LMFDB - Embedded newform 363.8.a.r.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [363,8,Mod(1,363)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(363, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 8, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("363.1"); S:= CuspForms(chi, 8); N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	363.a (trivial)

Newform invariants

comment:select newform

sage:traces = [14,23] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$113.395764251$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} - 1289 x^{12} + 2366 x^{11} + 623758 x^{10} - 908404 x^{9} - 141535137 x^{8} + \cdots - 20874968128476 $ x^14 - 2x^13 - 1289x^12 + 2366x^11 + 623758x^10 - 908404x^9 - 141535137x^8 + 122490614x^7 + 15472711238x^6 - 831247148x^5 - 774565663469x^4 - 859523952378x^3 + 14942261922049x^2 + 32570153376222*x - 20874968128476
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{4}\cdot 11^{8} $
Twist minimal:	no (minimal twist has level 33)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-11.5294$ of defining polynomial
Character	$\chi$	$=$	363.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-8.91136 q^{2} +27.0000 q^{3} -48.5876 q^{4} -136.704 q^{5} -240.607 q^{6} +36.0476 q^{7} +1573.64 q^{8} +729.000 q^{9} +1218.22 q^{10} -1311.87 q^{12} -13419.3 q^{13} -321.233 q^{14} -3691.02 q^{15} -7804.03 q^{16} +31127.1 q^{17} -6496.38 q^{18} -48101.7 q^{19} +6642.14 q^{20} +973.285 q^{21} +76581.4 q^{23} +42488.2 q^{24} -59436.9 q^{25} +119584. q^{26} +19683.0 q^{27} -1751.47 q^{28} +142915. q^{29} +32892.0 q^{30} -22704.4 q^{31} -131881. q^{32} -277385. q^{34} -4927.87 q^{35} -35420.4 q^{36} -262940. q^{37} +428652. q^{38} -362320. q^{39} -215123. q^{40} -591395. q^{41} -8673.30 q^{42} +750154. q^{43} -99657.5 q^{45} -682445. q^{46} -105979. q^{47} -210709. q^{48} -822244. q^{49} +529664. q^{50} +840433. q^{51} +652011. q^{52} -910703. q^{53} -175402. q^{54} +56725.8 q^{56} -1.29875e6 q^{57} -1.27357e6 q^{58} -1.29394e6 q^{59} +179338. q^{60} +1.21870e6 q^{61} +202327. q^{62} +26278.7 q^{63} +2.17415e6 q^{64} +1.83447e6 q^{65} -1.79922e6 q^{67} -1.51239e6 q^{68} +2.06770e6 q^{69} +43914.0 q^{70} +1.10830e6 q^{71} +1.14718e6 q^{72} +231610. q^{73} +2.34316e6 q^{74} -1.60480e6 q^{75} +2.33715e6 q^{76} +3.22877e6 q^{78} +3.82577e6 q^{79} +1.06684e6 q^{80} +531441. q^{81} +5.27013e6 q^{82} +2.44422e6 q^{83} -47289.6 q^{84} -4.25522e6 q^{85} -6.68490e6 q^{86} +3.85871e6 q^{87} +1.91429e6 q^{89} +888084. q^{90} -483733. q^{91} -3.72091e6 q^{92} -613018. q^{93} +944414. q^{94} +6.57572e6 q^{95} -3.56078e6 q^{96} -1.44172e7 q^{97} +7.32731e6 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 23 q^{2} + 378 q^{3} + 845 q^{4} + 69 q^{5} + 621 q^{6} + 3278 q^{7} + 4602 q^{8} + 10206 q^{9} + 5320 q^{10} + 22815 q^{12} + 32188 q^{13} - 7794 q^{14} + 1863 q^{15} + 86137 q^{16} + 42917 q^{17}+ \cdots - 70266089 q^{98}+O(q^{100}) $ 14 * q + 23 * q^2 + 378 * q^3 + 845 * q^4 + 69 * q^5 + 621 * q^6 + 3278 * q^7 + 4602 * q^8 + 10206 * q^9 + 5320 * q^10 + 22815 * q^12 + 32188 * q^13 - 7794 * q^14 + 1863 * q^15 + 86137 * q^16 + 42917 * q^17 + 16767 * q^18 + 50419 * q^19 + 54475 * q^20 + 88506 * q^21 - 83492 * q^23 + 124254 * q^24 + 336991 * q^25 + 234897 * q^26 + 275562 * q^27 + 697184 * q^28 + 227028 * q^29 + 143640 * q^30 - 36481 * q^31 + 151749 * q^32 - 614562 * q^34 - 258783 * q^35 + 616005 * q^36 + 634524 * q^37 - 662891 * q^38 + 869076 * q^39 + 1585604 * q^40 + 1286544 * q^41 - 210438 * q^42 + 2632644 * q^43 + 50301 * q^45 + 1290627 * q^46 - 1692245 * q^47 + 2325699 * q^48 + 842030 * q^49 + 7870914 * q^50 + 1158759 * q^51 + 6419781 * q^52 + 1211317 * q^53 + 452709 * q^54 - 9100953 * q^56 + 1361313 * q^57 - 6265711 * q^58 + 2551943 * q^59 + 1470825 * q^60 + 10221163 * q^61 + 5723657 * q^62 + 2389662 * q^63 + 6349332 * q^64 + 7684087 * q^65 - 3570631 * q^67 + 13112925 * q^68 - 2254284 * q^69 + 3559265 * q^70 + 4528437 * q^71 + 3354858 * q^72 + 13052276 * q^73 + 4896205 * q^74 + 9098757 * q^75 + 9845214 * q^76 + 6342219 * q^78 + 14911090 * q^79 - 9395382 * q^80 + 7440174 * q^81 + 17478001 * q^82 + 7068900 * q^83 + 18823968 * q^84 + 24423120 * q^85 + 12792479 * q^86 + 6129756 * q^87 + 4800832 * q^89 + 3878280 * q^90 - 15295476 * q^91 - 3195753 * q^92 - 984987 * q^93 - 43320002 * q^94 + 7614177 * q^95 + 4097223 * q^96 - 11578773 * q^97 - 70266089 * q^98

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 $

$2$	−8.91136	−0.787661	−0.393830	−	0.919183i	$-0.628850\pi$
$2$	−8.91136	−0.787661	−0.393830	+	0.919183i	$0.628850\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	−48.5876	−0.379591
$5$	−136.704	−0.489088	−0.244544	−	0.969638i	$-0.578638\pi$
$5$	−136.704	−0.489088	−0.244544	+	0.969638i	$0.578638\pi$
$6$	−240.607	−0.454756
$7$	36.0476	0.0397222	0.0198611	−	0.999803i	$-0.493678\pi$
$7$	36.0476	0.0397222	0.0198611	+	0.999803i	$0.493678\pi$
$8$	1573.64	1.08665
$9$	729.000	0.333333
$10$	1218.22	0.385236
$11$	0	0
$11$	0	0
$12$	−1311.87	−0.219157
$13$	−13419.3	−1.69405	−0.847027	−	0.531550i	$-0.821610\pi$
$13$	−13419.3	−1.69405	−0.847027	+	0.531550i	$0.821610\pi$
$14$	−321.233	−0.0312876
$15$	−3691.02	−0.282375
$16$	−7804.03	−0.476320
$17$	31127.1	1.53663	0.768313	−	0.640075i	$-0.221097\pi$
$17$	31127.1	1.53663	0.768313	+	0.640075i	$0.221097\pi$
$18$	−6496.38	−0.262554
$19$	−48101.7	−1.60888	−0.804439	−	0.594035i	$-0.797534\pi$
$19$	−48101.7	−1.60888	−0.804439	+	0.594035i	$0.797534\pi$
$20$	6642.14	0.185653
$21$	973.285	0.0229336
$22$	0	0
$23$	76581.4	1.31243	0.656215	−	0.754574i	$-0.272156\pi$
$23$	76581.4	1.31243	0.656215	+	0.754574i	$0.272156\pi$
$24$	42488.2	0.627377
$25$	−59436.9	−0.760793
$26$	119584.	1.33434
$27$	19683.0	0.192450
$28$	−1751.47	−0.0150782
$29$	142915.	1.08814	0.544071	−	0.839039i	$-0.316882\pi$
$29$	142915.	1.08814	0.544071	+	0.839039i	$0.316882\pi$
$30$	32892.0	0.222416
$31$	−22704.4	−0.136881	−0.0684405	−	0.997655i	$-0.521802\pi$
$31$	−22704.4	−0.136881	−0.0684405	+	0.997655i	$0.521802\pi$
$32$	−131881.	−0.711471
$33$	0	0
$34$	−277385.	−1.21034
$35$	−4927.87	−0.0194277
$36$	−35420.4	−0.126530
$37$	−262940.	−0.853397	−0.426698	−	0.904394i	$-0.640323\pi$
$37$	−262940.	−0.853397	−0.426698	+	0.904394i	$0.640323\pi$
$38$	428652.	1.26725
$39$	−362320.	−0.978063
$40$	−215123.	−0.531468
$41$	−591395.	−1.34009	−0.670045	−	0.742321i	$-0.733725\pi$
$41$	−591395.	−1.34009	−0.670045	+	0.742321i	$0.733725\pi$
$42$	−8673.30	−0.0180639
$43$	750154.	1.43883	0.719417	−	0.694578i	$-0.244409\pi$
$43$	750154.	1.43883	0.719417	+	0.694578i	$0.244409\pi$
$44$	0	0
$45$	−99657.5	−0.163029
$46$	−682445.	−1.03375
$47$	−105979.	−0.148893	−0.0744467	−	0.997225i	$-0.523719\pi$
$47$	−105979.	−0.148893	−0.0744467	+	0.997225i	$0.523719\pi$
$48$	−210709.	−0.275004
$49$	−822244.	−0.998422
$50$	529664.	0.599246
$51$	840433.	0.887171
$52$	652011.	0.643047
$53$	−910703.	−0.840255	−0.420128	−	0.907465i	$-0.638015\pi$
$53$	−910703.	−0.840255	−0.420128	+	0.907465i	$0.638015\pi$
$54$	−175402.	−0.151585
$55$	0	0
$56$	56725.8	0.0431641
$57$	−1.29875e6	−0.928886
$58$	−1.27357e6	−0.857087
$59$	−1.29394e6	−0.820220	−0.410110	−	0.912036i	$-0.634510\pi$
$59$	−1.29394e6	−0.820220	−0.410110	+	0.912036i	$0.634510\pi$
$60$	179338.	0.107187
$61$	1.21870e6	0.687452	0.343726	−	0.939070i	$-0.388311\pi$
$61$	1.21870e6	0.687452	0.343726	+	0.939070i	$0.388311\pi$
$62$	202327.	0.107816
$63$	26278.7	0.0132407
$64$	2.17415e6	1.03672
$65$	1.83447e6	0.828542
$66$	0	0
$67$	−1.79922e6	−0.730842	−0.365421	−	0.930842i	$-0.619075\pi$
$67$	−1.79922e6	−0.730842	−0.365421	+	0.930842i	$0.619075\pi$
$68$	−1.51239e6	−0.583289
$69$	2.06770e6	0.757732
$70$	43914.0	0.0153024
$71$	1.10830e6	0.367497	0.183749	−	0.982973i	$-0.441177\pi$
$71$	1.10830e6	0.367497	0.183749	+	0.982973i	$0.441177\pi$
$72$	1.14718e6	0.362216
$73$	231610.	0.0696831	0.0348416	−	0.999393i	$-0.488907\pi$
$73$	231610.	0.0696831	0.0348416	+	0.999393i	$0.488907\pi$
$74$	2.34316e6	0.672187
$75$	−1.60480e6	−0.439244
$76$	2.33715e6	0.610715
$77$	0	0
$78$	3.22877e6	0.770381
$79$	3.82577e6	0.873020	0.436510	−	0.899699i	$-0.356214\pi$
$79$	3.82577e6	0.873020	0.436510	+	0.899699i	$0.356214\pi$
$80$	1.06684e6	0.232963
$81$	531441.	0.111111
$82$	5.27013e6	1.05554
$83$	2.44422e6	0.469210	0.234605	−	0.972091i	$-0.424620\pi$
$83$	2.44422e6	0.469210	0.234605	+	0.972091i	$0.424620\pi$
$84$	−47289.6	−0.00870539
$85$	−4.25522e6	−0.751546
$86$	−6.68490e6	−1.13331
$87$	3.85871e6	0.628239
$88$	0	0
$89$	1.91429e6	0.287834	0.143917	−	0.989590i	$-0.454030\pi$
$89$	1.91429e6	0.287834	0.143917	+	0.989590i	$0.454030\pi$
$90$	888084.	0.128412
$91$	−483733.	−0.0672916
$92$	−3.72091e6	−0.498186
$93$	−613018.	−0.0790283
$94$	944414.	0.117278
$95$	6.57572e6	0.786884
$96$	−3.56078e6	−0.410768
$97$	−1.44172e7	−1.60391	−0.801957	−	0.597382i	$-0.796208\pi$
$97$	−1.44172e7	−1.60391	−0.801957	+	0.597382i	$0.796208\pi$
$98$	7.32731e6	0.786418
$99$	0	0
$100$	2.88790e6	0.288790
$101$	−1.27715e7	−1.23344	−0.616718	−	0.787184i	$-0.711538\pi$
$101$	−1.27715e7	−1.23344	−0.616718	+	0.787184i	$0.711538\pi$
$102$	−7.48940e6	−0.698790
$103$	−1.39946e7	−1.26192	−0.630958	−	0.775817i	$-0.717338\pi$
$103$	−1.39946e7	−1.26192	−0.630958	+	0.775817i	$0.717338\pi$
$104$	−2.11171e7	−1.84084
$105$	−133052.	−0.0112166
$106$	8.11560e6	0.661836
$107$	1.23764e7	0.976680	0.488340	−	0.872653i	$-0.337603\pi$
$107$	1.23764e7	0.976680	0.488340	+	0.872653i	$0.337603\pi$
$108$	−956350.	−0.0730523
$109$	1.12352e7	0.830978	0.415489	−	0.909598i	$-0.363610\pi$
$109$	1.12352e7	0.830978	0.415489	+	0.909598i	$0.363610\pi$
$110$	0	0
$111$	−7.09939e6	−0.492709
$112$	−281317.	−0.0189205
$113$	6.82108e6	0.444712	0.222356	−	0.974966i	$-0.428625\pi$
$113$	6.82108e6	0.444712	0.222356	+	0.974966i	$0.428625\pi$
$114$	1.15736e7	0.731647
$115$	−1.04690e7	−0.641894
$116$	−6.94391e6	−0.413049
$117$	−9.78265e6	−0.564685
$118$	1.15307e7	0.646055
$119$	1.12206e6	0.0610381
$120$	−5.80832e6	−0.306843
$121$	0	0
$122$	−1.08603e7	−0.541479
$123$	−1.59677e7	−0.773701
$124$	1.10315e6	0.0519588
$125$	1.88053e7	0.861183
$126$	−234179.	−0.0104292
$127$	−1.15772e7	−0.501521	−0.250760	−	0.968049i	$-0.580681\pi$
$127$	−1.15772e7	−0.501521	−0.250760	+	0.968049i	$0.580681\pi$
$128$	−2.49392e6	−0.105111
$129$	2.02542e7	0.830712
$130$	−1.63477e7	−0.652610
$131$	2.50834e6	0.0974849	0.0487424	−	0.998811i	$-0.484479\pi$
$131$	2.50834e6	0.0974849	0.0487424	+	0.998811i	$0.484479\pi$
$132$	0	0
$133$	−1.73395e6	−0.0639082
$134$	1.60335e7	0.575655
$135$	−2.69075e6	−0.0941251
$136$	4.89828e7	1.66977
$137$	4.20739e7	1.39795	0.698973	−	0.715148i	$-0.253641\pi$
$137$	4.20739e7	1.39795	0.698973	+	0.715148i	$0.253641\pi$
$138$	−1.84260e7	−0.596835
$139$	5.45687e7	1.72342	0.861712	−	0.507398i	$-0.169393\pi$
$139$	5.45687e7	1.72342	0.861712	+	0.507398i	$0.169393\pi$
$140$	239433.	0.00737456
$141$	−2.86142e6	−0.0859637
$142$	−9.87649e6	−0.289463
$143$	0	0
$144$	−5.68914e6	−0.158773
$145$	−1.95371e7	−0.532198
$146$	−2.06396e6	−0.0548866
$147$	−2.22006e7	−0.576439
$148$	1.27756e7	0.323942
$149$	−2.75160e6	−0.0681449	−0.0340725	−	0.999419i	$-0.510848\pi$
$149$	−2.75160e6	−0.0681449	−0.0340725	+	0.999419i	$0.510848\pi$
$150$	1.43009e7	0.345975
$151$	−7.36855e6	−0.174166	−0.0870828	−	0.996201i	$-0.527754\pi$
$151$	−7.36855e6	−0.174166	−0.0870828	+	0.996201i	$0.527754\pi$
$152$	−7.56946e7	−1.74829
$153$	2.26917e7	0.512208
$154$	0	0
$155$	3.10378e6	0.0669469
$156$	1.76043e7	0.371264
$157$	4.42410e7	0.912381	0.456191	−	0.889882i	$-0.349214\pi$
$157$	4.42410e7	0.912381	0.456191	+	0.889882i	$0.349214\pi$
$158$	−3.40928e7	−0.687644
$159$	−2.45890e7	−0.485122
$160$	1.80287e7	0.347972
$161$	2.76058e6	0.0521326
$162$	−4.73586e6	−0.0875178
$163$	−1.01430e6	−0.0183447	−0.00917235	−	0.999958i	$-0.502920\pi$
$163$	−1.01430e6	−0.0183447	−0.00917235	+	0.999958i	$0.502920\pi$
$164$	2.87345e7	0.508686
$165$	0	0
$166$	−2.17813e7	−0.369578
$167$	2.57109e7	0.427178	0.213589	−	0.976924i	$-0.431485\pi$
$167$	2.57109e7	0.427178	0.213589	+	0.976924i	$0.431485\pi$
$168$	1.53160e6	0.0249208
$169$	1.17328e8	1.86982
$170$	3.79198e7	0.591963
$171$	−3.50662e7	−0.536293
$172$	−3.64482e7	−0.546168
$173$	1.11743e8	1.64081	0.820404	−	0.571784i	$-0.193748\pi$
$173$	1.11743e8	1.64081	0.820404	+	0.571784i	$0.193748\pi$
$174$	−3.43864e7	−0.494839
$175$	−2.14256e6	−0.0302204
$176$	0	0
$177$	−3.49363e7	−0.473554
$178$	−1.70589e7	−0.226715
$179$	−2.45048e7	−0.319349	−0.159675	−	0.987170i	$-0.551045\pi$
$179$	−2.45048e7	−0.319349	−0.159675	+	0.987170i	$0.551045\pi$
$180$	4.84212e6	0.0618845
$181$	1.21746e8	1.52609	0.763047	−	0.646344i	$-0.223703\pi$
$181$	1.21746e8	1.52609	0.763047	+	0.646344i	$0.223703\pi$
$182$	4.31072e6	0.0530029
$183$	3.29049e7	0.396901
$184$	1.20511e8	1.42615
$185$	3.59451e7	0.417387
$186$	5.46282e6	0.0622475
$187$	0	0
$188$	5.14925e6	0.0565186
$189$	709525.	0.00764454
$190$	−5.85986e7	−0.619797
$191$	1.33978e8	1.39129	0.695646	−	0.718385i	$-0.255118\pi$
$191$	1.33978e8	1.39129	0.695646	+	0.718385i	$0.255118\pi$
$192$	5.87022e7	0.598549
$193$	8.31747e7	0.832799	0.416400	−	0.909182i	$-0.363292\pi$
$193$	8.31747e7	0.832799	0.416400	+	0.909182i	$0.363292\pi$
$194$	1.28477e8	1.26334
$195$	4.95308e7	0.478359
$196$	3.99509e7	0.378992
$197$	−8.27669e7	−0.771303	−0.385652	−	0.922644i	$-0.626023\pi$
$197$	−8.27669e7	−0.771303	−0.385652	+	0.922644i	$0.626023\pi$
$198$	0	0
$199$	5.05775e7	0.454958	0.227479	−	0.973783i	$-0.426952\pi$
$199$	5.05775e7	0.454958	0.227479	+	0.973783i	$0.426952\pi$
$200$	−9.35321e7	−0.826715
$201$	−4.85790e7	−0.421952
$202$	1.13811e8	0.971530
$203$	5.15175e6	0.0432234
$204$	−4.08346e7	−0.336762
$205$	8.08462e7	0.655422
$206$	1.24711e8	0.993961
$207$	5.58279e7	0.437477
$208$	1.04724e8	0.806912
$209$	0	0
$210$	1.18568e6	0.00883485
$211$	2.03447e8	1.49095	0.745476	−	0.666532i	$-0.232222\pi$
$211$	2.03447e8	1.49095	0.745476	+	0.666532i	$0.232222\pi$
$212$	4.42489e7	0.318953
$213$	2.99242e7	0.212175
$214$	−1.10291e8	−0.769292
$215$	−1.02549e8	−0.703717
$216$	3.09739e7	0.209126
$217$	−818438.	−0.00543722
$218$	−1.00121e8	−0.654529
$219$	6.25347e6	0.0402316
$220$	0	0
$221$	−4.17704e8	−2.60313
$222$	6.32652e7	0.388087
$223$	−1.61600e8	−0.975831	−0.487915	−	0.872891i	$-0.662243\pi$
$223$	−1.61600e8	−0.975831	−0.487915	+	0.872891i	$0.662243\pi$
$224$	−4.75399e6	−0.0282612
$225$	−4.33295e7	−0.253598
$226$	−6.07851e7	−0.350282
$227$	2.52390e8	1.43213	0.716064	−	0.698034i	$-0.245942\pi$
$227$	2.52390e8	1.43213	0.716064	+	0.698034i	$0.245942\pi$
$228$	6.31030e7	0.352597
$229$	−3.40759e8	−1.87509	−0.937547	−	0.347860i	$-0.886909\pi$
$229$	−3.40759e8	−1.87509	−0.937547	+	0.347860i	$0.886909\pi$
$230$	9.32932e7	0.505595
$231$	0	0
$232$	2.24897e8	1.18243
$233$	3.30373e7	0.171103	0.0855517	−	0.996334i	$-0.472735\pi$
$233$	3.30373e7	0.171103	0.0855517	+	0.996334i	$0.472735\pi$
$234$	8.71767e7	0.444780
$235$	1.44877e7	0.0728221
$236$	6.28692e7	0.311348
$237$	1.03296e8	0.504039
$238$	−9.99907e6	−0.0480773
$239$	1.79272e8	0.849413	0.424706	−	0.905331i	$-0.360377\pi$
$239$	1.79272e8	0.849413	0.424706	+	0.905331i	$0.360377\pi$
$240$	2.88048e7	0.134501
$241$	2.24679e8	1.03396	0.516978	−	0.855998i	$-0.327057\pi$
$241$	2.24679e8	1.03396	0.516978	+	0.855998i	$0.327057\pi$
$242$	0	0
$243$	1.43489e7	0.0641500
$244$	−5.92137e7	−0.260951
$245$	1.12404e8	0.488317
$246$	1.42294e8	0.609414
$247$	6.45490e8	2.72553
$248$	−3.57284e7	−0.148742
$249$	6.59940e7	0.270898
$250$	−1.67581e8	−0.678320
$251$	2.02643e8	0.808861	0.404431	−	0.914569i	$-0.367470\pi$
$251$	2.02643e8	0.808861	0.404431	+	0.914569i	$0.367470\pi$
$252$	−1.27682e6	−0.00502606
$253$	0	0
$254$	1.03168e8	0.395028
$255$	−1.14891e8	−0.433905
$256$	−2.56068e8	−0.953926
$257$	1.44536e8	0.531140	0.265570	−	0.964092i	$-0.414440\pi$
$257$	1.44536e8	0.531140	0.265570	+	0.964092i	$0.414440\pi$
$258$	−1.80492e8	−0.654319
$259$	−9.47837e6	−0.0338988
$260$	−8.91327e7	−0.314507
$261$	1.04185e8	0.362714
$262$	−2.23527e7	−0.0767850
$263$	1.67215e8	0.566801	0.283401	−	0.959002i	$-0.408537\pi$
$263$	1.67215e8	0.566801	0.283401	+	0.959002i	$0.408537\pi$
$264$	0	0
$265$	1.24497e8	0.410959
$266$	1.54519e7	0.0503379
$267$	5.16857e7	0.166181
$268$	8.74200e7	0.277421
$269$	−1.08827e8	−0.340882	−0.170441	−	0.985368i	$-0.554519\pi$
$269$	−1.08827e8	−0.340882	−0.170441	+	0.985368i	$0.554519\pi$
$270$	2.39783e7	0.0741386
$271$	−3.07657e8	−0.939019	−0.469510	−	0.882927i	$-0.655569\pi$
$271$	−3.07657e8	−0.939019	−0.469510	+	0.882927i	$0.655569\pi$
$272$	−2.42917e8	−0.731925
$273$	−1.30608e7	−0.0388508
$274$	−3.74936e8	−1.10111
$275$	0	0
$276$	−1.00465e8	−0.287628
$277$	3.37254e8	0.953405	0.476703	−	0.879065i	$-0.341832\pi$
$277$	3.37254e8	0.953405	0.476703	+	0.879065i	$0.341832\pi$
$278$	−4.86282e8	−1.35747
$279$	−1.65515e7	−0.0456270
$280$	−7.75467e6	−0.0211111
$281$	1.22459e8	0.329245	0.164622	−	0.986357i	$-0.447359\pi$
$281$	1.22459e8	0.329245	0.164622	+	0.986357i	$0.447359\pi$
$282$	2.54992e7	0.0677102
$283$	2.25751e8	0.592076	0.296038	−	0.955176i	$-0.404335\pi$
$283$	2.25751e8	0.592076	0.296038	+	0.955176i	$0.404335\pi$
$284$	−5.38498e7	−0.139499
$285$	1.77544e8	0.454307
$286$	0	0
$287$	−2.13184e7	−0.0532313
$288$	−9.61412e7	−0.237157
$289$	5.58560e8	1.36122
$290$	1.74103e8	0.419191
$291$	−3.89265e8	−0.926020
$292$	−1.12534e7	−0.0264511
$293$	−9.33223e7	−0.216745	−0.108372	−	0.994110i	$-0.534564\pi$
$293$	−9.33223e7	−0.216745	−0.108372	+	0.994110i	$0.534564\pi$
$294$	1.97837e8	0.454039
$295$	1.76887e8	0.401160
$296$	−4.13772e8	−0.927343
$297$	0	0
$298$	2.45205e7	0.0536751
$299$	−1.02767e9	−2.22333
$300$	7.79733e7	0.166733
$301$	2.70413e7	0.0571537
$302$	6.56638e7	0.137183
$303$	−3.44830e8	−0.712125
$304$	3.75387e8	0.766341
$305$	−1.66602e8	−0.336225
$306$	−2.02214e8	−0.403446
$307$	1.74160e8	0.343529	0.171765	−	0.985138i	$-0.445053\pi$
$307$	1.74160e8	0.343529	0.171765	+	0.985138i	$0.445053\pi$
$308$	0	0
$309$	−3.77854e8	−0.728567
$310$	−2.76590e7	−0.0527315
$311$	5.96455e8	1.12439	0.562194	−	0.827005i	$-0.309957\pi$
$311$	5.96455e8	1.12439	0.562194	+	0.827005i	$0.309957\pi$
$312$	−5.70160e8	−1.06281
$313$	−4.68345e8	−0.863297	−0.431649	−	0.902042i	$-0.642068\pi$
$313$	−4.68345e8	−0.863297	−0.431649	+	0.902042i	$0.642068\pi$
$314$	−3.94248e8	−0.718647
$315$	−3.59241e6	−0.00647589
$316$	−1.85885e8	−0.331390
$317$	−2.38689e8	−0.420848	−0.210424	−	0.977610i	$-0.567484\pi$
$317$	−2.38689e8	−0.420848	−0.210424	+	0.977610i	$0.567484\pi$
$318$	2.19121e8	0.382111
$319$	0	0
$320$	−2.97216e8	−0.507047
$321$	3.34164e8	0.563886
$322$	−2.46005e7	−0.0410628
$323$	−1.49727e9	−2.47224
$324$	−2.58215e7	−0.0421768
$325$	7.97600e8	1.28882
$326$	9.03882e6	0.0144494
$327$	3.03352e8	0.479766
$328$	−9.30640e8	−1.45621
$329$	−3.82027e6	−0.00591438
$330$	0	0
$331$	8.95317e8	1.35700	0.678498	−	0.734602i	$-0.262631\pi$
$331$	8.95317e8	1.35700	0.678498	+	0.734602i	$0.262631\pi$
$332$	−1.18759e8	−0.178108
$333$	−1.91683e8	−0.284466
$334$	−2.29119e8	−0.336471
$335$	2.45962e8	0.357446
$336$	−7.59555e6	−0.0109237
$337$	−8.59820e8	−1.22378	−0.611890	−	0.790943i	$-0.709590\pi$
$337$	−8.59820e8	−1.22378	−0.611890	+	0.790943i	$0.709590\pi$
$338$	−1.04556e9	−1.47278
$339$	1.84169e8	0.256754
$340$	2.06751e8	0.285280
$341$	0	0
$342$	3.12487e8	0.422417
$343$	−5.93267e7	−0.0793817
$344$	1.18047e9	1.56351
$345$	−2.82663e8	−0.370598
$346$	−9.95780e8	−1.29240
$347$	−6.33708e7	−0.0814209	−0.0407105	−	0.999171i	$-0.512962\pi$
$347$	−6.33708e7	−0.0814209	−0.0407105	+	0.999171i	$0.512962\pi$
$348$	−1.87486e8	−0.238474
$349$	−9.21131e8	−1.15993	−0.579966	−	0.814641i	$-0.696934\pi$
$349$	−9.21131e8	−1.15993	−0.579966	+	0.814641i	$0.696934\pi$
$350$	1.90931e7	0.0238034
$351$	−2.64132e8	−0.326021
$352$	0	0
$353$	−6.19912e8	−0.750099	−0.375050	−	0.927005i	$-0.622374\pi$
$353$	−6.19912e8	−0.750099	−0.375050	+	0.927005i	$0.622374\pi$
$354$	3.11330e8	0.373000
$355$	−1.51510e8	−0.179739
$356$	−9.30106e7	−0.109259
$357$	3.02956e7	0.0352404
$358$	2.18371e8	0.251539
$359$	3.35550e8	0.382761	0.191380	−	0.981516i	$-0.438704\pi$
$359$	3.35550e8	0.382761	0.191380	+	0.981516i	$0.438704\pi$
$360$	−1.56825e8	−0.177156
$361$	1.41990e9	1.58849
$362$	−1.08493e9	−1.20204
$363$	0	0
$364$	2.35034e7	0.0255433
$365$	−3.16621e7	−0.0340812
$366$	−2.93228e8	−0.312623
$367$	1.76126e8	0.185991	0.0929956	−	0.995667i	$-0.470356\pi$
$367$	1.76126e8	0.185991	0.0929956	+	0.995667i	$0.470356\pi$
$368$	−5.97644e8	−0.625137
$369$	−4.31127e8	−0.446697
$370$	−3.20320e8	−0.328759
$371$	−3.28287e7	−0.0333768
$372$	2.97851e7	0.0299984
$373$	3.71682e7	0.0370843	0.0185422	−	0.999828i	$-0.494098\pi$
$373$	3.71682e7	0.0370843	0.0185422	+	0.999828i	$0.494098\pi$
$374$	0	0
$375$	5.07743e8	0.497204
$376$	−1.66772e8	−0.161795
$377$	−1.91782e9	−1.84337
$378$	−6.32283e6	−0.00602130
$379$	4.96879e7	0.0468828	0.0234414	−	0.999725i	$-0.492538\pi$
$379$	4.96879e7	0.0468828	0.0234414	+	0.999725i	$0.492538\pi$
$380$	−3.19498e8	−0.298694
$381$	−3.12583e8	−0.289553
$382$	−1.19393e9	−1.09587
$383$	4.27413e8	0.388733	0.194367	−	0.980929i	$-0.437735\pi$
$383$	4.27413e8	0.388733	0.194367	+	0.980929i	$0.437735\pi$
$384$	−6.73358e7	−0.0606858
$385$	0	0
$386$	−7.41200e8	−0.655963
$387$	5.46862e8	0.479612
$388$	7.00499e8	0.608831
$389$	−9.12549e8	−0.786018	−0.393009	−	0.919535i	$-0.628566\pi$
$389$	−9.12549e8	−0.786018	−0.393009	+	0.919535i	$0.628566\pi$
$390$	−4.41387e8	−0.376785
$391$	2.38376e9	2.01671
$392$	−1.29391e9	−1.08493
$393$	6.77252e7	0.0562829
$394$	7.37566e8	0.607525
$395$	−5.23000e8	−0.426984
$396$	0	0
$397$	1.80271e9	1.44597	0.722983	−	0.690865i	$-0.242770\pi$
$397$	1.80271e9	1.44597	0.722983	+	0.690865i	$0.242770\pi$
$398$	−4.50714e8	−0.358352
$399$	−4.68167e7	−0.0368974
$400$	4.63847e8	0.362381
$401$	8.33627e8	0.645604	0.322802	−	0.946466i	$-0.395375\pi$
$401$	8.33627e8	0.645604	0.322802	+	0.946466i	$0.395375\pi$
$402$	4.32905e8	0.332355
$403$	3.04676e8	0.231884
$404$	6.20537e8	0.468201
$405$	−7.26503e7	−0.0543432
$406$	−4.59091e7	−0.0340454
$407$	0	0
$408$	1.32254e9	0.964044
$409$	2.52002e8	0.182126	0.0910631	−	0.995845i	$-0.470973\pi$
$409$	2.52002e8	0.182126	0.0910631	+	0.995845i	$0.470973\pi$
$410$	−7.20450e8	−0.516250
$411$	1.13599e9	0.807105
$412$	6.79964e8	0.479011
$413$	−4.66433e7	−0.0325810
$414$	−4.97502e8	−0.344583
$415$	−3.34136e8	−0.229485
$416$	1.76975e9	1.20527
$417$	1.47336e9	0.995019
$418$	0	0
$419$	−8.72485e8	−0.579441	−0.289720	−	0.957111i	$-0.593562\pi$
$419$	−8.72485e8	−0.579441	−0.289720	+	0.957111i	$0.593562\pi$
$420$	6.46470e6	0.00425771
$421$	2.96770e8	0.193835	0.0969175	−	0.995292i	$-0.469102\pi$
$421$	2.96770e8	0.193835	0.0969175	+	0.995292i	$0.469102\pi$
$422$	−1.81299e9	−1.17436
$423$	−7.72584e7	−0.0496311
$424$	−1.43312e9	−0.913063
$425$	−1.85010e9	−1.16905
$426$	−2.66665e8	−0.167122
$427$	4.39312e7	0.0273071
$428$	−6.01341e8	−0.370739
$429$	0	0
$430$	9.13854e8	0.554290
$431$	−2.04430e9	−1.22991	−0.614955	−	0.788562i	$-0.710826\pi$
$431$	−2.04430e9	−1.22991	−0.614955	+	0.788562i	$0.710826\pi$
$432$	−1.53607e8	−0.0916678
$433$	−1.24093e9	−0.734582	−0.367291	−	0.930106i	$-0.619715\pi$
$433$	−1.24093e9	−0.734582	−0.367291	+	0.930106i	$0.619715\pi$
$434$	7.29340e6	0.00428268
$435$	−5.27503e8	−0.307264
$436$	−5.45894e8	−0.315432
$437$	−3.68370e9	−2.11154
$438$	−5.57270e7	−0.0316888
$439$	3.43514e8	0.193785	0.0968923	−	0.995295i	$-0.469110\pi$
$439$	3.43514e8	0.193785	0.0968923	+	0.995295i	$0.469110\pi$
$440$	0	0
$441$	−5.99416e8	−0.332807
$442$	3.72231e9	2.05038
$443$	3.17949e9	1.73758	0.868791	−	0.495180i	$-0.164898\pi$
$443$	3.17949e9	1.73758	0.868791	+	0.495180i	$0.164898\pi$
$444$	3.44942e8	0.187028
$445$	−2.61691e8	−0.140776
$446$	1.44008e9	0.768623
$447$	−7.42932e7	−0.0393435
$448$	7.83731e7	0.0411807
$449$	1.99556e9	1.04041	0.520203	−	0.854043i	$-0.325856\pi$
$449$	1.99556e9	1.04041	0.520203	+	0.854043i	$0.325856\pi$
$450$	3.86125e8	0.199749
$451$	0	0
$452$	−3.31420e8	−0.168808
$453$	−1.98951e8	−0.100555
$454$	−2.24914e9	−1.12803
$455$	6.61284e7	0.0329115
$456$	−2.04375e9	−1.00937
$457$	−3.66922e9	−1.79832	−0.899159	−	0.437622i	$-0.855821\pi$
$457$	−3.66922e9	−1.79832	−0.899159	+	0.437622i	$0.855821\pi$
$458$	3.03662e9	1.47694
$459$	6.12675e8	0.295724
$460$	5.08665e8	0.243657
$461$	−1.09387e9	−0.520010	−0.260005	−	0.965607i	$-0.583724\pi$
$461$	−1.09387e9	−0.520010	−0.260005	+	0.965607i	$0.583724\pi$
$462$	0	0
$463$	−3.35862e9	−1.57263	−0.786317	−	0.617824i	$-0.788015\pi$
$463$	−3.35862e9	−1.57263	−0.786317	+	0.617824i	$0.788015\pi$
$464$	−1.11531e9	−0.518304
$465$	8.38022e7	0.0386518
$466$	−2.94407e8	−0.134771
$467$	3.62609e9	1.64752	0.823758	−	0.566942i	$-0.191874\pi$
$467$	3.62609e9	1.64752	0.823758	+	0.566942i	$0.191874\pi$
$468$	4.75316e8	0.214349
$469$	−6.48577e7	−0.0290306
$470$	−1.29105e8	−0.0573591
$471$	1.19451e9	0.526764
$472$	−2.03618e9	−0.891292
$473$	0	0
$474$	−9.20507e8	−0.397011
$475$	2.85902e9	1.22402
$476$	−5.45182e7	−0.0231695
$477$	−6.63902e8	−0.280085
$478$	−1.59755e9	−0.669049
$479$	1.75250e9	0.728589	0.364294	−	0.931284i	$-0.381310\pi$
$479$	1.75250e9	0.728589	0.364294	+	0.931284i	$0.381310\pi$
$480$	4.86775e8	0.200902
$481$	3.52847e9	1.44570
$482$	−2.00219e9	−0.814407
$483$	7.45356e7	0.0300988
$484$	0	0
$485$	1.97090e9	0.784456
$486$	−1.27868e8	−0.0505285
$487$	−3.46090e9	−1.35780	−0.678902	−	0.734229i	$-0.737544\pi$
$487$	−3.46090e9	−1.35780	−0.678902	+	0.734229i	$0.737544\pi$
$488$	1.91779e9	0.747019
$489$	−2.73862e7	−0.0105913
$490$	−1.00168e9	−0.384628
$491$	−2.35598e9	−0.898228	−0.449114	−	0.893475i	$-0.648260\pi$
$491$	−2.35598e9	−0.898228	−0.449114	+	0.893475i	$0.648260\pi$
$492$	7.75830e8	0.293690
$493$	4.44854e9	1.67207
$494$	−5.75220e9	−2.14679
$495$	0	0
$496$	1.77185e8	0.0651992
$497$	3.99517e7	0.0145978
$498$	−5.88096e8	−0.213376
$499$	−2.56638e7	−0.00924632	−0.00462316	−	0.999989i	$-0.501472\pi$
$499$	−2.56638e7	−0.00924632	−0.00462316	+	0.999989i	$0.501472\pi$
$500$	−9.13705e8	−0.326897
$501$	6.94193e8	0.246631
$502$	−1.80583e9	−0.637108
$503$	−1.52399e9	−0.533941	−0.266970	−	0.963705i	$-0.586023\pi$
$503$	−1.52399e9	−0.533941	−0.266970	+	0.963705i	$0.586023\pi$
$504$	4.13531e7	0.0143880
$505$	1.74592e9	0.603260
$506$	0	0
$507$	3.16787e9	1.07954
$508$	5.62506e8	0.190373
$509$	2.20253e9	0.740304	0.370152	−	0.928971i	$-0.379306\pi$
$509$	2.20253e9	0.740304	0.370152	+	0.928971i	$0.379306\pi$
$510$	1.02383e9	0.341770
$511$	8.34899e6	0.00276797
$512$	2.60113e9	0.856481
$513$	−9.46786e8	−0.309629
$514$	−1.28801e9	−0.418358
$515$	1.91312e9	0.617188
$516$	−9.84101e8	−0.315330
$517$	0	0
$518$	8.44652e7	0.0267008
$519$	3.01705e9	0.947321
$520$	2.88679e9	0.900335
$521$	1.05738e9	0.327567	0.163784	−	0.986496i	$-0.447630\pi$
$521$	1.05738e9	0.327567	0.163784	+	0.986496i	$0.447630\pi$
$522$	−9.28432e8	−0.285696
$523$	2.17638e9	0.665239	0.332620	−	0.943061i	$-0.392067\pi$
$523$	2.17638e9	0.665239	0.332620	+	0.943061i	$0.392067\pi$
$524$	−1.21874e8	−0.0370044
$525$	−5.78491e7	−0.0174477
$526$	−1.49012e9	−0.446447
$527$	−7.06722e8	−0.210335
$528$	0	0
$529$	2.45989e9	0.722472
$530$	−1.10944e9	−0.323696
$531$	−9.43279e8	−0.273407
$532$	8.42486e7	0.0242589
$533$	7.93609e9	2.27018
$534$	−4.60590e8	−0.130894
$535$	−1.69191e9	−0.477683
$536$	−2.83132e9	−0.794169
$537$	−6.61630e8	−0.184376
$538$	9.69799e8	0.268500
$539$	0	0
$540$	1.30737e8	0.0357290
$541$	−6.40721e9	−1.73972	−0.869859	−	0.493301i	$-0.835790\pi$
$541$	−6.40721e9	−1.73972	−0.869859	+	0.493301i	$0.835790\pi$
$542$	2.74164e9	0.739629
$543$	3.28715e9	0.881090
$544$	−4.10508e9	−1.09326
$545$	−1.53591e9	−0.406422
$546$	1.16389e8	0.0306012
$547$	3.36465e9	0.878991	0.439496	−	0.898245i	$-0.355157\pi$
$547$	3.36465e9	0.878991	0.439496	+	0.898245i	$0.355157\pi$
$548$	−2.04427e9	−0.530648
$549$	8.88433e8	0.229151
$550$	0	0
$551$	−6.87447e9	−1.75069
$552$	3.25381e9	0.823389
$553$	1.37910e8	0.0346783
$554$	−3.00539e9	−0.750960
$555$	9.70517e8	0.240978
$556$	−2.65136e9	−0.654196
$557$	6.38004e9	1.56434	0.782169	−	0.623067i	$-0.214114\pi$
$557$	6.38004e9	1.56434	0.782169	+	0.623067i	$0.214114\pi$
$558$	1.47496e8	0.0359386
$559$	−1.00665e10	−2.43746
$560$	3.84572e7	0.00925379
$561$	0	0
$562$	−1.09128e9	−0.259333
$563$	−2.77212e9	−0.654686	−0.327343	−	0.944906i	$-0.606153\pi$
$563$	−2.77212e9	−0.654686	−0.327343	+	0.944906i	$0.606153\pi$
$564$	1.39030e8	0.0326310
$565$	−9.32471e8	−0.217503
$566$	−2.01175e9	−0.466355
$567$	1.91572e7	0.00441358
$568$	1.74407e9	0.399341
$569$	2.62697e9	0.597808	0.298904	−	0.954283i	$-0.403379\pi$
$569$	2.62697e9	0.597808	0.298904	+	0.954283i	$0.403379\pi$
$570$	−1.58216e9	−0.357840
$571$	4.02057e9	0.903776	0.451888	−	0.892075i	$-0.350751\pi$
$571$	4.02057e9	0.903776	0.451888	+	0.892075i	$0.350751\pi$
$572$	0	0
$573$	3.61742e9	0.803263
$574$	1.89976e8	0.0419282
$575$	−4.55176e9	−0.998487
$576$	1.58496e9	0.345573
$577$	−5.02115e9	−1.08815	−0.544074	−	0.839037i	$-0.683119\pi$
$577$	−5.02115e9	−1.08815	−0.544074	+	0.839037i	$0.683119\pi$
$578$	−4.97753e9	−1.07218
$579$	2.24572e9	0.480817
$580$	9.49263e8	0.202017
$581$	8.81083e7	0.0186380
$582$	3.46889e9	0.729390
$583$	0	0
$584$	3.64470e8	0.0757211
$585$	1.33733e9	0.276181
$586$	8.31629e8	0.170721
$587$	−5.84178e9	−1.19210	−0.596049	−	0.802948i	$-0.703264\pi$
$587$	−5.84178e9	−1.19210	−0.596049	+	0.802948i	$0.703264\pi$
$588$	1.07867e9	0.218811
$589$	1.09212e9	0.220225
$590$	−1.57630e9	−0.315978
$591$	−2.23471e9	−0.445312
$592$	2.05199e9	0.406490
$593$	−7.36520e9	−1.45042	−0.725208	−	0.688529i	$-0.758257\pi$
$593$	−7.36520e9	−1.45042	−0.725208	+	0.688529i	$0.758257\pi$
$594$	0	0
$595$	−1.53390e8	−0.0298530
$596$	1.33694e8	0.0258672
$597$	1.36559e9	0.262670
$598$	9.15792e9	1.75123
$599$	2.36658e9	0.449912	0.224956	−	0.974369i	$-0.427776\pi$
$599$	2.36658e9	0.449912	0.224956	+	0.974369i	$0.427776\pi$
$600$	−2.52537e9	−0.477304
$601$	1.92050e9	0.360871	0.180436	−	0.983587i	$-0.442249\pi$
$601$	1.92050e9	0.360871	0.180436	+	0.983587i	$0.442249\pi$
$602$	−2.40974e8	−0.0450177
$603$	−1.31163e9	−0.243614
$604$	3.58020e8	0.0661117
$605$	0	0
$606$	3.07291e9	0.560913
$607$	−2.53705e8	−0.0460435	−0.0230217	−	0.999735i	$-0.507329\pi$
$607$	−2.53705e8	−0.0460435	−0.0230217	+	0.999735i	$0.507329\pi$
$608$	6.34370e9	1.14467
$609$	1.39097e8	0.0249550
$610$	1.48465e9	0.264831
$611$	1.42216e9	0.252234
$612$	−1.10253e9	−0.194430
$613$	5.54411e9	0.972120	0.486060	−	0.873925i	$-0.338434\pi$
$613$	5.54411e9	0.972120	0.486060	+	0.873925i	$0.338434\pi$
$614$	−1.55200e9	−0.270585
$615$	2.18285e9	0.378408
$616$	0	0
$617$	−1.00616e10	−1.72453	−0.862265	−	0.506457i	$-0.830955\pi$
$617$	−1.00616e10	−1.72453	−0.862265	+	0.506457i	$0.830955\pi$
$618$	3.36720e9	0.573864
$619$	1.41349e9	0.239539	0.119770	−	0.992802i	$-0.461784\pi$
$619$	1.41349e9	0.239539	0.119770	+	0.992802i	$0.461784\pi$
$620$	−1.50806e8	−0.0254124
$621$	1.50735e9	0.252577
$622$	−5.31523e9	−0.885637
$623$	6.90054e7	0.0114334
$624$	2.82756e9	0.465871
$625$	2.07274e9	0.339598
$626$	4.17359e9	0.679985
$627$	0	0
$628$	−2.14957e9	−0.346332
$629$	−8.18458e9	−1.31135
$630$	3.20133e7	0.00510080
$631$	2.16250e9	0.342653	0.171326	−	0.985214i	$-0.445195\pi$
$631$	2.16250e9	0.342653	0.171326	+	0.985214i	$0.445195\pi$
$632$	6.02037e9	0.948667
$633$	5.49308e9	0.860802
$634$	2.12704e9	0.331485
$635$	1.58265e9	0.245288
$636$	1.19472e9	0.184148
$637$	1.10339e10	1.69138
$638$	0	0
$639$	8.07953e8	0.122499
$640$	3.40930e8	0.0514085
$641$	−9.66792e9	−1.44987	−0.724937	−	0.688816i	$-0.758131\pi$
$641$	−9.66792e9	−1.44987	−0.724937	+	0.688816i	$0.758131\pi$
$642$	−2.97785e9	−0.444151
$643$	−4.33710e9	−0.643370	−0.321685	−	0.946847i	$-0.604249\pi$
$643$	−4.33710e9	−0.643370	−0.321685	+	0.946847i	$0.604249\pi$
$644$	−1.34130e8	−0.0197891
$645$	−2.76883e9	−0.406291
$646$	1.33427e10	1.94729
$647$	−7.24369e9	−1.05147	−0.525733	−	0.850650i	$-0.676209\pi$
$647$	−7.24369e9	−1.05147	−0.525733	+	0.850650i	$0.676209\pi$
$648$	8.36295e8	0.120739
$649$	0	0
$650$	−7.10770e9	−1.01516
$651$	−2.20978e7	−0.00313918
$652$	4.92825e7	0.00696348
$653$	6.02648e9	0.846968	0.423484	−	0.905903i	$-0.360807\pi$
$653$	6.02648e9	0.846968	0.423484	+	0.905903i	$0.360807\pi$
$654$	−2.70328e9	−0.377892
$655$	−3.42901e8	−0.0476787
$656$	4.61526e9	0.638312
$657$	1.68844e8	0.0232277
$658$	3.40438e7	0.00465852
$659$	1.16210e10	1.58178	0.790888	−	0.611961i	$-0.209619\pi$
$659$	1.16210e10	1.58178	0.790888	+	0.611961i	$0.209619\pi$
$660$	0	0
$661$	5.58371e9	0.752000	0.376000	−	0.926620i	$-0.377299\pi$
$661$	5.58371e9	0.752000	0.376000	+	0.926620i	$0.377299\pi$
$662$	−7.97849e9	−1.06885
$663$	−1.12780e10	−1.50292
$664$	3.84631e9	0.509867
$665$	2.37039e8	0.0312567
$666$	1.70816e9	0.224062
$667$	1.09447e10	1.42811
$668$	−1.24923e9	−0.162153
$669$	−4.36320e9	−0.563396
$670$	−2.19185e9	−0.281546
$671$	0	0
$672$	−1.28358e8	−0.0163166
$673$	−1.87107e9	−0.236612	−0.118306	−	0.992977i	$-0.537746\pi$
$673$	−1.87107e9	−0.236612	−0.118306	+	0.992977i	$0.537746\pi$
$674$	7.66217e9	0.963923
$675$	−1.16990e9	−0.146415
$676$	−5.70071e9	−0.709766
$677$	1.13083e10	1.40068	0.700339	−	0.713810i	$-0.253032\pi$
$677$	1.13083e10	1.40068	0.700339	+	0.713810i	$0.253032\pi$
$678$	−1.64120e9	−0.202235
$679$	−5.19707e8	−0.0637110
$680$	−6.69616e9	−0.816666
$681$	6.81454e9	0.826840
$682$	0	0
$683$	1.18365e10	1.42151	0.710757	−	0.703437i	$-0.248352\pi$
$683$	1.18365e10	1.42151	0.710757	+	0.703437i	$0.248352\pi$
$684$	1.70378e9	0.203572
$685$	−5.75168e9	−0.683720
$686$	5.28681e8	0.0625259
$687$	−9.20049e9	−1.08259
$688$	−5.85422e9	−0.685346
$689$	1.22210e10	1.42344
$690$	2.51892e9	0.291905
$691$	−1.39695e10	−1.61068	−0.805338	−	0.592817i	$-0.798016\pi$
$691$	−1.39695e10	−1.61068	−0.805338	+	0.592817i	$0.798016\pi$
$692$	−5.42931e9	−0.622836
$693$	0	0
$694$	5.64720e8	0.0641320
$695$	−7.45978e9	−0.842907
$696$	6.07221e9	0.682676
$697$	−1.84084e10	−2.05922
$698$	8.20853e9	0.913633
$699$	8.92007e8	0.0987866
$700$	1.04102e8	0.0114714
$701$	−1.70615e10	−1.87070	−0.935349	−	0.353726i	$-0.884914\pi$
$701$	−1.70615e10	−1.87070	−0.935349	+	0.353726i	$0.884914\pi$
$702$	2.35377e9	0.256794
$703$	1.26479e10	1.37301
$704$	0	0
$705$	3.91169e8	0.0420438
$706$	5.52426e9	0.590824
$707$	−4.60382e8	−0.0489948
$708$	1.69747e9	0.179757
$709$	8.65719e9	0.912252	0.456126	−	0.889915i	$-0.349237\pi$
$709$	8.65719e9	0.912252	0.456126	+	0.889915i	$0.349237\pi$
$710$	1.35016e9	0.141573
$711$	2.78899e9	0.291007
$712$	3.01239e9	0.312774
$713$	−1.73873e9	−0.179647
$714$	−2.69975e8	−0.0277575
$715$	0	0
$716$	1.19063e9	0.121222
$717$	4.84033e9	0.490409
$718$	−2.99021e9	−0.301485
$719$	1.03963e10	1.04310	0.521550	−	0.853221i	$-0.325354\pi$
$719$	1.03963e10	1.04310	0.521550	+	0.853221i	$0.325354\pi$
$720$	7.77730e8	0.0776542
$721$	−5.04472e8	−0.0501260
$722$	−1.26533e10	−1.25119
$723$	6.06633e9	0.596955
$724$	−5.91537e9	−0.579291
$725$	−8.49444e9	−0.827850
$726$	0	0
$727$	−1.58088e10	−1.52591	−0.762954	−	0.646452i	$-0.776252\pi$
$727$	−1.58088e10	−1.52591	−0.762954	+	0.646452i	$0.776252\pi$
$728$	−7.61219e8	−0.0731223
$729$	3.87420e8	0.0370370
$730$	2.82153e8	0.0268444
$731$	2.33501e10	2.21095
$732$	−1.59877e9	−0.150660
$733$	1.23275e10	1.15614	0.578071	−	0.815986i	$-0.303806\pi$
$733$	1.23275e10	1.15614	0.578071	+	0.815986i	$0.303806\pi$
$734$	−1.56952e9	−0.146498
$735$	3.03492e9	0.281930
$736$	−1.00996e10	−0.933755
$737$	0	0
$738$	3.84193e9	0.351845
$739$	1.16220e10	1.05932	0.529658	−	0.848211i	$-0.322320\pi$
$739$	1.16220e10	1.05932	0.529658	+	0.848211i	$0.322320\pi$
$740$	−1.74649e9	−0.158436
$741$	1.74282e10	1.57358
$742$	2.92548e8	0.0262896
$743$	7.00441e9	0.626485	0.313243	−	0.949673i	$-0.398585\pi$
$743$	7.00441e9	0.626485	0.313243	+	0.949673i	$0.398585\pi$
$744$	−9.64667e8	−0.0858761
$745$	3.76156e8	0.0333289
$746$	−3.31219e8	−0.0292099
$747$	1.78184e9	0.156403
$748$	0	0
$749$	4.46141e8	0.0387959
$750$	−4.52469e9	−0.391628
$751$	1.13785e10	0.980269	0.490135	−	0.871647i	$-0.336948\pi$
$751$	1.13785e10	0.980269	0.490135	+	0.871647i	$0.336948\pi$
$752$	8.27060e8	0.0709209
$753$	5.47137e9	0.466996
$754$	1.70904e10	1.45195
$755$	1.00731e9	0.0851824
$756$	−3.44741e7	−0.00290180
$757$	4.98421e9	0.417600	0.208800	−	0.977958i	$-0.433044\pi$
$757$	4.98421e9	0.417600	0.208800	+	0.977958i	$0.433044\pi$
$758$	−4.42787e8	−0.0369277
$759$	0	0
$760$	1.03478e10	0.855066
$761$	1.08756e10	0.894555	0.447278	−	0.894395i	$-0.352394\pi$
$761$	1.08756e10	0.894555	0.447278	+	0.894395i	$0.352394\pi$
$762$	2.78554e9	0.228070
$763$	4.05004e8	0.0330083
$764$	−6.50969e9	−0.528121
$765$	−3.10205e9	−0.250515
$766$	−3.80883e9	−0.306190
$767$	1.73637e10	1.38950
$768$	−6.91382e9	−0.550749
$769$	9.12903e9	0.723906	0.361953	−	0.932196i	$-0.382110\pi$
$769$	9.12903e9	0.723906	0.361953	+	0.932196i	$0.382110\pi$
$770$	0	0
$771$	3.90246e9	0.306654
$772$	−4.04126e9	−0.316123
$773$	−6.46587e9	−0.503499	−0.251749	−	0.967792i	$-0.581006\pi$
$773$	−6.46587e9	−0.503499	−0.251749	+	0.967792i	$0.581006\pi$
$774$	−4.87329e9	−0.377771
$775$	1.34948e9	0.104138
$776$	−2.26875e10	−1.74289
$777$	−2.55916e8	−0.0195715
$778$	8.13206e9	0.619116
$779$	2.84471e10	2.15604
$780$	−2.40658e9	−0.181581
$781$	0	0
$782$	−2.12426e10	−1.58849
$783$	2.81300e9	0.209413
$784$	6.41681e9	0.475569
$785$	−6.04794e9	−0.446235
$786$	−6.03524e8	−0.0443318
$787$	−1.41699e10	−1.03623	−0.518113	−	0.855312i	$-0.673365\pi$
$787$	−1.41699e10	−1.03623	−0.518113	+	0.855312i	$0.673365\pi$
$788$	4.02145e9	0.292780
$789$	4.51481e9	0.327243
$790$	4.66064e9	0.336319
$791$	2.45883e8	0.0176649
$792$	0	0
$793$	−1.63541e10	−1.16458
$794$	−1.60646e10	−1.13893
$795$	3.36142e9	0.237267
$796$	−2.45744e9	−0.172698
$797$	−1.43127e10	−1.00142	−0.500712	−	0.865614i	$-0.666929\pi$
$797$	−1.43127e10	−1.00142	−0.500712	+	0.865614i	$0.666929\pi$
$798$	4.17201e8	0.0290626
$799$	−3.29881e9	−0.228793
$800$	7.83860e9	0.541282
$801$	1.39551e9	0.0959446
$802$	−7.42875e9	−0.508517
$803$	0	0
$804$	2.36034e9	0.160169
$805$	−3.77383e8	−0.0254975
$806$	−2.71508e9	−0.182646
$807$	−2.93834e9	−0.196809
$808$	−2.00977e10	−1.34031
$809$	−4.79015e9	−0.318075	−0.159038	−	0.987273i	$-0.550839\pi$
$809$	−4.79015e9	−0.318075	−0.159038	+	0.987273i	$0.550839\pi$
$810$	6.47413e8	0.0428040
$811$	−7.82863e8	−0.0515362	−0.0257681	−	0.999668i	$-0.508203\pi$
$811$	−7.82863e8	−0.0515362	−0.0257681	+	0.999668i	$0.508203\pi$
$812$	−2.50311e8	−0.0164072
$813$	−8.30674e9	−0.542143
$814$	0	0
$815$	1.38660e8	0.00897218
$816$	−6.55876e9	−0.422577
$817$	−3.60837e10	−2.31491
$818$	−2.24568e9	−0.143454
$819$	−3.52641e8	−0.0224305
$820$	−3.92813e9	−0.248792
$821$	3.46070e9	0.218254	0.109127	−	0.994028i	$-0.465194\pi$
$821$	3.46070e9	0.218254	0.109127	+	0.994028i	$0.465194\pi$
$822$	−1.01233e10	−0.635725
$823$	1.74239e10	1.08955	0.544774	−	0.838583i	$-0.316615\pi$
$823$	1.74239e10	1.08955	0.544774	+	0.838583i	$0.316615\pi$
$824$	−2.20224e10	−1.37126
$825$	0	0
$826$	4.15655e8	0.0256627
$827$	−5.32736e9	−0.327524	−0.163762	−	0.986500i	$-0.552363\pi$
$827$	−5.32736e9	−0.327524	−0.163762	+	0.986500i	$0.552363\pi$
$828$	−2.71254e9	−0.166062
$829$	2.38657e10	1.45490	0.727451	−	0.686160i	$-0.240705\pi$
$829$	2.38657e10	1.45490	0.727451	+	0.686160i	$0.240705\pi$
$830$	2.97760e9	0.180756
$831$	9.10585e9	0.550449
$832$	−2.91756e10	−1.75626
$833$	−2.55941e10	−1.53420
$834$	−1.31296e10	−0.783737
$835$	−3.51479e9	−0.208928
$836$	0	0
$837$	−4.46890e8	−0.0263428
$838$	7.77503e9	0.456403
$839$	2.29941e10	1.34415	0.672077	−	0.740481i	$-0.265402\pi$
$839$	2.29941e10	1.34415	0.672077	+	0.740481i	$0.265402\pi$
$840$	−2.09376e8	−0.0121885
$841$	3.17489e9	0.184053
$842$	−2.64462e9	−0.152676
$843$	3.30640e9	0.190090
$844$	−9.88503e9	−0.565952
$845$	−1.60393e10	−0.914507
$846$	6.88477e8	0.0390925
$847$	0	0
$848$	7.10715e9	0.400230
$849$	6.09528e9	0.341835
$850$	1.64869e10	0.920817
$851$	−2.01363e10	−1.12002
$852$	−1.45394e9	−0.0805395
$853$	2.38161e10	1.31386	0.656931	−	0.753951i	$-0.271854\pi$
$853$	2.38161e10	1.31386	0.656931	+	0.753951i	$0.271854\pi$
$854$	−3.91487e8	−0.0215087
$855$	4.79370e9	0.262295
$856$	1.94760e10	1.06131
$857$	−7.02104e8	−0.0381038	−0.0190519	−	0.999818i	$-0.506065\pi$
$857$	−7.02104e8	−0.0381038	−0.0190519	+	0.999818i	$0.506065\pi$
$858$	0	0
$859$	2.82931e10	1.52302	0.761508	−	0.648155i	$-0.224459\pi$
$859$	2.82931e10	1.52302	0.761508	+	0.648155i	$0.224459\pi$
$860$	4.98263e9	0.267125
$861$	−5.75596e8	−0.0307331
$862$	1.82175e10	0.968752
$863$	3.62273e9	0.191866	0.0959331	−	0.995388i	$-0.469417\pi$
$863$	3.62273e9	0.191866	0.0959331	+	0.995388i	$0.469417\pi$
$864$	−2.59581e9	−0.136923
$865$	−1.52757e10	−0.802501
$866$	1.10584e10	0.578601
$867$	1.50811e10	0.785899
$868$	3.97659e7	0.00206392
$869$	0	0
$870$	4.70077e9	0.242020
$871$	2.41443e10	1.23809
$872$	1.76802e10	0.902982
$873$	−1.05102e10	−0.534638
$874$	3.28268e10	1.66318
$875$	6.77887e8	0.0342081
$876$	−3.03841e8	−0.0152715
$877$	−2.06676e10	−1.03464	−0.517322	−	0.855791i	$-0.673071\pi$
$877$	−2.06676e10	−1.03464	−0.517322	+	0.855791i	$0.673071\pi$
$878$	−3.06118e9	−0.152636
$879$	−2.51970e9	−0.125138
$880$	0	0
$881$	−2.28892e10	−1.12776	−0.563879	−	0.825857i	$-0.690692\pi$
$881$	−2.28892e10	−1.12776	−0.563879	+	0.825857i	$0.690692\pi$
$882$	5.34161e9	0.262139
$883$	−5.89842e9	−0.288319	−0.144159	−	0.989554i	$-0.546048\pi$
$883$	−5.89842e9	−0.288319	−0.144159	+	0.989554i	$0.546048\pi$
$884$	2.02952e10	0.988123
$885$	4.77594e9	0.231610
$886$	−2.83336e10	−1.36862
$887$	−2.84463e9	−0.136865	−0.0684326	−	0.997656i	$-0.521800\pi$
$887$	−2.84463e9	−0.136865	−0.0684326	+	0.997656i	$0.521800\pi$
$888$	−1.11719e10	−0.535402
$889$	−4.17329e8	−0.0199215
$890$	2.33202e9	0.110884
$891$	0	0
$892$	7.85176e9	0.370416
$893$	5.09775e9	0.239551
$894$	6.62054e8	0.0309893
$895$	3.34992e9	0.156190
$896$	−8.98998e7	−0.00417523
$897$	−2.77470e10	−1.28364
$898$	−1.77832e10	−0.819486
$899$	−3.24480e9	−0.148946
$900$	2.10528e9	0.0962633
$901$	−2.83476e10	−1.29116
$902$	0	0
$903$	7.30114e8	0.0329977
$904$	1.07339e10	0.483245
$905$	−1.66433e10	−0.746394
$906$	1.77292e9	0.0792029
$907$	−1.73926e10	−0.773997	−0.386999	−	0.922080i	$-0.626488\pi$
$907$	−1.73926e10	−0.773997	−0.386999	+	0.922080i	$0.626488\pi$
$908$	−1.22630e10	−0.543623
$909$	−9.31042e9	−0.411146
$910$	−5.89294e8	−0.0259231
$911$	1.38544e10	0.607119	0.303559	−	0.952813i	$-0.401825\pi$
$911$	1.38544e10	0.607119	0.303559	+	0.952813i	$0.401825\pi$
$912$	1.01355e10	0.442447
$913$	0	0
$914$	3.26977e10	1.41646
$915$	−4.49824e9	−0.194120
$916$	1.65567e10	0.711768
$917$	9.04197e7	0.00387231
$918$	−5.45977e9	−0.232930
$919$	3.93168e10	1.67099	0.835495	−	0.549497i	$-0.185181\pi$
$919$	3.93168e10	1.67099	0.835495	+	0.549497i	$0.185181\pi$
$920$	−1.64744e10	−0.697514
$921$	4.70232e9	0.198337
$922$	9.74785e9	0.409591
$923$	−1.48726e10	−0.622560
$924$	0	0
$925$	1.56284e10	0.649258
$926$	2.99299e10	1.23870
$927$	−1.02021e10	−0.420638
$928$	−1.88478e10	−0.774181
$929$	−2.99302e10	−1.22477	−0.612386	−	0.790559i	$-0.709790\pi$
$929$	−2.99302e10	−1.22477	−0.612386	+	0.790559i	$0.709790\pi$
$930$	−7.46792e8	−0.0304445
$931$	3.95513e10	1.60634
$932$	−1.60520e9	−0.0649493
$933$	1.61043e10	0.649166
$934$	−3.23134e10	−1.29768
$935$	0	0
$936$	−1.53943e10	−0.613614
$937$	−2.71339e10	−1.07752	−0.538759	−	0.842460i	$-0.681107\pi$
$937$	−2.71339e10	−1.07752	−0.538759	+	0.842460i	$0.681107\pi$
$938$	5.77971e8	0.0228663
$939$	−1.26453e10	−0.498425
$940$	−7.03925e8	−0.0276426
$941$	7.19172e9	0.281364	0.140682	−	0.990055i	$-0.455070\pi$
$941$	7.19172e9	0.281364	0.140682	+	0.990055i	$0.455070\pi$
$942$	−1.06447e10	−0.414911
$943$	−4.52899e10	−1.75877
$944$	1.00979e10	0.390687
$945$	−9.69952e7	−0.00373886
$946$	0	0
$947$	2.04057e10	0.780774	0.390387	−	0.920651i	$-0.372341\pi$
$947$	2.04057e10	0.780774	0.390387	+	0.920651i	$0.372341\pi$
$948$	−5.01890e9	−0.191328
$949$	−3.10804e9	−0.118047
$950$	−2.54777e10	−0.964114
$951$	−6.44460e9	−0.242976
$952$	1.76571e9	0.0663270
$953$	−2.32200e10	−0.869034	−0.434517	−	0.900664i	$-0.643081\pi$
$953$	−2.32200e10	−0.869034	−0.434517	+	0.900664i	$0.643081\pi$
$954$	5.91628e9	0.220612
$955$	−1.83154e10	−0.680465
$956$	−8.71038e9	−0.322429
$957$	0	0
$958$	−1.56171e10	−0.573881
$959$	1.51666e9	0.0555295
$960$	−8.02484e9	−0.292743
$961$	−2.69971e10	−0.981264
$962$	−3.14435e10	−1.13872
$963$	9.02242e9	0.325560
$964$	−1.09166e10	−0.392480
$965$	−1.13703e10	−0.407313
$966$	−6.64214e8	−0.0237076
$967$	2.01004e10	0.714845	0.357422	−	0.933943i	$-0.383656\pi$
$967$	2.01004e10	0.714845	0.357422	+	0.933943i	$0.383656\pi$
$968$	0	0
$969$	−4.04263e10	−1.42735
$970$	−1.75634e10	−0.617885
$971$	−4.08237e10	−1.43102	−0.715510	−	0.698603i	$-0.753805\pi$
$971$	−4.08237e10	−1.43102	−0.715510	+	0.698603i	$0.753805\pi$
$972$	−6.97179e8	−0.0243508
$973$	1.96707e9	0.0684582
$974$	3.08413e10	1.06949
$975$	2.15352e10	0.744103
$976$	−9.51077e9	−0.327447
$977$	3.68949e10	1.26571	0.632857	−	0.774268i	$-0.281882\pi$
$977$	3.68949e10	1.26571	0.632857	+	0.774268i	$0.281882\pi$
$978$	2.44048e8	0.00834237
$979$	0	0
$980$	−5.46146e9	−0.185361
$981$	8.19049e9	0.276993
$982$	2.09950e10	0.707499
$983$	−2.14087e10	−0.718874	−0.359437	−	0.933169i	$-0.617031\pi$
$983$	−2.14087e10	−0.718874	−0.359437	+	0.933169i	$0.617031\pi$
$984$	−2.51273e10	−0.840742
$985$	1.13146e10	0.377235
$986$	−3.96426e10	−1.31702
$987$	−1.03147e8	−0.00341467
$988$	−3.13628e10	−1.03458
$989$	5.74479e10	1.88837
$990$	0	0
$991$	4.09883e10	1.33783	0.668917	−	0.743337i	$-0.266758\pi$
$991$	4.09883e10	1.33783	0.668917	+	0.743337i	$0.266758\pi$
$992$	2.99427e9	0.0973869
$993$	2.41735e10	0.783462
$994$	−3.56024e8	−0.0114981
$995$	−6.91416e9	−0.222515
$996$	−3.20649e9	−0.102831
$997$	1.43146e10	0.457453	0.228727	−	0.973491i	$-0.426544\pi$
$997$	1.43146e10	0.457453	0.228727	+	0.973491i	$0.426544\pi$
$998$	2.28699e8	0.00728296
$999$	−5.17545e9	−0.164236

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.8.a.r.1.4		14
11.7	odd	10		33.8.e.b.16.6	✓	28
11.8	odd	10		33.8.e.b.31.6	yes	28
11.10	odd	2		363.8.a.o.1.11		14
33.8	even	10		99.8.f.b.64.2		28
33.29	even	10		99.8.f.b.82.2		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.e.b.16.6	✓	28	11.7	odd	10
33.8.e.b.31.6	yes	28	11.8	odd	10
99.8.f.b.64.2		28	33.8	even	10
99.8.f.b.82.2		28	33.29	even	10
363.8.a.o.1.11		14	11.10	odd	2
363.8.a.r.1.4		14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	363.a (trivial)

\(f(q)\)	\(=\)	\(q-8.91136 q^{2} +27.0000 q^{3} -48.5876 q^{4} -136.704 q^{5} -240.607 q^{6} +36.0476 q^{7} +1573.64 q^{8} +729.000 q^{9} +1218.22 q^{10} -1311.87 q^{12} -13419.3 q^{13} -321.233 q^{14} -3691.02 q^{15} -7804.03 q^{16} +31127.1 q^{17} -6496.38 q^{18} -48101.7 q^{19} +6642.14 q^{20} +973.285 q^{21} +76581.4 q^{23} +42488.2 q^{24} -59436.9 q^{25} +119584. q^{26} +19683.0 q^{27} -1751.47 q^{28} +142915. q^{29} +32892.0 q^{30} -22704.4 q^{31} -131881. q^{32} -277385. q^{34} -4927.87 q^{35} -35420.4 q^{36} -262940. q^{37} +428652. q^{38} -362320. q^{39} -215123. q^{40} -591395. q^{41} -8673.30 q^{42} +750154. q^{43} -99657.5 q^{45} -682445. q^{46} -105979. q^{47} -210709. q^{48} -822244. q^{49} +529664. q^{50} +840433. q^{51} +652011. q^{52} -910703. q^{53} -175402. q^{54} +56725.8 q^{56} -1.29875e6 q^{57} -1.27357e6 q^{58} -1.29394e6 q^{59} +179338. q^{60} +1.21870e6 q^{61} +202327. q^{62} +26278.7 q^{63} +2.17415e6 q^{64} +1.83447e6 q^{65} -1.79922e6 q^{67} -1.51239e6 q^{68} +2.06770e6 q^{69} +43914.0 q^{70} +1.10830e6 q^{71} +1.14718e6 q^{72} +231610. q^{73} +2.34316e6 q^{74} -1.60480e6 q^{75} +2.33715e6 q^{76} +3.22877e6 q^{78} +3.82577e6 q^{79} +1.06684e6 q^{80} +531441. q^{81} +5.27013e6 q^{82} +2.44422e6 q^{83} -47289.6 q^{84} -4.25522e6 q^{85} -6.68490e6 q^{86} +3.85871e6 q^{87} +1.91429e6 q^{89} +888084. q^{90} -483733. q^{91} -3.72091e6 q^{92} -613018. q^{93} +944414. q^{94} +6.57572e6 q^{95} -3.56078e6 q^{96} -1.44172e7 q^{97} +7.32731e6 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 23 q^{2} + 378 q^{3} + 845 q^{4} + 69 q^{5} + 621 q^{6} + 3278 q^{7} + 4602 q^{8} + 10206 q^{9} + 5320 q^{10} + 22815 q^{12} + 32188 q^{13} - 7794 q^{14} + 1863 q^{15} + 86137 q^{16} + 42917 q^{17}+ \cdots - 70266089 q^{98}+O(q^{100}) \) 14 * q + 23 * q^2 + 378 * q^3 + 845 * q^4 + 69 * q^5 + 621 * q^6 + 3278 * q^7 + 4602 * q^8 + 10206 * q^9 + 5320 * q^10 + 22815 * q^12 + 32188 * q^13 - 7794 * q^14 + 1863 * q^15 + 86137 * q^16 + 42917 * q^17 + 16767 * q^18 + 50419 * q^19 + 54475 * q^20 + 88506 * q^21 - 83492 * q^23 + 124254 * q^24 + 336991 * q^25 + 234897 * q^26 + 275562 * q^27 + 697184 * q^28 + 227028 * q^29 + 143640 * q^30 - 36481 * q^31 + 151749 * q^32 - 614562 * q^34 - 258783 * q^35 + 616005 * q^36 + 634524 * q^37 - 662891 * q^38 + 869076 * q^39 + 1585604 * q^40 + 1286544 * q^41 - 210438 * q^42 + 2632644 * q^43 + 50301 * q^45 + 1290627 * q^46 - 1692245 * q^47 + 2325699 * q^48 + 842030 * q^49 + 7870914 * q^50 + 1158759 * q^51 + 6419781 * q^52 + 1211317 * q^53 + 452709 * q^54 - 9100953 * q^56 + 1361313 * q^57 - 6265711 * q^58 + 2551943 * q^59 + 1470825 * q^60 + 10221163 * q^61 + 5723657 * q^62 + 2389662 * q^63 + 6349332 * q^64 + 7684087 * q^65 - 3570631 * q^67 + 13112925 * q^68 - 2254284 * q^69 + 3559265 * q^70 + 4528437 * q^71 + 3354858 * q^72 + 13052276 * q^73 + 4896205 * q^74 + 9098757 * q^75 + 9845214 * q^76 + 6342219 * q^78 + 14911090 * q^79 - 9395382 * q^80 + 7440174 * q^81 + 17478001 * q^82 + 7068900 * q^83 + 18823968 * q^84 + 24423120 * q^85 + 12792479 * q^86 + 6129756 * q^87 + 4800832 * q^89 + 3878280 * q^90 - 15295476 * q^91 - 3195753 * q^92 - 984987 * q^93 - 43320002 * q^94 + 7614177 * q^95 + 4097223 * q^96 - 11578773 * q^97 - 70266089 * q^98

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