LMFDB - Embedded newform 150.8.c.b.49.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [150,8,Mod(49,150)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("150.49"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(150, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1])) N = Newforms(chi, 8, names="a")

Level:	$N$	$=$	$150 = 2 \cdot 3 \cdot 5^{2}$
Weight:	$k$	$=$	$8$
Character orbit:	$[\chi]$	$=$	150.c (of order $2$ , degree $1$ , not minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,0,-128,0,-432,0,0,-1458,0,-120] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$46.8577538226$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{2} + 1$ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			49.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	150.49
Dual form			150.8.c.b.49.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+8.00000i q^{2} +27.0000i q^{3} -64.0000 q^{4} -216.000 q^{6} +232.000i q^{7} -512.000i q^{8} -729.000 q^{9} -60.0000 q^{11} -1728.00i q^{12} +14054.0i q^{13} -1856.00 q^{14} +4096.00 q^{16} -13938.0i q^{17} -5832.00i q^{18} -53564.0 q^{19} -6264.00 q^{21} -480.000i q^{22} -27000.0i q^{23} +13824.0 q^{24} -112432. q^{26} -19683.0i q^{27} -14848.0i q^{28} +88554.0 q^{29} -120352. q^{31} +32768.0i q^{32} -1620.00i q^{33} +111504. q^{34} +46656.0 q^{36} -469646. i q^{37} -428512. i q^{38} -379458. q^{39} -510246. q^{41} -50112.0i q^{42} +145412. i q^{43} +3840.00 q^{44} +216000. q^{46} -304560. i q^{47} +110592. i q^{48} +769719. q^{49} +376326. q^{51} -899456. i q^{52} +94398.0i q^{53} +157464. q^{54} +118784. q^{56} -1.44623e6i q^{57} +708432. i q^{58} +1.88574e6 q^{59} -271690. q^{61} -962816. i q^{62} -169128. i q^{63} -262144. q^{64} +12960.0 q^{66} -1.07467e6i q^{67} +892032. i q^{68} +729000. q^{69} -2.50548e6 q^{71} +373248. i q^{72} -2.95457e6i q^{73} +3.75717e6 q^{74} +3.42810e6 q^{76} -13920.0i q^{77} -3.03566e6i q^{78} +7.35477e6 q^{79} +531441. q^{81} -4.08197e6i q^{82} -3.84676e6i q^{83} +400896. q^{84} -1.16330e6 q^{86} +2.39096e6i q^{87} +30720.0i q^{88} -5.68516e6 q^{89} -3.26053e6 q^{91} +1.72800e6i q^{92} -3.24950e6i q^{93} +2.43648e6 q^{94} -884736. q^{96} -7.98135e6i q^{97} +6.15775e6i q^{98} +43740.0 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2 q - 128 q^{4} - 432 q^{6} - 1458 q^{9} - 120 q^{11} - 3712 q^{14} + 8192 q^{16} - 107128 q^{19} - 12528 q^{21} + 27648 q^{24} - 224864 q^{26} + 177108 q^{29} - 240704 q^{31} + 223008 q^{34} + 93312 q^{36}+ \cdots + 87480 q^{99}+O(q^{100})$ 2 * q - 128 * q^4 - 432 * q^6 - 1458 * q^9 - 120 * q^11 - 3712 * q^14 + 8192 * q^16 - 107128 * q^19 - 12528 * q^21 + 27648 * q^24 - 224864 * q^26 + 177108 * q^29 - 240704 * q^31 + 223008 * q^34 + 93312 * q^36 - 758916 * q^39 - 1020492 * q^41 + 7680 * q^44 + 432000 * q^46 + 1539438 * q^49 + 752652 * q^51 + 314928 * q^54 + 237568 * q^56 + 3771480 * q^59 - 543380 * q^61 - 524288 * q^64 + 25920 * q^66 + 1458000 * q^69 - 5010960 * q^71 + 7514336 * q^74 + 6856192 * q^76 + 14709536 * q^79 + 1062882 * q^81 + 801792 * q^84 - 2326592 * q^86 - 11370324 * q^89 - 6521056 * q^91 + 4872960 * q^94 - 1769472 * q^96 + 87480 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$ .

$n$	$101$	$127$
$\chi(n)$	$1$	$-1$

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

)

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

$2$	8.00000i	0.707107i
$2$	8.00000i	0.707107i
$3$	27.0000i	0.577350i
$3$	27.0000i	0.577350i
$4$	−64.0000	−0.500000
$5$	0	0
$5$	0	0
$6$	−216.000	−0.408248
$7$	232.000i	0.255649i	0.991797	+	0.127825i	$0.0407995\pi$
$7$	232.000i	0.255649i	−0.991797	+	0.127825i	$0.959201\pi$
$8$	− 512.000i	− 0.353553i
$9$	−729.000	−0.333333
$10$	0	0
$11$	−60.0000	−0.0135918	−0.00679590	−	0.999977i	$-0.502163\pi$
$11$	−60.0000	−0.0135918	−0.00679590	+	0.999977i	$0.502163\pi$
$12$	− 1728.00i	− 0.288675i
$13$	14054.0i	1.77418i	0.461594	+	0.887091i	$0.347278\pi$
$13$	14054.0i	1.77418i	−0.461594	+	0.887091i	$0.652722\pi$
$14$	−1856.00	−0.180771
$15$	0	0
$16$	4096.00	0.250000
$17$	− 13938.0i	− 0.688065i	−0.938958	−	0.344032i	$-0.888207\pi$
$17$	− 13938.0i	− 0.688065i	0.938958	−	0.344032i	$-0.111793\pi$
$18$	− 5832.00i	− 0.235702i
$19$	−53564.0	−1.79158	−0.895788	−	0.444481i	$-0.853388\pi$
$19$	−53564.0	−1.79158	−0.895788	+	0.444481i	$0.853388\pi$
$20$	0	0
$21$	−6264.00	−0.147599
$22$	− 480.000i	− 0.00961085i
$23$	− 27000.0i	− 0.462718i	−0.972868	−	0.231359i	$-0.925683\pi$
$23$	− 27000.0i	− 0.462718i	0.972868	−	0.231359i	$-0.0743172\pi$
$24$	13824.0	0.204124
$25$	0	0
$26$	−112432.	−1.25454
$27$	− 19683.0i	− 0.192450i
$28$	− 14848.0i	− 0.127825i
$29$	88554.0	0.674241	0.337121	−	0.941461i	$-0.390547\pi$
$29$	88554.0	0.674241	0.337121	+	0.941461i	$0.390547\pi$
$30$	0	0
$31$	−120352.	−0.725583	−0.362792	−	0.931870i	$-0.618176\pi$
$31$	−120352.	−0.725583	−0.362792	+	0.931870i	$0.618176\pi$
$32$	32768.0i	0.176777i
$33$	− 1620.00i	− 0.00784723i
$34$	111504.	0.486535
$35$	0	0
$36$	46656.0	0.166667
$37$	− 469646.i	− 1.52428i	−0.647413	−	0.762140i	$-0.724149\pi$
$37$	− 469646.i	− 1.52428i	0.647413	−	0.762140i	$-0.275851\pi$
$38$	− 428512.i	− 1.26684i
$39$	−379458.	−1.02432
$40$	0	0
$41$	−510246.	−1.15621	−0.578104	−	0.815963i	$-0.696207\pi$
$41$	−510246.	−1.15621	−0.578104	+	0.815963i	$0.696207\pi$
$42$	− 50112.0i	− 0.104368i
$43$	145412.i	0.278908i	0.990229	+	0.139454i	$0.0445347\pi$
$43$	145412.i	0.278908i	−0.990229	+	0.139454i	$0.955465\pi$
$44$	3840.00	0.00679590
$45$	0	0
$46$	216000.	0.327191
$47$	− 304560.i	− 0.427888i	−0.976846	−	0.213944i	$-0.931369\pi$
$47$	− 304560.i	− 0.427888i	0.976846	−	0.213944i	$-0.0686310\pi$
$48$	110592.i	0.144338i
$49$	769719.	0.934643
$50$	0	0
$51$	376326.	0.397254
$52$	− 899456.i	− 0.887091i
$53$	94398.0i	0.0870958i	0.999051	+	0.0435479i	$0.0138661\pi$
$53$	94398.0i	0.0870958i	−0.999051	+	0.0435479i	$0.986134\pi$
$54$	157464.	0.136083
$55$	0	0
$56$	118784.	0.0903857
$57$	− 1.44623e6i	− 1.03437i
$58$	708432.i	0.476760i
$59$	1.88574e6	1.19536	0.597681	−	0.801734i	$-0.296089\pi$
$59$	1.88574e6	1.19536	0.597681	+	0.801734i	$0.296089\pi$
$60$	0	0
$61$	−271690.	−0.153257	−0.0766283	−	0.997060i	$-0.524415\pi$
$61$	−271690.	−0.153257	−0.0766283	+	0.997060i	$0.524415\pi$
$62$	− 962816.i	− 0.513065i
$63$	− 169128.i	− 0.0852165i
$64$	−262144.	−0.125000
$65$	0	0
$66$	12960.0	0.00554883
$67$	− 1.07467e6i	− 0.436528i	−0.975890	−	0.218264i	$-0.929961\pi$
$67$	− 1.07467e6i	− 0.436528i	0.975890	−	0.218264i	$-0.0700395\pi$
$68$	892032.i	0.344032i
$69$	729000.	0.267150
$70$	0	0
$71$	−2.50548e6	−0.830781	−0.415391	−	0.909643i	$-0.636355\pi$
$71$	−2.50548e6	−0.830781	−0.415391	+	0.909643i	$0.636355\pi$
$72$	373248.i	0.117851i
$73$	− 2.95457e6i	− 0.888922i	−0.895798	−	0.444461i	$-0.853395\pi$
$73$	− 2.95457e6i	− 0.888922i	0.895798	−	0.444461i	$-0.146605\pi$
$74$	3.75717e6	1.07783
$75$	0	0
$76$	3.42810e6	0.895788
$77$	− 13920.0i	− 0.00347474i
$78$	− 3.03566e6i	− 0.724307i
$79$	7.35477e6	1.67832	0.839159	−	0.543886i	$-0.183048\pi$
$79$	7.35477e6	1.67832	0.839159	+	0.543886i	$0.183048\pi$
$80$	0	0
$81$	531441.	0.111111
$82$	− 4.08197e6i	− 0.817563i
$83$	− 3.84676e6i	− 0.738450i	−0.929340	−	0.369225i	$-0.879623\pi$
$83$	− 3.84676e6i	− 0.738450i	0.929340	−	0.369225i	$-0.120377\pi$
$84$	400896.	0.0737996
$85$	0	0
$86$	−1.16330e6	−0.197218
$87$	2.39096e6i	0.389273i
$88$	30720.0i	0.00480543i
$89$	−5.68516e6	−0.854826	−0.427413	−	0.904056i	$-0.640575\pi$
$89$	−5.68516e6	−0.854826	−0.427413	+	0.904056i	$0.640575\pi$
$90$	0	0
$91$	−3.26053e6	−0.453569
$92$	1.72800e6i	0.231359i
$93$	− 3.24950e6i	− 0.418916i
$94$	2.43648e6	0.302563
$95$	0	0
$96$	−884736.	−0.102062
$97$	− 7.98135e6i	− 0.887923i	−0.896046	−	0.443961i	$-0.853573\pi$
$97$	− 7.98135e6i	− 0.887923i	0.896046	−	0.443961i	$-0.146427\pi$
$98$	6.15775e6i	0.660893i
$99$	43740.0	0.00453060
$100$	0	0
$101$	1.54628e7	1.49336	0.746678	−	0.665186i	$-0.231648\pi$
$101$	1.54628e7	1.49336	0.746678	+	0.665186i	$0.231648\pi$
$102$	3.01061e6i	0.280901i
$103$	− 2.09024e7i	− 1.88480i	−0.334483	−	0.942402i	$-0.608562\pi$
$103$	− 2.09024e7i	− 1.88480i	0.334483	−	0.942402i	$-0.391438\pi$
$104$	7.19565e6	0.627268
$105$	0	0
$106$	−755184.	−0.0615860
$107$	− 2.05645e7i	− 1.62284i	−0.584466	−	0.811418i	$-0.698696\pi$
$107$	− 2.05645e7i	− 1.62284i	0.584466	−	0.811418i	$-0.301304\pi$
$108$	1.25971e6i	0.0962250i
$109$	−1.39850e7	−1.03436	−0.517179	−	0.855877i	$-0.673018\pi$
$109$	−1.39850e7	−1.03436	−0.517179	+	0.855877i	$0.673018\pi$
$110$	0	0
$111$	1.26804e7	0.880043
$112$	950272.i	0.0639124i
$113$	2.64438e7i	1.72405i	0.506868	+	0.862024i	$0.330803\pi$
$113$	2.64438e7i	1.72405i	−0.506868	+	0.862024i	$0.669197\pi$
$114$	1.15698e7	0.731408
$115$	0	0
$116$	−5.66746e6	−0.337121
$117$	− 1.02454e7i	− 0.591394i
$118$	1.50859e7i	0.845249i
$119$	3.23362e6	0.175903
$120$	0	0
$121$	−1.94836e7	−0.999815
$122$	− 2.17352e6i	− 0.108369i
$123$	− 1.37766e7i	− 0.667537i
$124$	7.70253e6	0.362792
$125$	0	0
$126$	1.35302e6	0.0602572
$127$	9.34000e6i	0.404607i	0.979323	+	0.202304i	$0.0648428\pi$
$127$	9.34000e6i	0.404607i	−0.979323	+	0.202304i	$0.935157\pi$
$128$	− 2.09715e6i	− 0.0883883i
$129$	−3.92612e6	−0.161027
$130$	0	0
$131$	−4.46795e7	−1.73644	−0.868219	−	0.496182i	$-0.834735\pi$
$131$	−4.46795e7	−1.73644	−0.868219	+	0.496182i	$0.834735\pi$
$132$	103680.i	0.00392361i
$133$	− 1.24268e7i	− 0.458016i
$134$	8.59734e6	0.308672
$135$	0	0
$136$	−7.13626e6	−0.243268
$137$	5.69929e7i	1.89365i	0.321755	+	0.946823i	$0.395727\pi$
$137$	5.69929e7i	1.89365i	−0.321755	+	0.946823i	$0.604273\pi$
$138$	5.83200e6i	0.188904i
$139$	−3.06822e7	−0.969026	−0.484513	−	0.874784i	$-0.661003\pi$
$139$	−3.06822e7	−0.969026	−0.484513	+	0.874784i	$0.661003\pi$
$140$	0	0
$141$	8.22312e6	0.247041
$142$	− 2.00438e7i	− 0.587451i
$143$	− 843240.i	− 0.0241143i
$144$	−2.98598e6	−0.0833333
$145$	0	0
$146$	2.36365e7	0.628563
$147$	2.07824e7i	0.539617i
$148$	3.00573e7i	0.762140i
$149$	−2.83628e7	−0.702422	−0.351211	−	0.936296i	$-0.614230\pi$
$149$	−2.83628e7	−0.702422	−0.351211	+	0.936296i	$0.614230\pi$
$150$	0	0
$151$	−3.45653e7	−0.816997	−0.408499	−	0.912759i	$-0.633948\pi$
$151$	−3.45653e7	−0.816997	−0.408499	+	0.912759i	$0.633948\pi$
$152$	2.74248e7i	0.633418i
$153$	1.01608e7i	0.229355i
$154$	111360.	0.00245701
$155$	0	0
$156$	2.42853e7	0.512162
$157$	− 5.00660e7i	− 1.03251i	−0.856435	−	0.516255i	$-0.827326\pi$
$157$	− 5.00660e7i	− 1.03251i	0.856435	−	0.516255i	$-0.172674\pi$
$158$	5.88381e7i	1.18675i
$159$	−2.54875e6	−0.0502848
$160$	0	0
$161$	6.26400e6	0.118294
$162$	4.25153e6i	0.0785674i
$163$	− 1.63359e6i	− 0.0295451i	−0.999891	−	0.0147726i	$-0.995298\pi$
$163$	− 1.63359e6i	− 0.0295451i	0.999891	−	0.0147726i	$-0.00470242\pi$
$164$	3.26557e7	0.578104
$165$	0	0
$166$	3.07740e7	0.522163
$167$	9.94818e7i	1.65286i	0.563040	+	0.826430i	$0.309632\pi$
$167$	9.94818e7i	1.65286i	−0.563040	+	0.826430i	$0.690368\pi$
$168$	3.20717e6i	0.0521842i
$169$	−1.34766e8	−2.14772
$170$	0	0
$171$	3.90482e7	0.597192
$172$	− 9.30637e6i	− 0.139454i
$173$	− 1.00775e8i	− 1.47976i	−0.672738	−	0.739881i	$-0.734882\pi$
$173$	− 1.00775e8i	− 1.47976i	0.672738	−	0.739881i	$-0.265118\pi$
$174$	−1.91277e7	−0.275258
$175$	0	0
$176$	−245760.	−0.00339795
$177$	5.09150e7i	0.690143i
$178$	− 4.54813e7i	− 0.604453i
$179$	−8.59163e7	−1.11967	−0.559835	−	0.828604i	$-0.689135\pi$
$179$	−8.59163e7	−1.11967	−0.559835	+	0.828604i	$0.689135\pi$
$180$	0	0
$181$	−7.34951e6	−0.0921262	−0.0460631	−	0.998939i	$-0.514668\pi$
$181$	−7.34951e6	−0.0921262	−0.0460631	+	0.998939i	$0.514668\pi$
$182$	− 2.60842e7i	− 0.320721i
$183$	− 7.33563e6i	− 0.0884827i
$184$	−1.38240e7	−0.163595
$185$	0	0
$186$	2.59960e7	0.296218
$187$	836280.i	0.00935203i
$188$	1.94918e7i	0.213944i
$189$	4.56646e6	0.0491998
$190$	0	0
$191$	2.55529e7	0.265353	0.132676	−	0.991159i	$-0.457643\pi$
$191$	2.55529e7	0.265353	0.132676	+	0.991159i	$0.457643\pi$
$192$	− 7.07789e6i	− 0.0721688i
$193$	1.36815e8i	1.36988i	0.728600	+	0.684940i	$0.240172\pi$
$193$	1.36815e8i	1.36988i	−0.728600	+	0.684940i	$0.759828\pi$
$194$	6.38508e7	0.627856
$195$	0	0
$196$	−4.92620e7	−0.467322
$197$	1.38053e8i	1.28651i	0.765652	+	0.643255i	$0.222417\pi$
$197$	1.38053e8i	1.28651i	−0.765652	+	0.643255i	$0.777583\pi$
$198$	349920.i	0.00320362i
$199$	−6.20415e6	−0.0558080	−0.0279040	−	0.999611i	$-0.508883\pi$
$199$	−6.20415e6	−0.0558080	−0.0279040	+	0.999611i	$0.508883\pi$
$200$	0	0
$201$	2.90160e7	0.252030
$202$	1.23702e8i	1.05596i
$203$	2.05445e7i	0.172369i
$204$	−2.40849e7	−0.198627
$205$	0	0
$206$	1.67219e8	1.33276
$207$	1.96830e7i	0.154239i
$208$	5.75652e7i	0.443546i
$209$	3.21384e6	0.0243507
$210$	0	0
$211$	−1.65042e8	−1.20950	−0.604750	−	0.796416i	$-0.706727\pi$
$211$	−1.65042e8	−1.20950	−0.604750	+	0.796416i	$0.706727\pi$
$212$	− 6.04147e6i	− 0.0435479i
$213$	− 6.76480e7i	− 0.479652i
$214$	1.64516e8	1.14752
$215$	0	0
$216$	−1.00777e7	−0.0680414
$217$	− 2.79217e7i	− 0.185495i
$218$	− 1.11880e8i	− 0.731401i
$219$	7.97733e7	0.513219
$220$	0	0
$221$	1.95885e8	1.22075
$222$	1.01444e8i	0.622284i
$223$	− 5.43117e7i	− 0.327964i	−0.986463	−	0.163982i	$-0.947566\pi$
$223$	− 5.43117e7i	− 0.327964i	0.986463	−	0.163982i	$-0.0524339\pi$
$224$	−7.60218e6	−0.0451929
$225$	0	0
$226$	−2.11550e8	−1.21909
$227$	− 1.33928e8i	− 0.759942i	−0.924998	−	0.379971i	$-0.875934\pi$
$227$	− 1.33928e8i	− 0.759942i	0.924998	−	0.379971i	$-0.124066\pi$
$228$	9.25586e7i	0.517184i
$229$	−2.09843e7	−0.115470	−0.0577351	−	0.998332i	$-0.518388\pi$
$229$	−2.09843e7	−0.115470	−0.0577351	+	0.998332i	$0.518388\pi$
$230$	0	0
$231$	375840.	0.00200614
$232$	− 4.53396e7i	− 0.238380i
$233$	1.21685e7i	0.0630217i	0.999503	+	0.0315109i	$0.0100319\pi$
$233$	1.21685e7i	0.0630217i	−0.999503	+	0.0315109i	$0.989968\pi$
$234$	8.19629e7	0.418179
$235$	0	0
$236$	−1.20687e8	−0.597681
$237$	1.98579e8i	0.968977i
$238$	2.58689e7i	0.124382i
$239$	4.69235e7	0.222330	0.111165	−	0.993802i	$-0.464542\pi$
$239$	4.69235e7	0.222330	0.111165	+	0.993802i	$0.464542\pi$
$240$	0	0
$241$	−2.29327e8	−1.05535	−0.527674	−	0.849447i	$-0.676936\pi$
$241$	−2.29327e8	−1.05535	−0.527674	+	0.849447i	$0.676936\pi$
$242$	− 1.55869e8i	− 0.706976i
$243$	1.43489e7i	0.0641500i
$244$	1.73882e7	0.0766283
$245$	0	0
$246$	1.10213e8	0.472020
$247$	− 7.52788e8i	− 3.17858i
$248$	6.16202e7i	0.256532i
$249$	1.03862e8	0.426345
$250$	0	0
$251$	4.50379e8	1.79771	0.898857	−	0.438242i	$-0.144399\pi$
$251$	4.50379e8	1.79771	0.898857	+	0.438242i	$0.144399\pi$
$252$	1.08242e7i	0.0426082i
$253$	1.62000e6i	0.00628917i
$254$	−7.47200e7	−0.286101
$255$	0	0
$256$	1.67772e7	0.0625000
$257$	− 6.65252e7i	− 0.244467i	−0.992501	−	0.122233i	$-0.960994\pi$
$257$	− 6.65252e7i	− 0.244467i	0.992501	−	0.122233i	$-0.0390057\pi$
$258$	− 3.14090e7i	− 0.113864i
$259$	1.08958e8	0.389681
$260$	0	0
$261$	−6.45559e7	−0.224747
$262$	− 3.57436e8i	− 1.22785i
$263$	− 1.10723e8i	− 0.375312i	−0.982235	−	0.187656i	$-0.939911\pi$
$263$	− 1.10723e8i	− 0.375312i	0.982235	−	0.187656i	$-0.0600890\pi$
$264$	−829440.	−0.00277441
$265$	0	0
$266$	9.94148e7	0.323866
$267$	− 1.53499e8i	− 0.493534i
$268$	6.87788e7i	0.218264i
$269$	1.31054e8	0.410504	0.205252	−	0.978709i	$-0.434199\pi$
$269$	1.31054e8	0.410504	0.205252	+	0.978709i	$0.434199\pi$
$270$	0	0
$271$	−5.66890e8	−1.73024	−0.865119	−	0.501566i	$-0.832757\pi$
$271$	−5.66890e8	−1.73024	−0.865119	+	0.501566i	$0.832757\pi$
$272$	− 5.70900e7i	− 0.172016i
$273$	− 8.80343e7i	− 0.261868i
$274$	−4.55943e8	−1.33901
$275$	0	0
$276$	−4.66560e7	−0.133575
$277$	− 1.30574e8i	− 0.369129i	−0.982820	−	0.184565i	$-0.940912\pi$
$277$	− 1.30574e8i	− 0.369129i	0.982820	−	0.184565i	$-0.0590875\pi$
$278$	− 2.45458e8i	− 0.685205i
$279$	8.77366e7	0.241861
$280$	0	0
$281$	−2.70368e8	−0.726914	−0.363457	−	0.931611i	$-0.618404\pi$
$281$	−2.70368e8	−0.726914	−0.363457	+	0.931611i	$0.618404\pi$
$282$	6.57850e7i	0.174685i
$283$	− 9.11074e7i	− 0.238947i	−0.992837	−	0.119473i	$-0.961879\pi$
$283$	− 9.11074e7i	− 0.238947i	0.992837	−	0.119473i	$-0.0381206\pi$
$284$	1.60351e8	0.415391
$285$	0	0
$286$	6.74592e6	0.0170514
$287$	− 1.18377e8i	− 0.295584i
$288$	− 2.38879e7i	− 0.0589256i
$289$	2.16071e8	0.526567
$290$	0	0
$291$	2.15496e8	0.512642
$292$	1.89092e8i	0.444461i
$293$	− 6.22671e8i	− 1.44618i	−0.690754	−	0.723090i	$-0.742721\pi$
$293$	− 6.22671e8i	− 1.44618i	0.690754	−	0.723090i	$-0.257279\pi$
$294$	−1.66259e8	−0.381567
$295$	0	0
$296$	−2.40459e8	−0.538914
$297$	1.18098e6i	0.00261574i
$298$	− 2.26903e8i	− 0.496687i
$299$	3.79458e8	0.820946
$300$	0	0
$301$	−3.37356e7	−0.0713026
$302$	− 2.76522e8i	− 0.577704i
$303$	4.17496e8i	0.862189i
$304$	−2.19398e8	−0.447894
$305$	0	0
$306$	−8.12864e7	−0.162178
$307$	1.13282e8i	0.223447i	0.993739	+	0.111724i	$0.0356371\pi$
$307$	1.13282e8i	0.223447i	−0.993739	+	0.111724i	$0.964363\pi$
$308$	890880.i	0.00173737i
$309$	5.64365e8	1.08819
$310$	0	0
$311$	3.78344e8	0.713222	0.356611	−	0.934253i	$-0.383932\pi$
$311$	3.78344e8	0.713222	0.356611	+	0.934253i	$0.383932\pi$
$312$	1.94282e8i	0.362153i
$313$	− 1.11400e8i	− 0.205344i	−0.994715	−	0.102672i	$-0.967261\pi$
$313$	− 1.11400e8i	− 0.205344i	0.994715	−	0.102672i	$-0.0327391\pi$
$314$	4.00528e8	0.730095
$315$	0	0
$316$	−4.70705e8	−0.839159
$317$	6.70098e8i	1.18149i	0.806857	+	0.590746i	$0.201167\pi$
$317$	6.70098e8i	1.18149i	−0.806857	+	0.590746i	$0.798833\pi$
$318$	− 2.03900e7i	− 0.0355567i
$319$	−5.31324e6	−0.00916415
$320$	0	0
$321$	5.55241e8	0.936945
$322$	5.01120e7i	0.0836462i
$323$	7.46575e8i	1.23272i
$324$	−3.40122e7	−0.0555556
$325$	0	0
$326$	1.30687e7	0.0208916
$327$	− 3.77596e8i	− 0.597187i
$328$	2.61246e8i	0.408781i
$329$	7.06579e7	0.109389
$330$	0	0
$331$	−5.44096e8	−0.824665	−0.412332	−	0.911033i	$-0.635286\pi$
$331$	−5.44096e8	−0.824665	−0.412332	+	0.911033i	$0.635286\pi$
$332$	2.46192e8i	0.369225i
$333$	3.42372e8i	0.508093i
$334$	−7.95854e8	−1.16875
$335$	0	0
$336$	−2.56573e7	−0.0368998
$337$	− 9.62374e8i	− 1.36974i	−0.728664	−	0.684872i	$-0.759858\pi$
$337$	− 9.62374e8i	− 1.36974i	0.728664	−	0.684872i	$-0.240142\pi$
$338$	− 1.07813e9i	− 1.51867i
$339$	−7.13982e8	−0.995379
$340$	0	0
$341$	7.22112e6	0.00986198
$342$	3.12385e8i	0.422279i
$343$	3.69637e8i	0.494590i
$344$	7.44509e7	0.0986088
$345$	0	0
$346$	8.06200e8	1.04635
$347$	5.92829e8i	0.761686i	0.924640	+	0.380843i	$0.124366\pi$
$347$	5.92829e8i	0.761686i	−0.924640	+	0.380843i	$0.875634\pi$
$348$	− 1.53021e8i	− 0.194637i
$349$	9.73268e8	1.22558	0.612792	−	0.790244i	$-0.290046\pi$
$349$	9.73268e8	1.22558	0.612792	+	0.790244i	$0.290046\pi$
$350$	0	0
$351$	2.76625e8	0.341442
$352$	− 1.96608e6i	− 0.00240271i
$353$	1.59127e9i	1.92545i	0.270491	+	0.962723i	$0.412814\pi$
$353$	1.59127e9i	1.92545i	−0.270491	+	0.962723i	$0.587186\pi$
$354$	−4.07320e8	−0.488005
$355$	0	0
$356$	3.63850e8	0.427413
$357$	8.73076e7i	0.101558i
$358$	− 6.87331e8i	− 0.791726i
$359$	−8.37928e8	−0.955820	−0.477910	−	0.878409i	$-0.658606\pi$
$359$	−8.37928e8	−0.955820	−0.477910	+	0.878409i	$0.658606\pi$
$360$	0	0
$361$	1.97523e9	2.20975
$362$	− 5.87960e7i	− 0.0651431i
$363$	− 5.26056e8i	− 0.577244i
$364$	2.08674e8	0.226784
$365$	0	0
$366$	5.86850e7	0.0625668
$367$	1.14448e9i	1.20858i	0.796765	+	0.604290i	$0.206543\pi$
$367$	1.14448e9i	1.20858i	−0.796765	+	0.604290i	$0.793457\pi$
$368$	− 1.10592e8i	− 0.115679i
$369$	3.71969e8	0.385403
$370$	0	0
$371$	−2.19003e7	−0.0222660
$372$	2.07968e8i	0.209458i
$373$	1.36673e9i	1.36365i	0.731516	+	0.681825i	$0.238813\pi$
$373$	1.36673e9i	1.36365i	−0.731516	+	0.681825i	$0.761187\pi$
$374$	−6.69024e6	−0.00661289
$375$	0	0
$376$	−1.55935e8	−0.151281
$377$	1.24454e9i	1.19623i
$378$	3.65316e7i	0.0347895i
$379$	4.91619e8	0.463865	0.231933	−	0.972732i	$-0.425495\pi$
$379$	4.91619e8	0.463865	0.231933	+	0.972732i	$0.425495\pi$
$380$	0	0
$381$	−2.52180e8	−0.233600
$382$	2.04423e8i	0.187633i
$383$	5.32012e8i	0.483867i	0.970293	+	0.241933i	$0.0777816\pi$
$383$	5.32012e8i	0.483867i	−0.970293	+	0.241933i	$0.922218\pi$
$384$	5.66231e7	0.0510310
$385$	0	0
$386$	−1.09452e9	−0.968651
$387$	− 1.06005e8i	− 0.0929693i
$388$	5.10806e8i	0.443961i
$389$	−6.83513e8	−0.588739	−0.294370	−	0.955692i	$-0.595110\pi$
$389$	−6.83513e8	−0.588739	−0.294370	+	0.955692i	$0.595110\pi$
$390$	0	0
$391$	−3.76326e8	−0.318380
$392$	− 3.94096e8i	− 0.330446i
$393$	− 1.20635e9i	− 1.00253i
$394$	−1.10442e9	−0.909701
$395$	0	0
$396$	−2.79936e6	−0.00226530
$397$	1.46842e9i	1.17784i	0.808193	+	0.588918i	$0.200446\pi$
$397$	1.46842e9i	1.17784i	−0.808193	+	0.588918i	$0.799554\pi$
$398$	− 4.96332e7i	− 0.0394622i
$399$	3.35525e8	0.264435
$400$	0	0
$401$	7.08292e8	0.548538	0.274269	−	0.961653i	$-0.411564\pi$
$401$	7.08292e8	0.548538	0.274269	+	0.961653i	$0.411564\pi$
$402$	2.32128e8i	0.178212i
$403$	− 1.69143e9i	− 1.28732i
$404$	−9.89619e8	−0.746678
$405$	0	0
$406$	−1.64356e8	−0.121884
$407$	2.81788e7i	0.0207177i
$408$	− 1.92679e8i	− 0.140451i
$409$	−2.13603e9	−1.54375	−0.771873	−	0.635777i	$-0.780680\pi$
$409$	−2.13603e9	−1.54375	−0.771873	+	0.635777i	$0.780680\pi$
$410$	0	0
$411$	−1.53881e9	−1.09330
$412$	1.33775e9i	0.942402i
$413$	4.37492e8i	0.305594i
$414$	−1.57464e8	−0.109064
$415$	0	0
$416$	−4.60521e8	−0.313634
$417$	− 8.28421e8i	− 0.559467i
$418$	2.57107e7i	0.0172186i
$419$	−1.22130e9	−0.811098	−0.405549	−	0.914073i	$-0.632920\pi$
$419$	−1.22130e9	−0.811098	−0.405549	+	0.914073i	$0.632920\pi$
$420$	0	0
$421$	−1.17754e8	−0.0769110	−0.0384555	−	0.999260i	$-0.512244\pi$
$421$	−1.17754e8	−0.0769110	−0.0384555	+	0.999260i	$0.512244\pi$
$422$	− 1.32033e9i	− 0.855245i
$423$	2.22024e8i	0.142629i
$424$	4.83318e7	0.0307930
$425$	0	0
$426$	5.41184e8	0.339165
$427$	− 6.30321e7i	− 0.0391800i
$428$	1.31613e9i	0.811418i
$429$	2.27675e7	0.0139224
$430$	0	0
$431$	−2.92749e9	−1.76127	−0.880634	−	0.473797i	$-0.842883\pi$
$431$	−2.92749e9	−1.76127	−0.880634	+	0.473797i	$0.842883\pi$
$432$	− 8.06216e7i	− 0.0481125i
$433$	− 9.22066e8i	− 0.545826i	−0.962039	−	0.272913i	$-0.912013\pi$
$433$	− 9.22066e8i	− 0.545826i	0.962039	−	0.272913i	$-0.0879871\pi$
$434$	2.23373e8	0.131165
$435$	0	0
$436$	8.95042e8	0.517179
$437$	1.44623e9i	0.828995i
$438$	6.38186e8i	0.362901i
$439$	2.69431e9	1.51992	0.759962	−	0.649967i	$-0.225217\pi$
$439$	2.69431e9	1.51992	0.759962	+	0.649967i	$0.225217\pi$
$440$	0	0
$441$	−5.61125e8	−0.311548
$442$	1.56708e9i	0.863202i
$443$	1.50928e9i	0.824815i	0.911000	+	0.412407i	$0.135312\pi$
$443$	1.50928e9i	0.824815i	−0.911000	+	0.412407i	$0.864688\pi$
$444$	−8.11548e8	−0.440022
$445$	0	0
$446$	4.34493e8	0.231906
$447$	− 7.65797e8i	− 0.405543i
$448$	− 6.08174e7i	− 0.0319562i
$449$	−7.94655e8	−0.414302	−0.207151	−	0.978309i	$-0.566419\pi$
$449$	−7.94655e8	−0.414302	−0.207151	+	0.978309i	$0.566419\pi$
$450$	0	0
$451$	3.06148e7	0.0157149
$452$	− 1.69240e9i	− 0.862024i
$453$	− 9.33262e8i	− 0.471694i
$454$	1.07142e9	0.537360
$455$	0	0
$456$	−7.40469e8	−0.365704
$457$	− 1.82270e9i	− 0.893324i	−0.894703	−	0.446662i	$-0.852613\pi$
$457$	− 1.82270e9i	− 0.893324i	0.894703	−	0.446662i	$-0.147387\pi$
$458$	− 1.67874e8i	− 0.0816497i
$459$	−2.74342e8	−0.132418
$460$	0	0
$461$	−1.79582e8	−0.0853711	−0.0426855	−	0.999089i	$-0.513591\pi$
$461$	−1.79582e8	−0.0853711	−0.0426855	+	0.999089i	$0.513591\pi$
$462$	3.00672e6i	0.00141855i
$463$	3.95891e8i	0.185371i	0.995695	+	0.0926855i	$0.0295451\pi$
$463$	3.95891e8i	0.185371i	−0.995695	+	0.0926855i	$0.970455\pi$
$464$	3.62717e8	0.168560
$465$	0	0
$466$	−9.73478e7	−0.0445631
$467$	− 5.70281e8i	− 0.259107i	−0.991572	−	0.129554i	$-0.958646\pi$
$467$	− 5.70281e8i	− 0.259107i	0.991572	−	0.129554i	$-0.0413545\pi$
$468$	6.55703e8i	0.295697i
$469$	2.49323e8	0.111598
$470$	0	0
$471$	1.35178e9	0.596120
$472$	− 9.65499e8i	− 0.422625i
$473$	− 8.72472e6i	− 0.00379086i
$474$	−1.58863e9	−0.685170
$475$	0	0
$476$	−2.06951e8	−0.0879517
$477$	− 6.88161e7i	− 0.0290319i
$478$	3.75388e8i	0.157211i
$479$	−4.36823e9	−1.81607	−0.908033	−	0.418900i	$-0.862416\pi$
$479$	−4.36823e9	−1.81607	−0.908033	+	0.418900i	$0.862416\pi$
$480$	0	0
$481$	6.60040e9	2.70435
$482$	− 1.83462e9i	− 0.746243i
$483$	1.69128e8i	0.0682968i
$484$	1.24695e9	0.499908
$485$	0	0
$486$	−1.14791e8	−0.0453609
$487$	− 3.29328e8i	− 0.129204i	−0.997911	−	0.0646022i	$-0.979422\pi$
$487$	− 3.29328e8i	− 0.129204i	0.997911	−	0.0646022i	$-0.0205779\pi$
$488$	1.39105e8i	0.0541844i
$489$	4.41069e7	0.0170579
$490$	0	0
$491$	−2.54666e9	−0.970924	−0.485462	−	0.874258i	$-0.661349\pi$
$491$	−2.54666e9	−0.970924	−0.485462	+	0.874258i	$0.661349\pi$
$492$	8.81705e8i	0.333769i
$493$	− 1.23427e9i	− 0.463921i
$494$	6.02231e9	2.24760
$495$	0	0
$496$	−4.92962e8	−0.181396
$497$	− 5.81271e8i	− 0.212389i
$498$	8.30899e8i	0.301471i
$499$	−1.42495e9	−0.513391	−0.256696	−	0.966492i	$-0.582634\pi$
$499$	−1.42495e9	−0.513391	−0.256696	+	0.966492i	$0.582634\pi$
$500$	0	0
$501$	−2.68601e9	−0.954279
$502$	3.60304e9i	1.27118i
$503$	− 2.18397e9i	− 0.765172i	−0.923920	−	0.382586i	$-0.875034\pi$
$503$	− 2.18397e9i	− 0.765172i	0.923920	−	0.382586i	$-0.124966\pi$
$504$	−8.65935e7	−0.0301286
$505$	0	0
$506$	−1.29600e7	−0.00444711
$507$	− 3.63869e9i	− 1.23999i
$508$	− 5.97760e8i	− 0.202304i
$509$	5.25623e9	1.76670	0.883349	−	0.468715i	$-0.155283\pi$
$509$	5.25623e9	1.76670	0.883349	+	0.468715i	$0.155283\pi$
$510$	0	0
$511$	6.85459e8	0.227252
$512$	1.34218e8i	0.0441942i
$513$	1.05430e9i	0.344789i
$514$	5.32201e8	0.172864
$515$	0	0
$516$	2.51272e8	0.0805137
$517$	1.82736e7i	0.00581577i
$518$	8.71663e8i	0.275546i
$519$	2.72093e9	0.854340
$520$	0	0
$521$	3.19481e9	0.989720	0.494860	−	0.868973i	$-0.335219\pi$
$521$	3.19481e9	0.989720	0.494860	+	0.868973i	$0.335219\pi$
$522$	− 5.16447e8i	− 0.158920i
$523$	− 1.92219e9i	− 0.587545i	−0.955875	−	0.293772i	$-0.905089\pi$
$523$	− 1.92219e9i	− 0.587545i	0.955875	−	0.293772i	$-0.0949108\pi$
$524$	2.85949e9	0.868219
$525$	0	0
$526$	8.85783e8	0.265386
$527$	1.67747e9i	0.499248i
$528$	− 6.63552e6i	− 0.00196181i
$529$	2.67583e9	0.785892
$530$	0	0
$531$	−1.37470e9	−0.398454
$532$	7.95318e8i	0.229008i
$533$	− 7.17100e9i	− 2.05132i
$534$	1.22799e9	0.348981
$535$	0	0
$536$	−5.50230e8	−0.154336
$537$	− 2.31974e9i	− 0.646442i
$538$	1.04843e9i	0.290270i
$539$	−4.61831e7	−0.0127035
$540$	0	0
$541$	1.62352e9	0.440826	0.220413	−	0.975407i	$-0.429259\pi$
$541$	1.62352e9	0.440826	0.220413	+	0.975407i	$0.429259\pi$
$542$	− 4.53512e9i	− 1.22346i
$543$	− 1.98437e8i	− 0.0531891i
$544$	4.56720e8	0.121634
$545$	0	0
$546$	7.04274e8	0.185169
$547$	8.76824e8i	0.229064i	0.993420	+	0.114532i	$0.0365368\pi$
$547$	8.76824e8i	0.229064i	−0.993420	+	0.114532i	$0.963463\pi$
$548$	− 3.64755e9i	− 0.946823i
$549$	1.98062e8	0.0510855
$550$	0	0
$551$	−4.74331e9	−1.20795
$552$	− 3.73248e8i	− 0.0944519i
$553$	1.70631e9i	0.429061i
$554$	1.04459e9	0.261014
$555$	0	0
$556$	1.96366e9	0.484513
$557$	2.29689e8i	0.0563179i	0.999603	+	0.0281590i	$0.00896446\pi$
$557$	2.29689e8i	0.0563179i	−0.999603	+	0.0281590i	$0.991036\pi$
$558$	7.01893e8i	0.171022i
$559$	−2.04362e9	−0.494833
$560$	0	0
$561$	−2.25796e7	−0.00539940
$562$	− 2.16294e9i	− 0.514006i
$563$	7.86151e8i	0.185664i	0.995682	+	0.0928318i	$0.0295919\pi$
$563$	7.86151e8i	0.185664i	−0.995682	+	0.0928318i	$0.970408\pi$
$564$	−5.26280e8	−0.123521
$565$	0	0
$566$	7.28859e8	0.168961
$567$	1.23294e8i	0.0284055i
$568$	1.28281e9i	0.293726i
$569$	−3.30088e9	−0.751166	−0.375583	−	0.926789i	$-0.622558\pi$
$569$	−3.30088e9	−0.751166	−0.375583	+	0.926789i	$0.622558\pi$
$570$	0	0
$571$	−1.54033e9	−0.346248	−0.173124	−	0.984900i	$-0.555386\pi$
$571$	−1.54033e9	−0.346248	−0.173124	+	0.984900i	$0.555386\pi$
$572$	5.39674e7i	0.0120572i
$573$	6.89928e8i	0.153201i
$574$	9.47017e8	0.209009
$575$	0	0
$576$	1.91103e8	0.0416667
$577$	3.79769e9i	0.823008i	0.911408	+	0.411504i	$0.134996\pi$
$577$	3.79769e9i	0.823008i	−0.911408	+	0.411504i	$0.865004\pi$
$578$	1.72857e9i	0.372339i
$579$	−3.69400e9	−0.790900
$580$	0	0
$581$	8.92447e8	0.188784
$582$	1.72397e9i	0.362493i
$583$	− 5.66388e6i	− 0.00118379i
$584$	−1.51274e9	−0.314281
$585$	0	0
$586$	4.98137e9	1.02260
$587$	− 8.29676e9i	− 1.69307i	−0.532332	−	0.846536i	$-0.678684\pi$
$587$	− 8.29676e9i	− 1.69307i	0.532332	−	0.846536i	$-0.321316\pi$
$588$	− 1.33007e9i	− 0.269808i
$589$	6.44653e9	1.29994
$590$	0	0
$591$	−3.72743e9	−0.742767
$592$	− 1.92367e9i	− 0.381070i
$593$	4.93196e9i	0.971243i	0.874169	+	0.485621i	$0.161407\pi$
$593$	4.93196e9i	0.971243i	−0.874169	+	0.485621i	$0.838593\pi$
$594$	−9.44784e6	−0.00184961
$595$	0	0
$596$	1.81522e9	0.351211
$597$	− 1.67512e8i	− 0.0322208i
$598$	3.03566e9i	0.580496i
$599$	−6.51152e9	−1.23791	−0.618954	−	0.785427i	$-0.712443\pi$
$599$	−6.51152e9	−1.23791	−0.618954	+	0.785427i	$0.712443\pi$
$600$	0	0
$601$	−4.17460e9	−0.784430	−0.392215	−	0.919874i	$-0.628291\pi$
$601$	−4.17460e9	−0.784430	−0.392215	+	0.919874i	$0.628291\pi$
$602$	− 2.69885e8i	− 0.0504186i
$603$	7.83433e8i	0.145509i
$604$	2.21218e9	0.408499
$605$	0	0
$606$	−3.33996e9	−0.609660
$607$	− 5.46979e9i	− 0.992682i	−0.868128	−	0.496341i	$-0.834677\pi$
$607$	− 5.46979e9i	− 0.992682i	0.868128	−	0.496341i	$-0.165323\pi$
$608$	− 1.75519e9i	− 0.316709i
$609$	−5.54702e8	−0.0995175
$610$	0	0
$611$	4.28029e9	0.759152
$612$	− 6.50291e8i	− 0.114677i
$613$	− 7.92764e9i	− 1.39006i	−0.718982	−	0.695028i	$-0.755392\pi$
$613$	− 7.92764e9i	− 1.39006i	0.718982	−	0.695028i	$-0.244608\pi$
$614$	−9.06252e8	−0.158001
$615$	0	0
$616$	−7.12704e6	−0.00122850
$617$	9.70277e9i	1.66302i	0.555510	+	0.831510i	$0.312523\pi$
$617$	9.70277e9i	1.66302i	−0.555510	+	0.831510i	$0.687477\pi$
$618$	4.51492e9i	0.769468i
$619$	−5.34840e8	−0.0906373	−0.0453186	−	0.998973i	$-0.514430\pi$
$619$	−5.34840e8	−0.0906373	−0.0453186	+	0.998973i	$0.514430\pi$
$620$	0	0
$621$	−5.31441e8	−0.0890501
$622$	3.02675e9i	0.504324i
$623$	− 1.31896e9i	− 0.218536i
$624$	−1.55426e9	−0.256081
$625$	0	0
$626$	8.91202e8	0.145200
$627$	8.67737e7i	0.0140589i
$628$	3.20422e9i	0.516255i
$629$	−6.54593e9	−1.04880
$630$	0	0
$631$	−8.98145e9	−1.42313	−0.711563	−	0.702622i	$-0.752013\pi$
$631$	−8.98145e9	−1.42313	−0.711563	+	0.702622i	$0.752013\pi$
$632$	− 3.76564e9i	− 0.593375i
$633$	− 4.45613e9i	− 0.698305i
$634$	−5.36079e9	−0.835441
$635$	0	0
$636$	1.63120e8	0.0251424
$637$	1.08176e10i	1.65823i
$638$	− 4.25059e7i	− 0.00648003i
$639$	1.82649e9	0.276927
$640$	0	0
$641$	6.81488e8	0.102201	0.0511005	−	0.998694i	$-0.483727\pi$
$641$	6.81488e8	0.102201	0.0511005	+	0.998694i	$0.483727\pi$
$642$	4.44193e9i	0.662520i
$643$	− 3.68007e9i	− 0.545906i	−0.962027	−	0.272953i	$-0.912000\pi$
$643$	− 3.68007e9i	− 0.545906i	0.962027	−	0.272953i	$-0.0880003\pi$
$644$	−4.00896e8	−0.0591468
$645$	0	0
$646$	−5.97260e9	−0.871665
$647$	− 9.03269e9i	− 1.31115i	−0.755131	−	0.655574i	$-0.772427\pi$
$647$	− 9.03269e9i	− 1.31115i	0.755131	−	0.655574i	$-0.227573\pi$
$648$	− 2.72098e8i	− 0.0392837i
$649$	−1.13144e8	−0.0162471
$650$	0	0
$651$	7.53885e8	0.107096
$652$	1.04550e8i	0.0147726i
$653$	2.90477e9i	0.408240i	0.978946	+	0.204120i	$0.0654333\pi$
$653$	2.90477e9i	0.408240i	−0.978946	+	0.204120i	$0.934567\pi$
$654$	3.02077e9	0.422275
$655$	0	0
$656$	−2.08997e9	−0.289052
$657$	2.15388e9i	0.296307i
$658$	5.65263e8i	0.0773500i
$659$	2.88225e8	0.0392313	0.0196157	−	0.999808i	$-0.493756\pi$
$659$	2.88225e8	0.0392313	0.0196157	+	0.999808i	$0.493756\pi$
$660$	0	0
$661$	4.04326e9	0.544536	0.272268	−	0.962221i	$-0.412226\pi$
$661$	4.04326e9	0.544536	0.272268	+	0.962221i	$0.412226\pi$
$662$	− 4.35277e9i	− 0.583126i
$663$	5.28889e9i	0.704802i
$664$	−1.96954e9	−0.261082
$665$	0	0
$666$	−2.73898e9	−0.359276
$667$	− 2.39096e9i	− 0.311983i
$668$	− 6.36684e9i	− 0.826430i
$669$	1.46642e9	0.189350
$670$	0	0
$671$	1.63014e7	0.00208303
$672$	− 2.05259e8i	− 0.0260921i
$673$	6.38900e9i	0.807942i	0.914772	+	0.403971i	$0.132370\pi$
$673$	6.38900e9i	0.807942i	−0.914772	+	0.403971i	$0.867630\pi$
$674$	7.69899e9	0.968555
$675$	0	0
$676$	8.62505e9	1.07386
$677$	1.08256e10i	1.34089i	0.741960	+	0.670445i	$0.233897\pi$
$677$	1.08256e10i	1.34089i	−0.741960	+	0.670445i	$0.766103\pi$
$678$	− 5.71186e9i	− 0.703839i
$679$	1.85167e9	0.226997
$680$	0	0
$681$	3.61605e9	0.438753
$682$	5.77690e7i	0.00697347i
$683$	8.81962e8i	0.105920i	0.998597	+	0.0529599i	$0.0168656\pi$
$683$	8.81962e8i	0.105920i	−0.998597	+	0.0529599i	$0.983134\pi$
$684$	−2.49908e9	−0.298596
$685$	0	0
$686$	−2.95709e9	−0.349728
$687$	− 5.66575e8i	− 0.0666667i
$688$	5.95608e8i	0.0697269i
$689$	−1.32667e9	−0.154524
$690$	0	0
$691$	5.36883e9	0.619022	0.309511	−	0.950896i	$-0.399835\pi$
$691$	5.36883e9	0.619022	0.309511	+	0.950896i	$0.399835\pi$
$692$	6.44960e9i	0.739881i
$693$	1.01477e7i	0.00115825i
$694$	−4.74263e9	−0.538593
$695$	0	0
$696$	1.22417e9	0.137629
$697$	7.11181e9i	0.795546i
$698$	7.78614e9i	0.866619i
$699$	−3.28549e8	−0.0363856
$700$	0	0
$701$	4.37341e9	0.479521	0.239760	−	0.970832i	$-0.422931\pi$
$701$	4.37341e9	0.479521	0.239760	+	0.970832i	$0.422931\pi$
$702$	2.21300e9i	0.241436i
$703$	2.51561e10i	2.73086i
$704$	1.57286e7	0.00169897
$705$	0	0
$706$	−1.27301e10	−1.36150
$707$	3.58737e9i	0.381776i
$708$	− 3.25856e9i	− 0.345072i
$709$	−4.60383e9	−0.485129	−0.242565	−	0.970135i	$-0.577989\pi$
$709$	−4.60383e9	−0.485129	−0.242565	+	0.970135i	$0.577989\pi$
$710$	0	0
$711$	−5.36163e9	−0.559439
$712$	2.91080e9i	0.302227i
$713$	3.24950e9i	0.335740i
$714$	−6.98461e8	−0.0718122
$715$	0	0
$716$	5.49864e9	0.559835
$717$	1.26693e9i	0.128362i
$718$	− 6.70343e9i	− 0.675867i
$719$	−5.78324e9	−0.580257	−0.290129	−	0.956988i	$-0.593698\pi$
$719$	−5.78324e9	−0.580257	−0.290129	+	0.956988i	$0.593698\pi$
$720$	0	0
$721$	4.84936e9	0.481849
$722$	1.58018e10i	1.56253i
$723$	− 6.19183e9i	− 0.609305i
$724$	4.70368e8	0.0460631
$725$	0	0
$726$	4.20845e9	0.408173
$727$	− 1.42871e10i	− 1.37903i	−0.724272	−	0.689514i	$-0.757824\pi$
$727$	− 1.42871e10i	− 1.37903i	0.724272	−	0.689514i	$-0.242176\pi$
$728$	1.66939e9i	0.160361i
$729$	−3.87420e8	−0.0370370
$730$	0	0
$731$	2.02675e9	0.191907
$732$	4.69480e8i	0.0442414i
$733$	− 1.18896e10i	− 1.11507i	−0.830153	−	0.557535i	$-0.811747\pi$
$733$	− 1.18896e10i	− 1.11507i	0.830153	−	0.557535i	$-0.188253\pi$
$734$	−9.15580e9	−0.854595
$735$	0	0
$736$	8.84736e8	0.0817977
$737$	6.44801e7i	0.00593321i
$738$	2.97575e9i	0.272521i
$739$	−1.41993e10	−1.29423	−0.647113	−	0.762394i	$-0.724024\pi$
$739$	−1.41993e10	−1.29423	−0.647113	+	0.762394i	$0.724024\pi$
$740$	0	0
$741$	2.03253e10	1.83516
$742$	− 1.75203e8i	− 0.0157444i
$743$	− 8.29539e9i	− 0.741953i	−0.928642	−	0.370976i	$-0.879023\pi$
$743$	− 8.29539e9i	− 0.741953i	0.928642	−	0.370976i	$-0.120977\pi$
$744$	−1.66375e9	−0.148109
$745$	0	0
$746$	−1.09339e10	−0.964246
$747$	2.80429e9i	0.246150i
$748$	− 5.35219e7i	− 0.00467602i
$749$	4.77096e9	0.414877
$750$	0	0
$751$	−1.07334e10	−0.924693	−0.462347	−	0.886699i	$-0.652992\pi$
$751$	−1.07334e10	−0.924693	−0.462347	+	0.886699i	$0.652992\pi$
$752$	− 1.24748e9i	− 0.106972i
$753$	1.21602e10i	1.03791i
$754$	−9.95630e9	−0.845860
$755$	0	0
$756$	−2.92253e8	−0.0245999
$757$	− 1.28389e9i	− 0.107570i	−0.998553	−	0.0537850i	$-0.982871\pi$
$757$	− 1.28389e9i	− 0.107570i	0.998553	−	0.0537850i	$-0.0171286\pi$
$758$	3.93296e9i	0.328002i
$759$	−4.37400e7	−0.00363105
$760$	0	0
$761$	1.13991e10	0.937616	0.468808	−	0.883300i	$-0.344684\pi$
$761$	1.13991e10	0.937616	0.468808	+	0.883300i	$0.344684\pi$
$762$	− 2.01744e9i	− 0.165180i
$763$	− 3.24453e9i	− 0.264433i
$764$	−1.63539e9	−0.132676
$765$	0	0
$766$	−4.25610e9	−0.342146
$767$	2.65022e10i	2.12079i
$768$	4.52985e8i	0.0360844i
$769$	1.26388e10	1.00222	0.501112	−	0.865383i	$-0.332925\pi$
$769$	1.26388e10	1.00222	0.501112	+	0.865383i	$0.332925\pi$
$770$	0	0
$771$	1.79618e9	0.141143
$772$	− 8.75615e9i	− 0.684940i
$773$	1.78935e10i	1.39337i	0.717375	+	0.696687i	$0.245343\pi$
$773$	1.78935e10i	1.39337i	−0.717375	+	0.696687i	$0.754657\pi$
$774$	8.48043e8	0.0657392
$775$	0	0
$776$	−4.08645e9	−0.313928
$777$	2.94186e9i	0.224983i
$778$	− 5.46810e9i	− 0.416302i
$779$	2.73308e10	2.07144
$780$	0	0
$781$	1.50329e8	0.0112918
$782$	− 3.01061e9i	− 0.225129i
$783$	− 1.74301e9i	− 0.129758i
$784$	3.15277e9	0.233661
$785$	0	0
$786$	9.65078e9	0.708898
$787$	− 1.65085e10i	− 1.20725i	−0.797270	−	0.603623i	$-0.793723\pi$
$787$	− 1.65085e10i	− 1.20725i	0.797270	−	0.603623i	$-0.206277\pi$
$788$	− 8.83538e9i	− 0.643255i
$789$	2.98952e9	0.216686
$790$	0	0
$791$	−6.13496e9	−0.440752
$792$	− 2.23949e7i	− 0.00160181i
$793$	− 3.81833e9i	− 0.271905i
$794$	−1.17474e10	−0.832856
$795$	0	0
$796$	3.97066e8	0.0279040
$797$	1.82052e9i	0.127377i	0.997970	+	0.0636886i	$0.0202864\pi$
$797$	1.82052e9i	0.127377i	−0.997970	+	0.0636886i	$0.979714\pi$
$798$	2.68420e9i	0.186984i
$799$	−4.24496e9	−0.294415
$800$	0	0
$801$	4.14448e9	0.284942
$802$	5.66634e9i	0.387875i
$803$	1.77274e8i	0.0120820i
$804$	−1.85703e9	−0.126015
$805$	0	0
$806$	1.35314e10	0.910271
$807$	3.53846e9i	0.237004i
$808$	− 7.91695e9i	− 0.527981i
$809$	2.17445e10	1.44388	0.721938	−	0.691958i	$-0.243252\pi$
$809$	2.17445e10	1.44388	0.721938	+	0.691958i	$0.243252\pi$
$810$	0	0
$811$	−1.93869e10	−1.27625	−0.638126	−	0.769932i	$-0.720290\pi$
$811$	−1.93869e10	−1.27625	−0.638126	+	0.769932i	$0.720290\pi$
$812$	− 1.31485e9i	− 0.0861847i
$813$	− 1.53060e10i	− 0.998954i
$814$	−2.25430e8	−0.0146496
$815$	0	0
$816$	1.54143e9	0.0993136
$817$	− 7.78885e9i	− 0.499685i
$818$	− 1.70882e10i	− 1.09159i
$819$	2.37692e9	0.151190
$820$	0	0
$821$	−1.16565e10	−0.735134	−0.367567	−	0.929997i	$-0.619809\pi$
$821$	−1.16565e10	−0.735134	−0.367567	+	0.929997i	$0.619809\pi$
$822$	− 1.23105e10i	− 0.773078i
$823$	− 4.64054e9i	− 0.290181i	−0.989418	−	0.145091i	$-0.953653\pi$
$823$	− 4.64054e9i	− 0.290181i	0.989418	−	0.145091i	$-0.0463474\pi$
$824$	−1.07020e10	−0.666379
$825$	0	0
$826$	−3.49993e9	−0.216087
$827$	− 1.00604e10i	− 0.618506i	−0.950980	−	0.309253i	$-0.899921\pi$
$827$	− 1.00604e10i	− 0.618506i	0.950980	−	0.309253i	$-0.100079\pi$
$828$	− 1.25971e9i	− 0.0771197i
$829$	−1.56256e10	−0.952566	−0.476283	−	0.879292i	$-0.658016\pi$
$829$	−1.56256e10	−0.952566	−0.476283	+	0.879292i	$0.658016\pi$
$830$	0	0
$831$	3.52551e9	0.213117
$832$	− 3.68417e9i	− 0.221773i
$833$	− 1.07283e10i	− 0.643095i
$834$	6.62736e9	0.395603
$835$	0	0
$836$	−2.05686e8	−0.0121754
$837$	2.36889e9i	0.139639i
$838$	− 9.77041e9i	− 0.573533i
$839$	2.83557e10	1.65757	0.828787	−	0.559564i	$-0.189032\pi$
$839$	2.83557e10	1.65757	0.828787	+	0.559564i	$0.189032\pi$
$840$	0	0
$841$	−9.40807e9	−0.545399
$842$	− 9.42032e8i	− 0.0543843i
$843$	− 7.29994e9i	− 0.419684i
$844$	1.05627e10	0.604750
$845$	0	0
$846$	−1.77619e9	−0.100854
$847$	− 4.52019e9i	− 0.255602i
$848$	3.86654e8i	0.0217740i
$849$	2.45990e9	0.137956
$850$	0	0
$851$	−1.26804e10	−0.705311
$852$	4.32947e9i	0.239826i
$853$	1.52072e10i	0.838933i	0.907771	+	0.419466i	$0.137783\pi$
$853$	1.52072e10i	0.838933i	−0.907771	+	0.419466i	$0.862217\pi$
$854$	5.04257e8	0.0277044
$855$	0	0
$856$	−1.05290e10	−0.573759
$857$	− 2.69776e10i	− 1.46410i	−0.681251	−	0.732049i	$-0.738564\pi$
$857$	− 2.69776e10i	− 1.46410i	0.681251	−	0.732049i	$-0.261436\pi$
$858$	1.82140e8i	0.00984463i
$859$	1.59964e10	0.861086	0.430543	−	0.902570i	$-0.358322\pi$
$859$	1.59964e10	0.861086	0.430543	+	0.902570i	$0.358322\pi$
$860$	0	0
$861$	3.19618e9	0.170656
$862$	− 2.34199e10i	− 1.24540i
$863$	2.22647e10i	1.17918i	0.807704	+	0.589588i	$0.200710\pi$
$863$	2.22647e10i	1.17918i	−0.807704	+	0.589588i	$0.799290\pi$
$864$	6.44973e8	0.0340207
$865$	0	0
$866$	7.37653e9	0.385957
$867$	5.83391e9i	0.304014i
$868$	1.78699e9i	0.0927475i
$869$	−4.41286e8	−0.0228114
$870$	0	0
$871$	1.51034e10	0.774481
$872$	7.16034e9i	0.365701i
$873$	5.81840e9i	0.295974i
$874$	−1.15698e10	−0.586188
$875$	0	0
$876$	−5.10549e9	−0.256610
$877$	− 2.08359e10i	− 1.04307i	−0.853230	−	0.521534i	$-0.825360\pi$
$877$	− 2.08359e10i	− 1.04307i	0.853230	−	0.521534i	$-0.174640\pi$
$878$	2.15545e10i	1.07475i
$879$	1.68121e10	0.834952
$880$	0	0
$881$	2.41363e10	1.18920	0.594601	−	0.804021i	$-0.297310\pi$
$881$	2.41363e10	1.18920	0.594601	+	0.804021i	$0.297310\pi$
$882$	− 4.48900e9i	− 0.220298i
$883$	8.17127e9i	0.399417i	0.979855	+	0.199709i	$0.0639996\pi$
$883$	8.17127e9i	0.399417i	−0.979855	+	0.199709i	$0.936000\pi$
$884$	−1.25366e10	−0.610376
$885$	0	0
$886$	−1.20742e10	−0.583232
$887$	− 2.64726e10i	− 1.27369i	−0.770991	−	0.636846i	$-0.780239\pi$
$887$	− 2.64726e10i	− 1.27369i	0.770991	−	0.636846i	$-0.219761\pi$
$888$	− 6.49239e9i	− 0.311142i
$889$	−2.16688e9	−0.103438
$890$	0	0
$891$	−3.18865e7	−0.00151020
$892$	3.47595e9i	0.163982i
$893$	1.63135e10i	0.766595i
$894$	6.12637e9	0.286762
$895$	0	0
$896$	4.86539e8	0.0225964
$897$	1.02454e10i	0.473973i
$898$	− 6.35724e9i	− 0.292956i
$899$	−1.06577e10	−0.489218
$900$	0	0
$901$	1.31572e9	0.0599275
$902$	2.44918e8i	0.0111121i
$903$	− 9.10861e8i	− 0.0411666i
$904$	1.35392e10	0.609543
$905$	0	0
$906$	7.46610e9	0.333538
$907$	− 3.84880e10i	− 1.71277i	−0.516335	−	0.856387i	$-0.672704\pi$
$907$	− 3.84880e10i	− 1.71277i	0.516335	−	0.856387i	$-0.327296\pi$
$908$	8.57138e9i	0.379971i
$909$	−1.12724e10	−0.497785
$910$	0	0
$911$	−8.73430e9	−0.382749	−0.191374	−	0.981517i	$-0.561294\pi$
$911$	−8.73430e9	−0.382749	−0.191374	+	0.981517i	$0.561294\pi$
$912$	− 5.92375e9i	− 0.258592i
$913$	2.30805e8i	0.0100369i
$914$	1.45816e10	0.631676
$915$	0	0
$916$	1.34299e9	0.0577351
$917$	− 1.03657e10i	− 0.443919i
$918$	− 2.19473e9i	− 0.0936337i
$919$	−1.91695e10	−0.814717	−0.407358	−	0.913268i	$-0.633550\pi$
$919$	−1.91695e10	−0.814717	−0.407358	+	0.913268i	$0.633550\pi$
$920$	0	0
$921$	−3.05860e9	−0.129007
$922$	− 1.43666e9i	− 0.0603665i
$923$	− 3.52120e10i	− 1.47396i
$924$	−2.40538e7	−0.00100307
$925$	0	0
$926$	−3.16713e9	−0.131077
$927$	1.52379e10i	0.628268i
$928$	2.90174e9i	0.119190i
$929$	−9.51352e9	−0.389302	−0.194651	−	0.980873i	$-0.562357\pi$
$929$	−9.51352e9	−0.389302	−0.194651	+	0.980873i	$0.562357\pi$
$930$	0	0
$931$	−4.12292e10	−1.67449
$932$	− 7.78782e8i	− 0.0315109i
$933$	1.02153e10i	0.411779i
$934$	4.56225e9	0.183217
$935$	0	0
$936$	−5.24563e9	−0.209089
$937$	2.09871e10i	0.833422i	0.909039	+	0.416711i	$0.136817\pi$
$937$	2.09871e10i	0.833422i	−0.909039	+	0.416711i	$0.863183\pi$
$938$	1.99458e9i	0.0789119i
$939$	3.00781e9	0.118555
$940$	0	0
$941$	1.92302e9	0.0752349	0.0376175	−	0.999292i	$-0.488023\pi$
$941$	1.92302e9	0.0752349	0.0376175	+	0.999292i	$0.488023\pi$
$942$	1.08143e10i	0.421520i
$943$	1.37766e10i	0.534998i
$944$	7.72399e9	0.298841
$945$	0	0
$946$	6.97978e7	0.00268054
$947$	− 1.52483e10i	− 0.583440i	−0.956504	−	0.291720i	$-0.905772\pi$
$947$	− 1.52483e10i	− 0.583440i	0.956504	−	0.291720i	$-0.0942275\pi$
$948$	− 1.27090e10i	− 0.484489i
$949$	4.15235e10	1.57711
$950$	0	0
$951$	−1.80927e10	−0.682135
$952$	− 1.65561e9i	− 0.0621912i
$953$	− 1.60051e10i	− 0.599011i	−0.954095	−	0.299505i	$-0.903178\pi$
$953$	− 1.60051e10i	− 0.599011i	0.954095	−	0.299505i	$-0.0968216\pi$
$954$	5.50529e8	0.0205287
$955$	0	0
$956$	−3.00310e9	−0.111165
$957$	− 1.43457e8i	− 0.00529092i
$958$	− 3.49459e10i	− 1.28415i
$959$	−1.32224e10	−0.484110
$960$	0	0
$961$	−1.30280e10	−0.473529
$962$	5.28032e10i	1.91226i
$963$	1.49915e10i	0.540945i
$964$	1.46769e10	0.527674
$965$	0	0
$966$	−1.35302e9	−0.0482932
$967$	3.05254e10i	1.08560i	0.839863	+	0.542798i	$0.182635\pi$
$967$	3.05254e10i	1.08560i	−0.839863	+	0.542798i	$0.817365\pi$
$968$	9.97559e9i	0.353488i
$969$	−2.01575e10	−0.711712
$970$	0	0
$971$	3.85732e10	1.35213	0.676066	−	0.736841i	$-0.263684\pi$
$971$	3.85732e10	1.35213	0.676066	+	0.736841i	$0.263684\pi$
$972$	− 9.18330e8i	− 0.0320750i
$973$	− 7.11828e9i	− 0.247731i
$974$	2.63462e9	0.0913613
$975$	0	0
$976$	−1.11284e9	−0.0383142
$977$	1.90805e10i	0.654575i	0.944925	+	0.327287i	$0.106134\pi$
$977$	1.90805e10i	0.654575i	−0.944925	+	0.327287i	$0.893866\pi$
$978$	3.52855e8i	0.0120617i
$979$	3.41110e8	0.0116186
$980$	0	0
$981$	1.01951e10	0.344786
$982$	− 2.03733e10i	− 0.686547i
$983$	− 4.88330e10i	− 1.63974i	−0.572546	−	0.819872i	$-0.694044\pi$
$983$	− 4.88330e10i	− 1.63974i	0.572546	−	0.819872i	$-0.305956\pi$
$984$	−7.05364e9	−0.236010
$985$	0	0
$986$	9.87413e9	0.328042
$987$	1.90776e9i	0.0631560i
$988$	4.81785e10i	1.58929i
$989$	3.92612e9	0.129056
$990$	0	0
$991$	3.83732e10	1.25248	0.626239	−	0.779631i	$-0.284593\pi$
$991$	3.83732e10	1.25248	0.626239	+	0.779631i	$0.284593\pi$
$992$	− 3.94369e9i	− 0.128266i
$993$	− 1.46906e10i	− 0.476120i
$994$	4.65017e9	0.150182
$995$	0	0
$996$	−6.64719e9	−0.213172
$997$	2.22521e10i	0.711111i	0.934655	+	0.355555i	$0.115708\pi$
$997$	2.22521e10i	0.711111i	−0.934655	+	0.355555i	$0.884292\pi$
$998$	− 1.13996e10i	− 0.363022i
$999$	−9.24404e9	−0.293348

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.8.c.b.49.2		2
3.2	odd	2		450.8.c.j.199.1		2
5.2	odd	4		30.8.a.c.1.1	✓	1
5.3	odd	4		150.8.a.k.1.1		1
5.4	even	2	inner	150.8.c.b.49.1		2
15.2	even	4		90.8.a.g.1.1		1
15.8	even	4		450.8.a.g.1.1		1
15.14	odd	2		450.8.c.j.199.2		2
20.7	even	4		240.8.a.e.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.8.a.c.1.1	✓	1	5.2	odd	4
90.8.a.g.1.1		1	15.2	even	4
150.8.a.k.1.1		1	5.3	odd	4
150.8.c.b.49.1		2	5.4	even	2	inner
150.8.c.b.49.2		2	1.1	even	1	trivial
240.8.a.e.1.1		1	20.7	even	4
450.8.a.g.1.1		1	15.8	even	4
450.8.c.j.199.1		2	3.2	odd	2
450.8.c.j.199.2		2	15.14	odd	2

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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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	150.8.c.b.49.2

Level	$150$
Weight	$8$
Character	150.49
Analytic conductor	$46.858$
Analytic rank	$0$
Dimension	$2$
Inner twists	$2$