LMFDB - Embedded newform 322.4.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [322,4,Mod(1,322)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(322, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("322.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 322 = 2 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	322.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$18.9986150218$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{8})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 2 $ x^2 - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.41421$ of defining polynomial
Character	$\chi$	$=$	322.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.00000 q^{2} +2.24264 q^{3} +4.00000 q^{4} +3.75736 q^{5} -4.48528 q^{6} +7.00000 q^{7} -8.00000 q^{8} -21.9706 q^{9} -7.51472 q^{10} +13.0294 q^{11} +8.97056 q^{12} +33.1716 q^{13} -14.0000 q^{14} +8.42641 q^{15} +16.0000 q^{16} +89.4386 q^{17} +43.9411 q^{18} +14.2843 q^{19} +15.0294 q^{20} +15.6985 q^{21} -26.0589 q^{22} +23.0000 q^{23} -17.9411 q^{24} -110.882 q^{25} -66.3431 q^{26} -109.823 q^{27} +28.0000 q^{28} -54.5442 q^{29} -16.8528 q^{30} +217.179 q^{31} -32.0000 q^{32} +29.2203 q^{33} -178.877 q^{34} +26.3015 q^{35} -87.8823 q^{36} +190.083 q^{37} -28.5685 q^{38} +74.3919 q^{39} -30.0589 q^{40} +483.588 q^{41} -31.3970 q^{42} -141.186 q^{43} +52.1177 q^{44} -82.5513 q^{45} -46.0000 q^{46} -187.453 q^{47} +35.8823 q^{48} +49.0000 q^{49} +221.765 q^{50} +200.579 q^{51} +132.686 q^{52} +13.1817 q^{53} +219.647 q^{54} +48.9563 q^{55} -56.0000 q^{56} +32.0345 q^{57} +109.088 q^{58} +828.080 q^{59} +33.7056 q^{60} +37.6842 q^{61} -434.357 q^{62} -153.794 q^{63} +64.0000 q^{64} +124.638 q^{65} -58.4407 q^{66} +458.333 q^{67} +357.754 q^{68} +51.5807 q^{69} -52.6030 q^{70} +901.200 q^{71} +175.765 q^{72} +665.024 q^{73} -380.167 q^{74} -248.669 q^{75} +57.1371 q^{76} +91.2061 q^{77} -148.784 q^{78} -1185.76 q^{79} +60.1177 q^{80} +346.911 q^{81} -967.176 q^{82} -607.200 q^{83} +62.7939 q^{84} +336.053 q^{85} +282.372 q^{86} -122.323 q^{87} -104.235 q^{88} +1547.15 q^{89} +165.103 q^{90} +232.201 q^{91} +92.0000 q^{92} +487.054 q^{93} +374.906 q^{94} +53.6711 q^{95} -71.7645 q^{96} -408.482 q^{97} -98.0000 q^{98} -286.264 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 4 q^{2} - 4 q^{3} + 8 q^{4} + 16 q^{5} + 8 q^{6} + 14 q^{7} - 16 q^{8} - 10 q^{9} - 32 q^{10} + 60 q^{11} - 16 q^{12} + 72 q^{13} - 28 q^{14} - 68 q^{15} + 32 q^{16} + 12 q^{17} + 20 q^{18} - 28 q^{19}+ \cdots + 276 q^{99}+O(q^{100}) $ 2 * q - 4 * q^2 - 4 * q^3 + 8 * q^4 + 16 * q^5 + 8 * q^6 + 14 * q^7 - 16 * q^8 - 10 * q^9 - 32 * q^10 + 60 * q^11 - 16 * q^12 + 72 * q^13 - 28 * q^14 - 68 * q^15 + 32 * q^16 + 12 * q^17 + 20 * q^18 - 28 * q^19 + 64 * q^20 - 28 * q^21 - 120 * q^22 + 46 * q^23 + 32 * q^24 - 86 * q^25 - 144 * q^26 - 16 * q^27 + 56 * q^28 - 160 * q^29 + 136 * q^30 + 160 * q^31 - 64 * q^32 - 264 * q^33 - 24 * q^34 + 112 * q^35 - 40 * q^36 + 284 * q^37 + 56 * q^38 - 168 * q^39 - 128 * q^40 + 492 * q^41 + 56 * q^42 + 272 * q^43 + 240 * q^44 + 64 * q^45 - 92 * q^46 + 352 * q^47 - 64 * q^48 + 98 * q^49 + 172 * q^50 + 684 * q^51 + 288 * q^52 + 428 * q^53 + 32 * q^54 + 624 * q^55 - 112 * q^56 + 296 * q^57 + 320 * q^58 + 884 * q^59 - 272 * q^60 + 576 * q^61 - 320 * q^62 - 70 * q^63 + 128 * q^64 + 600 * q^65 + 528 * q^66 + 532 * q^67 + 48 * q^68 - 92 * q^69 - 224 * q^70 + 688 * q^71 + 80 * q^72 + 12 * q^73 - 568 * q^74 - 404 * q^75 - 112 * q^76 + 420 * q^77 + 336 * q^78 - 748 * q^79 + 256 * q^80 - 562 * q^81 - 984 * q^82 - 100 * q^83 - 112 * q^84 - 612 * q^85 - 544 * q^86 + 536 * q^87 - 480 * q^88 + 676 * q^89 - 128 * q^90 + 504 * q^91 + 184 * q^92 + 844 * q^93 - 704 * q^94 - 464 * q^95 + 128 * q^96 - 124 * q^97 - 196 * q^98 + 276 * q^99

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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	2.24264	0.431596	0.215798	−	0.976438i	$-0.430765\pi$
$3$	2.24264	0.431596	0.215798	+	0.976438i	$0.430765\pi$
$4$	4.00000	0.500000
$5$	3.75736	0.336068	0.168034	−	0.985781i	$-0.446258\pi$
$5$	3.75736	0.336068	0.168034	+	0.985781i	$0.446258\pi$
$6$	−4.48528	−0.305185
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	−21.9706	−0.813725
$10$	−7.51472	−0.237636
$11$	13.0294	0.357138	0.178569	−	0.983927i	$-0.442853\pi$
$11$	13.0294	0.357138	0.178569	+	0.983927i	$0.442853\pi$
$12$	8.97056	0.215798
$13$	33.1716	0.707703	0.353851	−	0.935302i	$-0.384872\pi$
$13$	33.1716	0.707703	0.353851	+	0.935302i	$0.384872\pi$
$14$	−14.0000	−0.267261
$15$	8.42641	0.145046
$16$	16.0000	0.250000
$17$	89.4386	1.27600	0.638001	−	0.770035i	$-0.279761\pi$
$17$	89.4386	1.27600	0.638001	+	0.770035i	$0.279761\pi$
$18$	43.9411	0.575390
$19$	14.2843	0.172476	0.0862378	−	0.996275i	$-0.472516\pi$
$19$	14.2843	0.172476	0.0862378	+	0.996275i	$0.472516\pi$
$20$	15.0294	0.168034
$21$	15.6985	0.163128
$22$	−26.0589	−0.252535
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−17.9411	−0.152592
$25$	−110.882	−0.887058
$26$	−66.3431	−0.500422
$27$	−109.823	−0.782797
$28$	28.0000	0.188982
$29$	−54.5442	−0.349262	−0.174631	−	0.984634i	$-0.555873\pi$
$29$	−54.5442	−0.349262	−0.174631	+	0.984634i	$0.555873\pi$
$30$	−16.8528	−0.102563
$31$	217.179	1.25827	0.629136	−	0.777295i	$-0.283409\pi$
$31$	217.179	1.25827	0.629136	+	0.777295i	$0.283409\pi$
$32$	−32.0000	−0.176777
$33$	29.2203	0.154140
$34$	−178.877	−0.902270
$35$	26.3015	0.127022
$36$	−87.8823	−0.406862
$37$	190.083	0.844581	0.422290	−	0.906461i	$-0.361226\pi$
$37$	190.083	0.844581	0.422290	+	0.906461i	$0.361226\pi$
$38$	−28.5685	−0.121959
$39$	74.3919	0.305442
$40$	−30.0589	−0.118818
$41$	483.588	1.84204	0.921021	−	0.389512i	$-0.127356\pi$
$41$	483.588	1.84204	0.921021	+	0.389512i	$0.127356\pi$
$42$	−31.3970	−0.115349
$43$	−141.186	−0.500713	−0.250356	−	0.968154i	$-0.580548\pi$
$43$	−141.186	−0.500713	−0.250356	+	0.968154i	$0.580548\pi$
$44$	52.1177	0.178569
$45$	−82.5513	−0.273467
$46$	−46.0000	−0.147442
$47$	−187.453	−0.581762	−0.290881	−	0.956759i	$-0.593948\pi$
$47$	−187.453	−0.581762	−0.290881	+	0.956759i	$0.593948\pi$
$48$	35.8823	0.107899
$49$	49.0000	0.142857
$50$	221.765	0.627245
$51$	200.579	0.550718
$52$	132.686	0.353851
$53$	13.1817	0.0341631	0.0170815	−	0.999854i	$-0.494563\pi$
$53$	13.1817	0.0341631	0.0170815	+	0.999854i	$0.494563\pi$
$54$	219.647	0.553521
$55$	48.9563	0.120023
$56$	−56.0000	−0.133631
$57$	32.0345	0.0744399
$58$	109.088	0.246965
$59$	828.080	1.82724	0.913618	−	0.406575i	$-0.133277\pi$
$59$	828.080	1.82724	0.913618	+	0.406575i	$0.133277\pi$
$60$	33.7056	0.0725230
$61$	37.6842	0.0790978	0.0395489	−	0.999218i	$-0.487408\pi$
$61$	37.6842	0.0790978	0.0395489	+	0.999218i	$0.487408\pi$
$62$	−434.357	−0.889733
$63$	−153.794	−0.307559
$64$	64.0000	0.125000
$65$	124.638	0.237837
$66$	−58.4407	−0.108993
$67$	458.333	0.835736	0.417868	−	0.908508i	$-0.362778\pi$
$67$	458.333	0.835736	0.417868	+	0.908508i	$0.362778\pi$
$68$	357.754	0.638001
$69$	51.5807	0.0899941
$70$	−52.6030	−0.0898181
$71$	901.200	1.50638	0.753189	−	0.657805i	$-0.228515\pi$
$71$	901.200	1.50638	0.753189	+	0.657805i	$0.228515\pi$
$72$	175.765	0.287695
$73$	665.024	1.06623	0.533117	−	0.846041i	$-0.321020\pi$
$73$	665.024	1.06623	0.533117	+	0.846041i	$0.321020\pi$
$74$	−380.167	−0.597209
$75$	−248.669	−0.382851
$76$	57.1371	0.0862378
$77$	91.2061	0.134986
$78$	−148.784	−0.215980
$79$	−1185.76	−1.68871	−0.844356	−	0.535782i	$-0.820017\pi$
$79$	−1185.76	−1.68871	−0.844356	+	0.535782i	$0.820017\pi$
$80$	60.1177	0.0840171
$81$	346.911	0.475872
$82$	−967.176	−1.30252
$83$	−607.200	−0.802998	−0.401499	−	0.915859i	$-0.631511\pi$
$83$	−607.200	−0.802998	−0.401499	+	0.915859i	$0.631511\pi$
$84$	62.7939	0.0815641
$85$	336.053	0.428824
$86$	282.372	0.354057
$87$	−122.323	−0.150740
$88$	−104.235	−0.126268
$89$	1547.15	1.84267	0.921336	−	0.388767i	$-0.127099\pi$
$89$	1547.15	1.84267	0.921336	+	0.388767i	$0.127099\pi$
$90$	165.103	0.193370
$91$	232.201	0.267487
$92$	92.0000	0.104257
$93$	487.054	0.543066
$94$	374.906	0.411368
$95$	53.6711	0.0579636
$96$	−71.7645	−0.0762962
$97$	−408.482	−0.427578	−0.213789	−	0.976880i	$-0.568581\pi$
$97$	−408.482	−0.427578	−0.213789	+	0.976880i	$0.568581\pi$
$98$	−98.0000	−0.101015
$99$	−286.264	−0.290612
$100$	−443.529	−0.443529
$101$	−193.367	−0.190502	−0.0952510	−	0.995453i	$-0.530365\pi$
$101$	−193.367	−0.190502	−0.0952510	+	0.995453i	$0.530365\pi$
$102$	−401.157	−0.389417
$103$	144.402	0.138139	0.0690697	−	0.997612i	$-0.477997\pi$
$103$	144.402	0.138139	0.0690697	+	0.997612i	$0.477997\pi$
$104$	−265.373	−0.250211
$105$	58.9848	0.0548222
$106$	−26.3633	−0.0241569
$107$	1713.82	1.54843	0.774213	−	0.632925i	$-0.218146\pi$
$107$	1713.82	1.54843	0.774213	+	0.632925i	$0.218146\pi$
$108$	−439.294	−0.391398
$109$	−308.599	−0.271178	−0.135589	−	0.990765i	$-0.543293\pi$
$109$	−308.599	−0.271178	−0.135589	+	0.990765i	$0.543293\pi$
$110$	−97.9126	−0.0848691
$111$	426.288	0.364518
$112$	112.000	0.0944911
$113$	−2160.23	−1.79838	−0.899191	−	0.437557i	$-0.855844\pi$
$113$	−2160.23	−1.79838	−0.899191	+	0.437557i	$0.855844\pi$
$114$	−64.0690	−0.0526369
$115$	86.4193	0.0700751
$116$	−218.177	−0.174631
$117$	−728.798	−0.575875
$118$	−1656.16	−1.29205
$119$	626.070	0.482284
$120$	−67.4113	−0.0512815
$121$	−1161.23	−0.872452
$122$	−75.3684	−0.0559306
$123$	1084.51	0.795019
$124$	868.715	0.629136
$125$	−886.294	−0.634181
$126$	307.588	0.217477
$127$	71.2304	0.0497691	0.0248846	−	0.999690i	$-0.492078\pi$
$127$	71.2304	0.0497691	0.0248846	+	0.999690i	$0.492078\pi$
$128$	−128.000	−0.0883883
$129$	−316.629	−0.216106
$130$	−249.275	−0.168176
$131$	−1137.93	−0.758944	−0.379472	−	0.925203i	$-0.623894\pi$
$131$	−1137.93	−0.758944	−0.379472	+	0.925203i	$0.623894\pi$
$132$	116.881	0.0770698
$133$	99.9899	0.0651897
$134$	−916.666	−0.590954
$135$	−412.646	−0.263073
$136$	−715.509	−0.451135
$137$	−2528.87	−1.57705	−0.788524	−	0.615004i	$-0.789154\pi$
$137$	−2528.87	−1.57705	−0.788524	+	0.615004i	$0.789154\pi$
$138$	−103.161	−0.0636354
$139$	−1289.58	−0.786915	−0.393457	−	0.919343i	$-0.628721\pi$
$139$	−1289.58	−0.786915	−0.393457	+	0.919343i	$0.628721\pi$
$140$	105.206	0.0635110
$141$	−420.389	−0.251086
$142$	−1802.40	−1.06517
$143$	432.207	0.252748
$144$	−351.529	−0.203431
$145$	−204.942	−0.117376
$146$	−1330.05	−0.753942
$147$	109.889	0.0616566
$148$	760.333	0.422290
$149$	−445.870	−0.245149	−0.122574	−	0.992459i	$-0.539115\pi$
$149$	−445.870	−0.245149	−0.122574	+	0.992459i	$0.539115\pi$
$150$	497.338	0.270717
$151$	−2442.35	−1.31626	−0.658132	−	0.752902i	$-0.728653\pi$
$151$	−2442.35	−1.31626	−0.658132	+	0.752902i	$0.728653\pi$
$152$	−114.274	−0.0609793
$153$	−1965.02	−1.03831
$154$	−182.412	−0.0954493
$155$	816.018	0.422866
$156$	297.568	0.152721
$157$	1091.42	0.554808	0.277404	−	0.960753i	$-0.410526\pi$
$157$	1091.42	0.554808	0.277404	+	0.960753i	$0.410526\pi$
$158$	2371.52	1.19410
$159$	29.5618	0.0147447
$160$	−120.235	−0.0594091
$161$	161.000	0.0788110
$162$	−693.822	−0.336492
$163$	2681.74	1.28865	0.644325	−	0.764751i	$-0.277138\pi$
$163$	2681.74	1.28865	0.644325	+	0.764751i	$0.277138\pi$
$164$	1934.35	0.921021
$165$	109.791	0.0518015
$166$	1214.40	0.567806
$167$	−848.332	−0.393089	−0.196545	−	0.980495i	$-0.562972\pi$
$167$	−848.332	−0.393089	−0.196545	+	0.980495i	$0.562972\pi$
$168$	−125.588	−0.0576745
$169$	−1096.65	−0.499156
$170$	−672.106	−0.303225
$171$	−313.833	−0.140348
$172$	−564.743	−0.250356
$173$	2662.58	1.17013	0.585064	−	0.810987i	$-0.301069\pi$
$173$	2662.58	1.17013	0.585064	+	0.810987i	$0.301069\pi$
$174$	244.646	0.106589
$175$	−776.176	−0.335276
$176$	208.471	0.0892846
$177$	1857.09	0.788628
$178$	−3094.31	−1.30297
$179$	−1472.38	−0.614809	−0.307404	−	0.951579i	$-0.599460\pi$
$179$	−1472.38	−0.614809	−0.307404	+	0.951579i	$0.599460\pi$
$180$	−330.205	−0.136734
$181$	−1917.05	−0.787256	−0.393628	−	0.919270i	$-0.628780\pi$
$181$	−1917.05	−0.787256	−0.393628	+	0.919270i	$0.628780\pi$
$182$	−464.402	−0.189142
$183$	84.5121	0.0341383
$184$	−184.000	−0.0737210
$185$	714.211	0.283837
$186$	−974.108	−0.384006
$187$	1165.33	0.455710
$188$	−749.812	−0.290881
$189$	−768.764	−0.295869
$190$	−107.342	−0.0409865
$191$	4397.54	1.66594	0.832970	−	0.553318i	$-0.186639\pi$
$191$	4397.54	1.66594	0.832970	+	0.553318i	$0.186639\pi$
$192$	143.529	0.0539496
$193$	−3290.01	−1.22705	−0.613523	−	0.789677i	$-0.710248\pi$
$193$	−3290.01	−1.22705	−0.613523	+	0.789677i	$0.710248\pi$
$194$	816.965	0.302344
$195$	279.517	0.102649
$196$	196.000	0.0714286
$197$	−785.712	−0.284161	−0.142080	−	0.989855i	$-0.545379\pi$
$197$	−785.712	−0.284161	−0.142080	+	0.989855i	$0.545379\pi$
$198$	572.528	0.205494
$199$	−3667.09	−1.30630	−0.653149	−	0.757229i	$-0.726553\pi$
$199$	−3667.09	−1.30630	−0.653149	+	0.757229i	$0.726553\pi$
$200$	887.058	0.313622
$201$	1027.88	0.360701
$202$	386.733	0.134705
$203$	−381.809	−0.132009
$204$	802.315	0.275359
$205$	1817.01	0.619052
$206$	−288.804	−0.0976793
$207$	−505.323	−0.169673
$208$	530.745	0.176926
$209$	186.116	0.0615977
$210$	−117.970	−0.0387652
$211$	−2814.18	−0.918182	−0.459091	−	0.888389i	$-0.651825\pi$
$211$	−2814.18	−0.918182	−0.459091	+	0.888389i	$0.651825\pi$
$212$	52.7267	0.0170815
$213$	2021.07	0.650147
$214$	−3427.65	−1.09490
$215$	−530.486	−0.168274
$216$	878.587	0.276761
$217$	1520.25	0.475582
$218$	617.198	0.191752
$219$	1491.41	0.460183
$220$	195.825	0.0600115
$221$	2966.82	0.903031
$222$	−852.577	−0.257753
$223$	623.289	0.187168	0.0935841	−	0.995611i	$-0.470168\pi$
$223$	623.289	0.187168	0.0935841	+	0.995611i	$0.470168\pi$
$224$	−224.000	−0.0668153
$225$	2436.15	0.721821
$226$	4320.46	1.27165
$227$	3802.36	1.11177	0.555884	−	0.831260i	$-0.312380\pi$
$227$	3802.36	1.11177	0.555884	+	0.831260i	$0.312380\pi$
$228$	128.138	0.0372199
$229$	−3973.52	−1.14663	−0.573313	−	0.819336i	$-0.694342\pi$
$229$	−3973.52	−1.14663	−0.573313	+	0.819336i	$0.694342\pi$
$230$	−172.839	−0.0495506
$231$	204.542	0.0582593
$232$	436.353	0.123483
$233$	−3225.41	−0.906881	−0.453441	−	0.891286i	$-0.649804\pi$
$233$	−3225.41	−0.906881	−0.453441	+	0.891286i	$0.649804\pi$
$234$	1457.60	0.407205
$235$	−704.328	−0.195512
$236$	3312.32	0.913618
$237$	−2659.23	−0.728842
$238$	−1252.14	−0.341026
$239$	4119.96	1.11505	0.557527	−	0.830159i	$-0.311750\pi$
$239$	4119.96	1.11505	0.557527	+	0.830159i	$0.311750\pi$
$240$	134.823	0.0362615
$241$	1742.43	0.465726	0.232863	−	0.972510i	$-0.425191\pi$
$241$	1742.43	0.465726	0.232863	+	0.972510i	$0.425191\pi$
$242$	2322.47	0.616917
$243$	3743.23	0.988182
$244$	150.737	0.0395489
$245$	184.111	0.0480098
$246$	−2169.03	−0.562163
$247$	473.832	0.122062
$248$	−1737.43	−0.444867
$249$	−1361.73	−0.346571
$250$	1772.59	0.448433
$251$	−4923.16	−1.23804	−0.619018	−	0.785377i	$-0.712469\pi$
$251$	−4923.16	−1.23804	−0.619018	+	0.785377i	$0.712469\pi$
$252$	−615.176	−0.153779
$253$	299.677	0.0744685
$254$	−142.461	−0.0351921
$255$	753.646	0.185079
$256$	256.000	0.0625000
$257$	4717.28	1.14496	0.572482	−	0.819917i	$-0.305980\pi$
$257$	4717.28	1.14496	0.572482	+	0.819917i	$0.305980\pi$
$258$	633.258	0.152810
$259$	1330.58	0.319222
$260$	498.550	0.118918
$261$	1198.37	0.284203
$262$	2275.86	0.536654
$263$	1811.49	0.424719	0.212360	−	0.977192i	$-0.431885\pi$
$263$	1811.49	0.424719	0.212360	+	0.977192i	$0.431885\pi$
$264$	−233.763	−0.0544966
$265$	49.5283	0.0114811
$266$	−199.980	−0.0460960
$267$	3469.71	0.795291
$268$	1833.33	0.417868
$269$	3173.02	0.719190	0.359595	−	0.933108i	$-0.382915\pi$
$269$	3173.02	0.719190	0.359595	+	0.933108i	$0.382915\pi$
$270$	825.292	0.186021
$271$	−3316.92	−0.743499	−0.371750	−	0.928333i	$-0.621242\pi$
$271$	−3316.92	−0.743499	−0.371750	+	0.928333i	$0.621242\pi$
$272$	1431.02	0.319001
$273$	520.743	0.115446
$274$	5057.73	1.11514
$275$	−1444.73	−0.316803
$276$	206.323	0.0449970
$277$	−6461.12	−1.40148	−0.700742	−	0.713415i	$-0.747148\pi$
$277$	−6461.12	−1.40148	−0.700742	+	0.713415i	$0.747148\pi$
$278$	2579.17	0.556433
$279$	−4771.54	−1.02389
$280$	−210.412	−0.0449090
$281$	−495.920	−0.105281	−0.0526407	−	0.998614i	$-0.516764\pi$
$281$	−495.920	−0.105281	−0.0526407	+	0.998614i	$0.516764\pi$
$282$	840.779	0.177545
$283$	714.309	0.150040	0.0750199	−	0.997182i	$-0.476098\pi$
$283$	714.309	0.150040	0.0750199	+	0.997182i	$0.476098\pi$
$284$	3604.80	0.753189
$285$	120.365	0.0250169
$286$	−864.414	−0.178720
$287$	3385.12	0.696227
$288$	703.058	0.143848
$289$	3086.26	0.628183
$290$	409.884	0.0829973
$291$	−916.079	−0.184541
$292$	2660.09	0.533117
$293$	−9322.33	−1.85876	−0.929380	−	0.369125i	$-0.879658\pi$
$293$	−9322.33	−1.85876	−0.929380	+	0.369125i	$0.879658\pi$
$294$	−219.779	−0.0435978
$295$	3111.40	0.614076
$296$	−1520.67	−0.298604
$297$	−1430.94	−0.279567
$298$	891.741	0.173346
$299$	762.946	0.147566
$300$	−994.676	−0.191426
$301$	−988.301	−0.189252
$302$	4884.71	0.930740
$303$	−433.652	−0.0822200
$304$	228.548	0.0431189
$305$	141.593	0.0265823
$306$	3930.03	0.734199
$307$	6636.06	1.23368	0.616840	−	0.787088i	$-0.288412\pi$
$307$	6636.06	1.23368	0.616840	+	0.787088i	$0.288412\pi$
$308$	364.824	0.0674928
$309$	323.842	0.0596204
$310$	−1632.04	−0.299011
$311$	−3975.74	−0.724899	−0.362449	−	0.932003i	$-0.618059\pi$
$311$	−3975.74	−0.724899	−0.362449	+	0.932003i	$0.618059\pi$
$312$	−595.135	−0.107990
$313$	−4431.10	−0.800193	−0.400097	−	0.916473i	$-0.631023\pi$
$313$	−4431.10	−0.800193	−0.400097	+	0.916473i	$0.631023\pi$
$314$	−2182.84	−0.392309
$315$	−577.859	−0.103361
$316$	−4743.03	−0.844356
$317$	5435.63	0.963077	0.481539	−	0.876425i	$-0.340078\pi$
$317$	5435.63	0.963077	0.481539	+	0.876425i	$0.340078\pi$
$318$	−59.1235	−0.0104260
$319$	−710.680	−0.124735
$320$	240.471	0.0420086
$321$	3843.49	0.668295
$322$	−322.000	−0.0557278
$323$	1277.57	0.220079
$324$	1387.64	0.237936
$325$	−3678.14	−0.627774
$326$	−5363.48	−0.911214
$327$	−692.076	−0.117039
$328$	−3868.70	−0.651260
$329$	−1312.17	−0.219885
$330$	−219.583	−0.0366292
$331$	−5587.24	−0.927801	−0.463901	−	0.885887i	$-0.653551\pi$
$331$	−5587.24	−0.927801	−0.463901	+	0.885887i	$0.653551\pi$
$332$	−2428.80	−0.401499
$333$	−4176.24	−0.687256
$334$	1696.66	0.277956
$335$	1722.12	0.280864
$336$	251.176	0.0407820
$337$	633.663	0.102427	0.0512134	−	0.998688i	$-0.483691\pi$
$337$	633.663	0.102427	0.0512134	+	0.998688i	$0.483691\pi$
$338$	2193.29	0.352957
$339$	−4844.61	−0.776175
$340$	1344.21	0.214412
$341$	2829.72	0.449378
$342$	627.667	0.0992408
$343$	343.000	0.0539949
$344$	1129.49	0.177029
$345$	193.807	0.0302442
$346$	−5325.16	−0.827405
$347$	8745.82	1.35303	0.676513	−	0.736431i	$-0.263490\pi$
$347$	8745.82	1.35303	0.676513	+	0.736431i	$0.263490\pi$
$348$	−489.292	−0.0753701
$349$	−10932.9	−1.67687	−0.838434	−	0.545002i	$-0.816529\pi$
$349$	−10932.9	−1.67687	−0.838434	+	0.545002i	$0.816529\pi$
$350$	1552.35	0.237076
$351$	−3643.01	−0.553988
$352$	−416.942	−0.0631338
$353$	−7386.27	−1.11369	−0.556843	−	0.830618i	$-0.687988\pi$
$353$	−7386.27	−1.11369	−0.556843	+	0.830618i	$0.687988\pi$
$354$	−3714.17	−0.557644
$355$	3386.13	0.506246
$356$	6188.61	0.921336
$357$	1404.05	0.208152
$358$	2944.76	0.434735
$359$	9258.66	1.36115	0.680576	−	0.732678i	$-0.261730\pi$
$359$	9258.66	1.36115	0.680576	+	0.732678i	$0.261730\pi$
$360$	660.410	0.0966852
$361$	−6654.96	−0.970252
$362$	3834.11	0.556674
$363$	−2604.23	−0.376547
$364$	928.804	0.133743
$365$	2498.73	0.358328
$366$	−169.024	−0.0241394
$367$	1466.51	0.208586	0.104293	−	0.994547i	$-0.466742\pi$
$367$	1466.51	0.208586	0.104293	+	0.994547i	$0.466742\pi$
$368$	368.000	0.0521286
$369$	−10624.7	−1.49892
$370$	−1428.42	−0.200703
$371$	92.2717	0.0129124
$372$	1948.22	0.271533
$373$	595.179	0.0826198	0.0413099	−	0.999146i	$-0.486847\pi$
$373$	595.179	0.0826198	0.0413099	+	0.999146i	$0.486847\pi$
$374$	−2330.67	−0.322235
$375$	−1987.64	−0.273710
$376$	1499.62	0.205684
$377$	−1809.32	−0.247174
$378$	1537.53	0.209211
$379$	14050.6	1.90431	0.952154	−	0.305620i	$-0.0988636\pi$
$379$	14050.6	1.90431	0.952154	+	0.305620i	$0.0988636\pi$
$380$	214.685	0.0289818
$381$	159.744	0.0214802
$382$	−8795.07	−1.17800
$383$	−538.612	−0.0718584	−0.0359292	−	0.999354i	$-0.511439\pi$
$383$	−538.612	−0.0718584	−0.0359292	+	0.999354i	$0.511439\pi$
$384$	−287.058	−0.0381481
$385$	342.694	0.0453644
$386$	6580.02	0.867653
$387$	3101.93	0.407442
$388$	−1633.93	−0.213789
$389$	−3807.18	−0.496226	−0.248113	−	0.968731i	$-0.579810\pi$
$389$	−3807.18	−0.496226	−0.248113	+	0.968731i	$0.579810\pi$
$390$	−559.034	−0.0725841
$391$	2057.09	0.266065
$392$	−392.000	−0.0505076
$393$	−2551.97	−0.327557
$394$	1571.42	0.200932
$395$	−4455.32	−0.567523
$396$	−1145.06	−0.145306
$397$	−4457.42	−0.563505	−0.281752	−	0.959487i	$-0.590916\pi$
$397$	−4457.42	−0.563505	−0.281752	+	0.959487i	$0.590916\pi$
$398$	7334.19	0.923693
$399$	224.241	0.0281356
$400$	−1774.12	−0.221765
$401$	5948.99	0.740844	0.370422	−	0.928864i	$-0.379213\pi$
$401$	5948.99	0.740844	0.370422	+	0.928864i	$0.379213\pi$
$402$	−2055.75	−0.255054
$403$	7204.16	0.890483
$404$	−773.467	−0.0952510
$405$	1303.47	0.159926
$406$	763.618	0.0933442
$407$	2476.68	0.301632
$408$	−1604.63	−0.194708
$409$	−10366.4	−1.25327	−0.626634	−	0.779314i	$-0.715568\pi$
$409$	−10366.4	−1.25327	−0.626634	+	0.779314i	$0.715568\pi$
$410$	−3634.03	−0.437736
$411$	−5671.34	−0.680648
$412$	577.608	0.0690697
$413$	5796.56	0.690630
$414$	1010.65	0.119977
$415$	−2281.47	−0.269862
$416$	−1061.49	−0.125105
$417$	−2892.08	−0.339630
$418$	−372.232	−0.0435561
$419$	−12122.8	−1.41346	−0.706729	−	0.707485i	$-0.749830\pi$
$419$	−12122.8	−1.41346	−0.706729	+	0.707485i	$0.749830\pi$
$420$	235.939	0.0274111
$421$	−757.168	−0.0876535	−0.0438268	−	0.999039i	$-0.513955\pi$
$421$	−757.168	−0.0876535	−0.0438268	+	0.999039i	$0.513955\pi$
$422$	5628.37	0.649253
$423$	4118.45	0.473394
$424$	−105.453	−0.0120785
$425$	−9917.15	−1.13189
$426$	−4042.14	−0.459723
$427$	263.789	0.0298962
$428$	6855.29	0.774213
$429$	969.285	0.109085
$430$	1060.97	0.118987
$431$	13485.2	1.50710	0.753548	−	0.657393i	$-0.228341\pi$
$431$	13485.2	1.50710	0.753548	+	0.657393i	$0.228341\pi$
$432$	−1757.17	−0.195699
$433$	−2790.51	−0.309708	−0.154854	−	0.987937i	$-0.549491\pi$
$433$	−2790.51	−0.309708	−0.154854	+	0.987937i	$0.549491\pi$
$434$	−3040.50	−0.336287
$435$	−459.611	−0.0506590
$436$	−1234.40	−0.135589
$437$	328.538	0.0359637
$438$	−2982.82	−0.325398
$439$	9806.47	1.06614	0.533072	−	0.846070i	$-0.321037\pi$
$439$	9806.47	1.06614	0.533072	+	0.846070i	$0.321037\pi$
$440$	−391.650	−0.0424345
$441$	−1076.56	−0.116246
$442$	−5933.64	−0.638539
$443$	420.068	0.0450519	0.0225260	−	0.999746i	$-0.492829\pi$
$443$	420.068	0.0450519	0.0225260	+	0.999746i	$0.492829\pi$
$444$	1705.15	0.182259
$445$	5813.21	0.619264
$446$	−1246.58	−0.132348
$447$	−999.927	−0.105805
$448$	448.000	0.0472456
$449$	−2320.84	−0.243936	−0.121968	−	0.992534i	$-0.538920\pi$
$449$	−2320.84	−0.243936	−0.121968	+	0.992534i	$0.538920\pi$
$450$	−4872.29	−0.510404
$451$	6300.88	0.657864
$452$	−8640.91	−0.899191
$453$	−5477.32	−0.568095
$454$	−7604.72	−0.786139
$455$	872.463	0.0898938
$456$	−256.276	−0.0263185
$457$	5158.96	0.528066	0.264033	−	0.964514i	$-0.414947\pi$
$457$	5158.96	0.528066	0.264033	+	0.964514i	$0.414947\pi$
$458$	7947.03	0.810787
$459$	−9822.45	−0.998851
$460$	345.677	0.0350376
$461$	−5040.74	−0.509263	−0.254632	−	0.967038i	$-0.581954\pi$
$461$	−5040.74	−0.509263	−0.254632	+	0.967038i	$0.581954\pi$
$462$	−409.085	−0.0411956
$463$	−17474.3	−1.75399	−0.876996	−	0.480498i	$-0.840456\pi$
$463$	−17474.3	−1.75399	−0.876996	+	0.480498i	$0.840456\pi$
$464$	−872.706	−0.0873155
$465$	1830.04	0.182507
$466$	6450.81	0.641262
$467$	−3438.75	−0.340742	−0.170371	−	0.985380i	$-0.554497\pi$
$467$	−3438.75	−0.340742	−0.170371	+	0.985380i	$0.554497\pi$
$468$	−2915.19	−0.287938
$469$	3208.33	0.315878
$470$	1408.66	0.138248
$471$	2447.66	0.239453
$472$	−6624.64	−0.646025
$473$	−1839.57	−0.178824
$474$	5318.46	0.515369
$475$	−1583.87	−0.152996
$476$	2504.28	0.241142
$477$	−289.609	−0.0277993
$478$	−8239.92	−0.788462
$479$	13432.4	1.28130	0.640648	−	0.767835i	$-0.278666\pi$
$479$	13432.4	1.28130	0.640648	+	0.767835i	$0.278666\pi$
$480$	−269.645	−0.0256407
$481$	6305.36	0.597712
$482$	−3484.87	−0.329318
$483$	361.065	0.0340146
$484$	−4644.94	−0.436226
$485$	−1534.81	−0.143696
$486$	−7486.45	−0.698750
$487$	10444.4	0.971832	0.485916	−	0.874006i	$-0.338486\pi$
$487$	10444.4	0.971832	0.485916	+	0.874006i	$0.338486\pi$
$488$	−301.474	−0.0279653
$489$	6014.18	0.556177
$490$	−368.221	−0.0339480
$491$	6996.55	0.643075	0.321537	−	0.946897i	$-0.395800\pi$
$491$	6996.55	0.643075	0.321537	+	0.946897i	$0.395800\pi$
$492$	4338.06	0.397509
$493$	−4878.35	−0.445659
$494$	−947.663	−0.0863105
$495$	−1075.60	−0.0976656
$496$	3474.86	0.314568
$497$	6308.40	0.569357
$498$	2723.46	0.245063
$499$	−9779.42	−0.877329	−0.438664	−	0.898651i	$-0.644548\pi$
$499$	−9779.42	−0.877329	−0.438664	+	0.898651i	$0.644548\pi$
$500$	−3545.18	−0.317090
$501$	−1902.50	−0.169656
$502$	9846.31	0.875423
$503$	11581.1	1.02660	0.513298	−	0.858210i	$-0.328424\pi$
$503$	11581.1	1.02660	0.513298	+	0.858210i	$0.328424\pi$
$504$	1230.35	0.108739
$505$	−726.548	−0.0640217
$506$	−599.354	−0.0526572
$507$	−2459.38	−0.215434
$508$	284.922	0.0248846
$509$	−15876.4	−1.38253	−0.691265	−	0.722601i	$-0.742946\pi$
$509$	−15876.4	−1.38253	−0.691265	+	0.722601i	$0.742946\pi$
$510$	−1507.29	−0.130871
$511$	4655.16	0.402999
$512$	−512.000	−0.0441942
$513$	−1568.75	−0.135013
$514$	−9434.56	−0.809612
$515$	542.570	0.0464243
$516$	−1266.52	−0.108053
$517$	−2442.41	−0.207770
$518$	−2661.17	−0.225724
$519$	5971.21	0.505023
$520$	−997.100	−0.0840879
$521$	−17634.3	−1.48286	−0.741431	−	0.671029i	$-0.765852\pi$
$521$	−17634.3	−1.48286	−0.741431	+	0.671029i	$0.765852\pi$
$522$	−2396.73	−0.200962
$523$	−4964.31	−0.415056	−0.207528	−	0.978229i	$-0.566542\pi$
$523$	−4964.31	−0.415056	−0.207528	+	0.978229i	$0.566542\pi$
$524$	−4551.73	−0.379472
$525$	−1740.68	−0.144704
$526$	−3622.98	−0.300322
$527$	19424.2	1.60556
$528$	467.526	0.0385349
$529$	529.000	0.0434783
$530$	−99.0566	−0.00811838
$531$	−18193.4	−1.48687
$532$	399.960	0.0325948
$533$	16041.4	1.30362
$534$	−6939.41	−0.562356
$535$	6439.45	0.520377
$536$	−3666.66	−0.295477
$537$	−3302.02	−0.265349
$538$	−6346.03	−0.508544
$539$	638.442	0.0510198
$540$	−1650.58	−0.131537
$541$	18581.1	1.47664	0.738320	−	0.674451i	$-0.235619\pi$
$541$	18581.1	1.47664	0.738320	+	0.674451i	$0.235619\pi$
$542$	6633.83	0.525734
$543$	−4299.26	−0.339777
$544$	−2862.04	−0.225568
$545$	−1159.52	−0.0911344
$546$	−1041.49	−0.0816328
$547$	−2158.56	−0.168727	−0.0843633	−	0.996435i	$-0.526886\pi$
$547$	−2158.56	−0.168727	−0.0843633	+	0.996435i	$0.526886\pi$
$548$	−10115.5	−0.788524
$549$	−827.943	−0.0643638
$550$	2889.47	0.224013
$551$	−779.124	−0.0602392
$552$	−412.646	−0.0318177
$553$	−8300.31	−0.638273
$554$	12922.2	0.990999
$555$	1601.72	0.122503
$556$	−5158.34	−0.393457
$557$	13879.0	1.05578	0.527891	−	0.849312i	$-0.322983\pi$
$557$	13879.0	1.05578	0.527891	+	0.849312i	$0.322983\pi$
$558$	9543.08	0.723998
$559$	−4683.36	−0.354356
$560$	420.824	0.0317555
$561$	2613.43	0.196683
$562$	991.840	0.0744453
$563$	2234.36	0.167259	0.0836297	−	0.996497i	$-0.473349\pi$
$563$	2234.36	0.167259	0.0836297	+	0.996497i	$0.473349\pi$
$564$	−1681.56	−0.125543
$565$	−8116.75	−0.604379
$566$	−1428.62	−0.106094
$567$	2428.38	0.179863
$568$	−7209.60	−0.532585
$569$	−18285.7	−1.34724	−0.673619	−	0.739079i	$-0.735261\pi$
$569$	−18285.7	−1.34724	−0.673619	+	0.739079i	$0.735261\pi$
$570$	−240.730	−0.0176896
$571$	26177.7	1.91857	0.959285	−	0.282441i	$-0.0911442\pi$
$571$	26177.7	1.91857	0.959285	+	0.282441i	$0.0911442\pi$
$572$	1728.83	0.126374
$573$	9862.09	0.719014
$574$	−6770.23	−0.492307
$575$	−2550.29	−0.184964
$576$	−1406.12	−0.101716
$577$	16737.7	1.20763	0.603814	−	0.797125i	$-0.293647\pi$
$577$	16737.7	1.20763	0.603814	+	0.797125i	$0.293647\pi$
$578$	−6172.53	−0.444192
$579$	−7378.31	−0.529589
$580$	−819.768	−0.0586880
$581$	−4250.40	−0.303505
$582$	1832.16	0.130490
$583$	171.750	0.0122009
$584$	−5320.19	−0.376971
$585$	−2738.36	−0.193534
$586$	18644.7	1.31434
$587$	1162.62	0.0817484	0.0408742	−	0.999164i	$-0.486986\pi$
$587$	1162.62	0.0817484	0.0408742	+	0.999164i	$0.486986\pi$
$588$	439.558	0.0308283
$589$	3102.24	0.217021
$590$	−6222.79	−0.434217
$591$	−1762.07	−0.122643
$592$	3041.33	0.211145
$593$	14361.5	0.994527	0.497263	−	0.867600i	$-0.334338\pi$
$593$	14361.5	0.994527	0.497263	+	0.867600i	$0.334338\pi$
$594$	2861.87	0.197684
$595$	2352.37	0.162080
$596$	−1783.48	−0.122574
$597$	−8223.98	−0.563794
$598$	−1525.89	−0.104345
$599$	−176.151	−0.0120156	−0.00600780	−	0.999982i	$-0.501912\pi$
$599$	−176.151	−0.0120156	−0.00600780	+	0.999982i	$0.501912\pi$
$600$	1989.35	0.135358
$601$	−6123.65	−0.415622	−0.207811	−	0.978169i	$-0.566634\pi$
$601$	−6123.65	−0.415622	−0.207811	+	0.978169i	$0.566634\pi$
$602$	1976.60	0.133821
$603$	−10069.8	−0.680059
$604$	−9769.42	−0.658132
$605$	−4363.17	−0.293204
$606$	867.304	0.0581383
$607$	17923.7	1.19852	0.599258	−	0.800556i	$-0.295462\pi$
$607$	17923.7	1.19852	0.599258	+	0.800556i	$0.295462\pi$
$608$	−457.097	−0.0304897
$609$	−856.261	−0.0569744
$610$	−283.186	−0.0187965
$611$	−6218.11	−0.411715
$612$	−7860.07	−0.519157
$613$	−16185.7	−1.06645	−0.533225	−	0.845974i	$-0.679020\pi$
$613$	−16185.7	−1.06645	−0.533225	+	0.845974i	$0.679020\pi$
$614$	−13272.1	−0.872344
$615$	4074.91	0.267181
$616$	−729.648	−0.0477246
$617$	−13212.3	−0.862087	−0.431044	−	0.902331i	$-0.641854\pi$
$617$	−13212.3	−0.862087	−0.431044	+	0.902331i	$0.641854\pi$
$618$	−647.684	−0.0421580
$619$	−12509.8	−0.812296	−0.406148	−	0.913807i	$-0.633128\pi$
$619$	−12509.8	−0.812296	−0.406148	+	0.913807i	$0.633128\pi$
$620$	3264.07	0.211433
$621$	−2525.94	−0.163224
$622$	7951.48	0.512581
$623$	10830.1	0.696465
$624$	1190.27	0.0763605
$625$	10530.2	0.673930
$626$	8862.20	0.565822
$627$	417.391	0.0265853
$628$	4365.68	0.277404
$629$	17000.8	1.07769
$630$	1155.72	0.0730872
$631$	10569.8	0.666840	0.333420	−	0.942778i	$-0.391797\pi$
$631$	10569.8	0.666840	0.333420	+	0.942778i	$0.391797\pi$
$632$	9486.07	0.597050
$633$	−6311.21	−0.396284
$634$	−10871.3	−0.680998
$635$	267.638	0.0167258
$636$	118.247	0.00737233
$637$	1625.41	0.101100
$638$	1421.36	0.0882009
$639$	−19799.9	−1.22578
$640$	−480.942	−0.0297045
$641$	6255.30	0.385444	0.192722	−	0.981253i	$-0.438268\pi$
$641$	6255.30	0.385444	0.192722	+	0.981253i	$0.438268\pi$
$642$	−7686.98	−0.472556
$643$	16065.9	0.985347	0.492673	−	0.870214i	$-0.336020\pi$
$643$	16065.9	0.985347	0.492673	+	0.870214i	$0.336020\pi$
$644$	644.000	0.0394055
$645$	−1189.69	−0.0726263
$646$	−2555.13	−0.155620
$647$	−6775.52	−0.411705	−0.205853	−	0.978583i	$-0.565997\pi$
$647$	−6775.52	−0.411705	−0.205853	+	0.978583i	$0.565997\pi$
$648$	−2775.29	−0.168246
$649$	10789.4	0.652576
$650$	7356.28	0.443903
$651$	3409.38	0.205260
$652$	10727.0	0.644325
$653$	27296.8	1.63584	0.817922	−	0.575329i	$-0.195126\pi$
$653$	27296.8	1.63584	0.817922	+	0.575329i	$0.195126\pi$
$654$	1384.15	0.0827594
$655$	−4275.62	−0.255057
$656$	7737.41	0.460511
$657$	−14610.9	−0.867621
$658$	2624.34	0.155482
$659$	−30855.2	−1.82390	−0.911948	−	0.410307i	$-0.865422\pi$
$659$	−30855.2	−1.82390	−0.911948	+	0.410307i	$0.865422\pi$
$660$	439.165	0.0259007
$661$	20147.1	1.18552	0.592762	−	0.805378i	$-0.298038\pi$
$661$	20147.1	1.18552	0.592762	+	0.805378i	$0.298038\pi$
$662$	11174.5	0.656055
$663$	6653.51	0.389745
$664$	4857.60	0.283903
$665$	375.698	0.0219082
$666$	8352.47	0.485964
$667$	−1254.52	−0.0728261
$668$	−3393.33	−0.196545
$669$	1397.81	0.0807811
$670$	−3444.24	−0.198601
$671$	491.004	0.0282489
$672$	−502.352	−0.0288372
$673$	−7360.51	−0.421585	−0.210792	−	0.977531i	$-0.567604\pi$
$673$	−7360.51	−0.421585	−0.210792	+	0.977531i	$0.567604\pi$
$674$	−1267.33	−0.0724267
$675$	12177.5	0.694386
$676$	−4386.59	−0.249578
$677$	−26322.8	−1.49434	−0.747169	−	0.664634i	$-0.768588\pi$
$677$	−26322.8	−1.49434	−0.747169	+	0.664634i	$0.768588\pi$
$678$	9689.23	0.548839
$679$	−2859.38	−0.161609
$680$	−2688.42	−0.151612
$681$	8527.32	0.479835
$682$	−5659.43	−0.317758
$683$	−1139.72	−0.0638509	−0.0319255	−	0.999490i	$-0.510164\pi$
$683$	−1139.72	−0.0638509	−0.0319255	+	0.999490i	$0.510164\pi$
$684$	−1255.33	−0.0701738
$685$	−9501.86	−0.529996
$686$	−686.000	−0.0381802
$687$	−8911.17	−0.494880
$688$	−2258.97	−0.125178
$689$	437.257	0.0241773
$690$	−387.615	−0.0213859
$691$	5132.22	0.282545	0.141273	−	0.989971i	$-0.454881\pi$
$691$	5132.22	0.282545	0.141273	+	0.989971i	$0.454881\pi$
$692$	10650.3	0.585064
$693$	−2003.85	−0.109841
$694$	−17491.6	−0.956734
$695$	−4845.43	−0.264457
$696$	978.584	0.0532947
$697$	43251.4	2.35045
$698$	21865.9	1.18573
$699$	−7233.43	−0.391407
$700$	−3104.70	−0.167638
$701$	18308.7	0.986462	0.493231	−	0.869898i	$-0.335816\pi$
$701$	18308.7	0.986462	0.493231	+	0.869898i	$0.335816\pi$
$702$	7286.03	0.391729
$703$	2715.20	0.145670
$704$	833.884	0.0446423
$705$	−1579.55	−0.0843822
$706$	14772.5	0.787495
$707$	−1353.57	−0.0720030
$708$	7428.35	0.394314
$709$	6698.80	0.354836	0.177418	−	0.984136i	$-0.443226\pi$
$709$	6698.80	0.354836	0.177418	+	0.984136i	$0.443226\pi$
$710$	−6772.27	−0.357970
$711$	26051.8	1.37415
$712$	−12377.2	−0.651483
$713$	4995.11	0.262368
$714$	−2808.10	−0.147186
$715$	1623.96	0.0849406
$716$	−5889.51	−0.307404
$717$	9239.59	0.481253
$718$	−18517.3	−0.962479
$719$	−5195.31	−0.269475	−0.134737	−	0.990881i	$-0.543019\pi$
$719$	−5195.31	−0.269475	−0.134737	+	0.990881i	$0.543019\pi$
$720$	−1320.82	−0.0683668
$721$	1010.81	0.0522118
$722$	13309.9	0.686072
$723$	3907.65	0.201006
$724$	−7668.21	−0.393628
$725$	6047.98	0.309816
$726$	5208.46	0.266259
$727$	20053.2	1.02302	0.511509	−	0.859278i	$-0.329087\pi$
$727$	20053.2	1.02302	0.511509	+	0.859278i	$0.329087\pi$
$728$	−1857.61	−0.0945708
$729$	−971.878	−0.0493765
$730$	−4997.46	−0.253376
$731$	−12627.5	−0.638911
$732$	338.048	0.0170692
$733$	−1125.01	−0.0566893	−0.0283446	−	0.999598i	$-0.509024\pi$
$733$	−1125.01	−0.0566893	−0.0283446	+	0.999598i	$0.509024\pi$
$734$	−2933.02	−0.147493
$735$	412.894	0.0207208
$736$	−736.000	−0.0368605
$737$	5971.82	0.298473
$738$	21249.4	1.05989
$739$	5866.92	0.292041	0.146020	−	0.989282i	$-0.453353\pi$
$739$	5866.92	0.292041	0.146020	+	0.989282i	$0.453353\pi$
$740$	2856.84	0.141919
$741$	1062.63	0.0526813
$742$	−184.543	−0.00913046
$743$	−194.632	−0.00961019	−0.00480510	−	0.999988i	$-0.501530\pi$
$743$	−194.632	−0.00961019	−0.00480510	+	0.999988i	$0.501530\pi$
$744$	−3896.43	−0.192003
$745$	−1675.30	−0.0823867
$746$	−1190.36	−0.0584210
$747$	13340.5	0.653420
$748$	4661.34	0.227855
$749$	11996.8	0.585250
$750$	3975.28	0.193542
$751$	−16766.6	−0.814675	−0.407338	−	0.913278i	$-0.633543\pi$
$751$	−16766.6	−0.814675	−0.407338	+	0.913278i	$0.633543\pi$
$752$	−2999.25	−0.145440
$753$	−11040.9	−0.534332
$754$	3618.63	0.174778
$755$	−9176.80	−0.442355
$756$	−3075.05	−0.147935
$757$	30799.2	1.47875	0.739376	−	0.673293i	$-0.235121\pi$
$757$	30799.2	1.47875	0.739376	+	0.673293i	$0.235121\pi$
$758$	−28101.3	−1.34655
$759$	672.068	0.0321403
$760$	−429.369	−0.0204932
$761$	16533.7	0.787575	0.393787	−	0.919202i	$-0.371165\pi$
$761$	16533.7	0.787575	0.393787	+	0.919202i	$0.371165\pi$
$762$	−319.489	−0.0151888
$763$	−2160.19	−0.102496
$764$	17590.1	0.832970
$765$	−7383.27	−0.348945
$766$	1077.22	0.0508116
$767$	27468.7	1.29314
$768$	574.116	0.0269748
$769$	−11711.7	−0.549198	−0.274599	−	0.961559i	$-0.588545\pi$
$769$	−11711.7	−0.549198	−0.274599	+	0.961559i	$0.588545\pi$
$770$	−685.388	−0.0320775
$771$	10579.2	0.494163
$772$	−13160.0	−0.613523
$773$	34203.9	1.59150	0.795750	−	0.605625i	$-0.207077\pi$
$773$	34203.9	1.59150	0.795750	+	0.605625i	$0.207077\pi$
$774$	−6203.87	−0.288105
$775$	−24081.3	−1.11616
$776$	3267.86	0.151172
$777$	2984.02	0.137775
$778$	7614.36	0.350885
$779$	6907.70	0.317707
$780$	1118.07	0.0513247
$781$	11742.1	0.537985
$782$	−4114.18	−0.188136
$783$	5990.22	0.273401
$784$	784.000	0.0357143
$785$	4100.86	0.186453
$786$	5103.95	0.231618
$787$	11099.7	0.502746	0.251373	−	0.967890i	$-0.419118\pi$
$787$	11099.7	0.502746	0.251373	+	0.967890i	$0.419118\pi$
$788$	−3142.85	−0.142080
$789$	4062.52	0.183307
$790$	8910.64	0.401299
$791$	−15121.6	−0.679724
$792$	2290.11	0.102747
$793$	1250.04	0.0559778
$794$	8914.84	0.398458
$795$	111.074	0.00495521
$796$	−14668.4	−0.653149
$797$	−37944.9	−1.68642	−0.843211	−	0.537583i	$-0.819337\pi$
$797$	−37944.9	−1.68642	−0.843211	+	0.537583i	$0.819337\pi$
$798$	−448.483	−0.0198949
$799$	−16765.5	−0.742330
$800$	3548.23	0.156811
$801$	−33991.8	−1.49943
$802$	−11898.0	−0.523856
$803$	8664.88	0.380793
$804$	4111.51	0.180350
$805$	604.935	0.0264859
$806$	−14408.3	−0.629667
$807$	7115.93	0.310400
$808$	1546.93	0.0673526
$809$	−6105.90	−0.265355	−0.132677	−	0.991159i	$-0.542357\pi$
$809$	−6105.90	−0.265355	−0.132677	+	0.991159i	$0.542357\pi$
$810$	−2606.94	−0.113084
$811$	346.069	0.0149841	0.00749207	−	0.999972i	$-0.497615\pi$
$811$	346.069	0.0149841	0.00749207	+	0.999972i	$0.497615\pi$
$812$	−1527.24	−0.0660043
$813$	−7438.65	−0.320892
$814$	−4953.36	−0.213286
$815$	10076.3	0.433075
$816$	3209.26	0.137680
$817$	−2016.74	−0.0863607
$818$	20732.8	0.886194
$819$	−5101.59	−0.217660
$820$	7268.05	0.309526
$821$	−27513.2	−1.16957	−0.584786	−	0.811188i	$-0.698821\pi$
$821$	−27513.2	−1.16957	−0.584786	+	0.811188i	$0.698821\pi$
$822$	11342.7	0.481291
$823$	130.449	0.00552510	0.00276255	−	0.999996i	$-0.499121\pi$
$823$	130.449	0.00552510	0.00276255	+	0.999996i	$0.499121\pi$
$824$	−1155.22	−0.0488396
$825$	−3240.02	−0.136731
$826$	−11593.1	−0.488349
$827$	−25203.0	−1.05973	−0.529863	−	0.848083i	$-0.677757\pi$
$827$	−25203.0	−1.05973	−0.529863	+	0.848083i	$0.677757\pi$
$828$	−2021.29	−0.0848366
$829$	−22862.7	−0.957848	−0.478924	−	0.877857i	$-0.658973\pi$
$829$	−22862.7	−0.957848	−0.478924	+	0.877857i	$0.658973\pi$
$830$	4562.94	0.190822
$831$	−14490.0	−0.604875
$832$	2122.98	0.0884629
$833$	4382.49	0.182286
$834$	5784.15	0.240154
$835$	−3187.49	−0.132105
$836$	744.464	0.0307988
$837$	−23851.3	−0.984972
$838$	24245.6	0.999465
$839$	−10880.7	−0.447727	−0.223863	−	0.974621i	$-0.571867\pi$
$839$	−10880.7	−0.447727	−0.223863	+	0.974621i	$0.571867\pi$
$840$	−471.879	−0.0193826
$841$	−21413.9	−0.878016
$842$	1514.34	0.0619804
$843$	−1112.17	−0.0454391
$844$	−11256.7	−0.459091
$845$	−4120.50	−0.167751
$846$	−8236.89	−0.334740
$847$	−8128.64	−0.329756
$848$	210.907	0.00854077
$849$	1601.94	0.0647567
$850$	19834.3	0.800366
$851$	4371.92	0.176107
$852$	8084.27	0.325073
$853$	42963.5	1.72455	0.862275	−	0.506440i	$-0.169039\pi$
$853$	42963.5	1.72455	0.862275	+	0.506440i	$0.169039\pi$
$854$	−527.579	−0.0211398
$855$	−1179.19	−0.0471664
$856$	−13710.6	−0.547451
$857$	17543.8	0.699284	0.349642	−	0.936883i	$-0.386303\pi$
$857$	17543.8	0.699284	0.349642	+	0.936883i	$0.386303\pi$
$858$	−1938.57	−0.0771348
$859$	−34293.4	−1.36214	−0.681068	−	0.732220i	$-0.738484\pi$
$859$	−34293.4	−1.36214	−0.681068	+	0.732220i	$0.738484\pi$
$860$	−2121.94	−0.0841368
$861$	7591.60	0.300489
$862$	−26970.4	−1.06568
$863$	5445.15	0.214780	0.107390	−	0.994217i	$-0.465751\pi$
$863$	5445.15	0.214780	0.107390	+	0.994217i	$0.465751\pi$
$864$	3514.35	0.138380
$865$	10004.3	0.393243
$866$	5581.02	0.218996
$867$	6921.38	0.271122
$868$	6081.00	0.237791
$869$	−15449.8	−0.603104
$870$	919.222	0.0358213
$871$	15203.6	0.591453
$872$	2468.79	0.0958759
$873$	8974.59	0.347931
$874$	−657.076	−0.0254301
$875$	−6204.06	−0.239698
$876$	5965.64	0.230091
$877$	−36247.6	−1.39566	−0.697830	−	0.716264i	$-0.745851\pi$
$877$	−36247.6	−1.39566	−0.697830	+	0.716264i	$0.745851\pi$
$878$	−19612.9	−0.753878
$879$	−20906.6	−0.802234
$880$	783.300	0.0300057
$881$	17847.1	0.682503	0.341251	−	0.939972i	$-0.389149\pi$
$881$	17847.1	0.682503	0.341251	+	0.939972i	$0.389149\pi$
$882$	2153.12	0.0821986
$883$	−27180.9	−1.03591	−0.517956	−	0.855407i	$-0.673307\pi$
$883$	−27180.9	−1.03591	−0.517956	+	0.855407i	$0.673307\pi$
$884$	11867.3	0.451515
$885$	6977.74	0.265033
$886$	−840.135	−0.0318565
$887$	−16712.3	−0.632631	−0.316315	−	0.948654i	$-0.602446\pi$
$887$	−16712.3	−0.632631	−0.316315	+	0.948654i	$0.602446\pi$
$888$	−3410.31	−0.128877
$889$	498.613	0.0188110
$890$	−11626.4	−0.437886
$891$	4520.05	0.169952
$892$	2493.16	0.0935841
$893$	−2677.63	−0.100340
$894$	1999.85	0.0748156
$895$	−5532.25	−0.206618
$896$	−896.000	−0.0334077
$897$	1711.01	0.0636891
$898$	4641.68	0.172489
$899$	−11845.8	−0.439467
$900$	9744.58	0.360910
$901$	1178.95	0.0435922
$902$	−12601.8	−0.465180
$903$	−2216.40	−0.0816803
$904$	17281.8	0.635824
$905$	−7203.06	−0.264572
$906$	10954.6	0.401704
$907$	−52905.3	−1.93681	−0.968407	−	0.249373i	$-0.919775\pi$
$907$	−52905.3	−1.93681	−0.968407	+	0.249373i	$0.919775\pi$
$908$	15209.4	0.555884
$909$	4248.37	0.155016
$910$	−1744.93	−0.0635645
$911$	16730.8	0.608469	0.304234	−	0.952597i	$-0.401599\pi$
$911$	16730.8	0.608469	0.304234	+	0.952597i	$0.401599\pi$
$912$	512.552	0.0186100
$913$	−7911.48	−0.286782
$914$	−10317.9	−0.373399
$915$	317.542	0.0114728
$916$	−15894.1	−0.573313
$917$	−7965.53	−0.286854
$918$	19644.9	0.706294
$919$	−2823.14	−0.101335	−0.0506674	−	0.998716i	$-0.516135\pi$
$919$	−2823.14	−0.101335	−0.0506674	+	0.998716i	$0.516135\pi$
$920$	−691.354	−0.0247753
$921$	14882.3	0.532452
$922$	10081.5	0.360104
$923$	29894.2	1.06607
$924$	818.170	0.0291297
$925$	−21076.9	−0.749192
$926$	34948.5	1.24026
$927$	−3172.59	−0.112407
$928$	1745.41	0.0617414
$929$	−37470.3	−1.32332	−0.661659	−	0.749805i	$-0.730147\pi$
$929$	−37470.3	−1.32332	−0.661659	+	0.749805i	$0.730147\pi$
$930$	−3660.07	−0.129052
$931$	699.929	0.0246394
$932$	−12901.6	−0.453441
$933$	−8916.15	−0.312864
$934$	6877.50	0.240941
$935$	4378.58	0.153150
$936$	5830.38	0.203603
$937$	3006.81	0.104833	0.0524164	−	0.998625i	$-0.483308\pi$
$937$	3006.81	0.104833	0.0524164	+	0.998625i	$0.483308\pi$
$938$	−6416.66	−0.223360
$939$	−9937.36	−0.345361
$940$	−2817.31	−0.0977559
$941$	20759.1	0.719159	0.359580	−	0.933114i	$-0.382920\pi$
$941$	20759.1	0.719159	0.359580	+	0.933114i	$0.382920\pi$
$942$	−4895.33	−0.169319
$943$	11122.5	0.384092
$944$	13249.3	0.456809
$945$	−2888.52	−0.0994324
$946$	3679.14	0.126447
$947$	−43409.2	−1.48955	−0.744777	−	0.667313i	$-0.767444\pi$
$947$	−43409.2	−1.48955	−0.744777	+	0.667313i	$0.767444\pi$
$948$	−10636.9	−0.364421
$949$	22059.9	0.754577
$950$	3167.74	0.108184
$951$	12190.2	0.415661
$952$	−5008.56	−0.170513
$953$	−15885.0	−0.539941	−0.269971	−	0.962869i	$-0.587014\pi$
$953$	−15885.0	−0.539941	−0.269971	+	0.962869i	$0.587014\pi$
$954$	579.218	0.0196571
$955$	16523.1	0.559870
$956$	16479.8	0.557527
$957$	−1593.80	−0.0538351
$958$	−26864.8	−0.906013
$959$	−17702.1	−0.596068
$960$	539.290	0.0181307
$961$	17375.6	0.583250
$962$	−12610.7	−0.422647
$963$	−37653.7	−1.25999
$964$	6969.74	0.232863
$965$	−12361.7	−0.412372
$966$	−722.130	−0.0240519
$967$	−22766.1	−0.757094	−0.378547	−	0.925582i	$-0.623576\pi$
$967$	−22766.1	−0.757094	−0.378547	+	0.925582i	$0.623576\pi$
$968$	9289.87	0.308458
$969$	2865.12	0.0949855
$970$	3069.63	0.101608
$971$	−18733.2	−0.619131	−0.309566	−	0.950878i	$-0.600184\pi$
$971$	−18733.2	−0.619131	−0.309566	+	0.950878i	$0.600184\pi$
$972$	14972.9	0.494091
$973$	−9027.09	−0.297426
$974$	−20888.9	−0.687189
$975$	−8248.74	−0.270945
$976$	602.947	0.0197745
$977$	−867.359	−0.0284025	−0.0142013	−	0.999899i	$-0.504521\pi$
$977$	−867.359	−0.0284025	−0.0142013	+	0.999899i	$0.504521\pi$
$978$	−12028.4	−0.393277
$979$	20158.5	0.658089
$980$	736.442	0.0240049
$981$	6780.09	0.220664
$982$	−13993.1	−0.454723
$983$	−15279.8	−0.495780	−0.247890	−	0.968788i	$-0.579737\pi$
$983$	−15279.8	−0.495780	−0.247890	+	0.968788i	$0.579737\pi$
$984$	−8676.11	−0.281082
$985$	−2952.20	−0.0954975
$986$	9756.71	0.315129
$987$	−2942.73	−0.0949017
$988$	1895.33	0.0610308
$989$	−3247.27	−0.104406
$990$	2151.19	0.0690600
$991$	−763.971	−0.0244887	−0.0122444	−	0.999925i	$-0.503898\pi$
$991$	−763.971	−0.0244887	−0.0122444	+	0.999925i	$0.503898\pi$
$992$	−6949.72	−0.222433
$993$	−12530.2	−0.400436
$994$	−12616.8	−0.402596
$995$	−13778.6	−0.439006
$996$	−5446.93	−0.173286
$997$	45215.8	1.43631	0.718154	−	0.695884i	$-0.244987\pi$
$997$	45215.8	1.43631	0.718154	+	0.695884i	$0.244987\pi$
$998$	19558.8	0.620365
$999$	−20875.6	−0.661135

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	322.4.a.a.1.2	✓	2
7.6	odd	2		2254.4.a.e.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
322.4.a.a.1.2	✓	2	1.1	even	1	trivial
2254.4.a.e.1.1		2	7.6	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	322.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +2.24264 q^{3} +4.00000 q^{4} +3.75736 q^{5} -4.48528 q^{6} +7.00000 q^{7} -8.00000 q^{8} -21.9706 q^{9} -7.51472 q^{10} +13.0294 q^{11} +8.97056 q^{12} +33.1716 q^{13} -14.0000 q^{14} +8.42641 q^{15} +16.0000 q^{16} +89.4386 q^{17} +43.9411 q^{18} +14.2843 q^{19} +15.0294 q^{20} +15.6985 q^{21} -26.0589 q^{22} +23.0000 q^{23} -17.9411 q^{24} -110.882 q^{25} -66.3431 q^{26} -109.823 q^{27} +28.0000 q^{28} -54.5442 q^{29} -16.8528 q^{30} +217.179 q^{31} -32.0000 q^{32} +29.2203 q^{33} -178.877 q^{34} +26.3015 q^{35} -87.8823 q^{36} +190.083 q^{37} -28.5685 q^{38} +74.3919 q^{39} -30.0589 q^{40} +483.588 q^{41} -31.3970 q^{42} -141.186 q^{43} +52.1177 q^{44} -82.5513 q^{45} -46.0000 q^{46} -187.453 q^{47} +35.8823 q^{48} +49.0000 q^{49} +221.765 q^{50} +200.579 q^{51} +132.686 q^{52} +13.1817 q^{53} +219.647 q^{54} +48.9563 q^{55} -56.0000 q^{56} +32.0345 q^{57} +109.088 q^{58} +828.080 q^{59} +33.7056 q^{60} +37.6842 q^{61} -434.357 q^{62} -153.794 q^{63} +64.0000 q^{64} +124.638 q^{65} -58.4407 q^{66} +458.333 q^{67} +357.754 q^{68} +51.5807 q^{69} -52.6030 q^{70} +901.200 q^{71} +175.765 q^{72} +665.024 q^{73} -380.167 q^{74} -248.669 q^{75} +57.1371 q^{76} +91.2061 q^{77} -148.784 q^{78} -1185.76 q^{79} +60.1177 q^{80} +346.911 q^{81} -967.176 q^{82} -607.200 q^{83} +62.7939 q^{84} +336.053 q^{85} +282.372 q^{86} -122.323 q^{87} -104.235 q^{88} +1547.15 q^{89} +165.103 q^{90} +232.201 q^{91} +92.0000 q^{92} +487.054 q^{93} +374.906 q^{94} +53.6711 q^{95} -71.7645 q^{96} -408.482 q^{97} -98.0000 q^{98} -286.264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} - 4 q^{3} + 8 q^{4} + 16 q^{5} + 8 q^{6} + 14 q^{7} - 16 q^{8} - 10 q^{9} - 32 q^{10} + 60 q^{11} - 16 q^{12} + 72 q^{13} - 28 q^{14} - 68 q^{15} + 32 q^{16} + 12 q^{17} + 20 q^{18} - 28 q^{19}+ \cdots + 276 q^{99}+O(q^{100}) \) 2 * q - 4 * q^2 - 4 * q^3 + 8 * q^4 + 16 * q^5 + 8 * q^6 + 14 * q^7 - 16 * q^8 - 10 * q^9 - 32 * q^10 + 60 * q^11 - 16 * q^12 + 72 * q^13 - 28 * q^14 - 68 * q^15 + 32 * q^16 + 12 * q^17 + 20 * q^18 - 28 * q^19 + 64 * q^20 - 28 * q^21 - 120 * q^22 + 46 * q^23 + 32 * q^24 - 86 * q^25 - 144 * q^26 - 16 * q^27 + 56 * q^28 - 160 * q^29 + 136 * q^30 + 160 * q^31 - 64 * q^32 - 264 * q^33 - 24 * q^34 + 112 * q^35 - 40 * q^36 + 284 * q^37 + 56 * q^38 - 168 * q^39 - 128 * q^40 + 492 * q^41 + 56 * q^42 + 272 * q^43 + 240 * q^44 + 64 * q^45 - 92 * q^46 + 352 * q^47 - 64 * q^48 + 98 * q^49 + 172 * q^50 + 684 * q^51 + 288 * q^52 + 428 * q^53 + 32 * q^54 + 624 * q^55 - 112 * q^56 + 296 * q^57 + 320 * q^58 + 884 * q^59 - 272 * q^60 + 576 * q^61 - 320 * q^62 - 70 * q^63 + 128 * q^64 + 600 * q^65 + 528 * q^66 + 532 * q^67 + 48 * q^68 - 92 * q^69 - 224 * q^70 + 688 * q^71 + 80 * q^72 + 12 * q^73 - 568 * q^74 - 404 * q^75 - 112 * q^76 + 420 * q^77 + 336 * q^78 - 748 * q^79 + 256 * q^80 - 562 * q^81 - 984 * q^82 - 100 * q^83 - 112 * q^84 - 612 * q^85 - 544 * q^86 + 536 * q^87 - 480 * q^88 + 676 * q^89 - 128 * q^90 + 504 * q^91 + 184 * q^92 + 844 * q^93 - 704 * q^94 - 464 * q^95 + 128 * q^96 - 124 * q^97 - 196 * q^98 + 276 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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