LMFDB - Embedded newform 950.2.b.g.799.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(799,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("950.799");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.b (of order $2$, degree $1$, not 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.4227136.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 9x^{4} + 22x^{2} + 9 $ x^6 + 9x^4 + 22x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			799.1
Root			$-2.19869i$ of defining polynomial
Character	$\chi$	$=$	950.799
Dual form			950.2.b.g.799.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} -3.03293i q^{3} -1.00000 q^{4} -3.03293 q^{6} -2.46980i q^{7} +1.00000i q^{8} -6.19869 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} -3.03293i q^{3} -1.00000 q^{4} -3.03293 q^{6} -2.46980i q^{7} +1.00000i q^{8} -6.19869 q^{9} +0.728896 q^{11} +3.03293i q^{12} -6.23163i q^{13} -2.46980 q^{14} +1.00000 q^{16} -0.563139i q^{17} +6.19869i q^{18} +1.00000 q^{19} -7.49073 q^{21} -0.728896i q^{22} +4.63555i q^{23} +3.03293 q^{24} -6.23163 q^{26} +9.70142i q^{27} +2.46980i q^{28} -10.2316 q^{29} +6.06587 q^{31} -1.00000i q^{32} -2.21069i q^{33} -0.563139 q^{34} +6.19869 q^{36} +5.72890i q^{37} -1.00000i q^{38} -18.9001 q^{39} +4.79476 q^{41} +7.49073i q^{42} +8.06587i q^{43} -0.728896 q^{44} +4.63555 q^{46} -8.12628i q^{47} -3.03293i q^{48} +0.900112 q^{49} -1.70796 q^{51} +6.23163i q^{52} -1.53020i q^{53} +9.70142 q^{54} +2.46980 q^{56} -3.03293i q^{57} +10.2316i q^{58} +5.76183 q^{59} +10.9396 q^{61} -6.06587i q^{62} +15.3095i q^{63} -1.00000 q^{64} -2.21069 q^{66} -12.9330i q^{67} +0.563139i q^{68} +14.0593 q^{69} -4.39738 q^{71} -6.19869i q^{72} -4.09334i q^{73} +5.72890 q^{74} -1.00000 q^{76} -1.80022i q^{77} +18.9001i q^{78} -15.3370 q^{79} +10.8277 q^{81} -4.79476i q^{82} +7.85517i q^{83} +7.49073 q^{84} +8.06587 q^{86} +31.0318i q^{87} +0.728896i q^{88} +10.0000 q^{89} -15.3908 q^{91} -4.63555i q^{92} -18.3974i q^{93} -8.12628 q^{94} -3.03293 q^{96} -11.0055i q^{97} -0.900112i q^{98} -4.51820 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} + 4 q^{6} - 26 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 + 4 * q^6 - 26 * q^9	$ 6 q - 6 q^{4} + 4 q^{6} - 26 q^{9} + 4 q^{11} - 4 q^{14} + 6 q^{16} + 6 q^{19} - 22 q^{21} - 4 q^{24} - 4 q^{26} - 28 q^{29} - 8 q^{31} + 8 q^{34} + 26 q^{36} - 58 q^{39} - 16 q^{41} - 4 q^{44} + 28 q^{46} - 50 q^{49} - 22 q^{51} + 14 q^{54} + 4 q^{56} + 12 q^{59} + 44 q^{61} - 6 q^{64} + 8 q^{66} - 16 q^{69} - 4 q^{71} + 34 q^{74} - 6 q^{76} - 48 q^{79} - 2 q^{81} + 22 q^{84} + 4 q^{86} + 60 q^{89} - 14 q^{91} - 26 q^{94} + 4 q^{96} - 48 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 + 4 * q^6 - 26 * q^9 + 4 * q^11 - 4 * q^14 + 6 * q^16 + 6 * q^19 - 22 * q^21 - 4 * q^24 - 4 * q^26 - 28 * q^29 - 8 * q^31 + 8 * q^34 + 26 * q^36 - 58 * q^39 - 16 * q^41 - 4 * q^44 + 28 * q^46 - 50 * q^49 - 22 * q^51 + 14 * q^54 + 4 * q^56 + 12 * q^59 + 44 * q^61 - 6 * q^64 + 8 * q^66 - 16 * q^69 - 4 * q^71 + 34 * q^74 - 6 * q^76 - 48 * q^79 - 2 * q^81 + 22 * q^84 + 4 * q^86 + 60 * q^89 - 14 * q^91 - 26 * q^94 + 4 * q^96 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$-1$	$1$

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 $

$2$	− 1.00000i	− 0.707107i
$2$	− 1.00000i	− 0.707107i
$3$	− 3.03293i	− 1.75107i	−0.483159	−	0.875533i	$-0.660511\pi$
$3$	− 3.03293i	− 1.75107i	0.483159	−	0.875533i	$-0.339489\pi$
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−3.03293	−1.23819
$7$	− 2.46980i	− 0.933495i	−0.884391	−	0.466747i	$-0.845426\pi$
$7$	− 2.46980i	− 0.933495i	0.884391	−	0.466747i	$-0.154574\pi$
$8$	1.00000i	0.353553i
$9$	−6.19869	−2.06623
$10$	0	0
$11$	0.728896	0.219770	0.109885	−	0.993944i	$-0.464952\pi$
$11$	0.728896	0.219770	0.109885	+	0.993944i	$0.464952\pi$
$12$	3.03293i	0.875533i
$13$	− 6.23163i	− 1.72834i	−0.503198	−	0.864171i	$-0.667843\pi$
$13$	− 6.23163i	− 1.72834i	0.503198	−	0.864171i	$-0.332157\pi$
$14$	−2.46980	−0.660081
$15$	0	0
$16$	1.00000	0.250000
$17$	− 0.563139i	− 0.136581i	−0.997665	−	0.0682907i	$-0.978245\pi$
$17$	− 0.563139i	− 0.136581i	0.997665	−	0.0682907i	$-0.0217545\pi$
$18$	6.19869i	1.46105i
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0	0
$21$	−7.49073	−1.63461
$22$	− 0.728896i	− 0.155401i
$23$	4.63555i	0.966579i	0.875460	+	0.483290i	$0.160558\pi$
$23$	4.63555i	0.966579i	−0.875460	+	0.483290i	$0.839442\pi$
$24$	3.03293	0.619095
$25$	0	0
$26$	−6.23163	−1.22212
$27$	9.70142i	1.86704i
$28$	2.46980i	0.466747i
$29$	−10.2316	−1.89997	−0.949983	−	0.312303i	$-0.898900\pi$
$29$	−10.2316	−1.89997	−0.949983	+	0.312303i	$0.898900\pi$
$30$	0	0
$31$	6.06587	1.08946	0.544731	−	0.838611i	$-0.316632\pi$
$31$	6.06587	1.08946	0.544731	+	0.838611i	$0.316632\pi$
$32$	− 1.00000i	− 0.176777i
$33$	− 2.21069i	− 0.384832i
$34$	−0.563139	−0.0965776
$35$	0	0
$36$	6.19869	1.03312
$37$	5.72890i	0.941825i	0.882180	+	0.470912i	$0.156075\pi$
$37$	5.72890i	0.941825i	−0.882180	+	0.470912i	$0.843925\pi$
$38$	− 1.00000i	− 0.162221i
$39$	−18.9001	−3.02644
$40$	0	0
$41$	4.79476	0.748816	0.374408	−	0.927264i	$-0.377846\pi$
$41$	4.79476	0.748816	0.374408	+	0.927264i	$0.377846\pi$
$42$	7.49073i	1.15584i
$43$	8.06587i	1.23003i	0.788514	+	0.615017i	$0.210851\pi$
$43$	8.06587i	1.23003i	−0.788514	+	0.615017i	$0.789149\pi$
$44$	−0.728896	−0.109885
$45$	0	0
$46$	4.63555	0.683475
$47$	− 8.12628i	− 1.18534i	−0.805446	−	0.592670i	$-0.798074\pi$
$47$	− 8.12628i	− 1.18534i	0.805446	−	0.592670i	$-0.201926\pi$
$48$	− 3.03293i	− 0.437766i
$49$	0.900112	0.128587
$50$	0	0
$51$	−1.70796	−0.239163
$52$	6.23163i	0.864171i
$53$	− 1.53020i	− 0.210190i	−0.994462	−	0.105095i	$-0.966485\pi$
$53$	− 1.53020i	− 0.210190i	0.994462	−	0.105095i	$-0.0335146\pi$
$54$	9.70142	1.32020
$55$	0	0
$56$	2.46980	0.330040
$57$	− 3.03293i	− 0.401722i
$58$	10.2316i	1.34348i
$59$	5.76183	0.750126	0.375063	−	0.926999i	$-0.377621\pi$
$59$	5.76183	0.750126	0.375063	+	0.926999i	$0.377621\pi$
$60$	0	0
$61$	10.9396	1.40067	0.700336	−	0.713814i	$-0.253034\pi$
$61$	10.9396	1.40067	0.700336	+	0.713814i	$0.253034\pi$
$62$	− 6.06587i	− 0.770366i
$63$	15.3095i	1.92882i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−2.21069	−0.272118
$67$	− 12.9330i	− 1.58002i	−0.613092	−	0.790012i	$-0.710074\pi$
$67$	− 12.9330i	− 1.58002i	0.613092	−	0.790012i	$-0.289926\pi$
$68$	0.563139i	0.0682907i
$69$	14.0593	1.69254
$70$	0	0
$71$	−4.39738	−0.521873	−0.260937	−	0.965356i	$-0.584031\pi$
$71$	−4.39738	−0.521873	−0.260937	+	0.965356i	$0.584031\pi$
$72$	− 6.19869i	− 0.730523i
$73$	− 4.09334i	− 0.479090i	−0.970885	−	0.239545i	$-0.923002\pi$
$73$	− 4.09334i	− 0.479090i	0.970885	−	0.239545i	$-0.0769982\pi$
$74$	5.72890	0.665971
$75$	0	0
$76$	−1.00000	−0.114708
$77$	− 1.80022i	− 0.205155i
$78$	18.9001i	2.14002i
$79$	−15.3370	−1.72554	−0.862772	−	0.505593i	$-0.831274\pi$
$79$	−15.3370	−1.72554	−0.862772	+	0.505593i	$0.831274\pi$
$80$	0	0
$81$	10.8277	1.20308
$82$	− 4.79476i	− 0.529493i
$83$	7.85517i	0.862217i	0.902300	+	0.431109i	$0.141877\pi$
$83$	7.85517i	0.862217i	−0.902300	+	0.431109i	$0.858123\pi$
$84$	7.49073	0.817305
$85$	0	0
$86$	8.06587	0.869765
$87$	31.0318i	3.32696i
$88$	0.728896i	0.0777006i
$89$	10.0000	1.06000	0.529999	−	0.847998i	$-0.322192\pi$
$89$	10.0000	1.06000	0.529999	+	0.847998i	$0.322192\pi$
$90$	0	0
$91$	−15.3908	−1.61340
$92$	− 4.63555i	− 0.483290i
$93$	− 18.3974i	− 1.90772i
$94$	−8.12628	−0.838162
$95$	0	0
$96$	−3.03293	−0.309548
$97$	− 11.0055i	− 1.11744i	−0.829358	−	0.558718i	$-0.811294\pi$
$97$	− 11.0055i	− 1.11744i	0.829358	−	0.558718i	$-0.188706\pi$
$98$	− 0.900112i	− 0.0909250i
$99$	−4.51820	−0.454096
$100$	0	0
$101$	−9.73436	−0.968605	−0.484302	−	0.874901i	$-0.660926\pi$
$101$	−9.73436	−0.968605	−0.484302	+	0.874901i	$0.660926\pi$
$102$	1.70796i	0.169114i
$103$	− 8.33151i	− 0.820928i	−0.911877	−	0.410464i	$-0.865367\pi$
$103$	− 8.33151i	− 0.820928i	0.911877	−	0.410464i	$-0.134633\pi$
$104$	6.23163	0.611061
$105$	0	0
$106$	−1.53020	−0.148627
$107$	15.0264i	1.45266i	0.687348	+	0.726328i	$0.258775\pi$
$107$	15.0264i	1.45266i	−0.687348	+	0.726328i	$0.741225\pi$
$108$	− 9.70142i	− 0.933520i
$109$	13.6619	1.30858	0.654288	−	0.756245i	$-0.272968\pi$
$109$	13.6619	1.30858	0.654288	+	0.756245i	$0.272968\pi$
$110$	0	0
$111$	17.3754	1.64920
$112$	− 2.46980i	− 0.233374i
$113$	1.20524i	0.113379i	0.998392	+	0.0566895i	$0.0180545\pi$
$113$	1.20524i	0.113379i	−0.998392	+	0.0566895i	$0.981945\pi$
$114$	−3.03293	−0.284060
$115$	0	0
$116$	10.2316	0.949983
$117$	38.6279i	3.57115i
$118$	− 5.76183i	− 0.530419i
$119$	−1.39084	−0.127498
$120$	0	0
$121$	−10.4687	−0.951701
$122$	− 10.9396i	− 0.990424i
$123$	− 14.5422i	− 1.31123i
$124$	−6.06587	−0.544731
$125$	0	0
$126$	15.3095	1.36388
$127$	− 9.52366i	− 0.845088i	−0.906342	−	0.422544i	$-0.861137\pi$
$127$	− 9.52366i	− 0.845088i	0.906342	−	0.422544i	$-0.138863\pi$
$128$	1.00000i	0.0883883i
$129$	24.4633	2.15387
$130$	0	0
$131$	−17.4028	−1.52049	−0.760247	−	0.649635i	$-0.774922\pi$
$131$	−17.4028	−1.52049	−0.760247	+	0.649635i	$0.774922\pi$
$132$	2.21069i	0.192416i
$133$	− 2.46980i	− 0.214158i
$134$	−12.9330	−1.11725
$135$	0	0
$136$	0.563139	0.0482888
$137$	− 2.25910i	− 0.193008i	−0.995333	−	0.0965040i	$-0.969234\pi$
$137$	− 2.25910i	− 0.193008i	0.995333	−	0.0965040i	$-0.0307661\pi$
$138$	− 14.0593i	− 1.19681i
$139$	−16.8606	−1.43010	−0.715050	−	0.699073i	$-0.753596\pi$
$139$	−16.8606	−1.43010	−0.715050	+	0.699073i	$0.753596\pi$
$140$	0	0
$141$	−24.6465	−2.07561
$142$	4.39738i	0.369020i
$143$	− 4.54221i	− 0.379838i
$144$	−6.19869	−0.516558
$145$	0	0
$146$	−4.09334	−0.338768
$147$	− 2.72998i	− 0.225165i
$148$	− 5.72890i	− 0.470912i
$149$	13.0055	1.06545	0.532724	−	0.846289i	$-0.321168\pi$
$149$	13.0055	1.06545	0.532724	+	0.846289i	$0.321168\pi$
$150$	0	0
$151$	17.5895	1.43142	0.715708	−	0.698400i	$-0.246104\pi$
$151$	17.5895	1.43142	0.715708	+	0.698400i	$0.246104\pi$
$152$	1.00000i	0.0811107i
$153$	3.49073i	0.282209i
$154$	−1.80022	−0.145066
$155$	0	0
$156$	18.9001	1.51322
$157$	− 9.52366i	− 0.760071i	−0.924972	−	0.380035i	$-0.875912\pi$
$157$	− 9.52366i	− 0.760071i	0.924972	−	0.380035i	$-0.124088\pi$
$158$	15.3370i	1.22014i
$159$	−4.64101	−0.368056
$160$	0	0
$161$	11.4489	0.902297
$162$	− 10.8277i	− 0.850704i
$163$	13.1921i	1.03329i	0.856200	+	0.516644i	$0.172819\pi$
$163$	13.1921i	1.03329i	−0.856200	+	0.516644i	$0.827181\pi$
$164$	−4.79476	−0.374408
$165$	0	0
$166$	7.85517	0.609680
$167$	− 1.81331i	− 0.140318i	−0.997536	−	0.0701591i	$-0.977649\pi$
$167$	− 1.81331i	− 0.140318i	0.997536	−	0.0701591i	$-0.0223507\pi$
$168$	− 7.49073i	− 0.577922i
$169$	−25.8332	−1.98717
$170$	0	0
$171$	−6.19869	−0.474026
$172$	− 8.06587i	− 0.615017i
$173$	− 12.5237i	− 0.952156i	−0.879403	−	0.476078i	$-0.842058\pi$
$173$	− 12.5237i	− 0.952156i	0.879403	−	0.476078i	$-0.157942\pi$
$174$	31.0318	2.35252
$175$	0	0
$176$	0.728896	0.0549426
$177$	− 17.4753i	− 1.31352i
$178$	− 10.0000i	− 0.749532i
$179$	−1.39738	−0.104445	−0.0522226	−	0.998635i	$-0.516631\pi$
$179$	−1.39738	−0.104445	−0.0522226	+	0.998635i	$0.516631\pi$
$180$	0	0
$181$	5.72890	0.425825	0.212913	−	0.977071i	$-0.431705\pi$
$181$	5.72890	0.425825	0.212913	+	0.977071i	$0.431705\pi$
$182$	15.3908i	1.14084i
$183$	− 33.1791i	− 2.45267i
$184$	−4.63555	−0.341737
$185$	0	0
$186$	−18.3974	−1.34896
$187$	− 0.410470i	− 0.0300165i
$188$	8.12628i	0.592670i
$189$	23.9605	1.74287
$190$	0	0
$191$	−27.0198	−1.95509	−0.977544	−	0.210733i	$-0.932415\pi$
$191$	−27.0198	−1.95509	−0.977544	+	0.210733i	$0.932415\pi$
$192$	3.03293i	0.218883i
$193$	− 23.0713i	− 1.66071i	−0.557234	−	0.830355i	$-0.688138\pi$
$193$	− 23.0713i	− 1.66071i	0.557234	−	0.830355i	$-0.311862\pi$
$194$	−11.0055	−0.790146
$195$	0	0
$196$	−0.900112	−0.0642937
$197$	− 0.794765i	− 0.0566247i	−0.999599	−	0.0283123i	$-0.990987\pi$
$197$	− 0.794765i	− 0.0566247i	0.999599	−	0.0283123i	$-0.00901330\pi$
$198$	4.51820i	0.321095i
$199$	−8.07241	−0.572238	−0.286119	−	0.958194i	$-0.592365\pi$
$199$	−8.07241	−0.572238	−0.286119	+	0.958194i	$0.592365\pi$
$200$	0	0
$201$	−39.2251	−2.76672
$202$	9.73436i	0.684907i
$203$	25.2700i	1.77361i
$204$	1.70796	0.119581
$205$	0	0
$206$	−8.33151	−0.580484
$207$	− 28.7344i	− 1.99718i
$208$	− 6.23163i	− 0.432085i
$209$	0.728896	0.0504188
$210$	0	0
$211$	−11.6410	−0.801400	−0.400700	−	0.916209i	$-0.631233\pi$
$211$	−11.6410	−0.801400	−0.400700	+	0.916209i	$0.631233\pi$
$212$	1.53020i	0.105095i
$213$	13.3370i	0.913834i
$214$	15.0264	1.02718
$215$	0	0
$216$	−9.70142	−0.660098
$217$	− 14.9815i	− 1.01701i
$218$	− 13.6619i	− 0.925304i
$219$	−12.4148	−0.838917
$220$	0	0
$221$	−3.50927	−0.236059
$222$	− 17.3754i	− 1.16616i
$223$	− 15.6554i	− 1.04836i	−0.851607	−	0.524182i	$-0.824371\pi$
$223$	− 15.6554i	− 1.04836i	0.851607	−	0.524182i	$-0.175629\pi$
$224$	−2.46980	−0.165020
$225$	0	0
$226$	1.20524	0.0801710
$227$	− 4.80131i	− 0.318674i	−0.987224	−	0.159337i	$-0.949064\pi$
$227$	− 4.80131i	− 0.318674i	0.987224	−	0.159337i	$-0.0509357\pi$
$228$	3.03293i	0.200861i
$229$	−2.79476	−0.184683	−0.0923416	−	0.995727i	$-0.529435\pi$
$229$	−2.79476	−0.184683	−0.0923416	+	0.995727i	$0.529435\pi$
$230$	0	0
$231$	−5.45996	−0.359239
$232$	− 10.2316i	− 0.671739i
$233$	11.5422i	0.756155i	0.925774	+	0.378078i	$0.123415\pi$
$233$	11.5422i	0.756155i	−0.925774	+	0.378078i	$0.876585\pi$
$234$	38.6279	2.52519
$235$	0	0
$236$	−5.76183	−0.375063
$237$	46.5160i	3.02154i
$238$	1.39084i	0.0901547i
$239$	26.2251	1.69636	0.848180	−	0.529708i	$-0.177699\pi$
$239$	26.2251	1.69636	0.848180	+	0.529708i	$0.177699\pi$
$240$	0	0
$241$	−12.0659	−0.777231	−0.388615	−	0.921400i	$-0.627047\pi$
$241$	−12.0659	−0.777231	−0.388615	+	0.921400i	$0.627047\pi$
$242$	10.4687i	0.672954i
$243$	− 3.73544i	− 0.239629i
$244$	−10.9396	−0.700336
$245$	0	0
$246$	−14.5422	−0.927177
$247$	− 6.23163i	− 0.396509i
$248$	6.06587i	0.385183i
$249$	23.8242	1.50980
$250$	0	0
$251$	13.5237	0.853606	0.426803	−	0.904345i	$-0.359640\pi$
$251$	13.5237	0.853606	0.426803	+	0.904345i	$0.359640\pi$
$252$	− 15.3095i	− 0.964408i
$253$	3.37884i	0.212426i
$254$	−9.52366	−0.597568
$255$	0	0
$256$	1.00000	0.0625000
$257$	− 22.7398i	− 1.41847i	−0.704972	−	0.709235i	$-0.749040\pi$
$257$	− 22.7398i	− 1.41847i	0.704972	−	0.709235i	$-0.250960\pi$
$258$	− 24.4633i	− 1.52302i
$259$	14.1492	0.879188
$260$	0	0
$261$	63.4227	3.92577
$262$	17.4028i	1.07515i
$263$	− 6.67395i	− 0.411533i	−0.978601	−	0.205767i	$-0.934031\pi$
$263$	− 6.67395i	− 0.411533i	0.978601	−	0.205767i	$-0.0659688\pi$
$264$	2.21069	0.136059
$265$	0	0
$266$	−2.46980	−0.151433
$267$	− 30.3293i	− 1.85613i
$268$	12.9330i	0.790012i
$269$	29.7398	1.81327	0.906634	−	0.421917i	$-0.138643\pi$
$269$	29.7398	1.81327	0.906634	+	0.421917i	$0.138643\pi$
$270$	0	0
$271$	1.11189	0.0675426	0.0337713	−	0.999430i	$-0.489248\pi$
$271$	1.11189	0.0675426	0.0337713	+	0.999430i	$0.489248\pi$
$272$	− 0.563139i	− 0.0341453i
$273$	46.6794i	2.82517i
$274$	−2.25910	−0.136477
$275$	0	0
$276$	−14.0593	−0.846272
$277$	− 13.1263i	− 0.788682i	−0.918964	−	0.394341i	$-0.870973\pi$
$277$	− 13.1263i	− 0.788682i	0.918964	−	0.394341i	$-0.129027\pi$
$278$	16.8606i	1.01123i
$279$	−37.6004	−2.25108
$280$	0	0
$281$	22.9265	1.36768	0.683840	−	0.729632i	$-0.260309\pi$
$281$	22.9265	1.36768	0.683840	+	0.729632i	$0.260309\pi$
$282$	24.6465i	1.46768i
$283$	0.860634i	0.0511594i	0.999673	+	0.0255797i	$0.00814315\pi$
$283$	0.860634i	0.0511594i	−0.999673	+	0.0255797i	$0.991857\pi$
$284$	4.39738	0.260937
$285$	0	0
$286$	−4.54221	−0.268586
$287$	− 11.8421i	− 0.699016i
$288$	6.19869i	0.365261i
$289$	16.6829	0.981346
$290$	0	0
$291$	−33.3788	−1.95670
$292$	4.09334i	0.239545i
$293$	19.8212i	1.15796i	0.815340	+	0.578982i	$0.196550\pi$
$293$	19.8212i	1.15796i	−0.815340	+	0.578982i	$0.803450\pi$
$294$	−2.72998	−0.159216
$295$	0	0
$296$	−5.72890	−0.332985
$297$	7.07133i	0.410320i
$298$	− 13.0055i	− 0.753386i
$299$	28.8870	1.67058
$300$	0	0
$301$	19.9210	1.14823
$302$	− 17.5895i	− 1.01216i
$303$	29.5237i	1.69609i
$304$	1.00000	0.0573539
$305$	0	0
$306$	3.49073	0.199552
$307$	16.8661i	0.962599i	0.876556	+	0.481299i	$0.159835\pi$
$307$	16.8661i	0.962599i	−0.876556	+	0.481299i	$0.840165\pi$
$308$	1.80022i	0.102577i
$309$	−25.2689	−1.43750
$310$	0	0
$311$	10.3250	0.585475	0.292738	−	0.956193i	$-0.405434\pi$
$311$	10.3250	0.585475	0.292738	+	0.956193i	$0.405434\pi$
$312$	− 18.9001i	− 1.07001i
$313$	− 15.7684i	− 0.891281i	−0.895212	−	0.445641i	$-0.852976\pi$
$313$	− 15.7684i	− 0.891281i	0.895212	−	0.445641i	$-0.147024\pi$
$314$	−9.52366	−0.537451
$315$	0	0
$316$	15.3370	0.862772
$317$	2.17230i	0.122009i	0.998138	+	0.0610043i	$0.0194303\pi$
$317$	2.17230i	0.122009i	−0.998138	+	0.0610043i	$0.980570\pi$
$318$	4.64101i	0.260255i
$319$	−7.45779	−0.417556
$320$	0	0
$321$	45.5741	2.54370
$322$	− 11.4489i	− 0.638020i
$323$	− 0.563139i	− 0.0313339i
$324$	−10.8277	−0.601539
$325$	0	0
$326$	13.1921	0.730645
$327$	− 41.4358i	− 2.29140i
$328$	4.79476i	0.264747i
$329$	−20.0702	−1.10651
$330$	0	0
$331$	11.9791	0.658429	0.329215	−	0.944255i	$-0.393216\pi$
$331$	11.9791	0.658429	0.329215	+	0.944255i	$0.393216\pi$
$332$	− 7.85517i	− 0.431109i
$333$	− 35.5117i	− 1.94603i
$334$	−1.81331	−0.0992200
$335$	0	0
$336$	−7.49073	−0.408653
$337$	11.1921i	0.609675i	0.952404	+	0.304838i	$0.0986022\pi$
$337$	11.1921i	0.609675i	−0.952404	+	0.304838i	$0.901398\pi$
$338$	25.8332i	1.40514i
$339$	3.65540	0.198534
$340$	0	0
$341$	4.42139	0.239432
$342$	6.19869i	0.335187i
$343$	− 19.5117i	− 1.05353i
$344$	−8.06587	−0.434883
$345$	0	0
$346$	−12.5237	−0.673276
$347$	20.3843i	1.09429i	0.837039	+	0.547143i	$0.184285\pi$
$347$	20.3843i	1.09429i	−0.837039	+	0.547143i	$0.815715\pi$
$348$	− 31.0318i	− 1.66348i
$349$	0.252557	0.0135191	0.00675954	−	0.999977i	$-0.497848\pi$
$349$	0.252557	0.0135191	0.00675954	+	0.999977i	$0.497848\pi$
$350$	0	0
$351$	60.4556	3.22688
$352$	− 0.728896i	− 0.0388503i
$353$	− 28.6434i	− 1.52453i	−0.647263	−	0.762267i	$-0.724086\pi$
$353$	− 28.6434i	− 1.52453i	0.647263	−	0.762267i	$-0.275914\pi$
$354$	−17.4753	−0.928799
$355$	0	0
$356$	−10.0000	−0.529999
$357$	4.21832i	0.223257i
$358$	1.39738i	0.0738540i
$359$	18.5741	0.980301	0.490151	−	0.871638i	$-0.336942\pi$
$359$	18.5741	0.980301	0.490151	+	0.871638i	$0.336942\pi$
$360$	0	0
$361$	1.00000	0.0526316
$362$	− 5.72890i	− 0.301104i
$363$	31.7509i	1.66649i
$364$	15.3908	0.806699
$365$	0	0
$366$	−33.1791	−1.73430
$367$	4.79476i	0.250285i	0.992139	+	0.125142i	$0.0399388\pi$
$367$	4.79476i	0.250285i	−0.992139	+	0.125142i	$0.960061\pi$
$368$	4.63555i	0.241645i
$369$	−29.7213	−1.54723
$370$	0	0
$371$	−3.77929	−0.196211
$372$	18.3974i	0.953860i
$373$	15.9485i	0.825783i	0.910780	+	0.412892i	$0.135481\pi$
$373$	15.9485i	0.825783i	−0.910780	+	0.412892i	$0.864519\pi$
$374$	−0.410470	−0.0212249
$375$	0	0
$376$	8.12628	0.419081
$377$	63.7597i	3.28379i
$378$	− 23.9605i	− 1.23240i
$379$	16.8013	0.863025	0.431513	−	0.902107i	$-0.357980\pi$
$379$	16.8013	0.863025	0.431513	+	0.902107i	$0.357980\pi$
$380$	0	0
$381$	−28.8846	−1.47980
$382$	27.0198i	1.38246i
$383$	26.7948i	1.36915i	0.728943	+	0.684574i	$0.240012\pi$
$383$	26.7948i	1.36915i	−0.728943	+	0.684574i	$0.759988\pi$
$384$	3.03293	0.154774
$385$	0	0
$386$	−23.0713	−1.17430
$387$	− 49.9978i	− 2.54153i
$388$	11.0055i	0.558718i
$389$	−18.3424	−0.929998	−0.464999	−	0.885311i	$-0.653945\pi$
$389$	−18.3424	−0.929998	−0.464999	+	0.885311i	$0.653945\pi$
$390$	0	0
$391$	2.61046	0.132017
$392$	0.900112i	0.0454625i
$393$	52.7817i	2.66248i
$394$	−0.794765	−0.0400397
$395$	0	0
$396$	4.51820	0.227048
$397$	− 21.2162i	− 1.06481i	−0.846490	−	0.532404i	$-0.821289\pi$
$397$	− 21.2162i	− 1.06481i	0.846490	−	0.532404i	$-0.178711\pi$
$398$	8.07241i	0.404633i
$399$	−7.49073	−0.375005
$400$	0	0
$401$	−27.8661	−1.39157	−0.695783	−	0.718252i	$-0.744943\pi$
$401$	−27.8661	−1.39157	−0.695783	+	0.718252i	$0.744943\pi$
$402$	39.2251i	1.95637i
$403$	− 37.8002i	− 1.88296i
$404$	9.73436	0.484302
$405$	0	0
$406$	25.2700	1.25413
$407$	4.17577i	0.206985i
$408$	− 1.70796i	− 0.0845568i
$409$	18.0899	0.894487	0.447243	−	0.894412i	$-0.352406\pi$
$409$	18.0899	0.894487	0.447243	+	0.894412i	$0.352406\pi$
$410$	0	0
$411$	−6.85171	−0.337970
$412$	8.33151i	0.410464i
$413$	− 14.2305i	− 0.700239i
$414$	−28.7344	−1.41222
$415$	0	0
$416$	−6.23163	−0.305531
$417$	51.1372i	2.50420i
$418$	− 0.728896i	− 0.0356515i
$419$	15.3370	0.749260	0.374630	−	0.927174i	$-0.377770\pi$
$419$	15.3370	0.749260	0.374630	+	0.927174i	$0.377770\pi$
$420$	0	0
$421$	−8.42486	−0.410602	−0.205301	−	0.978699i	$-0.565817\pi$
$421$	−8.42486	−0.410602	−0.205301	+	0.978699i	$0.565817\pi$
$422$	11.6410i	0.566676i
$423$	50.3723i	2.44918i
$424$	1.53020	0.0743133
$425$	0	0
$426$	13.3370	0.646178
$427$	− 27.0185i	− 1.30752i
$428$	− 15.0264i	− 0.726328i
$429$	−13.7762	−0.665122
$430$	0	0
$431$	16.2766	0.784014	0.392007	−	0.919962i	$-0.371781\pi$
$431$	16.2766	0.784014	0.392007	+	0.919962i	$0.371781\pi$
$432$	9.70142i	0.466760i
$433$	− 18.1976i	− 0.874521i	−0.899335	−	0.437261i	$-0.855949\pi$
$433$	− 18.1976i	− 0.874521i	0.899335	−	0.437261i	$-0.144051\pi$
$434$	−14.9815	−0.719133
$435$	0	0
$436$	−13.6619	−0.654288
$437$	4.63555i	0.221749i
$438$	12.4148i	0.593204i
$439$	−20.4214	−0.974660	−0.487330	−	0.873218i	$-0.662029\pi$
$439$	−20.4214	−0.974660	−0.487330	+	0.873218i	$0.662029\pi$
$440$	0	0
$441$	−5.57952	−0.265691
$442$	3.50927i	0.166919i
$443$	21.6685i	1.02950i	0.857340	+	0.514750i	$0.172115\pi$
$443$	21.6685i	1.02950i	−0.857340	+	0.514750i	$0.827885\pi$
$444$	−17.3754	−0.824598
$445$	0	0
$446$	−15.6554	−0.741305
$447$	− 39.4447i	− 1.86567i
$448$	2.46980i	0.116687i
$449$	−23.8133	−1.12382	−0.561910	−	0.827198i	$-0.689933\pi$
$449$	−23.8133	−1.12382	−0.561910	+	0.827198i	$0.689933\pi$
$450$	0	0
$451$	3.49489	0.164568
$452$	− 1.20524i	− 0.0566895i
$453$	− 53.3479i	− 2.50650i
$454$	−4.80131	−0.225337
$455$	0	0
$456$	3.03293	0.142030
$457$	− 9.15813i	− 0.428399i	−0.976790	−	0.214200i	$-0.931286\pi$
$457$	− 9.15813i	− 0.428399i	0.976790	−	0.214200i	$-0.0687143\pi$
$458$	2.79476i	0.130591i
$459$	5.46325	0.255003
$460$	0	0
$461$	−7.78931	−0.362784	−0.181392	−	0.983411i	$-0.558060\pi$
$461$	−7.78931	−0.362784	−0.181392	+	0.983411i	$0.558060\pi$
$462$	5.45996i	0.254020i
$463$	0.405011i	0.0188225i	0.999956	+	0.00941123i	$0.00299573\pi$
$463$	0.405011i	0.0188225i	−0.999956	+	0.00941123i	$0.997004\pi$
$464$	−10.2316	−0.474991
$465$	0	0
$466$	11.5422	0.534682
$467$	1.95814i	0.0906118i	0.998973	+	0.0453059i	$0.0144262\pi$
$467$	1.95814i	0.0906118i	−0.998973	+	0.0453059i	$0.985574\pi$
$468$	− 38.6279i	− 1.78558i
$469$	−31.9420	−1.47494
$470$	0	0
$471$	−28.8846	−1.33093
$472$	5.76183i	0.265210i
$473$	5.87918i	0.270325i
$474$	46.5160	2.13655
$475$	0	0
$476$	1.39084	0.0637490
$477$	9.48527i	0.434301i
$478$	− 26.2251i	− 1.19951i
$479$	22.9210	1.04729	0.523645	−	0.851937i	$-0.324572\pi$
$479$	22.9210	1.04729	0.523645	+	0.851937i	$0.324572\pi$
$480$	0	0
$481$	35.7003	1.62780
$482$	12.0659i	0.549585i
$483$	− 34.7237i	− 1.57998i
$484$	10.4687	0.475850
$485$	0	0
$486$	−3.73544	−0.169443
$487$	23.9450i	1.08505i	0.840038	+	0.542527i	$0.182532\pi$
$487$	23.9450i	1.08505i	−0.840038	+	0.542527i	$0.817468\pi$
$488$	10.9396i	0.495212i
$489$	40.0109	1.80936
$490$	0	0
$491$	3.86826	0.174572	0.0872861	−	0.996183i	$-0.472181\pi$
$491$	3.86826	0.174572	0.0872861	+	0.996183i	$0.472181\pi$
$492$	14.5422i	0.655613i
$493$	5.76183i	0.259500i
$494$	−6.23163	−0.280374
$495$	0	0
$496$	6.06587	0.272366
$497$	10.8606i	0.487166i
$498$	− 23.8242i	− 1.06759i
$499$	7.92104	0.354595	0.177297	−	0.984157i	$-0.443265\pi$
$499$	7.92104	0.354595	0.177297	+	0.984157i	$0.443265\pi$
$500$	0	0
$501$	−5.49966	−0.245706
$502$	− 13.5237i	− 0.603591i
$503$	− 16.6949i	− 0.744388i	−0.928155	−	0.372194i	$-0.878606\pi$
$503$	− 16.6949i	− 0.744388i	0.928155	−	0.372194i	$-0.121394\pi$
$504$	−15.3095	−0.681939
$505$	0	0
$506$	3.37884	0.150208
$507$	78.3503i	3.47966i
$508$	9.52366i	0.422544i
$509$	−24.4028	−1.08164	−0.540818	−	0.841139i	$-0.681885\pi$
$509$	−24.4028	−1.08164	−0.540818	+	0.841139i	$0.681885\pi$
$510$	0	0
$511$	−10.1097	−0.447228
$512$	− 1.00000i	− 0.0441942i
$513$	9.70142i	0.428328i
$514$	−22.7398	−1.00301
$515$	0	0
$516$	−24.4633	−1.07693
$517$	− 5.92321i	− 0.260503i
$518$	− 14.1492i	− 0.621680i
$519$	−37.9834	−1.66729
$520$	0	0
$521$	26.0659	1.14197	0.570983	−	0.820962i	$-0.306562\pi$
$521$	26.0659	1.14197	0.570983	+	0.820962i	$0.306562\pi$
$522$	− 63.4227i	− 2.77594i
$523$	17.8726i	0.781516i	0.920493	+	0.390758i	$0.127787\pi$
$523$	17.8726i	0.781516i	−0.920493	+	0.390758i	$0.872213\pi$
$524$	17.4028	0.760247
$525$	0	0
$526$	−6.67395	−0.290998
$527$	− 3.41593i	− 0.148800i
$528$	− 2.21069i	− 0.0962081i
$529$	1.51166	0.0657243
$530$	0	0
$531$	−35.7158	−1.54993
$532$	2.46980i	0.107079i
$533$	− 29.8792i	− 1.29421i
$534$	−30.3293	−1.31248
$535$	0	0
$536$	12.9330	0.558623
$537$	4.23817i	0.182891i
$538$	− 29.7398i	− 1.28217i
$539$	0.656088	0.0282597
$540$	0	0
$541$	23.0604	0.991444	0.495722	−	0.868481i	$-0.334903\pi$
$541$	23.0604	0.991444	0.495722	+	0.868481i	$0.334903\pi$
$542$	− 1.11189i	− 0.0477598i
$543$	− 17.3754i	− 0.745648i
$544$	−0.563139	−0.0241444
$545$	0	0
$546$	46.6794	1.99769
$547$	27.7584i	1.18686i	0.804885	+	0.593431i	$0.202227\pi$
$547$	27.7584i	1.18686i	−0.804885	+	0.593431i	$0.797773\pi$
$548$	2.25910i	0.0965040i
$549$	−67.8111	−2.89411
$550$	0	0
$551$	−10.2316	−0.435882
$552$	14.0593i	0.598405i
$553$	37.8792i	1.61079i
$554$	−13.1263	−0.557682
$555$	0	0
$556$	16.8606	0.715050
$557$	8.60808i	0.364736i	0.983230	+	0.182368i	$0.0583762\pi$
$557$	8.60808i	0.364736i	−0.983230	+	0.182368i	$0.941624\pi$
$558$	37.6004i	1.59175i
$559$	50.2635	2.12592
$560$	0	0
$561$	−1.24493	−0.0525609
$562$	− 22.9265i	− 0.967096i
$563$	7.93959i	0.334614i	0.985905	+	0.167307i	$0.0535071\pi$
$563$	7.93959i	0.334614i	−0.985905	+	0.167307i	$0.946493\pi$
$564$	24.6465	1.03780
$565$	0	0
$566$	0.860634	0.0361751
$567$	− 26.7422i	− 1.12307i
$568$	− 4.39738i	− 0.184510i
$569$	1.65757	0.0694889	0.0347444	−	0.999396i	$-0.488938\pi$
$569$	1.65757	0.0694889	0.0347444	+	0.999396i	$0.488938\pi$
$570$	0	0
$571$	−14.0528	−0.588091	−0.294045	−	0.955791i	$-0.595002\pi$
$571$	−14.0528	−0.588091	−0.294045	+	0.955791i	$0.595002\pi$
$572$	4.54221i	0.189919i
$573$	81.9494i	3.42349i
$574$	−11.8421	−0.494279
$575$	0	0
$576$	6.19869	0.258279
$577$	1.36445i	0.0568027i	0.999597	+	0.0284014i	$0.00904165\pi$
$577$	1.36445i	0.0568027i	−0.999597	+	0.0284014i	$0.990958\pi$
$578$	− 16.6829i	− 0.693916i
$579$	−69.9738	−2.90801
$580$	0	0
$581$	19.4007	0.804876
$582$	33.3788i	1.38360i
$583$	− 1.11536i	− 0.0461935i
$584$	4.09334	0.169384
$585$	0	0
$586$	19.8212	0.818804
$587$	24.6609i	1.01786i	0.860807	+	0.508931i	$0.169959\pi$
$587$	24.6609i	1.01786i	−0.860807	+	0.508931i	$0.830041\pi$
$588$	2.72998i	0.112583i
$589$	6.06587	0.249940
$590$	0	0
$591$	−2.41047	−0.0991535
$592$	5.72890i	0.235456i
$593$	− 0.747443i	− 0.0306938i	−0.999882	−	0.0153469i	$-0.995115\pi$
$593$	− 0.747443i	− 0.0306938i	0.999882	−	0.0153469i	$-0.00488526\pi$
$594$	7.07133	0.290140
$595$	0	0
$596$	−13.0055	−0.532724
$597$	24.4831i	1.00203i
$598$	− 28.8870i	− 1.18128i
$599$	−1.40501	−0.0574072	−0.0287036	−	0.999588i	$-0.509138\pi$
$599$	−1.40501	−0.0574072	−0.0287036	+	0.999588i	$0.509138\pi$
$600$	0	0
$601$	29.7453	1.21334	0.606668	−	0.794956i	$-0.292506\pi$
$601$	29.7453	1.21334	0.606668	+	0.794956i	$0.292506\pi$
$602$	− 19.9210i	− 0.811921i
$603$	80.1680i	3.26469i
$604$	−17.5895	−0.715708
$605$	0	0
$606$	29.5237	1.19932
$607$	− 5.66849i	− 0.230077i	−0.993361	−	0.115038i	$-0.963301\pi$
$607$	− 5.66849i	− 0.230077i	0.993361	−	0.115038i	$-0.0366991\pi$
$608$	− 1.00000i	− 0.0405554i
$609$	76.6423	3.10570
$610$	0	0
$611$	−50.6399	−2.04867
$612$	− 3.49073i	− 0.141104i
$613$	− 2.99454i	− 0.120948i	−0.998170	−	0.0604742i	$-0.980739\pi$
$613$	− 2.99454i	− 0.120948i	0.998170	−	0.0604742i	$-0.0192613\pi$
$614$	16.8661	0.680660
$615$	0	0
$616$	1.80022	0.0725331
$617$	32.3370i	1.30184i	0.759147	+	0.650919i	$0.225616\pi$
$617$	32.3370i	1.30184i	−0.759147	+	0.650919i	$0.774384\pi$
$618$	25.2689i	1.01647i
$619$	20.9265	0.841107	0.420554	−	0.907268i	$-0.361836\pi$
$619$	20.9265	0.841107	0.420554	+	0.907268i	$0.361836\pi$
$620$	0	0
$621$	−44.9714	−1.80464
$622$	− 10.3250i	− 0.413994i
$623$	− 24.6980i	− 0.989503i
$624$	−18.9001	−0.756610
$625$	0	0
$626$	−15.7684	−0.630231
$627$	− 2.21069i	− 0.0882866i
$628$	9.52366i	0.380035i
$629$	3.22617	0.128636
$630$	0	0
$631$	22.8002	0.907663	0.453831	−	0.891088i	$-0.350057\pi$
$631$	22.8002	0.907663	0.453831	+	0.891088i	$0.350057\pi$
$632$	− 15.3370i	− 0.610072i
$633$	35.3064i	1.40330i
$634$	2.17230	0.0862731
$635$	0	0
$636$	4.64101	0.184028
$637$	− 5.60916i	− 0.222243i
$638$	7.45779i	0.295257i
$639$	27.2580	1.07831
$640$	0	0
$641$	36.3184	1.43449	0.717246	−	0.696820i	$-0.245402\pi$
$641$	36.3184	1.43449	0.717246	+	0.696820i	$0.245402\pi$
$642$	− 45.5741i	− 1.79866i
$643$	13.6135i	0.536865i	0.963298	+	0.268433i	$0.0865057\pi$
$643$	13.6135i	0.536865i	−0.963298	+	0.268433i	$0.913494\pi$
$644$	−11.4489	−0.451148
$645$	0	0
$646$	−0.563139	−0.0221564
$647$	0.0724126i	0.00284683i	0.999999	+	0.00142342i	$0.000453088\pi$
$647$	0.0724126i	0.00284683i	−0.999999	+	0.00142342i	$0.999547\pi$
$648$	10.8277i	0.425352i
$649$	4.19978	0.164856
$650$	0	0
$651$	−45.4378	−1.78085
$652$	− 13.1921i	− 0.516644i
$653$	− 43.5346i	− 1.70364i	−0.523835	−	0.851820i	$-0.675499\pi$
$653$	− 43.5346i	− 1.70364i	0.523835	−	0.851820i	$-0.324501\pi$
$654$	−41.4358	−1.62027
$655$	0	0
$656$	4.79476	0.187204
$657$	25.3734i	0.989910i
$658$	20.0702i	0.782420i
$659$	33.4512	1.30308	0.651538	−	0.758616i	$-0.274124\pi$
$659$	33.4512	1.30308	0.651538	+	0.758616i	$0.274124\pi$
$660$	0	0
$661$	−2.89465	−0.112589	−0.0562945	−	0.998414i	$-0.517929\pi$
$661$	−2.89465	−0.112589	−0.0562945	+	0.998414i	$0.517929\pi$
$662$	− 11.9791i	− 0.465580i
$663$	10.6434i	0.413355i
$664$	−7.85517	−0.304840
$665$	0	0
$666$	−35.5117	−1.37605
$667$	− 47.4292i	− 1.83647i
$668$	1.81331i	0.0701591i
$669$	−47.4818	−1.83575
$670$	0	0
$671$	7.97382	0.307826
$672$	7.49073i	0.288961i
$673$	42.8475i	1.65165i	0.563925	+	0.825826i	$0.309291\pi$
$673$	42.8475i	1.65165i	−0.563925	+	0.825826i	$0.690709\pi$
$674$	11.1921	0.431105
$675$	0	0
$676$	25.8332	0.993583
$677$	− 34.4567i	− 1.32428i	−0.749381	−	0.662139i	$-0.769649\pi$
$677$	− 34.4567i	− 1.32428i	0.749381	−	0.662139i	$-0.230351\pi$
$678$	− 3.65540i	− 0.140385i
$679$	−27.1812	−1.04312
$680$	0	0
$681$	−14.5621	−0.558019
$682$	− 4.42139i	− 0.169304i
$683$	− 2.73436i	− 0.104627i	−0.998631	−	0.0523136i	$-0.983340\pi$
$683$	− 2.73436i	− 0.104627i	0.998631	−	0.0523136i	$-0.0166595\pi$
$684$	6.19869	0.237013
$685$	0	0
$686$	−19.5117	−0.744959
$687$	8.47634i	0.323393i
$688$	8.06587i	0.307508i
$689$	−9.53566	−0.363280
$690$	0	0
$691$	−4.74198	−0.180394	−0.0901968	−	0.995924i	$-0.528750\pi$
$691$	−4.74198	−0.180394	−0.0901968	+	0.995924i	$0.528750\pi$
$692$	12.5237i	0.476078i
$693$	11.1590i	0.423897i
$694$	20.3843	0.773777
$695$	0	0
$696$	−31.0318	−1.17626
$697$	− 2.70012i	− 0.102274i
$698$	− 0.252557i	− 0.00955943i
$699$	35.0068	1.32408
$700$	0	0
$701$	33.1372	1.25157	0.625787	−	0.779994i	$-0.284778\pi$
$701$	33.1372	1.25157	0.625787	+	0.779994i	$0.284778\pi$
$702$	− 60.4556i	− 2.28175i
$703$	5.72890i	0.216069i
$704$	−0.728896	−0.0274713
$705$	0	0
$706$	−28.6434	−1.07801
$707$	24.0419i	0.904187i
$708$	17.4753i	0.656760i
$709$	−5.37884	−0.202006	−0.101003	−	0.994886i	$-0.532205\pi$
$709$	−5.37884	−0.202006	−0.101003	+	0.994886i	$0.532205\pi$
$710$	0	0
$711$	95.0692	3.56537
$712$	10.0000i	0.374766i
$713$	28.1187i	1.05305i
$714$	4.21832	0.157867
$715$	0	0
$716$	1.39738	0.0522226
$717$	− 79.5390i	− 2.97044i
$718$	− 18.5741i	− 0.693178i
$719$	−33.0857	−1.23389	−0.616944	−	0.787007i	$-0.711630\pi$
$719$	−33.0857	−1.23389	−0.616944	+	0.787007i	$0.711630\pi$
$720$	0	0
$721$	−20.5771	−0.766332
$722$	− 1.00000i	− 0.0372161i
$723$	36.5950i	1.36098i
$724$	−5.72890	−0.212913
$725$	0	0
$726$	31.7509	1.17839
$727$	− 2.62463i	− 0.0973423i	−0.998815	−	0.0486711i	$-0.984501\pi$
$727$	− 2.62463i	− 0.0973423i	0.998815	−	0.0486711i	$-0.0154986\pi$
$728$	− 15.3908i	− 0.570422i
$729$	21.1538	0.783472
$730$	0	0
$731$	4.54221	0.168000
$732$	33.1791i	1.22633i
$733$	0.608077i	0.0224598i	0.999937	+	0.0112299i	$0.00357467\pi$
$733$	0.608077i	0.0224598i	−0.999937	+	0.0112299i	$0.996425\pi$
$734$	4.79476	0.176978
$735$	0	0
$736$	4.63555	0.170869
$737$	− 9.42685i	− 0.347242i
$738$	29.7213i	1.09405i
$739$	−36.3974	−1.33890	−0.669450	−	0.742857i	$-0.733470\pi$
$739$	−36.3974	−1.33890	−0.669450	+	0.742857i	$0.733470\pi$
$740$	0	0
$741$	−18.9001	−0.694313
$742$	3.77929i	0.138742i
$743$	− 23.0713i	− 0.846405i	−0.906035	−	0.423202i	$-0.860906\pi$
$743$	− 23.0713i	− 0.846405i	0.906035	−	0.423202i	$-0.139094\pi$
$744$	18.3974	0.674481
$745$	0	0
$746$	15.9485	0.583917
$747$	− 48.6918i	− 1.78154i
$748$	0.410470i	0.0150083i
$749$	37.1121	1.35605
$750$	0	0
$751$	4.75290	0.173436	0.0867179	−	0.996233i	$-0.472362\pi$
$751$	4.75290	0.173436	0.0867179	+	0.996233i	$0.472362\pi$
$752$	− 8.12628i	− 0.296335i
$753$	− 41.0164i	− 1.49472i
$754$	63.7597	2.32199
$755$	0	0
$756$	−23.9605	−0.871436
$757$	− 26.8057i	− 0.974269i	−0.873327	−	0.487135i	$-0.838042\pi$
$757$	− 26.8057i	− 0.974269i	0.873327	−	0.487135i	$-0.161958\pi$
$758$	− 16.8013i	− 0.610251i
$759$	10.2478	0.371971
$760$	0	0
$761$	25.4478	0.922481	0.461241	−	0.887275i	$-0.347404\pi$
$761$	25.4478	0.922481	0.461241	+	0.887275i	$0.347404\pi$
$762$	28.8846i	1.04638i
$763$	− 33.7422i	− 1.22155i
$764$	27.0198	0.977544
$765$	0	0
$766$	26.7948	0.968134
$767$	− 35.9056i	− 1.29648i
$768$	− 3.03293i	− 0.109442i
$769$	14.6421	0.528007	0.264004	−	0.964522i	$-0.414957\pi$
$769$	14.6421	0.528007	0.264004	+	0.964522i	$0.414957\pi$
$770$	0	0
$771$	−68.9684	−2.48384
$772$	23.0713i	0.830355i
$773$	− 16.8462i	− 0.605917i	−0.953004	−	0.302959i	$-0.902026\pi$
$773$	− 16.8462i	− 0.605917i	0.953004	−	0.302959i	$-0.0979744\pi$
$774$	−49.9978	−1.79713
$775$	0	0
$776$	11.0055	0.395073
$777$	− 42.9136i	− 1.53952i
$778$	18.3424i	0.657608i
$779$	4.79476	0.171790
$780$	0	0
$781$	−3.20524	−0.114692
$782$	− 2.61046i	− 0.0933499i
$783$	− 99.2613i	− 3.54731i
$784$	0.900112	0.0321469
$785$	0	0
$786$	52.7817	1.88266
$787$	− 18.7367i	− 0.667893i	−0.942592	−	0.333946i	$-0.891620\pi$
$787$	− 18.7367i	− 0.667893i	0.942592	−	0.333946i	$-0.108380\pi$
$788$	0.794765i	0.0283123i
$789$	−20.2416	−0.720621
$790$	0	0
$791$	2.97668	0.105839
$792$	− 4.51820i	− 0.160547i
$793$	− 68.1714i	− 2.42084i
$794$	−21.2162	−0.752933
$795$	0	0
$796$	8.07241	0.286119
$797$	37.9900i	1.34567i	0.739791	+	0.672837i	$0.234925\pi$
$797$	37.9900i	1.34567i	−0.739791	+	0.672837i	$0.765075\pi$
$798$	7.49073i	0.265169i
$799$	−4.57623	−0.161895
$800$	0	0
$801$	−61.9869	−2.19020
$802$	27.8661i	0.983986i
$803$	− 2.98362i	− 0.105290i
$804$	39.2251	1.38336
$805$	0	0
$806$	−37.8002	−1.33146
$807$	− 90.1989i	− 3.17515i
$808$	− 9.73436i	− 0.342453i
$809$	−21.8857	−0.769461	−0.384731	−	0.923029i	$-0.625706\pi$
$809$	−21.8857	−0.769461	−0.384731	+	0.923029i	$0.625706\pi$
$810$	0	0
$811$	37.8595	1.32943	0.664714	−	0.747098i	$-0.268553\pi$
$811$	37.8595	1.32943	0.664714	+	0.747098i	$0.268553\pi$
$812$	− 25.2700i	− 0.886804i
$813$	− 3.37229i	− 0.118271i
$814$	4.17577	0.146361
$815$	0	0
$816$	−1.70796	−0.0597907
$817$	8.06587i	0.282189i
$818$	− 18.0899i	− 0.632498i
$819$	95.4031	3.33365
$820$	0	0
$821$	−20.1976	−0.704901	−0.352451	−	0.935830i	$-0.614652\pi$
$821$	−20.1976	−0.704901	−0.352451	+	0.935830i	$0.614652\pi$
$822$	6.85171i	0.238981i
$823$	− 4.34590i	− 0.151489i	−0.997127	−	0.0757443i	$-0.975867\pi$
$823$	− 4.34590i	− 0.151489i	0.997127	−	0.0757443i	$-0.0241333\pi$
$824$	8.33151	0.290242
$825$	0	0
$826$	−14.2305	−0.495144
$827$	56.8375i	1.97643i	0.153057	+	0.988217i	$0.451088\pi$
$827$	56.8375i	1.97643i	−0.153057	+	0.988217i	$0.548912\pi$
$828$	28.7344i	0.998588i
$829$	17.4543	0.606214	0.303107	−	0.952957i	$-0.401976\pi$
$829$	17.4543	0.606214	0.303107	+	0.952957i	$0.401976\pi$
$830$	0	0
$831$	−39.8111	−1.38103
$832$	6.23163i	0.216043i
$833$	− 0.506888i	− 0.0175626i
$834$	51.1372	1.77074
$835$	0	0
$836$	−0.728896	−0.0252094
$837$	58.8475i	2.03407i
$838$	− 15.3370i	− 0.529807i
$839$	−1.77622	−0.0613219	−0.0306609	−	0.999530i	$-0.509761\pi$
$839$	−1.77622	−0.0613219	−0.0306609	+	0.999530i	$0.509761\pi$
$840$	0	0
$841$	75.6862	2.60987
$842$	8.42486i	0.290340i
$843$	− 69.5346i	− 2.39490i
$844$	11.6410	0.400700
$845$	0	0
$846$	50.3723	1.73184
$847$	25.8556i	0.888408i
$848$	− 1.53020i	− 0.0525475i
$849$	2.61025	0.0895834
$850$	0	0
$851$	−26.5566	−0.910348
$852$	− 13.3370i	− 0.456917i
$853$	− 16.1187i	− 0.551892i	−0.961173	−	0.275946i	$-0.911009\pi$
$853$	− 16.1187i	− 0.551892i	0.961173	−	0.275946i	$-0.0889911\pi$
$854$	−27.0185	−0.924556
$855$	0	0
$856$	−15.0264	−0.513591
$857$	47.2031i	1.61243i	0.591625	+	0.806213i	$0.298486\pi$
$857$	47.2031i	1.61243i	−0.591625	+	0.806213i	$0.701514\pi$
$858$	13.7762i	0.470312i
$859$	−37.3239	−1.27347	−0.636737	−	0.771081i	$-0.719716\pi$
$859$	−37.3239	−1.27347	−0.636737	+	0.771081i	$0.719716\pi$
$860$	0	0
$861$	−35.9163	−1.22402
$862$	− 16.2766i	− 0.554382i
$863$	− 1.33697i	− 0.0455111i	−0.999741	−	0.0227555i	$-0.992756\pi$
$863$	− 1.33697i	− 0.0455111i	0.999741	−	0.0227555i	$-0.00724394\pi$
$864$	9.70142	0.330049
$865$	0	0
$866$	−18.1976	−0.618380
$867$	− 50.5981i	− 1.71840i
$868$	14.9815i	0.508504i
$869$	−11.1791	−0.379224
$870$	0	0
$871$	−80.5939	−2.73082
$872$	13.6619i	0.462652i
$873$	68.2194i	2.30888i
$874$	4.63555	0.156800
$875$	0	0
$876$	12.4148	0.419459
$877$	− 13.1647i	− 0.444539i	−0.974985	−	0.222270i	$-0.928653\pi$
$877$	− 13.1647i	− 0.444539i	0.974985	−	0.222270i	$-0.0713465\pi$
$878$	20.4214i	0.689188i
$879$	60.1163	2.02767
$880$	0	0
$881$	−10.2052	−0.343823	−0.171912	−	0.985112i	$-0.554994\pi$
$881$	−10.2052	−0.343823	−0.171912	+	0.985112i	$0.554994\pi$
$882$	5.57952i	0.187872i
$883$	1.49966i	0.0504674i	0.999682	+	0.0252337i	$0.00803299\pi$
$883$	1.49966i	0.0504674i	−0.999682	+	0.0252337i	$0.991967\pi$
$884$	3.50927	0.118030
$885$	0	0
$886$	21.6685	0.727967
$887$	46.9505i	1.57644i	0.615391	+	0.788222i	$0.288998\pi$
$887$	46.9505i	1.57644i	−0.615391	+	0.788222i	$0.711002\pi$
$888$	17.3754i	0.583079i
$889$	−23.5215	−0.788886
$890$	0	0
$891$	7.89227	0.264401
$892$	15.6554i	0.524182i
$893$	− 8.12628i	− 0.271936i
$894$	−39.4447	−1.31923
$895$	0	0
$896$	2.46980	0.0825101
$897$	− 87.6125i	− 2.92529i
$898$	23.8133i	0.794661i
$899$	−62.0637	−2.06994
$900$	0	0
$901$	−0.861719	−0.0287080
$902$	− 3.49489i	− 0.116367i
$903$	− 60.4192i	− 2.01063i
$904$	−1.20524	−0.0400855
$905$	0	0
$906$	−53.3479	−1.77236
$907$	− 16.3668i	− 0.543452i	−0.962375	−	0.271726i	$-0.912406\pi$
$907$	− 16.3668i	− 0.543452i	0.962375	−	0.271726i	$-0.0875944\pi$
$908$	4.80131i	0.159337i
$909$	60.3403	2.00136
$910$	0	0
$911$	32.3293	1.07112	0.535559	−	0.844498i	$-0.320101\pi$
$911$	32.3293	1.07112	0.535559	+	0.844498i	$0.320101\pi$
$912$	− 3.03293i	− 0.100430i
$913$	5.72561i	0.189490i
$914$	−9.15813	−0.302924
$915$	0	0
$916$	2.79476	0.0923416
$917$	42.9815i	1.41937i
$918$	− 5.46325i	− 0.180314i
$919$	22.8157	0.752620	0.376310	−	0.926494i	$-0.377193\pi$
$919$	22.8157	0.752620	0.376310	+	0.926494i	$0.377193\pi$
$920$	0	0
$921$	51.1538	1.68557
$922$	7.78931i	0.256527i
$923$	27.4028i	0.901976i
$924$	5.45996	0.179620
$925$	0	0
$926$	0.405011	0.0133095
$927$	51.6445i	1.69623i
$928$	10.2316i	0.335870i
$929$	27.2436	0.893834	0.446917	−	0.894575i	$-0.352522\pi$
$929$	27.2436	0.893834	0.446917	+	0.894575i	$0.352522\pi$
$930$	0	0
$931$	0.900112	0.0295000
$932$	− 11.5422i	− 0.378078i
$933$	− 31.3150i	− 1.02521i
$934$	1.95814	0.0640722
$935$	0	0
$936$	−38.6279	−1.26259
$937$	51.5006i	1.68245i	0.540685	+	0.841225i	$0.318165\pi$
$937$	51.5006i	1.68245i	−0.540685	+	0.841225i	$0.681835\pi$
$938$	31.9420i	1.04294i
$939$	−47.8244	−1.56069
$940$	0	0
$941$	−40.8541	−1.33181	−0.665903	−	0.746039i	$-0.731953\pi$
$941$	−40.8541	−1.33181	−0.665903	+	0.746039i	$0.731953\pi$
$942$	28.8846i	0.941112i
$943$	22.2264i	0.723791i
$944$	5.76183	0.187532
$945$	0	0
$946$	5.87918	0.191149
$947$	− 38.2526i	− 1.24304i	−0.783398	−	0.621521i	$-0.786515\pi$
$947$	− 38.2526i	− 1.24304i	0.783398	−	0.621521i	$-0.213485\pi$
$948$	− 46.5160i	− 1.51077i
$949$	−25.5082	−0.828031
$950$	0	0
$951$	6.58845	0.213645
$952$	− 1.39084i	− 0.0450773i
$953$	54.1187i	1.75308i	0.481334	+	0.876538i	$0.340153\pi$
$953$	54.1187i	1.75308i	−0.481334	+	0.876538i	$0.659847\pi$
$954$	9.48527	0.307097
$955$	0	0
$956$	−26.2251	−0.848180
$957$	22.6190i	0.731168i
$958$	− 22.9210i	− 0.740545i
$959$	−5.57952	−0.180172
$960$	0	0
$961$	5.79476	0.186928
$962$	− 35.7003i	− 1.15103i
$963$	− 93.1440i	− 3.00152i
$964$	12.0659	0.388615
$965$	0	0
$966$	−34.7237	−1.11722
$967$	− 28.4214i	− 0.913970i	−0.889474	−	0.456985i	$-0.848929\pi$
$967$	− 28.4214i	− 0.913970i	0.889474	−	0.456985i	$-0.151071\pi$
$968$	− 10.4687i	− 0.336477i
$969$	−1.70796	−0.0548677
$970$	0	0
$971$	30.8057	0.988601	0.494301	−	0.869291i	$-0.335424\pi$
$971$	30.8057	0.988601	0.494301	+	0.869291i	$0.335424\pi$
$972$	3.73544i	0.119814i
$973$	41.6423i	1.33499i
$974$	23.9450	0.767249
$975$	0	0
$976$	10.9396	0.350168
$977$	− 37.6554i	− 1.20470i	−0.798231	−	0.602351i	$-0.794231\pi$
$977$	− 37.6554i	− 1.20470i	0.798231	−	0.602351i	$-0.205769\pi$
$978$	− 40.0109i	− 1.27941i
$979$	7.28896	0.232956
$980$	0	0
$981$	−84.6862	−2.70382
$982$	− 3.86826i	− 0.123441i
$983$	− 38.7948i	− 1.23736i	−0.785643	−	0.618680i	$-0.787668\pi$
$983$	− 38.7948i	− 1.23736i	0.785643	−	0.618680i	$-0.212332\pi$
$984$	14.5422	0.463589
$985$	0	0
$986$	5.76183	0.183494
$987$	60.8717i	1.93757i
$988$	6.23163i	0.198254i
$989$	−37.3898	−1.18893
$990$	0	0
$991$	−15.0295	−0.477427	−0.238713	−	0.971090i	$-0.576726\pi$
$991$	−15.0295	−0.477427	−0.238713	+	0.971090i	$0.576726\pi$
$992$	− 6.06587i	− 0.192592i
$993$	− 36.3317i	− 1.15295i
$994$	10.8606	0.344478
$995$	0	0
$996$	−23.8242	−0.754900
$997$	− 1.18123i	− 0.0374099i	−0.999825	−	0.0187050i	$-0.994046\pi$
$997$	− 1.18123i	− 0.0374099i	0.999825	−	0.0187050i	$-0.00595432\pi$
$998$	− 7.92104i	− 0.250736i
$999$	−55.5784	−1.75842

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.b.g.799.1		6
5.2	odd	4		950.2.a.m.1.1	yes	3
5.3	odd	4		950.2.a.k.1.3	✓	3
5.4	even	2	inner	950.2.b.g.799.6		6
15.2	even	4		8550.2.a.cj.1.2		3
15.8	even	4		8550.2.a.co.1.2		3
20.3	even	4		7600.2.a.cb.1.1		3
20.7	even	4		7600.2.a.bm.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.a.k.1.3	✓	3	5.3	odd	4
950.2.a.m.1.1	yes	3	5.2	odd	4
950.2.b.g.799.1		6	1.1	even	1	trivial
950.2.b.g.799.6		6	5.4	even	2	inner
7600.2.a.bm.1.3		3	20.7	even	4
7600.2.a.cb.1.1		3	20.3	even	4
8550.2.a.cj.1.2		3	15.2	even	4
8550.2.a.co.1.2		3	15.8	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} -3.03293i q^{3} -1.00000 q^{4} -3.03293 q^{6} -2.46980i q^{7} +1.00000i q^{8} -6.19869 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} -3.03293i q^{3} -1.00000 q^{4} -3.03293 q^{6} -2.46980i q^{7} +1.00000i q^{8} -6.19869 q^{9} +0.728896 q^{11} +3.03293i q^{12} -6.23163i q^{13} -2.46980 q^{14} +1.00000 q^{16} -0.563139i q^{17} +6.19869i q^{18} +1.00000 q^{19} -7.49073 q^{21} -0.728896i q^{22} +4.63555i q^{23} +3.03293 q^{24} -6.23163 q^{26} +9.70142i q^{27} +2.46980i q^{28} -10.2316 q^{29} +6.06587 q^{31} -1.00000i q^{32} -2.21069i q^{33} -0.563139 q^{34} +6.19869 q^{36} +5.72890i q^{37} -1.00000i q^{38} -18.9001 q^{39} +4.79476 q^{41} +7.49073i q^{42} +8.06587i q^{43} -0.728896 q^{44} +4.63555 q^{46} -8.12628i q^{47} -3.03293i q^{48} +0.900112 q^{49} -1.70796 q^{51} +6.23163i q^{52} -1.53020i q^{53} +9.70142 q^{54} +2.46980 q^{56} -3.03293i q^{57} +10.2316i q^{58} +5.76183 q^{59} +10.9396 q^{61} -6.06587i q^{62} +15.3095i q^{63} -1.00000 q^{64} -2.21069 q^{66} -12.9330i q^{67} +0.563139i q^{68} +14.0593 q^{69} -4.39738 q^{71} -6.19869i q^{72} -4.09334i q^{73} +5.72890 q^{74} -1.00000 q^{76} -1.80022i q^{77} +18.9001i q^{78} -15.3370 q^{79} +10.8277 q^{81} -4.79476i q^{82} +7.85517i q^{83} +7.49073 q^{84} +8.06587 q^{86} +31.0318i q^{87} +0.728896i q^{88} +10.0000 q^{89} -15.3908 q^{91} -4.63555i q^{92} -18.3974i q^{93} -8.12628 q^{94} -3.03293 q^{96} -11.0055i q^{97} -0.900112i q^{98} -4.51820 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} + 4 q^{6} - 26 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 + 4 * q^6 - 26 * q^9	\( 6 q - 6 q^{4} + 4 q^{6} - 26 q^{9} + 4 q^{11} - 4 q^{14} + 6 q^{16} + 6 q^{19} - 22 q^{21} - 4 q^{24} - 4 q^{26} - 28 q^{29} - 8 q^{31} + 8 q^{34} + 26 q^{36} - 58 q^{39} - 16 q^{41} - 4 q^{44} + 28 q^{46} - 50 q^{49} - 22 q^{51} + 14 q^{54} + 4 q^{56} + 12 q^{59} + 44 q^{61} - 6 q^{64} + 8 q^{66} - 16 q^{69} - 4 q^{71} + 34 q^{74} - 6 q^{76} - 48 q^{79} - 2 q^{81} + 22 q^{84} + 4 q^{86} + 60 q^{89} - 14 q^{91} - 26 q^{94} + 4 q^{96} - 48 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 + 4 * q^6 - 26 * q^9 + 4 * q^11 - 4 * q^14 + 6 * q^16 + 6 * q^19 - 22 * q^21 - 4 * q^24 - 4 * q^26 - 28 * q^29 - 8 * q^31 + 8 * q^34 + 26 * q^36 - 58 * q^39 - 16 * q^41 - 4 * q^44 + 28 * q^46 - 50 * q^49 - 22 * q^51 + 14 * q^54 + 4 * q^56 + 12 * q^59 + 44 * q^61 - 6 * q^64 + 8 * q^66 - 16 * q^69 - 4 * q^71 + 34 * q^74 - 6 * q^76 - 48 * q^79 - 2 * q^81 + 22 * q^84 + 4 * q^86 + 60 * q^89 - 14 * q^91 - 26 * q^94 + 4 * q^96 - 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more