39.4969i	− 1.87023i
$447$	− 1.20536i	− 0.0570115i
$448$	−5.13706	−0.242703
$449$	19.4233i	0.916641i	0.888787	+	0.458320i	$0.151549\pi$
$449$	19.4233i	0.916641i	−0.888787	+	0.458320i	$0.848451\pi$
$450$	24.6015i	1.15973i
$451$	1.15346	0.0543142
$452$	10.7748i	0.506804i
$453$	1.08383i	0.0509230i
$454$	32.9366i	1.54579i
$455$	−7.49396	−0.351322
$456$	1.23729i	0.0579415i
$457$	12.4209	0.581024	0.290512	−	0.956871i	$-0.406174\pi$
$457$	12.4209	0.581024	0.290512	+	0.956871i	$0.406174\pi$
$458$	−28.8756	−1.34927
$459$	−2.86592	−0.133770
$460$	−1.84117	−0.0858448
$461$	21.9463i	1.02214i	0.859539	+	0.511070i	$0.170751\pi$
$461$	21.9463i	1.02214i	−0.859539	+	0.511070i	$0.829249\pi$
$462$	− 9.45473i	− 0.439874i
$463$	33.0073	1.53398	0.766990	−	0.641660i	$-0.221754\pi$
$463$	33.0073	1.53398	0.766990	+	0.641660i	$0.221754\pi$
$464$	0	0
$465$	−1.00969	−0.0468232
$466$	− 3.52542i	− 0.163312i
$467$	− 26.1032i	− 1.20791i	−0.797017	−	0.603956i	$-0.793590\pi$
$467$	− 26.1032i	− 1.20791i	0.797017	−	0.603956i	$-0.206410\pi$
$468$	18.1196	0.837579
$469$	1.51573	0.0699899
$470$	−5.01746	−0.231438
$471$	7.86725	0.362504
$472$	12.3612i	0.568971i
$473$	−16.7168	−0.768638
$474$	− 0.476501i	− 0.0218864i
$475$	− 9.98361i	− 0.458079i
$476$	5.60388i	0.256853i
$477$	−12.2078	−0.558955
$478$	16.1511i	0.738732i
$479$	− 33.0659i	− 1.51082i	−0.655253	−	0.755410i	$-0.727438\pi$
$479$	− 33.0659i	− 1.51082i	0.655253	−	0.755410i	$-0.272562\pi$
$480$	0.982542	0.0448467
$481$	− 15.1008i	− 0.688538i
$482$	35.8582i	1.63329i
$483$	7.45473i	0.339202i
$484$	−3.14377	−0.142899
$485$	5.62133i	0.255252i
$486$	19.7778	0.897138
$487$	−10.1564	−0.460232	−0.230116	−	0.973163i	$-0.573911\pi$
$487$	−10.1564	−0.460232	−0.230116	+	0.973163i	$0.573911\pi$
$488$	−8.20775	−0.371547
$489$	−2.21014	−0.0999462
$490$	6.04115i	0.272911i
$491$	19.6819i	0.888230i	0.895970	+	0.444115i	$0.146482\pi$
$491$	19.6819i	0.888230i	−0.895970	+	0.444115i	$0.853518\pi$
$492$	−0.219833	−0.00991082
$493$	0	0
$494$	−19.1468	−0.861453
$495$	− 2.91185i	− 0.130878i
$496$	31.3967i	1.40975i
$497$	−46.1812	−2.07151
$498$	−7.56465	−0.338980
$499$	−27.8495	−1.24672	−0.623358	−	0.781937i	$-0.714232\pi$
$499$	−27.8495	−1.24672	−0.623358	+	0.781937i	$0.714232\pi$
$500$	−4.39373	−0.196494
$501$	− 6.43727i	− 0.287596i
$502$	46.4989	2.07535
$503$	0.225209i	0.0100416i	0.999987	+	0.00502079i	$0.00159818\pi$
$503$	0.225209i	0.0100416i	−0.999987	+	0.00502079i	$0.998402\pi$
$504$	15.3937i	0.685691i
$505$	6.22521i	0.277018i
$506$	−21.7071	−0.964998
$507$	6.18359i	0.274623i
$508$	− 13.0586i	− 0.579382i
$509$	−25.3032	−1.12154	−0.560772	−	0.827970i	$-0.689496\pi$
$509$	−25.3032	−1.12154	−0.560772	+	0.827970i	$0.689496\pi$
$510$	− 0.317667i	− 0.0140665i
$511$	− 36.2325i	− 1.60283i
$512$	− 17.1491i	− 0.757892i
$513$	−5.29052	−0.233582
$514$	− 21.5351i	− 0.949873i
$515$	1.00431	0.0442553
$516$	3.18598	0.140255
$517$	−22.7181	−0.999141
$518$	−21.2446	−0.933434
$519$	− 4.67887i	− 0.205380i
$520$	− 2.51142i	− 0.110133i
$521$	−23.5797	−1.03305	−0.516523	−	0.856273i	$-0.672774\pi$
$521$	−23.5797	−1.03305	−0.516523	+	0.856273i	$0.672774\pi$
$522$	0	0
$523$	3.96508	0.173381	0.0866905	−	0.996235i	$-0.472371\pi$
$523$	3.96508	0.173381	0.0866905	+	0.996235i	$0.472371\pi$
$524$	− 0.567040i	− 0.0247712i
$525$	8.78017i	0.383198i
$526$	−0.599564	−0.0261422
$527$	7.05562	0.307348
$528$	6.40044	0.278543
$529$	−5.88471	−0.255857
$530$	− 2.80194i	− 0.121708i
$531$	−25.5254	−1.10771
$532$	10.3448i	0.448505i
$533$	2.05429i	0.0889814i
$534$	1.14138i	0.0493921i
$535$	2.66248	0.115109
$536$	0.507960i	0.0219405i
$537$	2.55496i	0.110255i
$538$	1.91723	0.0826577
$539$	27.3532i	1.17818i
$540$	1.14914i	0.0494513i
$541$	− 24.6601i	− 1.06022i	−0.847929	−	0.530110i	$-0.822151\pi$
$541$	− 24.6601i	− 1.06022i	0.847929	−	0.530110i	$-0.177849\pi$
$542$	29.6679	1.27434
$543$	− 2.95539i	− 0.126828i
$544$	−6.86592	−0.294374
$545$	−0.589875	−0.0252675
$546$	16.8388	0.720633
$547$	24.8412	1.06213	0.531066	−	0.847331i	$-0.321792\pi$
$547$	24.8412	1.06213	0.531066	+	0.847331i	$0.321792\pi$
$548$	16.5104i	0.705287i
$549$	− 16.9487i	− 0.723352i
$550$	−25.5666	−1.09016
$551$	0	0
$552$	−2.49827	−0.106333
$553$	2.40581i	0.102306i
$554$	− 11.8823i	− 0.504831i
$555$	0.462500	0.0196320
$556$	3.48725	0.147893
$557$	−7.76510	−0.329018	−0.164509	−	0.986376i	$-0.552604\pi$
$557$	−7.76510	−0.329018	−0.164509	+	0.986376i	$0.552604\pi$
$558$	−32.0954	−1.35871
$559$	− 29.7724i	− 1.25924i
$560$	−7.13706	−0.301596
$561$	− 1.43834i	− 0.0607266i
$562$	55.0224i	2.32098i
$563$	− 20.8009i	− 0.876652i	−0.898816	−	0.438326i	$-0.855571\pi$
$563$	− 20.8009i	− 0.876652i	0.898816	−	0.438326i	$-0.144429\pi$
$564$	4.32975	0.182315
$565$	3.08383i	0.129738i
$566$	− 6.40581i	− 0.269256i
$567$	−29.3817	−1.23391
$568$	− 15.4765i	− 0.649380i
$569$	− 2.80923i	− 0.117769i	−0.998265	−	0.0588846i	$-0.981246\pi$
$569$	− 2.80923i	− 0.117769i	0.998265	−	0.0588846i	$-0.0187544\pi$
$570$	− 0.586417i	− 0.0245623i
$571$	2.89248	0.121046	0.0605232	−	0.998167i	$-0.480723\pi$
$571$	2.89248	0.121046	0.0605232	+	0.998167i	$0.480723\pi$
$572$	18.8304i	0.787339i
$573$	8.37196	0.349744
$574$	2.89008	0.120630
$575$	20.1584	0.840662
$576$	3.55496	0.148123
$577$	− 7.18896i	− 0.299281i	−0.988741	−	0.149640i	$-0.952188\pi$
$577$	− 7.18896i	− 0.299281i	0.988741	−	0.149640i	$-0.0478116\pi$
$578$	− 28.4131i	− 1.18183i
$579$	−4.84415	−0.201316
$580$	0	0
$581$	38.1933	1.58452
$582$	− 12.6310i	− 0.523573i
$583$	− 12.6866i	− 0.525427i
$584$	12.1424	0.502458
$585$	5.18598	0.214414
$586$	59.2476	2.44749
$587$	−31.0368	−1.28103	−0.640514	−	0.767947i	$-0.721279\pi$
$587$	−31.0368	−1.28103	−0.640514	+	0.767947i	$0.721279\pi$
$588$	− 5.21313i	− 0.214986i
$589$	13.0248	0.536676
$590$	− 5.85862i	− 0.241196i
$591$	− 3.73855i	− 0.153783i
$592$	− 14.3817i	− 0.591082i
$593$	−36.4674	−1.49754	−0.748768	−	0.662832i	$-0.769354\pi$
$593$	−36.4674	−1.49754	−0.748768	+	0.662832i	$0.769354\pi$
$594$	13.5483i	0.555892i
$595$	1.60388i	0.0657525i
$596$	3.37734	0.138341
$597$	− 2.94677i	− 0.120603i
$598$	− 38.6601i	− 1.58093i
$599$	30.0683i	1.22856i	0.789089	+	0.614279i	$0.210553\pi$
$599$	30.0683i	1.22856i	−0.789089	+	0.614279i	$0.789447\pi$
$600$	−2.94246	−0.120125
$601$	− 33.1860i	− 1.35368i	−0.736128	−	0.676842i	$-0.763348\pi$
$601$	− 33.1860i	− 1.35368i	0.736128	−	0.676842i	$-0.236652\pi$
$602$	−41.8853	−1.70712
$603$	−1.04892	−0.0427152
$604$	−3.03684	−0.123567
$605$	−0.899772	−0.0365810
$606$	− 13.9879i	− 0.568220i
$607$	15.1202i	0.613710i	0.951756	+	0.306855i	$0.0992766\pi$
$607$	15.1202i	0.613710i	−0.951756	+	0.306855i	$0.900723\pi$
$608$	−12.6746	−0.514021
$609$	0	0
$610$	3.89008	0.157505
$611$	− 40.4607i	− 1.63686i
$612$	− 3.87800i	− 0.156759i
$613$	−3.75541	−0.151680	−0.0758399	−	0.997120i	$-0.524164\pi$
$613$	−3.75541	−0.151680	−0.0758399	+	0.997120i	$0.524164\pi$
$614$	26.4349	1.06682
$615$	−0.0629179	−0.00253709
$616$	−15.9976	−0.644562
$617$	− 29.8562i	− 1.20197i	−0.799262	−	0.600983i	$-0.794776\pi$
$617$	− 29.8562i	− 1.20197i	0.799262	−	0.600983i	$-0.205224\pi$
$618$	−2.25667	−0.0907765
$619$	46.1178i	1.85363i	0.375517	+	0.926816i	$0.377465\pi$
$619$	46.1178i	1.85363i	−0.375517	+	0.926816i	$0.622535\pi$
$620$	− 2.82908i	− 0.113619i
$621$	− 10.6823i	− 0.428667i
$622$	33.3836	1.33856
$623$	− 5.76271i	− 0.230878i
$624$	11.3991i	0.456330i
$625$	23.1056	0.924224
$626$	− 41.4306i	− 1.65590i
$627$	− 2.65519i	− 0.106038i
$628$	22.0435i	0.879633i
$629$	−3.23191	−0.128865
$630$	− 7.29590i	− 0.290675i
$631$	−12.6300	−0.502791	−0.251395	−	0.967884i	$-0.580889\pi$
$631$	−12.6300	−0.502791	−0.251395	+	0.967884i	$0.580889\pi$
$632$	−0.806250	−0.0320709
$633$	−3.60494	−0.143284
$634$	−25.3327	−1.00609
$635$	− 3.73748i	− 0.148317i
$636$	2.41789i	0.0958758i
$637$	−48.7157	−1.93019
$638$	0	0
$639$	31.9584	1.26425
$640$	− 3.59956i	− 0.142285i
$641$	39.0019i	1.54048i	0.637752	+	0.770242i	$0.279864\pi$
$641$	39.0019i	1.54048i	−0.637752	+	0.770242i	$0.720136\pi$
$642$	−5.98254	−0.236112
$643$	−41.2965	−1.62857	−0.814287	−	0.580462i	$-0.802872\pi$
$643$	−41.2965	−1.62857	−0.814287	+	0.580462i	$0.802872\pi$
$644$	−20.8877	−0.823090
$645$	0.911854	0.0359042
$646$	4.09783i	0.161227i
$647$	17.9105	0.704135	0.352068	−	0.935975i	$-0.385479\pi$
$647$	17.9105	0.704135	0.352068	+	0.935975i	$0.385479\pi$
$648$	− 9.84654i	− 0.386809i
$649$	− 26.5267i	− 1.04127i
$650$	− 45.5338i	− 1.78598i
$651$	−11.4547	−0.448946
$652$	− 6.19269i	− 0.242524i
$653$	13.3207i	0.521277i	0.965436	+	0.260639i	$0.0839331\pi$
$653$	13.3207i	0.521277i	−0.965436	+	0.260639i	$0.916067\pi$
$654$	1.32544	0.0518287
$655$	− 0.162291i	− 0.00634125i
$656$	1.95646i	0.0763869i
$657$	25.0737i	0.978217i
$658$	−56.9221	−2.21906
$659$	18.7657i	0.731008i	0.930810	+	0.365504i	$0.119103\pi$
$659$	18.7657i	0.731008i	−0.930810	+	0.365504i	$0.880897\pi$
$660$	−0.576728	−0.0224491
$661$	−24.7289	−0.961841	−0.480921	−	0.876764i	$-0.659697\pi$
$661$	−24.7289	−0.961841	−0.480921	+	0.876764i	$0.659697\pi$
$662$	−25.1487	−0.977431
$663$	2.56166	0.0994867
$664$	12.7995i	0.496719i
$665$	2.96077i	0.114814i
$666$	14.7017	0.569680
$667$	0	0
$668$	18.0368	0.697866
$669$	9.75494i	0.377148i
$670$	− 0.240749i	− 0.00930094i
$671$	17.6136	0.679964
$672$	11.1468	0.429995
$673$	−25.4426	−0.980742	−0.490371	−	0.871514i	$-0.663139\pi$
$673$	−25.4426	−0.980742	−0.490371	+	0.871514i	$0.663139\pi$
$674$	25.2228	0.971547
$675$	− 12.5816i	− 0.484267i
$676$	−17.3260	−0.666386
$677$	− 0.616548i	− 0.0236959i	−0.999930	−	0.0118479i	$-0.996229\pi$
$677$	− 0.616548i	− 0.0236959i	0.999930	−	0.0118479i	$-0.00377140\pi$
$678$	− 6.92931i	− 0.266119i
$679$	63.7730i	2.44738i
$680$	−0.537500	−0.0206122
$681$	− 8.13467i	− 0.311721i
$682$	− 33.3545i	− 1.27721i
$683$	18.0218	0.689584	0.344792	−	0.938679i	$-0.387949\pi$
$683$	18.0218	0.689584	0.344792	+	0.938679i	$0.387949\pi$
$684$	− 7.15883i	− 0.273725i
$685$	4.72540i	0.180548i
$686$	17.4644i	0.666795i
$687$	7.13169	0.272091
$688$	− 28.3545i	− 1.08101i
$689$	22.5948	0.860792
$690$	1.18406	0.0450765
$691$	12.3461	0.469669	0.234835	−	0.972035i	$-0.424545\pi$
$691$	12.3461	0.469669	0.234835	+	0.972035i	$0.424545\pi$
$692$	13.1099	0.498364
$693$	− 33.0344i	− 1.25487i
$694$	− 35.7754i	− 1.35801i
$695$	0.998081	0.0378594
$696$	0	0
$697$	0.439665	0.0166535
$698$	48.5086i	1.83608i
$699$	0.870706i	0.0329331i
$700$	−24.6015	−0.929849
$701$	34.0974	1.28784	0.643920	−	0.765093i	$-0.277307\pi$
$701$	34.0974	1.28784	0.643920	+	0.765093i	$0.277307\pi$
$702$	−24.1293	−0.910702
$703$	−5.96615	−0.225018
$704$	3.69441i	0.139238i
$705$	1.23921	0.0466713
$706$	− 7.23490i	− 0.272289i
$707$	70.6238i	2.65608i
$708$	5.05562i	0.190002i
$709$	−42.0954	−1.58093	−0.790464	−	0.612509i	$-0.790160\pi$
$709$	−42.0954	−1.58093	−0.790464	+	0.612509i	$0.790160\pi$
$710$	7.33513i	0.275282i
$711$	− 1.66487i	− 0.0624377i
$712$	1.93123	0.0723760
$713$	26.2989i	0.984901i
$714$	− 3.60388i	− 0.134872i
$715$	5.38942i	0.201553i
$716$	−7.15883	−0.267538
$717$	− 3.98898i	− 0.148971i
$718$	−1.34481	−0.0501880
$719$	−52.2543	−1.94876	−0.974378	−	0.224917i	$-0.927789\pi$
$719$	−52.2543	−1.94876	−0.974378	+	0.224917i	$0.927789\pi$
$720$	4.93900	0.184066
$721$	11.3937	0.424325
$722$	− 26.6722i	− 0.992635i
$723$	− 8.85623i	− 0.329367i
$724$	8.28083	0.307755
$725$	0	0
$726$	2.02177	0.0750349
$727$	29.9849i	1.11208i	0.831156	+	0.556040i	$0.187680\pi$
$727$	29.9849i	1.11208i	−0.831156	+	0.556040i	$0.812320\pi$
$728$	− 28.4916i	− 1.05597i
$729$	16.8853	0.625381
$730$	−5.75494	−0.213000
$731$	−6.37196	−0.235676
$732$	−3.35690	−0.124074
$733$	− 3.01447i	− 0.111342i	−0.998449	−	0.0556711i	$-0.982270\pi$
$733$	− 3.01447i	− 0.111342i	0.998449	−	0.0556711i	$-0.0177298\pi$
$734$	−61.3540	−2.26462
$735$	− 1.49204i	− 0.0550347i
$736$	− 25.5918i	− 0.943326i
$737$	− 1.09006i	− 0.0401531i
$738$	−2.00000	−0.0736210
$739$	− 20.8374i	− 0.766518i	−0.923641	−	0.383259i	$-0.874802\pi$
$739$	− 20.8374i	− 0.766518i	0.923641	−	0.383259i	$-0.125198\pi$
$740$	1.29590i	0.0476381i
$741$	4.72886	0.173719
$742$	− 31.7875i	− 1.16695i
$743$	30.7657i	1.12868i	0.825541	+	0.564342i	$0.190870\pi$
$743$	30.7657i	1.12868i	−0.825541	+	0.564342i	$0.809130\pi$
$744$	− 3.83877i	− 0.140736i
$745$	0.966622	0.0354143
$746$	− 50.4553i	− 1.84730i
$747$	−26.4306	−0.967044
$748$	4.03013	0.147356
$749$	30.2054	1.10368
$750$	2.82563	0.103177
$751$	4.46921i	0.163084i	0.996670	+	0.0815418i	$0.0259844\pi$
$751$	4.46921i	0.163084i	−0.996670	+	0.0815418i	$0.974016\pi$
$752$	− 38.5338i	− 1.40518i
$753$	−11.4843	−0.418510
$754$	0	0
$755$	−0.869167	−0.0316322
$756$	13.0368i	0.474145i
$757$	− 8.45580i	− 0.307331i	−0.988123	−	0.153666i	$-0.950892\pi$
$757$	− 8.45580i	− 0.307331i	0.988123	−	0.153666i	$-0.0491078\pi$
$758$	41.2301	1.49755
$759$	5.36121	0.194600
$760$	−0.992230	−0.0359920
$761$	24.6950	0.895193	0.447597	−	0.894236i	$-0.352280\pi$
$761$	24.6950	0.895193	0.447597	+	0.894236i	$0.352280\pi$
$762$	8.39804i	0.304229i
$763$	−6.69202	−0.242267
$764$	23.4577i	0.848670i
$765$	− 1.10992i	− 0.0401291i
$766$	21.3676i	0.772045i
$767$	47.2438	1.70588
$768$	9.21744i	0.332606i
$769$	− 30.1430i	− 1.08699i	−0.839414	−	0.543493i	$-0.817102\pi$
$769$	− 30.1430i	− 1.08699i	0.839414	−	0.543493i	$-0.182898\pi$
$770$	7.58211	0.273240
$771$	5.31873i	0.191549i
$772$	− 13.5730i	− 0.488503i
$773$	5.67696i	0.204186i	0.994775	+	0.102093i	$0.0325539\pi$
$773$	5.67696i	0.204186i	−0.994775	+	0.102093i	$0.967446\pi$
$774$	28.9855	1.04186
$775$	30.9748i	1.11265i
$776$	−21.3720	−0.767209
$777$	5.24698	0.188234
$778$	18.7245	0.671307
$779$	0.811626	0.0290795
$780$	− 1.02715i	− 0.0367778i
$781$	33.2121i	1.18842i
$782$	−8.27413	−0.295882
$783$	0	0
$784$	−46.3957	−1.65699
$785$	6.30904i	0.225179i
$786$	0.364666i	0.0130072i
$787$	3.60925	0.128656	0.0643280	−	0.997929i	$-0.479510\pi$
$787$	3.60925	0.128656	0.0643280	+	0.997929i	$0.479510\pi$
$788$	10.4752	0.373163
$789$	0.148080	0.00527179
$790$	0.382124	0.0135954
$791$	34.9855i	1.24394i
$792$	11.0707	0.393380
$793$	31.3696i	1.11397i
$794$	− 14.8073i	− 0.525492i
$795$	0.692021i	0.0245435i
$796$	8.25667	0.292650
$797$	− 30.7832i	− 1.09040i	−0.838308	−	0.545198i	$-0.816455\pi$
$797$	− 30.7832i	− 1.09040i	0.838308	−	0.545198i	$-0.183545\pi$
$798$	− 6.65279i	− 0.235506i
$799$	−8.65950	−0.306351
$800$	− 30.1420i	− 1.06568i
$801$	3.98792i	0.140906i
$802$	− 44.8340i	− 1.58314i
$803$	−26.0573	−0.919541
$804$	0.207751i	0.00732681i
$805$	−5.97823	−0.210705
$806$	59.4040	2.09242
$807$	−0.473517	−0.0166686
$808$	−23.6679	−0.832632
$809$	− 5.23729i	− 0.184133i	−0.995753	−	0.0920667i	$-0.970653\pi$
$809$	− 5.23729i	− 0.184133i	0.995753	−	0.0920667i	$-0.0293473\pi$
$810$	4.66679i	0.163974i
$811$	−41.8646	−1.47006	−0.735032	−	0.678032i	$-0.762833\pi$
$811$	−41.8646	−1.47006	−0.735032	+	0.678032i	$0.762833\pi$
$812$	0	0
$813$	−7.32736	−0.256982
$814$	15.2784i	0.535509i
$815$	− 1.77240i	− 0.0620844i
$816$	2.43967	0.0854054
$817$	−11.7627	−0.411525
$818$	34.0484	1.19048
$819$	58.8340	2.05583
$820$	− 0.176292i	− 0.00615638i
$821$	−15.4058	−0.537667	−0.268833	−	0.963187i	$-0.586638\pi$
$821$	−15.4058	−0.537667	−0.268833	+	0.963187i	$0.586638\pi$
$822$	− 10.6179i	− 0.370341i
$823$	− 35.6558i	− 1.24288i	−0.783461	−	0.621441i	$-0.786548\pi$
$823$	− 35.6558i	− 1.24288i	0.783461	−	0.621441i	$-0.213452\pi$
$824$	3.81833i	0.133018i
$825$	6.31442	0.219840
$826$	− 66.4650i	− 2.31261i
$827$	52.0538i	1.81009i	0.425317	+	0.905044i	$0.360163\pi$
$827$	52.0538i	1.81009i	−0.425317	+	0.905044i	$0.639837\pi$
$828$	14.4547	0.502337
$829$	− 13.4168i	− 0.465986i	−0.972478	−	0.232993i	$-0.925148\pi$
$829$	− 13.4168i	− 0.465986i	0.972478	−	0.232993i	$-0.0748519\pi$
$830$	− 6.06638i	− 0.210567i
$831$	2.93469i	0.101803i
$832$	−6.57971	−0.228110
$833$	10.4263i	0.361248i
$834$	−2.24267	−0.0776572
$835$	5.16229	0.178648
$836$	7.43967	0.257306
$837$	16.4142	0.567357
$838$	− 19.6276i	− 0.678023i
$839$	31.0513i	1.07201i	0.844215	+	0.536005i	$0.180067\pi$
$839$	31.0513i	1.07201i	−0.844215	+	0.536005i	$0.819933\pi$
$840$	0.872625	0.0301084
$841$	0	0
$842$	35.9681	1.23954
$843$	− 13.5894i	− 0.468044i
$844$	− 10.1008i	− 0.347685i
$845$	−4.95885	−0.170590
$846$	39.3913	1.35430
$847$	−10.2078	−0.350742
$848$	21.5187	0.738956
$849$	1.58211i	0.0542977i
$850$	−9.74525	−0.334259
$851$	− 12.0465i	− 0.412950i
$852$	− 6.32975i	− 0.216854i
$853$	− 21.3357i	− 0.730521i	−0.930905	−	0.365261i	$-0.880980\pi$
$853$	− 21.3357i	− 0.730521i	0.930905	−	0.365261i	$-0.119020\pi$
$854$	44.1323	1.51018
$855$	− 2.04892i	− 0.0700715i
$856$	10.1226i	0.345983i
$857$	−9.83207	−0.335857	−0.167929	−	0.985799i	$-0.553708\pi$
$857$	−9.83207	−0.335857	−0.167929	+	0.985799i	$0.553708\pi$
$858$	− 12.1099i	− 0.413426i
$859$	51.7837i	1.76684i	0.468583	+	0.883419i	$0.344765\pi$
$859$	51.7837i	1.76684i	−0.468583	+	0.883419i	$0.655235\pi$
$860$	2.55496i	0.0871233i
$861$	−0.713792	−0.0243260
$862$	54.4010i	1.85291i
$863$	16.2747	0.553998	0.276999	−	0.960870i	$-0.410660\pi$
$863$	16.2747	0.553998	0.276999	+	0.960870i	$0.410660\pi$
$864$	−15.9729	−0.543407
$865$	3.75217	0.127577
$866$	36.3836	1.23636
$867$	7.01746i	0.238325i
$868$	− 32.0954i	− 1.08939i
$869$	1.73019	0.0586925
$870$	0	0
$871$	1.94139	0.0657816
$872$	− 2.24267i	− 0.0759463i
$873$	− 44.1323i	− 1.49365i
$874$	−15.2741	−0.516655
$875$	−14.2664	−0.482291
$876$	4.96615	0.167791
$877$	14.8062	0.499972	0.249986	−	0.968250i	$-0.419574\pi$
$877$	14.8062	0.499972	0.249986	+	0.968250i	$0.419574\pi$
$878$	− 19.2174i	− 0.648557i
$879$	−14.6329	−0.493557
$880$	5.13275i	0.173025i
$881$	− 18.6377i	− 0.627921i	−0.949436	−	0.313960i	$-0.898344\pi$
$881$	− 18.6377i	− 0.627921i	0.949436	−	0.313960i	$-0.101656\pi$
$882$	− 47.4282i	− 1.59699i
$883$	32.3937	1.09014	0.545068	−	0.838392i	$-0.316504\pi$
$883$	32.3937	1.09014	0.545068	+	0.838392i	$0.316504\pi$
$884$	7.17762i	0.241409i
$885$	1.44696i	0.0486391i
$886$	36.6698	1.23195
$887$	− 6.16288i	− 0.206929i	−0.994633	−	0.103465i	$-0.967007\pi$
$887$	− 6.16288i	− 0.206929i	0.994633	−	0.103465i	$-0.0329929\pi$
$888$	1.75840i	0.0590079i
$889$	− 42.4010i	− 1.42208i
$890$	−0.915312	−0.0306813
$891$	21.1304i	0.707894i
$892$	−27.3327	−0.915168
$893$	−15.9855	−0.534935
$894$	−2.17198	−0.0726419
$895$	−2.04892	−0.0684878
$896$	− 40.8364i	− 1.36425i
$897$	9.54825i	0.318807i
$898$	34.9995	1.16795
$899$	0	0
$900$	17.0248	0.567492
$901$	− 4.83579i	− 0.161104i
$902$	− 2.07846i	− 0.0692051i
$903$	10.3448	0.344254
$904$	−11.7245	−0.389953
$905$	2.37004	0.0787829
$906$	1.95300	0.0648841
$907$	− 43.9842i	− 1.46047i	−0.683195	−	0.730236i	$-0.739410\pi$
$907$	− 43.9842i	− 1.46047i	0.683195	−	0.730236i	$-0.260590\pi$
$908$	22.7928	0.756407
$909$	− 48.8732i	− 1.62102i
$910$	13.5036i	0.447642i
$911$	25.6233i	0.848936i	0.905443	+	0.424468i	$0.139539\pi$
$911$	25.6233i	0.848936i	−0.905443	+	0.424468i	$0.860461\pi$
$912$	4.50365	0.149131
$913$	− 27.4674i	− 0.909038i
$914$	− 22.3817i	− 0.740319i
$915$	−0.960771	−0.0317621
$916$	19.9825i	0.660242i
$917$	− 1.84117i	− 0.0608007i
$918$	5.16421i	0.170444i
$919$	−6.24160	−0.205891	−0.102946	−	0.994687i	$-0.532827\pi$
$919$	−6.24160	−0.205891	−0.102946	+	0.994687i	$0.532827\pi$
$920$	− 2.00346i	− 0.0660520i
$921$	−6.52888	−0.215134
$922$	39.5459	1.30237
$923$	−59.1503	−1.94696
$924$	−6.54288	−0.215245
$925$	− 14.1884i	− 0.466511i
$926$	− 59.4771i	− 1.95454i
$927$	−7.88471	−0.258968
$928$	0	0
$929$	−24.5133	−0.804256	−0.402128	−	0.915583i	$-0.631729\pi$
$929$	−24.5133	−0.804256	−0.402128	+	0.915583i	$0.631729\pi$
$930$	1.81940i	0.0596603i
$931$	19.2470i	0.630794i
$932$	−2.43967	−0.0799139
$933$	−8.24506	−0.269931
$934$	−47.0364	−1.53908
$935$	1.15346	0.0377221
$936$	19.7168i	0.644463i
$937$	4.08947	0.133597	0.0667986	−	0.997766i	$-0.478721\pi$
$937$	4.08947	0.133597	0.0667986	+	0.997766i	$0.478721\pi$
$938$	− 2.73125i	− 0.0891785i
$939$	10.2325i	0.333925i
$940$	3.47219i	0.113250i
$941$	−6.16315	−0.200913	−0.100456	−	0.994941i	$-0.532030\pi$
$941$	−6.16315	−0.200913	−0.100456	+	0.994941i	$0.532030\pi$
$942$	− 14.1763i	− 0.461889i
$943$	1.63879i	0.0533664i
$944$	44.9939	1.46443
$945$	3.73125i	0.121378i
$946$	30.1226i	0.979370i
$947$	− 49.7023i	− 1.61511i	−0.589794	−	0.807554i	$-0.700791\pi$
$947$	− 49.7023i	− 1.61511i	0.589794	−	0.807554i	$-0.299209\pi$
$948$	−0.329749	−0.0107097
$949$	− 46.4077i	− 1.50646i
$950$	−17.9898	−0.583667
$951$	6.25667	0.202886
$952$	−6.09783	−0.197632
$953$	17.6856	0.572892	0.286446	−	0.958096i	$-0.407526\pi$
$953$	17.6856	0.572892	0.286446	+	0.958096i	$0.407526\pi$
$954$	21.9976i	0.712199i
$955$	6.71379i	0.217253i
$956$	11.1769	0.361486
$957$	0	0
$958$	−59.5827	−1.92503
$959$	53.6088i	1.73112i
$960$	− 0.201520i	− 0.00650403i
$961$	−9.41013	−0.303552
$962$	−27.2107	−0.877309
$963$	−20.9028	−0.673582
$964$	24.8146	0.799225
$965$	− 3.88471i	− 0.125053i
$966$	13.4330	0.432198
$967$	12.8933i	0.414622i	0.978275	+	0.207311i	$0.0664711\pi$
$967$	12.8933i	0.414622i	−0.978275	+	0.207311i	$0.933529\pi$
$968$	− 3.42088i	− 0.109951i
$969$	− 1.01208i	− 0.0325127i
$970$	10.1293	0.325232
$971$	4.83745i	0.155241i	0.996983	+	0.0776205i	$0.0247323\pi$
$971$	4.83745i	0.155241i	−0.996983	+	0.0776205i	$0.975268\pi$
$972$	− 13.6866i	− 0.438999i
$973$	11.3230	0.363000
$974$	18.3013i	0.586411i
$975$	11.2459i	0.360158i
$976$	29.8756i	0.956295i
$977$	16.4421	0.526028	0.263014	−	0.964792i	$-0.415283\pi$
$977$	16.4421	0.526028	0.263014	+	0.964792i	$0.415283\pi$
$978$	3.98254i	0.127348i
$979$	−4.14436	−0.132454
$980$	4.18060	0.133544
$981$	4.63102	0.147857
$982$	35.4655	1.13175
$983$	− 26.4993i	− 0.845198i	−0.906317	−	0.422599i	$-0.861118\pi$
$983$	− 26.4993i	− 0.845198i	0.906317	−	0.422599i	$-0.138882\pi$
$984$	− 0.239210i	− 0.00762573i
$985$	2.99808	0.0955268
$986$	0	0
$987$	14.0586	0.447490
$988$	13.2500i	0.421537i
$989$	− 23.7506i	− 0.755226i
$990$	−5.24698	−0.166760
$991$	−40.4064	−1.28355	−0.641776	−	0.766892i	$-0.721802\pi$
$991$	−40.4064	−1.28355	−0.641776	+	0.766892i	$0.721802\pi$
$992$	39.3236	1.24853
$993$	6.21121	0.197107
$994$	83.2156i	2.63944i
$995$	2.36313	0.0749162
$996$	5.23490i	0.165874i
$997$	− 23.4553i	− 0.742837i	−0.928465	−	0.371419i	$-0.878871\pi$
$997$	− 23.4553i	− 0.742837i	0.928465	−	0.371419i	$-0.121129\pi$
$998$	50.1831i	1.58852i
$999$	−7.51871	−0.237882

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	841.2.b.c.840.1		6
29.2	odd	28		841.2.d.b.605.1		6
29.3	odd	28		841.2.d.e.571.1		6
29.4	even	14		841.2.e.b.651.2		12
29.5	even	14		841.2.e.c.236.1		12
29.6	even	14		841.2.e.c.196.2		12
29.7	even	7		841.2.e.b.270.2		12
29.8	odd	28		841.2.d.d.574.1		6
29.9	even	14		841.2.e.d.267.2		12
29.10	odd	28		841.2.d.a.190.1		6
29.11	odd	28		29.2.d.a.24.1	yes	6
29.12	odd	4		841.2.a.f.1.3		3
29.13	even	14		841.2.e.d.63.1		12
29.14	odd	28		841.2.d.b.645.1		6
29.15	odd	28		841.2.d.c.645.1		6
29.16	even	7		841.2.e.d.63.2		12
29.17	odd	4		841.2.a.e.1.1		3
29.18	odd	28		841.2.d.d.778.1		6
29.19	odd	28		841.2.d.e.190.1		6
29.20	even	7		841.2.e.d.267.1		12
29.21	odd	28		29.2.d.a.23.1	✓	6
29.22	even	14		841.2.e.b.270.1		12
29.23	even	7		841.2.e.c.196.1		12
29.24	even	7		841.2.e.c.236.2		12
29.25	even	7		841.2.e.b.651.1		12
29.26	odd	28		841.2.d.a.571.1		6
29.27	odd	28		841.2.d.c.605.1		6
29.28	even	2	inner	841.2.b.c.840.6		6
87.11	even	28		261.2.k.a.82.1		6
87.17	even	4		7569.2.a.r.1.3		3
87.41	even	4		7569.2.a.p.1.1		3
87.50	even	28		261.2.k.a.226.1		6
116.11	even	28		464.2.u.f.401.1		6
116.79	even	28		464.2.u.f.81.1		6
145.69	odd	28		725.2.l.b.401.1		6
145.79	odd	28		725.2.l.b.226.1		6
145.98	even	28		725.2.r.b.24.1		12
145.108	even	28		725.2.r.b.574.2		12
145.127	even	28		725.2.r.b.24.2		12
145.137	even	28		725.2.r.b.574.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.2.d.a.23.1	✓	6	29.21	odd	28
29.2.d.a.24.1	yes	6	29.11	odd	28
261.2.k.a.82.1		6	87.11	even	28
261.2.k.a.226.1		6	87.50	even	28
464.2.u.f.81.1		6	116.79	even	28
464.2.u.f.401.1		6	116.11	even	28
725.2.l.b.226.1		6	145.79	odd	28
725.2.l.b.401.1		6	145.69	odd	28
725.2.r.b.24.1		12	145.98	even	28
725.2.r.b.24.2		12	145.127	even	28
725.2.r.b.574.1		12	145.137	even	28
725.2.r.b.574.2		12	145.108	even	28
841.2.a.e.1.1		3	29.17	odd	4
841.2.a.f.1.3		3	29.12	odd	4
841.2.b.c.840.1		6	1.1	even	1	trivial
841.2.b.c.840.6		6	29.28	even	2	inner
841.2.d.a.190.1		6	29.10	odd	28
841.2.d.a.571.1		6	29.26	odd	28
841.2.d.b.605.1		6	29.2	odd	28
841.2.d.b.645.1		6	29.14	odd	28
841.2.d.c.605.1		6	29.27	odd	28
841.2.d.c.645.1		6	29.15	odd	28
841.2.d.d.574.1		6	29.8	odd	28
841.2.d.d.778.1		6	29.18	odd	28
841.2.d.e.190.1		6	29.19	odd	28
841.2.d.e.571.1		6	29.3	odd	28
841.2.e.b.270.1		12	29.22	even	14
841.2.e.b.270.2		12	29.7	even	7
841.2.e.b.651.1		12	29.25	even	7
841.2.e.b.651.2		12	29.4	even	14
841.2.e.c.196.1		12	29.23	even	7
841.2.e.c.196.2		12	29.6	even	14
841.2.e.c.236.1		12	29.5	even	14
841.2.e.c.236.2		12	29.24	even	7
841.2.e.d.63.1		12	29.13	even	14
841.2.e.d.63.2		12	29.16	even	7
841.2.e.d.267.1		12	29.20	even	7
841.2.e.d.267.2		12	29.9	even	14
7569.2.a.p.1.1		3	87.41	even	4
7569.2.a.r.1.3		3	87.17	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 841 = 29^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	841.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.80194i q^{2} +0.445042i q^{3} -1.24698 q^{4} -0.356896 q^{5} +0.801938 q^{6} -4.04892 q^{7} -1.35690i q^{8} +2.80194 q^{9} +0.643104i q^{10} +2.91185i q^{11} -0.554958i q^{12} -5.18598 q^{13} +7.29590i q^{14} -0.158834i q^{15} -4.93900 q^{16} +1.10992i q^{17} -5.04892i q^{18} +2.04892i q^{19} +0.445042 q^{20} -1.80194i q^{21} +5.24698 q^{22} -4.13706 q^{23} +0.603875 q^{24} -4.87263 q^{25} +9.34481i q^{26} +2.58211i q^{27} +5.04892 q^{28} -0.286208 q^{30} -6.35690i q^{31} +6.18598i q^{32} -1.29590 q^{33} +2.00000 q^{34} +1.44504 q^{35} -3.49396 q^{36} +2.91185i q^{37} +3.69202 q^{38} -2.30798i q^{39} +0.484271i q^{40} -0.396125i q^{41} -3.24698 q^{42} +5.74094i q^{43} -3.63102i q^{44} -1.00000 q^{45} +7.45473i q^{46} +7.80194i q^{47} -2.19806i q^{48} +9.39373 q^{49} +8.78017i q^{50} -0.493959 q^{51} +6.46681 q^{52} -4.35690 q^{53} +4.65279 q^{54} -1.03923i q^{55} +5.49396i q^{56} -0.911854 q^{57} -9.10992 q^{59} +0.198062i q^{60} -6.04892i q^{61} -11.4547 q^{62} -11.3448 q^{63} +1.26875 q^{64} +1.85086 q^{65} +2.33513i q^{66} -0.374354 q^{67} -1.38404i q^{68} -1.84117i q^{69} -2.60388i q^{70} +11.4058 q^{71} -3.80194i q^{72} +8.94869i q^{73} +5.24698 q^{74} -2.16852i q^{75} -2.55496i q^{76} -11.7899i q^{77} -4.15883 q^{78} -0.594187i q^{79} +1.76271 q^{80} +7.25667 q^{81} -0.713792 q^{82} -9.43296 q^{83} +2.24698i q^{84} -0.396125i q^{85} +10.3448 q^{86} +3.95108 q^{88} +1.42327i q^{89} +1.80194i q^{90} +20.9976 q^{91} +5.15883 q^{92} +2.82908 q^{93} +14.0586 q^{94} -0.731250i q^{95} -2.75302 q^{96} -15.7506i q^{97} -16.9269i q^{98} +8.15883i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{4} + 6 q^{5} - 4 q^{6} - 6 q^{7} + 8 q^{9} - 2 q^{13} - 10 q^{16} + 2 q^{20} + 22 q^{22} - 14 q^{23} - 14 q^{24} + 4 q^{25} + 12 q^{28} - 18 q^{30} + 20 q^{33} + 12 q^{34} + 8 q^{35} - 2 q^{36}+ \cdots - 26 q^{96}+O(q^{100}) \) 6 * q + 2 * q^4 + 6 * q^5 - 4 * q^6 - 6 * q^7 + 8 * q^9 - 2 * q^13 - 10 * q^16 + 2 * q^20 + 22 * q^22 - 14 * q^23 - 14 * q^24 + 4 * q^25 + 12 * q^28 - 18 * q^30 + 20 * q^33 + 12 * q^34 + 8 * q^35 - 2 * q^36 + 12 * q^38 - 10 * q^42 - 6 * q^45 - 8 * q^49 + 16 * q^51 + 32 * q^52 - 18 * q^53 - 8 * q^54 + 2 * q^57 - 56 * q^59 - 24 * q^62 - 22 * q^63 - 8 * q^64 - 16 * q^65 - 26 * q^67 + 42 * q^71 + 22 * q^74 - 8 * q^78 - 24 * q^80 - 10 * q^81 + 12 * q^82 - 18 * q^83 + 16 * q^86 + 42 * q^88 + 44 * q^91 + 14 * q^92 - 4 * q^93 + 22 * q^94 - 26 * q^96

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