LMFDB - Embedded newform 322.4.a.a.1.1

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			1.1
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)

$f(q)$	$=$	\(q-2.00000 q^{2} -6.24264 q^{3} +4.00000 q^{4} +12.2426 q^{5} +12.4853 q^{6} +7.00000 q^{7} -8.00000 q^{8} +11.9706 q^{9} -24.4853 q^{10} +46.9706 q^{11} -24.9706 q^{12} +38.8284 q^{13} -14.0000 q^{14} -76.4264 q^{15} +16.0000 q^{16} -77.4386 q^{17} -23.9411 q^{18} -42.2843 q^{19} +48.9706 q^{20} -43.6985 q^{21} -93.9411 q^{22} +23.0000 q^{23} +49.9411 q^{24} +24.8823 q^{25} -77.6569 q^{26} +93.8234 q^{27} +28.0000 q^{28} -105.456 q^{29} +152.853 q^{30} -57.1787 q^{31} -32.0000 q^{32} -293.220 q^{33} +154.877 q^{34} +85.6985 q^{35} +47.8823 q^{36} +93.9167 q^{37} +84.5685 q^{38} -242.392 q^{39} -97.9411 q^{40} +8.41212 q^{41} +87.3970 q^{42} +413.186 q^{43} +187.882 q^{44} +146.551 q^{45} -46.0000 q^{46} +539.453 q^{47} -99.8823 q^{48} +49.0000 q^{49} -49.7645 q^{50} +483.421 q^{51} +155.314 q^{52} +414.818 q^{53} -187.647 q^{54} +575.044 q^{55} -56.0000 q^{56} +263.966 q^{57} +210.912 q^{58} +55.9197 q^{59} -305.706 q^{60} +538.316 q^{61} +114.357 q^{62} +83.7939 q^{63} +64.0000 q^{64} +475.362 q^{65} +586.441 q^{66} +73.6670 q^{67} -309.754 q^{68} -143.581 q^{69} -171.397 q^{70} -213.200 q^{71} -95.7645 q^{72} -653.024 q^{73} -187.833 q^{74} -155.331 q^{75} -169.137 q^{76} +328.794 q^{77} +484.784 q^{78} +437.759 q^{79} +195.882 q^{80} -908.911 q^{81} -16.8242 q^{82} +507.200 q^{83} -174.794 q^{84} -948.053 q^{85} -826.372 q^{86} +658.323 q^{87} -375.765 q^{88} -871.153 q^{89} -293.103 q^{90} +271.799 q^{91} +92.0000 q^{92} +356.946 q^{93} -1078.91 q^{94} -517.671 q^{95} +199.765 q^{96} +284.482 q^{97} -98.0000 q^{98} +562.264 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−6.24264	−1.20140	−0.600698	−	0.799476i	$-0.705111\pi$
$3$	−6.24264	−1.20140	−0.600698	+	0.799476i	$0.705111\pi$
$4$	4.00000	0.500000
$5$	12.2426	1.09502	0.547508	−	0.836801i	$-0.315577\pi$
$5$	12.2426	1.09502	0.547508	+	0.836801i	$0.315577\pi$
$6$	12.4853	0.849516
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	11.9706	0.443354
$10$	−24.4853	−0.774293
$11$	46.9706	1.28747	0.643734	−	0.765249i	$-0.277384\pi$
$11$	46.9706	1.28747	0.643734	+	0.765249i	$0.277384\pi$
$12$	−24.9706	−0.600698
$13$	38.8284	0.828390	0.414195	−	0.910188i	$-0.364063\pi$
$13$	38.8284	0.828390	0.414195	+	0.910188i	$0.364063\pi$
$14$	−14.0000	−0.267261
$15$	−76.4264	−1.31555
$16$	16.0000	0.250000
$17$	−77.4386	−1.10480	−0.552401	−	0.833579i	$-0.686288\pi$
$17$	−77.4386	−1.10480	−0.552401	+	0.833579i	$0.686288\pi$
$18$	−23.9411	−0.313499
$19$	−42.2843	−0.510562	−0.255281	−	0.966867i	$-0.582168\pi$
$19$	−42.2843	−0.510562	−0.255281	+	0.966867i	$0.582168\pi$
$20$	48.9706	0.547508
$21$	−43.6985	−0.454085
$22$	−93.9411	−0.910378
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	49.9411	0.424758
$25$	24.8823	0.199058
$26$	−77.6569	−0.585760
$27$	93.8234	0.668752
$28$	28.0000	0.188982
$29$	−105.456	−0.675264	−0.337632	−	0.941278i	$-0.609626\pi$
$29$	−105.456	−0.675264	−0.337632	+	0.941278i	$0.609626\pi$
$30$	152.853	0.930233
$31$	−57.1787	−0.331277	−0.165639	−	0.986187i	$-0.552969\pi$
$31$	−57.1787	−0.331277	−0.165639	+	0.986187i	$0.552969\pi$
$32$	−32.0000	−0.176777
$33$	−293.220	−1.54676
$34$	154.877	0.781212
$35$	85.6985	0.413877
$36$	47.8823	0.221677
$37$	93.9167	0.417292	0.208646	−	0.977991i	$-0.433094\pi$
$37$	93.9167	0.417292	0.208646	+	0.977991i	$0.433094\pi$
$38$	84.5685	0.361022
$39$	−242.392	−0.995225
$40$	−97.9411	−0.387146
$41$	8.41212	0.0320427	0.0160214	−	0.999872i	$-0.494900\pi$
$41$	8.41212	0.0320427	0.0160214	+	0.999872i	$0.494900\pi$
$42$	87.3970	0.321087
$43$	413.186	1.46535	0.732677	−	0.680576i	$-0.238270\pi$
$43$	413.186	1.46535	0.732677	+	0.680576i	$0.238270\pi$
$44$	187.882	0.643734
$45$	146.551	0.485480
$46$	−46.0000	−0.147442
$47$	539.453	1.67420	0.837099	−	0.547052i	$-0.184250\pi$
$47$	539.453	1.67420	0.837099	+	0.547052i	$0.184250\pi$
$48$	−99.8823	−0.300349
$49$	49.0000	0.142857
$50$	−49.7645	−0.140755
$51$	483.421	1.32730
$52$	155.314	0.414195
$53$	414.818	1.07509	0.537544	−	0.843236i	$-0.319352\pi$
$53$	414.818	1.07509	0.537544	+	0.843236i	$0.319352\pi$
$54$	−187.647	−0.472879
$55$	575.044	1.40980
$56$	−56.0000	−0.133631
$57$	263.966	0.613387
$58$	210.912	0.477484
$59$	55.9197	0.123392	0.0616960	−	0.998095i	$-0.480349\pi$
$59$	55.9197	0.123392	0.0616960	+	0.998095i	$0.480349\pi$
$60$	−305.706	−0.657774
$61$	538.316	1.12991	0.564953	−	0.825123i	$-0.308894\pi$
$61$	538.316	1.12991	0.564953	+	0.825123i	$0.308894\pi$
$62$	114.357	0.234249
$63$	83.7939	0.167572
$64$	64.0000	0.125000
$65$	475.362	0.907099
$66$	586.441	1.09373
$67$	73.6670	0.134326	0.0671631	−	0.997742i	$-0.478605\pi$
$67$	73.6670	0.134326	0.0671631	+	0.997742i	$0.478605\pi$
$68$	−309.754	−0.552401
$69$	−143.581	−0.250509
$70$	−171.397	−0.292655
$71$	−213.200	−0.356369	−0.178185	−	0.983997i	$-0.557022\pi$
$71$	−213.200	−0.356369	−0.178185	+	0.983997i	$0.557022\pi$
$72$	−95.7645	−0.156749
$73$	−653.024	−1.04699	−0.523497	−	0.852027i	$-0.675373\pi$
$73$	−653.024	−1.04699	−0.523497	+	0.852027i	$0.675373\pi$
$74$	−187.833	−0.295070
$75$	−155.331	−0.239148
$76$	−169.137	−0.255281
$77$	328.794	0.486617
$78$	484.784	0.703730
$79$	437.759	0.623439	0.311720	−	0.950174i	$-0.399095\pi$
$79$	437.759	0.623439	0.311720	+	0.950174i	$0.399095\pi$
$80$	195.882	0.273754
$81$	−908.911	−1.24679
$82$	−16.8242	−0.0226576
$83$	507.200	0.670752	0.335376	−	0.942084i	$-0.391137\pi$
$83$	507.200	0.670752	0.335376	+	0.942084i	$0.391137\pi$
$84$	−174.794	−0.227043
$85$	−948.053	−1.20977
$86$	−826.372	−1.03616
$87$	658.323	0.811260
$88$	−375.765	−0.455189
$89$	−871.153	−1.03755	−0.518775	−	0.854911i	$-0.673612\pi$
$89$	−871.153	−1.03755	−0.518775	+	0.854911i	$0.673612\pi$
$90$	−293.103	−0.343286
$91$	271.799	0.313102
$92$	92.0000	0.104257
$93$	356.946	0.397996
$94$	−1078.91	−1.18384
$95$	−517.671	−0.559073
$96$	199.765	0.212379
$97$	284.482	0.297781	0.148891	−	0.988854i	$-0.452430\pi$
$97$	284.482	0.297781	0.148891	+	0.988854i	$0.452430\pi$
$98$	−98.0000	−0.101015
$99$	562.264	0.570805
$100$	99.5290	0.0995290
$101$	1113.37	1.09687	0.548436	−	0.836192i	$-0.315223\pi$
$101$	1113.37	1.09687	0.548436	+	0.836192i	$0.315223\pi$
$102$	−966.843	−0.938546
$103$	223.598	0.213901	0.106950	−	0.994264i	$-0.465891\pi$
$103$	223.598	0.213901	0.106950	+	0.994264i	$0.465891\pi$
$104$	−310.627	−0.292880
$105$	−534.985	−0.497230
$106$	−829.637	−0.760202
$107$	1510.18	1.36443	0.682216	−	0.731150i	$-0.261016\pi$
$107$	1510.18	1.36443	0.682216	+	0.731150i	$0.261016\pi$
$108$	375.294	0.334376
$109$	−1383.40	−1.21565	−0.607825	−	0.794071i	$-0.707958\pi$
$109$	−1383.40	−1.21565	−0.607825	+	0.794071i	$0.707958\pi$
$110$	−1150.09	−0.996878
$111$	−586.288	−0.501334
$112$	112.000	0.0944911
$113$	1228.23	1.02250	0.511248	−	0.859433i	$-0.329184\pi$
$113$	1228.23	1.02250	0.511248	+	0.859433i	$0.329184\pi$
$114$	−527.931	−0.433730
$115$	281.581	0.228326
$116$	−421.823	−0.337632
$117$	464.798	0.367270
$118$	−111.839	−0.0872513
$119$	−542.070	−0.417576
$120$	611.411	0.465116
$121$	875.234	0.657576
$122$	−1076.63	−0.798964
$123$	−52.5139	−0.0384961
$124$	−228.715	−0.165639
$125$	−1225.71	−0.877044
$126$	−167.588	−0.118491
$127$	144.770	0.101151	0.0505757	−	0.998720i	$-0.483894\pi$
$127$	144.770	0.101151	0.0505757	+	0.998720i	$0.483894\pi$
$128$	−128.000	−0.0883883
$129$	−2579.37	−1.76047
$130$	−950.725	−0.641416
$131$	957.932	0.638893	0.319446	−	0.947604i	$-0.396503\pi$
$131$	957.932	0.638893	0.319446	+	0.947604i	$0.396503\pi$
$132$	−1172.88	−0.773380
$133$	−295.990	−0.192974
$134$	−147.334	−0.0949829
$135$	1148.65	0.732294
$136$	619.509	0.390606
$137$	508.865	0.317338	0.158669	−	0.987332i	$-0.449280\pi$
$137$	508.865	0.317338	0.158669	+	0.987332i	$0.449280\pi$
$138$	287.161	0.177136
$139$	−138.415	−0.0844620	−0.0422310	−	0.999108i	$-0.513447\pi$
$139$	−138.415	−0.0844620	−0.0422310	+	0.999108i	$0.513447\pi$
$140$	342.794	0.206938
$141$	−3367.61	−2.01138
$142$	426.400	0.251991
$143$	1823.79	1.06653
$144$	191.529	0.110839
$145$	−1291.06	−0.739424
$146$	1306.05	0.740337
$147$	−305.889	−0.171628
$148$	375.667	0.208646
$149$	2393.87	1.31620	0.658099	−	0.752931i	$-0.271361\pi$
$149$	2393.87	1.31620	0.658099	+	0.752931i	$0.271361\pi$
$150$	310.662	0.169103
$151$	2722.35	1.46717	0.733583	−	0.679600i	$-0.237847\pi$
$151$	2722.35	1.46717	0.733583	+	0.679600i	$0.237847\pi$
$152$	338.274	0.180511
$153$	−926.984	−0.489818
$154$	−657.588	−0.344091
$155$	−700.018	−0.362754
$156$	−969.568	−0.497612
$157$	−3131.42	−1.59181	−0.795906	−	0.605420i	$-0.793005\pi$
$157$	−3131.42	−1.59181	−0.795906	+	0.605420i	$0.793005\pi$
$158$	−875.517	−0.440838
$159$	−2589.56	−1.29161
$160$	−391.765	−0.193573
$161$	161.000	0.0788110
$162$	1817.82	0.881615
$163$	2574.26	1.23700	0.618502	−	0.785783i	$-0.287740\pi$
$163$	2574.26	1.23700	0.618502	+	0.785783i	$0.287740\pi$
$164$	33.6485	0.0160214
$165$	−3589.79	−1.69373
$166$	−1014.40	−0.474294
$167$	−2095.67	−0.971064	−0.485532	−	0.874219i	$-0.661374\pi$
$167$	−2095.67	−0.971064	−0.485532	+	0.874219i	$0.661374\pi$
$168$	349.588	0.160543
$169$	−689.353	−0.313770
$170$	1896.11	0.855439
$171$	−506.167	−0.226360
$172$	1652.74	0.732677
$173$	2945.42	1.29443	0.647215	−	0.762308i	$-0.275934\pi$
$173$	2945.42	1.29443	0.647215	+	0.762308i	$0.275934\pi$
$174$	−1316.65	−0.573648
$175$	174.176	0.0752369
$176$	751.529	0.321867
$177$	−349.087	−0.148243
$178$	1742.31	0.733659
$179$	3856.38	1.61028	0.805138	−	0.593088i	$-0.202091\pi$
$179$	3856.38	1.61028	0.805138	+	0.593088i	$0.202091\pi$
$180$	586.205	0.242740
$181$	−3418.95	−1.40402	−0.702012	−	0.712165i	$-0.747715\pi$
$181$	−3418.95	−1.40402	−0.702012	+	0.712165i	$0.747715\pi$
$182$	−543.598	−0.221397
$183$	−3360.51	−1.35747
$184$	−184.000	−0.0737210
$185$	1149.79	0.456941
$186$	−713.892	−0.281425
$187$	−3637.33	−1.42240
$188$	2157.81	0.837099
$189$	656.764	0.252765
$190$	1035.34	0.395324
$191$	−365.536	−0.138478	−0.0692388	−	0.997600i	$-0.522057\pi$
$191$	−365.536	−0.138478	−0.0692388	+	0.997600i	$0.522057\pi$
$192$	−399.529	−0.150175
$193$	−1377.99	−0.513938	−0.256969	−	0.966420i	$-0.582724\pi$
$193$	−1377.99	−0.513938	−0.256969	+	0.966420i	$0.582724\pi$
$194$	−568.965	−0.210563
$195$	−2967.52	−1.08979
$196$	196.000	0.0714286
$197$	3773.71	1.36480	0.682401	−	0.730978i	$-0.260936\pi$
$197$	3773.71	1.36480	0.682401	+	0.730978i	$0.260936\pi$
$198$	−1124.53	−0.403620
$199$	451.095	0.160690	0.0803449	−	0.996767i	$-0.474398\pi$
$199$	451.095	0.160690	0.0803449	+	0.996767i	$0.474398\pi$
$200$	−199.058	−0.0703776
$201$	−459.876	−0.161379
$202$	−2226.73	−0.775606
$203$	−738.191	−0.255226
$204$	1933.69	0.663652
$205$	102.987	0.0350873
$206$	−447.196	−0.151251
$207$	275.323	0.0924457
$208$	621.255	0.207097
$209$	−1986.12	−0.657333
$210$	1069.97	0.351595
$211$	−1105.82	−0.360794	−0.180397	−	0.983594i	$-0.557738\pi$
$211$	−1105.82	−0.360794	−0.180397	+	0.983594i	$0.557738\pi$
$212$	1659.27	0.537544
$213$	1330.93	0.428141
$214$	−3020.35	−0.964800
$215$	5058.49	1.60459
$216$	−750.587	−0.236440
$217$	−400.251	−0.125211
$218$	2766.80	0.859594
$219$	4076.59	1.25786
$220$	2300.17	0.704899
$221$	−3006.82	−0.915206
$222$	1172.58	0.354496
$223$	−3175.29	−0.953512	−0.476756	−	0.879036i	$-0.658187\pi$
$223$	−3175.29	−0.953512	−0.476756	+	0.879036i	$0.658187\pi$
$224$	−224.000	−0.0668153
$225$	297.855	0.0882532
$226$	−2456.46	−0.723013
$227$	−2318.36	−0.677863	−0.338931	−	0.940811i	$-0.610065\pi$
$227$	−2318.36	−0.677863	−0.338931	+	0.940811i	$0.610065\pi$
$228$	1055.86	0.306694
$229$	3213.52	0.927315	0.463658	−	0.886014i	$-0.346537\pi$
$229$	3213.52	0.927315	0.463658	+	0.886014i	$0.346537\pi$
$230$	−563.161	−0.161451
$231$	−2052.54	−0.584621
$232$	843.647	0.238742
$233$	4377.41	1.23079	0.615394	−	0.788220i	$-0.288997\pi$
$233$	4377.41	1.23079	0.615394	+	0.788220i	$0.288997\pi$
$234$	−929.596	−0.259699
$235$	6604.33	1.83327
$236$	223.679	0.0616960
$237$	−2732.77	−0.748998
$238$	1084.14	0.295271
$239$	−5343.96	−1.44633	−0.723163	−	0.690677i	$-0.757313\pi$
$239$	−5343.96	−1.44633	−0.723163	+	0.690677i	$0.757313\pi$
$240$	−1222.82	−0.328887
$241$	−4194.43	−1.12111	−0.560554	−	0.828118i	$-0.689412\pi$
$241$	−4194.43	−1.12111	−0.560554	+	0.828118i	$0.689412\pi$
$242$	−1750.47	−0.464977
$243$	3140.77	0.829138
$244$	2153.26	0.564953
$245$	599.889	0.156431
$246$	105.028	0.0272208
$247$	−1641.83	−0.422944
$248$	457.430	0.117124
$249$	−3166.27	−0.805840
$250$	2451.41	0.620163
$251$	−5488.84	−1.38029	−0.690145	−	0.723671i	$-0.742453\pi$
$251$	−5488.84	−1.38029	−0.690145	+	0.723671i	$0.742453\pi$
$252$	335.176	0.0837861
$253$	1080.32	0.268456
$254$	−289.539	−0.0715248
$255$	5918.35	1.45342
$256$	256.000	0.0625000
$257$	1198.72	0.290949	0.145475	−	0.989362i	$-0.453529\pi$
$257$	1198.72	0.290949	0.145475	+	0.989362i	$0.453529\pi$
$258$	5158.74	1.24484
$259$	657.417	0.157722
$260$	1901.45	0.453550
$261$	−1262.37	−0.299381
$262$	−1915.86	−0.451765
$263$	5256.51	1.23244	0.616218	−	0.787576i	$-0.288664\pi$
$263$	5256.51	1.23244	0.616218	+	0.787576i	$0.288664\pi$
$264$	2345.76	0.546863
$265$	5078.47	1.17724
$266$	591.980	0.136453
$267$	5438.29	1.24651
$268$	294.668	0.0671631
$269$	−1805.02	−0.409122	−0.204561	−	0.978854i	$-0.565577\pi$
$269$	−1805.02	−0.409122	−0.204561	+	0.978854i	$0.565577\pi$
$270$	−2297.29	−0.517810
$271$	−627.083	−0.140563	−0.0702815	−	0.997527i	$-0.522390\pi$
$271$	−627.083	−0.140563	−0.0702815	+	0.997527i	$0.522390\pi$
$272$	−1239.02	−0.276200
$273$	−1696.74	−0.376160
$274$	−1017.73	−0.224392
$275$	1168.73	0.256281
$276$	−574.323	−0.125254
$277$	−2178.88	−0.472622	−0.236311	−	0.971677i	$-0.575938\pi$
$277$	−2178.88	−0.472622	−0.236311	+	0.971677i	$0.575938\pi$
$278$	276.830	0.0597236
$279$	−684.461	−0.146873
$280$	−685.588	−0.146328
$281$	8243.92	1.75015	0.875073	−	0.483991i	$-0.160813\pi$
$281$	8243.92	1.75015	0.875073	+	0.483991i	$0.160813\pi$
$282$	6735.22	1.42226
$283$	−5078.31	−1.06669	−0.533347	−	0.845897i	$-0.679066\pi$
$283$	−5078.31	−1.06669	−0.533347	+	0.845897i	$0.679066\pi$
$284$	−852.801	−0.178185
$285$	3231.63	0.671669
$286$	−3647.59	−0.754148
$287$	58.8849	0.0121110
$288$	−383.058	−0.0783747
$289$	1083.74	0.220586
$290$	2582.12	0.522852
$291$	−1775.92	−0.357754
$292$	−2612.09	−0.523497
$293$	−1733.67	−0.345672	−0.172836	−	0.984951i	$-0.555293\pi$
$293$	−1733.67	−0.345672	−0.172836	+	0.984951i	$0.555293\pi$
$294$	611.779	0.121359
$295$	684.605	0.135116
$296$	−751.334	−0.147535
$297$	4406.94	0.860998
$298$	−4787.74	−0.930693
$299$	893.054	0.172731
$300$	−621.324	−0.119574
$301$	2892.30	0.553852
$302$	−5444.71	−1.03744
$303$	−6950.35	−1.31778
$304$	−676.548	−0.127640
$305$	6590.41	1.23726
$306$	1853.97	0.346354
$307$	5071.94	0.942902	0.471451	−	0.881892i	$-0.343730\pi$
$307$	5071.94	0.942902	0.471451	+	0.881892i	$0.343730\pi$
$308$	1315.18	0.243309
$309$	−1395.84	−0.256980
$310$	1400.04	0.256506
$311$	7951.74	1.44984	0.724922	−	0.688831i	$-0.241876\pi$
$311$	7951.74	1.44984	0.724922	+	0.688831i	$0.241876\pi$
$312$	1939.14	0.351865
$313$	10155.1	1.83387	0.916933	−	0.399041i	$-0.130657\pi$
$313$	10155.1	1.83387	0.916933	+	0.399041i	$0.130657\pi$
$314$	6262.84	1.12558
$315$	1025.86	0.183494
$316$	1751.03	0.311720
$317$	−10171.6	−1.80219	−0.901097	−	0.433617i	$-0.857237\pi$
$317$	−10171.6	−1.80219	−0.901097	+	0.433617i	$0.857237\pi$
$318$	5179.12	0.913304
$319$	−4953.32	−0.869381
$320$	783.529	0.136877
$321$	−9427.49	−1.63922
$322$	−322.000	−0.0557278
$323$	3274.43	0.564069
$324$	−3635.64	−0.623396
$325$	966.139	0.164898
$326$	−5148.52	−0.874694
$327$	8636.08	1.46048
$328$	−67.2970	−0.0113288
$329$	3776.17	0.632787
$330$	7179.58	1.19765
$331$	867.235	0.144011	0.0720054	−	0.997404i	$-0.477060\pi$
$331$	867.235	0.144011	0.0720054	+	0.997404i	$0.477060\pi$
$332$	2028.80	0.335376
$333$	1124.24	0.185008
$334$	4191.34	0.686646
$335$	901.878	0.147089
$336$	−699.176	−0.113521
$337$	−3597.66	−0.581535	−0.290767	−	0.956794i	$-0.593911\pi$
$337$	−3597.66	−0.581535	−0.290767	+	0.956794i	$0.593911\pi$
$338$	1378.71	0.221869
$339$	−7667.39	−1.22842
$340$	−3792.21	−0.604887
$341$	−2685.72	−0.426509
$342$	1012.33	0.160061
$343$	343.000	0.0539949
$344$	−3305.49	−0.518081
$345$	−1757.81	−0.274311
$346$	−5890.84	−0.915300
$347$	−3953.82	−0.611678	−0.305839	−	0.952083i	$-0.598937\pi$
$347$	−3953.82	−0.611678	−0.305839	+	0.952083i	$0.598937\pi$
$348$	2633.29	0.405630
$349$	−5491.05	−0.842204	−0.421102	−	0.907013i	$-0.638357\pi$
$349$	−5491.05	−0.842204	−0.421102	+	0.907013i	$0.638357\pi$
$350$	−348.352	−0.0532005
$351$	3643.01	0.553988
$352$	−1503.06	−0.227594
$353$	7870.27	1.18666	0.593332	−	0.804958i	$-0.297812\pi$
$353$	7870.27	1.18666	0.593332	+	0.804958i	$0.297812\pi$
$354$	698.173	0.104823
$355$	−2610.13	−0.390229
$356$	−3484.61	−0.518775
$357$	3383.95	0.501674
$358$	−7712.76	−1.13864
$359$	7137.34	1.04929	0.524644	−	0.851322i	$-0.324198\pi$
$359$	7137.34	1.04929	0.524644	+	0.851322i	$0.324198\pi$
$360$	−1172.41	−0.171643
$361$	−5071.04	−0.739326
$362$	6837.89	0.992795
$363$	−5463.77	−0.790010
$364$	1087.20	0.156551
$365$	−7994.73	−1.14648
$366$	6721.02	0.959873
$367$	−6594.51	−0.937958	−0.468979	−	0.883209i	$-0.655378\pi$
$367$	−6594.51	−0.937958	−0.468979	+	0.883209i	$0.655378\pi$
$368$	368.000	0.0521286
$369$	100.698	0.0142063
$370$	−2299.58	−0.323106
$371$	2903.73	0.406345
$372$	1427.78	0.198998
$373$	−9191.18	−1.27587	−0.637937	−	0.770088i	$-0.720212\pi$
$373$	−9191.18	−1.27587	−0.637937	+	0.770088i	$0.720212\pi$
$374$	7274.67	1.00579
$375$	7651.64	1.05368
$376$	−4315.62	−0.591918
$377$	−4094.68	−0.559382
$378$	−1313.53	−0.178732
$379$	−5974.63	−0.809753	−0.404876	−	0.914371i	$-0.632685\pi$
$379$	−5974.63	−0.809753	−0.404876	+	0.914371i	$0.632685\pi$
$380$	−2070.68	−0.279537
$381$	−903.744	−0.121523
$382$	731.071	0.0979185
$383$	−12197.4	−1.62730	−0.813652	−	0.581352i	$-0.802524\pi$
$383$	−12197.4	−1.62730	−0.813652	+	0.581352i	$0.802524\pi$
$384$	799.058	0.106189
$385$	4025.31	0.532853
$386$	2755.98	0.363409
$387$	4946.07	0.649671
$388$	1137.93	0.148891
$389$	1363.18	0.177676	0.0888382	−	0.996046i	$-0.471685\pi$
$389$	1363.18	0.177676	0.0888382	+	0.996046i	$0.471685\pi$
$390$	5935.03	0.770595
$391$	−1781.09	−0.230367
$392$	−392.000	−0.0505076
$393$	−5980.03	−0.767563
$394$	−7547.42	−0.965060
$395$	5359.32	0.682675
$396$	2249.06	0.285402
$397$	−7438.58	−0.940382	−0.470191	−	0.882565i	$-0.655815\pi$
$397$	−7438.58	−0.940382	−0.470191	+	0.882565i	$0.655815\pi$
$398$	−902.190	−0.113625
$399$	1847.76	0.231839
$400$	398.116	0.0497645
$401$	−2128.99	−0.265129	−0.132565	−	0.991174i	$-0.542321\pi$
$401$	−2128.99	−0.265129	−0.132565	+	0.991174i	$0.542321\pi$
$402$	919.753	0.114112
$403$	−2220.16	−0.274427
$404$	4453.47	0.548436
$405$	−11127.5	−1.36526
$406$	1476.38	0.180472
$407$	4411.32	0.537251
$408$	−3867.37	−0.469273
$409$	−9885.58	−1.19514	−0.597568	−	0.801818i	$-0.703866\pi$
$409$	−9885.58	−1.19514	−0.597568	+	0.801818i	$0.703866\pi$
$410$	−205.973	−0.0248105
$411$	−3176.66	−0.381249
$412$	894.392	0.106950
$413$	391.438	0.0466378
$414$	−550.646	−0.0653690
$415$	6209.47	0.734484
$416$	−1242.51	−0.146440
$417$	864.076	0.101472
$418$	3972.23	0.464804
$419$	−8457.18	−0.986063	−0.493031	−	0.870012i	$-0.664111\pi$
$419$	−8457.18	−0.986063	−0.493031	+	0.870012i	$0.664111\pi$
$420$	−2139.94	−0.248615
$421$	−9598.83	−1.11121	−0.555604	−	0.831447i	$-0.687513\pi$
$421$	−9598.83	−1.11121	−0.555604	+	0.831447i	$0.687513\pi$
$422$	2211.63	0.255120
$423$	6457.55	0.742263
$424$	−3318.55	−0.380101
$425$	−1926.85	−0.219920
$426$	−2661.86	−0.302741
$427$	3768.21	0.427064
$428$	6040.71	0.682216
$429$	−11385.3	−1.28132
$430$	−10117.0	−1.13461
$431$	−2829.18	−0.316188	−0.158094	−	0.987424i	$-0.550535\pi$
$431$	−2829.18	−0.316188	−0.158094	+	0.987424i	$0.550535\pi$
$432$	1501.17	0.167188
$433$	12474.5	1.38450	0.692248	−	0.721660i	$-0.256620\pi$
$433$	12474.5	1.38450	0.692248	+	0.721660i	$0.256620\pi$
$434$	800.502	0.0885376
$435$	8059.61	0.888342
$436$	−5533.60	−0.607825
$437$	−972.538	−0.106460
$438$	−8153.18	−0.889439
$439$	−12614.5	−1.37143	−0.685713	−	0.727872i	$-0.740509\pi$
$439$	−12614.5	−1.37143	−0.685713	+	0.727872i	$0.740509\pi$
$440$	−4600.35	−0.498439
$441$	586.558	0.0633363
$442$	6013.64	0.647148
$443$	12027.9	1.28999	0.644994	−	0.764188i	$-0.276860\pi$
$443$	12027.9	1.28999	0.644994	+	0.764188i	$0.276860\pi$
$444$	−2345.15	−0.250667
$445$	−10665.2	−1.13613
$446$	6350.58	0.674234
$447$	−14944.1	−1.58128
$448$	448.000	0.0472456
$449$	16312.8	1.71459	0.857295	−	0.514826i	$-0.172144\pi$
$449$	16312.8	1.71459	0.857295	+	0.514826i	$0.172144\pi$
$450$	−595.709	−0.0624044
$451$	395.122	0.0412540
$452$	4912.91	0.511248
$453$	−16994.7	−1.76265
$454$	4636.72	0.479321
$455$	3327.54	0.342851
$456$	−2111.72	−0.216865
$457$	10301.0	1.05440	0.527202	−	0.849740i	$-0.323241\pi$
$457$	10301.0	1.05440	0.527202	+	0.849740i	$0.323241\pi$
$458$	−6427.03	−0.655711
$459$	−7265.55	−0.738839
$460$	1126.32	0.114163
$461$	−4735.26	−0.478402	−0.239201	−	0.970970i	$-0.576885\pi$
$461$	−4735.26	−0.478402	−0.239201	+	0.970970i	$0.576885\pi$
$462$	4105.08	0.413389
$463$	7970.27	0.800021	0.400010	−	0.916511i	$-0.369007\pi$
$463$	7970.27	0.800021	0.400010	+	0.916511i	$0.369007\pi$
$464$	−1687.29	−0.168816
$465$	4369.96	0.435811
$466$	−8754.81	−0.870298
$467$	−10453.2	−1.03580	−0.517900	−	0.855441i	$-0.673286\pi$
$467$	−10453.2	−1.03580	−0.517900	+	0.855441i	$0.673286\pi$
$468$	1859.19	0.183635
$469$	515.669	0.0507705
$470$	−13208.7	−1.29632
$471$	19548.3	1.91240
$472$	−447.358	−0.0436256
$473$	19407.6	1.88660
$474$	5465.54	0.529621
$475$	−1052.13	−0.101631
$476$	−2168.28	−0.208788
$477$	4965.61	0.476645
$478$	10687.9	1.02271
$479$	−18800.4	−1.79334	−0.896671	−	0.442697i	$-0.854022\pi$
$479$	−18800.4	−1.79334	−0.896671	+	0.442697i	$0.854022\pi$
$480$	2445.65	0.232558
$481$	3646.64	0.345681
$482$	8388.87	0.792744
$483$	−1005.07	−0.0946833
$484$	3500.94	0.328788
$485$	3482.81	0.326075
$486$	−6281.55	−0.586289
$487$	−10972.4	−1.02096	−0.510481	−	0.859889i	$-0.670532\pi$
$487$	−10972.4	−1.02096	−0.510481	+	0.859889i	$0.670532\pi$
$488$	−4306.53	−0.399482
$489$	−16070.2	−1.48613
$490$	−1199.78	−0.110613
$491$	17235.5	1.58417	0.792083	−	0.610414i	$-0.208997\pi$
$491$	17235.5	1.58417	0.792083	+	0.610414i	$0.208997\pi$
$492$	−210.055	−0.0192480
$493$	8166.35	0.746033
$494$	3283.66	0.299067
$495$	6883.60	0.625040
$496$	−914.859	−0.0828194
$497$	−1492.40	−0.134695
$498$	6332.54	0.569815
$499$	−660.575	−0.0592614	−0.0296307	−	0.999561i	$-0.509433\pi$
$499$	−660.575	−0.0592614	−0.0296307	+	0.999561i	$0.509433\pi$
$500$	−4902.82	−0.438522
$501$	13082.5	1.16663
$502$	10977.7	0.976012
$503$	−1701.15	−0.150796	−0.0753980	−	0.997154i	$-0.524023\pi$
$503$	−1701.15	−0.150796	−0.0753980	+	0.997154i	$0.524023\pi$
$504$	−670.352	−0.0592457
$505$	13630.5	1.20109
$506$	−2160.65	−0.189827
$507$	4303.38	0.376963
$508$	579.078	0.0505757
$509$	−15163.6	−1.32046	−0.660231	−	0.751062i	$-0.729542\pi$
$509$	−15163.6	−1.32046	−0.660231	+	0.751062i	$0.729542\pi$
$510$	−11836.7	−1.02772
$511$	−4571.16	−0.395727
$512$	−512.000	−0.0441942
$513$	−3967.25	−0.341440
$514$	−2397.44	−0.205732
$515$	2737.43	0.234224
$516$	−10317.5	−0.880236
$517$	25338.4	2.15548
$518$	−1314.83	−0.111526
$519$	−18387.2	−1.55512
$520$	−3802.90	−0.320708
$521$	−17065.7	−1.43506	−0.717528	−	0.696530i	$-0.754726\pi$
$521$	−17065.7	−1.43506	−0.717528	+	0.696530i	$0.754726\pi$
$522$	2524.73	0.211694
$523$	−1479.69	−0.123714	−0.0618569	−	0.998085i	$-0.519702\pi$
$523$	−1479.69	−0.123714	−0.0618569	+	0.998085i	$0.519702\pi$
$524$	3831.73	0.319446
$525$	−1087.32	−0.0903893
$526$	−10513.0	−0.871463
$527$	4427.84	0.365996
$528$	−4691.53	−0.386690
$529$	529.000	0.0434783
$530$	−10156.9	−0.832433
$531$	669.390	0.0547063
$532$	−1183.96	−0.0964871
$533$	326.629	0.0265439
$534$	−10876.6	−0.881416
$535$	18488.5	1.49407
$536$	−589.336	−0.0474915
$537$	−24074.0	−1.93458
$538$	3610.03	0.289293
$539$	2301.56	0.183924
$540$	4594.58	0.366147
$541$	778.940	0.0619025	0.0309512	−	0.999521i	$-0.490146\pi$
$541$	778.940	0.0619025	0.0309512	+	0.999521i	$0.490146\pi$
$542$	1254.17	0.0993931
$543$	21343.3	1.68679
$544$	2478.04	0.195303
$545$	−16936.5	−1.33115
$546$	3393.49	0.265985
$547$	12758.6	0.997288	0.498644	−	0.866807i	$-0.333831\pi$
$547$	12758.6	0.997288	0.498644	+	0.866807i	$0.333831\pi$
$548$	2035.46	0.158669
$549$	6443.94	0.500949
$550$	−2337.47	−0.181218
$551$	4459.12	0.344764
$552$	1148.65	0.0885681
$553$	3064.31	0.235638
$554$	4357.76	0.334194
$555$	−7177.72	−0.548968
$556$	−553.660	−0.0422310
$557$	−11147.0	−0.847957	−0.423978	−	0.905672i	$-0.639367\pi$
$557$	−11147.0	−0.847957	−0.423978	+	0.905672i	$0.639367\pi$
$558$	1368.92	0.103855
$559$	16043.4	1.21388
$560$	1371.18	0.103469
$561$	22706.6	1.70886
$562$	−16487.8	−1.23754
$563$	−15030.4	−1.12514	−0.562570	−	0.826749i	$-0.690187\pi$
$563$	−15030.4	−1.12514	−0.562570	+	0.826749i	$0.690187\pi$
$564$	−13470.4	−1.00569
$565$	15036.8	1.11965
$566$	10156.6	0.754266
$567$	−6362.38	−0.471243
$568$	1705.60	0.125995
$569$	−6078.25	−0.447827	−0.223914	−	0.974609i	$-0.571883\pi$
$569$	−6078.25	−0.447827	−0.223914	+	0.974609i	$0.571883\pi$
$570$	−6463.27	−0.474941
$571$	3550.29	0.260202	0.130101	−	0.991501i	$-0.458470\pi$
$571$	3550.29	0.260202	0.130101	+	0.991501i	$0.458470\pi$
$572$	7295.17	0.533263
$573$	2281.91	0.166367
$574$	−117.770	−0.00856378
$575$	572.292	0.0415065
$576$	766.116	0.0554193
$577$	18938.3	1.36640	0.683198	−	0.730234i	$-0.260589\pi$
$577$	18938.3	1.36640	0.683198	+	0.730234i	$0.260589\pi$
$578$	−2167.47	−0.155978
$579$	8602.31	0.617443
$580$	−5164.23	−0.369712
$581$	3550.40	0.253521
$582$	3551.84	0.252970
$583$	19484.3	1.38414
$584$	5224.19	0.370169
$585$	5690.36	0.402166
$586$	3467.33	0.244427
$587$	21377.4	1.50313	0.751567	−	0.659657i	$-0.229299\pi$
$587$	21377.4	1.50313	0.751567	+	0.659657i	$0.229299\pi$
$588$	−1223.56	−0.0858141
$589$	2417.76	0.169138
$590$	−1369.21	−0.0955415
$591$	−23557.9	−1.63967
$592$	1502.67	0.104323
$593$	−7021.45	−0.486234	−0.243117	−	0.969997i	$-0.578170\pi$
$593$	−7021.45	−0.486234	−0.243117	+	0.969997i	$0.578170\pi$
$594$	−8813.87	−0.608818
$595$	−6636.37	−0.457252
$596$	9575.48	0.658099
$597$	−2816.02	−0.193052
$598$	−1786.11	−0.122139
$599$	7336.15	0.500412	0.250206	−	0.968193i	$-0.419502\pi$
$599$	7336.15	0.500412	0.250206	+	0.968193i	$0.419502\pi$
$600$	1242.65	0.0845515
$601$	10999.6	0.746564	0.373282	−	0.927718i	$-0.378232\pi$
$601$	10999.6	0.746564	0.373282	+	0.927718i	$0.378232\pi$
$602$	−5784.60	−0.391633
$603$	881.835	0.0595541
$604$	10889.4	0.733583
$605$	10715.2	0.720056
$606$	13900.7	0.931811
$607$	−15403.7	−1.03001	−0.515005	−	0.857187i	$-0.672210\pi$
$607$	−15403.7	−1.03001	−0.515005	+	0.857187i	$0.672210\pi$
$608$	1353.10	0.0902555
$609$	4608.26	0.306627
$610$	−13180.8	−0.874878
$611$	20946.1	1.38689
$612$	−3707.93	−0.244909
$613$	−23890.3	−1.57410	−0.787048	−	0.616892i	$-0.788392\pi$
$613$	−23890.3	−1.57410	−0.787048	+	0.616892i	$0.788392\pi$
$614$	−10143.9	−0.666732
$615$	−642.908	−0.0421538
$616$	−2630.35	−0.172045
$617$	−3199.68	−0.208775	−0.104388	−	0.994537i	$-0.533288\pi$
$617$	−3199.68	−0.208775	−0.104388	+	0.994537i	$0.533288\pi$
$618$	2791.68	0.181712
$619$	−7854.20	−0.509995	−0.254998	−	0.966942i	$-0.582075\pi$
$619$	−7854.20	−0.509995	−0.254998	+	0.966942i	$0.582075\pi$
$620$	−2800.07	−0.181377
$621$	2157.94	0.139445
$622$	−15903.5	−1.02520
$623$	−6098.07	−0.392157
$624$	−3878.27	−0.248806
$625$	−18116.2	−1.15943
$626$	−20310.2	−1.29674
$627$	12398.6	0.789717
$628$	−12525.7	−0.795906
$629$	−7272.78	−0.461025
$630$	−2051.72	−0.129750
$631$	−15253.8	−0.962350	−0.481175	−	0.876624i	$-0.659790\pi$
$631$	−15253.8	−0.962350	−0.481175	+	0.876624i	$0.659790\pi$
$632$	−3502.07	−0.220419
$633$	6903.21	0.433456
$634$	20343.3	1.27434
$635$	1772.36	0.110762
$636$	−10358.2	−0.645804
$637$	1902.59	0.118341
$638$	9906.64	0.614746
$639$	−2552.13	−0.157998
$640$	−1567.06	−0.0967866
$641$	−21067.3	−1.29814	−0.649071	−	0.760728i	$-0.724842\pi$
$641$	−21067.3	−1.29814	−0.649071	+	0.760728i	$0.724842\pi$
$642$	18855.0	1.15911
$643$	8282.08	0.507953	0.253976	−	0.967210i	$-0.418261\pi$
$643$	8282.08	0.507953	0.253976	+	0.967210i	$0.418261\pi$
$644$	644.000	0.0394055
$645$	−31578.3	−1.92774
$646$	−6548.87	−0.398857
$647$	1367.52	0.0830955	0.0415478	−	0.999137i	$-0.486771\pi$
$647$	1367.52	0.0830955	0.0415478	+	0.999137i	$0.486771\pi$
$648$	7271.29	0.440807
$649$	2626.58	0.158863
$650$	−1932.28	−0.116600
$651$	2498.62	0.150428
$652$	10297.0	0.618502
$653$	−10988.8	−0.658537	−0.329269	−	0.944236i	$-0.606802\pi$
$653$	−10988.8	−0.658537	−0.329269	+	0.944236i	$0.606802\pi$
$654$	−17272.2	−1.03271
$655$	11727.6	0.699597
$656$	134.594	0.00801069
$657$	−7817.06	−0.464190
$658$	−7552.34	−0.447448
$659$	−25288.8	−1.49486	−0.747430	−	0.664340i	$-0.768713\pi$
$659$	−25288.8	−1.49486	−0.747430	+	0.664340i	$0.768713\pi$
$660$	−14359.2	−0.846863
$661$	−20387.1	−1.19965	−0.599823	−	0.800133i	$-0.704762\pi$
$661$	−20387.1	−1.19965	−0.599823	+	0.800133i	$0.704762\pi$
$662$	−1734.47	−0.101831
$663$	18770.5	1.09953
$664$	−4057.60	−0.237147
$665$	−3623.70	−0.211310
$666$	−2248.47	−0.130821
$667$	−2425.48	−0.140802
$668$	−8382.67	−0.485532
$669$	19822.2	1.14555
$670$	−1803.76	−0.104008
$671$	25285.0	1.45472
$672$	1398.35	0.0802717
$673$	−16015.5	−0.917313	−0.458657	−	0.888614i	$-0.651669\pi$
$673$	−16015.5	−0.917313	−0.458657	+	0.888614i	$0.651669\pi$
$674$	7195.33	0.411207
$675$	2334.54	0.133121
$676$	−2757.41	−0.156885
$677$	13594.8	0.771773	0.385887	−	0.922546i	$-0.373896\pi$
$677$	13594.8	0.771773	0.385887	+	0.922546i	$0.373896\pi$
$678$	15334.8	0.868626
$679$	1991.38	0.112551
$680$	7584.42	0.427720
$681$	14472.7	0.814382
$682$	5371.43	0.301588
$683$	5331.72	0.298701	0.149350	−	0.988784i	$-0.452282\pi$
$683$	5331.72	0.298701	0.149350	+	0.988784i	$0.452282\pi$
$684$	−2024.67	−0.113180
$685$	6229.86	0.347490
$686$	−686.000	−0.0381802
$687$	−20060.8	−1.11407
$688$	6610.97	0.366339
$689$	16106.7	0.890592
$690$	3515.61	0.193967
$691$	16431.8	0.904623	0.452311	−	0.891860i	$-0.350600\pi$
$691$	16431.8	0.904623	0.452311	+	0.891860i	$0.350600\pi$
$692$	11781.7	0.647215
$693$	3935.85	0.215744
$694$	7907.64	0.432521
$695$	−1694.57	−0.0924871
$696$	−5266.58	−0.286824
$697$	−651.423	−0.0354009
$698$	10982.1	0.595528
$699$	−27326.6	−1.47866
$700$	696.703	0.0376184
$701$	12759.3	0.687464	0.343732	−	0.939068i	$-0.388309\pi$
$701$	12759.3	0.687464	0.343732	+	0.939068i	$0.388309\pi$
$702$	−7286.03	−0.391729
$703$	−3971.20	−0.213054
$704$	3006.12	0.160934
$705$	−41228.4	−2.20249
$706$	−15740.5	−0.839098
$707$	7793.57	0.414579
$708$	−1396.35	−0.0741213
$709$	16649.2	0.881910	0.440955	−	0.897529i	$-0.354640\pi$
$709$	16649.2	0.881910	0.440955	+	0.897529i	$0.354640\pi$
$710$	5220.27	0.275934
$711$	5240.22	0.276404
$712$	6969.22	0.366829
$713$	−1315.11	−0.0690761
$714$	−6767.90	−0.354737
$715$	22328.0	1.16786
$716$	15425.5	0.805138
$717$	33360.4	1.73761
$718$	−14274.7	−0.741959
$719$	2427.31	0.125902	0.0629508	−	0.998017i	$-0.479949\pi$
$719$	2427.31	0.125902	0.0629508	+	0.998017i	$0.479949\pi$
$720$	2344.82	0.121370
$721$	1565.19	0.0808468
$722$	10142.1	0.522783
$723$	26184.3	1.34690
$724$	−13675.8	−0.702012
$725$	−2623.98	−0.134417
$726$	10927.5	0.558621
$727$	34930.8	1.78199	0.890997	−	0.454008i	$-0.150006\pi$
$727$	34930.8	1.78199	0.890997	+	0.454008i	$0.150006\pi$
$728$	−2174.39	−0.110698
$729$	4933.88	0.250667
$730$	15989.5	0.810680
$731$	−31996.5	−1.61893
$732$	−13442.0	−0.678733
$733$	6837.01	0.344517	0.172258	−	0.985052i	$-0.444894\pi$
$733$	6837.01	0.344517	0.172258	+	0.985052i	$0.444894\pi$
$734$	13189.0	0.663236
$735$	−3744.89	−0.187935
$736$	−736.000	−0.0368605
$737$	3460.18	0.172941
$738$	−201.396	−0.0100454
$739$	−26314.9	−1.30989	−0.654946	−	0.755676i	$-0.727309\pi$
$739$	−26314.9	−1.30989	−0.654946	+	0.755676i	$0.727309\pi$
$740$	4599.16	0.228471
$741$	10249.4	0.508124
$742$	−5807.46	−0.287329
$743$	38854.6	1.91849	0.959245	−	0.282575i	$-0.0911887\pi$
$743$	38854.6	1.91849	0.959245	+	0.282575i	$0.0911887\pi$
$744$	−2855.57	−0.140713
$745$	29307.3	1.44126
$746$	18382.4	0.902180
$747$	6071.47	0.297381
$748$	−14549.3	−0.711199
$749$	10571.2	0.515707
$750$	−15303.3	−0.745062
$751$	26570.6	1.29104	0.645522	−	0.763742i	$-0.276640\pi$
$751$	26570.6	1.29104	0.645522	+	0.763742i	$0.276640\pi$
$752$	8631.25	0.418549
$753$	34264.9	1.65828
$754$	8189.37	0.395543
$755$	33328.8	1.60657
$756$	2627.05	0.126382
$757$	−8595.17	−0.412677	−0.206339	−	0.978481i	$-0.566155\pi$
$757$	−8595.17	−0.412677	−0.206339	+	0.978481i	$0.566155\pi$
$758$	11949.3	0.572582
$759$	−6744.07	−0.322522
$760$	4141.37	0.197662
$761$	22094.3	1.05246	0.526228	−	0.850343i	$-0.323606\pi$
$761$	22094.3	1.05246	0.526228	+	0.850343i	$0.323606\pi$
$762$	1807.49	0.0859297
$763$	−9683.81	−0.459472
$764$	−1462.14	−0.0692388
$765$	−11348.7	−0.536358
$766$	24394.8	1.15068
$767$	2171.27	0.102217
$768$	−1598.12	−0.0750873
$769$	−836.349	−0.0392191	−0.0196096	−	0.999808i	$-0.506242\pi$
$769$	−836.349	−0.0392191	−0.0196096	+	0.999808i	$0.506242\pi$
$770$	−8050.61	−0.376784
$771$	−7483.17	−0.349546
$772$	−5511.97	−0.256969
$773$	−13259.9	−0.616981	−0.308490	−	0.951227i	$-0.599824\pi$
$773$	−13259.9	−0.616981	−0.308490	+	0.951227i	$0.599824\pi$
$774$	−9892.13	−0.459387
$775$	−1422.74	−0.0659434
$776$	−2275.86	−0.105282
$777$	−4104.02	−0.189486
$778$	−2726.36	−0.125636
$779$	−355.700	−0.0163598
$780$	−11870.1	−0.544893
$781$	−10014.1	−0.458814
$782$	3562.18	0.162894
$783$	−9894.22	−0.451585
$784$	784.000	0.0357143
$785$	−38336.9	−1.74306
$786$	11960.1	0.542749
$787$	6704.31	0.303663	0.151832	−	0.988406i	$-0.451483\pi$
$787$	6704.31	0.303663	0.151832	+	0.988406i	$0.451483\pi$
$788$	15094.8	0.682401
$789$	−32814.5	−1.48064
$790$	−10718.6	−0.482724
$791$	8597.59	0.386467
$792$	−4498.11	−0.201810
$793$	20902.0	0.936003
$794$	14877.2	0.664951
$795$	−31703.1	−1.41433
$796$	1804.38	0.0803449
$797$	−20847.1	−0.926526	−0.463263	−	0.886221i	$-0.653322\pi$
$797$	−20847.1	−0.926526	−0.463263	+	0.886221i	$0.653322\pi$
$798$	−3695.52	−0.163935
$799$	−41774.5	−1.84966
$800$	−796.232	−0.0351888
$801$	−10428.2	−0.460002
$802$	4257.99	0.187475
$803$	−30672.9	−1.34797
$804$	−1839.51	−0.0806895
$805$	1971.07	0.0862993
$806$	4440.32	0.194049
$807$	11268.1	0.491518
$808$	−8906.93	−0.387803
$809$	−17906.1	−0.778177	−0.389088	−	0.921200i	$-0.627210\pi$
$809$	−17906.1	−0.778177	−0.389088	+	0.921200i	$0.627210\pi$
$810$	22254.9	0.965381
$811$	−8702.07	−0.376783	−0.188391	−	0.982094i	$-0.560327\pi$
$811$	−8702.07	−0.376783	−0.188391	+	0.982094i	$0.560327\pi$
$812$	−2952.76	−0.127613
$813$	3914.65	0.168872
$814$	−8822.64	−0.379894
$815$	31515.7	1.35454
$816$	7734.74	0.331826
$817$	−17471.3	−0.748154
$818$	19771.2	0.845089
$819$	3253.59	0.138815
$820$	411.946	0.0175436
$821$	15473.2	0.657758	0.328879	−	0.944372i	$-0.393329\pi$
$821$	15473.2	0.657758	0.328879	+	0.944372i	$0.393329\pi$
$822$	6353.33	0.269584
$823$	16597.6	0.702982	0.351491	−	0.936191i	$-0.385675\pi$
$823$	16597.6	0.702982	0.351491	+	0.936191i	$0.385675\pi$
$824$	−1788.78	−0.0756253
$825$	−7295.98	−0.307895
$826$	−782.876	−0.0329779
$827$	36683.0	1.54243	0.771217	−	0.636573i	$-0.219648\pi$
$827$	36683.0	1.54243	0.771217	+	0.636573i	$0.219648\pi$
$828$	1101.29	0.0462229
$829$	17798.7	0.745688	0.372844	−	0.927894i	$-0.378383\pi$
$829$	17798.7	0.745688	0.372844	+	0.927894i	$0.378383\pi$
$830$	−12418.9	−0.519359
$831$	13602.0	0.567806
$832$	2485.02	0.103549
$833$	−3794.49	−0.157829
$834$	−1728.15	−0.0717518
$835$	−25656.5	−1.06333
$836$	−7944.46	−0.328666
$837$	−5364.70	−0.221543
$838$	16914.4	0.697252
$839$	1592.68	0.0655369	0.0327685	−	0.999463i	$-0.489568\pi$
$839$	1592.68	0.0655369	0.0327685	+	0.999463i	$0.489568\pi$
$840$	4279.88	0.175797
$841$	−13268.1	−0.544018
$842$	19197.7	0.785742
$843$	−51463.8	−2.10262
$844$	−4423.26	−0.180397
$845$	−8439.50	−0.343583
$846$	−12915.1	−0.524859
$847$	6126.64	0.248540
$848$	6637.09	0.268772
$849$	31702.1	1.28152
$850$	3853.69	0.155507
$851$	2160.08	0.0870115
$852$	5323.73	0.214070
$853$	46012.5	1.84694	0.923469	−	0.383672i	$-0.125341\pi$
$853$	46012.5	1.84694	0.923469	+	0.383672i	$0.125341\pi$
$854$	−7536.42	−0.301980
$855$	−6196.81	−0.247867
$856$	−12081.4	−0.482400
$857$	−8771.84	−0.349639	−0.174819	−	0.984601i	$-0.555934\pi$
$857$	−8771.84	−0.349639	−0.174819	+	0.984601i	$0.555934\pi$
$858$	22770.6	0.906031
$859$	−27134.6	−1.07779	−0.538895	−	0.842373i	$-0.681158\pi$
$859$	−27134.6	−1.07779	−0.538895	+	0.842373i	$0.681158\pi$
$860$	20233.9	0.802293
$861$	−367.597	−0.0145501
$862$	5658.37	0.223579
$863$	−22245.2	−0.877443	−0.438722	−	0.898623i	$-0.644569\pi$
$863$	−22245.2	−0.877443	−0.438722	+	0.898623i	$0.644569\pi$
$864$	−3002.35	−0.118220
$865$	36059.7	1.41742
$866$	−24949.0	−0.978986
$867$	−6765.38	−0.265011
$868$	−1601.00	−0.0626056
$869$	20561.8	0.802658
$870$	−16119.2	−0.628153
$871$	2860.37	0.111274
$872$	11067.2	0.429797
$873$	3405.41	0.132023
$874$	1945.08	0.0752783
$875$	−8579.94	−0.331491
$876$	16306.4	0.628928
$877$	−2504.43	−0.0964295	−0.0482147	−	0.998837i	$-0.515353\pi$
$877$	−2504.43	−0.0964295	−0.0482147	+	0.998837i	$0.515353\pi$
$878$	25228.9	0.969744
$879$	10822.6	0.415289
$880$	9200.70	0.352449
$881$	24428.9	0.934199	0.467100	−	0.884205i	$-0.345299\pi$
$881$	24428.9	0.934199	0.467100	+	0.884205i	$0.345299\pi$
$882$	−1173.12	−0.0447855
$883$	−43235.1	−1.64776	−0.823882	−	0.566761i	$-0.808196\pi$
$883$	−43235.1	−1.64776	−0.823882	+	0.566761i	$0.808196\pi$
$884$	−12027.3	−0.457603
$885$	−4273.74	−0.162328
$886$	−24055.9	−0.912159
$887$	−41927.7	−1.58714	−0.793571	−	0.608478i	$-0.791780\pi$
$887$	−41927.7	−1.58714	−0.793571	+	0.608478i	$0.791780\pi$
$888$	4690.31	0.177248
$889$	1013.39	0.0382316
$890$	21330.4	0.803368
$891$	−42692.1	−1.60520
$892$	−12701.2	−0.476756
$893$	−22810.4	−0.854782
$894$	29888.1	1.11813
$895$	47212.3	1.76328
$896$	−896.000	−0.0334077
$897$	−5575.01	−0.207519
$898$	−32625.7	−1.21240
$899$	6029.83	0.223700
$900$	1191.42	0.0441266
$901$	−32123.0	−1.18776
$902$	−790.244	−0.0291710
$903$	−18055.6	−0.665396
$904$	−9825.82	−0.361507
$905$	−41856.9	−1.53743
$906$	33989.4	1.24638
$907$	−13646.7	−0.499594	−0.249797	−	0.968298i	$-0.580364\pi$
$907$	−13646.7	−0.499594	−0.249797	+	0.968298i	$0.580364\pi$
$908$	−9273.43	−0.338931
$909$	13327.6	0.486303
$910$	−6655.07	−0.242433
$911$	−10246.8	−0.372657	−0.186329	−	0.982487i	$-0.559659\pi$
$911$	−10246.8	−0.372657	−0.186329	+	0.982487i	$0.559659\pi$
$912$	4223.45	0.153347
$913$	23823.5	0.863573
$914$	−20602.1	−0.745576
$915$	−41141.5	−1.48645
$916$	12854.1	0.463658
$917$	6705.53	0.241479
$918$	14531.1	0.522438
$919$	−32764.9	−1.17608	−0.588038	−	0.808834i	$-0.700099\pi$
$919$	−32764.9	−1.17608	−0.588038	+	0.808834i	$0.700099\pi$
$920$	−2252.65	−0.0807256
$921$	−31662.3	−1.13280
$922$	9470.53	0.338281
$923$	−8278.23	−0.295212
$924$	−8210.17	−0.292310
$925$	2336.86	0.0830654
$926$	−15940.5	−0.565700
$927$	2676.59	0.0948337
$928$	3374.59	0.119371
$929$	−43613.7	−1.54028	−0.770139	−	0.637876i	$-0.779813\pi$
$929$	−43613.7	−1.54028	−0.770139	+	0.637876i	$0.779813\pi$
$930$	−8739.93	−0.308165
$931$	−2071.93	−0.0729374
$932$	17509.6	0.615394
$933$	−49639.8	−1.74184
$934$	20906.5	0.732421
$935$	−44530.6	−1.55755
$936$	−3718.38	−0.129850
$937$	−378.814	−0.0132074	−0.00660368	−	0.999978i	$-0.502102\pi$
$937$	−378.814	−0.0132074	−0.00660368	+	0.999978i	$0.502102\pi$
$938$	−1031.34	−0.0359002
$939$	−63394.6	−2.20320
$940$	26417.3	0.916636
$941$	49464.9	1.71361	0.856806	−	0.515640i	$-0.172446\pi$
$941$	49464.9	1.71361	0.856806	+	0.515640i	$0.172446\pi$
$942$	−39096.7	−1.35227
$943$	193.479	0.00668137
$944$	894.715	0.0308480
$945$	8040.52	0.276781
$946$	−38815.1	−1.33403
$947$	−42622.8	−1.46257	−0.731286	−	0.682071i	$-0.761080\pi$
$947$	−42622.8	−1.46257	−0.731286	+	0.682071i	$0.761080\pi$
$948$	−10931.1	−0.374499
$949$	−25355.9	−0.867320
$950$	2104.26	0.0718643
$951$	63497.8	2.16515
$952$	4336.56	0.147635
$953$	−10839.0	−0.368427	−0.184214	−	0.982886i	$-0.558974\pi$
$953$	−10839.0	−0.368427	−0.184214	+	0.982886i	$0.558974\pi$
$954$	−9931.22	−0.337039
$955$	−4475.12	−0.151635
$956$	−21375.8	−0.723163
$957$	30921.8	1.04447
$958$	37600.8	1.26808
$959$	3562.06	0.119942
$960$	−4891.29	−0.164443
$961$	−26521.6	−0.890255
$962$	−7293.28	−0.244433
$963$	18077.7	0.604927
$964$	−16777.7	−0.560554
$965$	−16870.3	−0.562770
$966$	2010.13	0.0669512
$967$	−24089.9	−0.801114	−0.400557	−	0.916272i	$-0.631183\pi$
$967$	−24089.9	−0.801114	−0.400557	+	0.916272i	$0.631183\pi$
$968$	−7001.87	−0.232488
$969$	−20441.1	−0.677671
$970$	−6965.63	−0.230570
$971$	−46038.8	−1.52158	−0.760791	−	0.648997i	$-0.775189\pi$
$971$	−46038.8	−1.52158	−0.760791	+	0.648997i	$0.775189\pi$
$972$	12563.1	0.414569
$973$	−968.906	−0.0319236
$974$	21944.9	0.721928
$975$	−6031.26	−0.198107
$976$	8613.05	0.282477
$977$	−28376.6	−0.929221	−0.464611	−	0.885515i	$-0.653806\pi$
$977$	−28376.6	−0.929221	−0.464611	+	0.885515i	$0.653806\pi$
$978$	32140.4	1.05085
$979$	−40918.5	−1.33581
$980$	2399.56	0.0782154
$981$	−16560.1	−0.538963
$982$	−34470.9	−1.12017
$983$	27751.8	0.900454	0.450227	−	0.892914i	$-0.351343\pi$
$983$	27751.8	0.900454	0.450227	+	0.892914i	$0.351343\pi$
$984$	420.111	0.0136104
$985$	46200.2	1.49448
$986$	−16332.7	−0.527525
$987$	−23573.3	−0.760229
$988$	−6567.33	−0.211472
$989$	9503.27	0.305548
$990$	−13767.2	−0.441970
$991$	44044.0	1.41181	0.705905	−	0.708307i	$-0.250541\pi$
$991$	44044.0	1.41181	0.705905	+	0.708307i	$0.250541\pi$
$992$	1829.72	0.0585621
$993$	−5413.84	−0.173014
$994$	2984.80	0.0952436
$995$	5522.59	0.175958
$996$	−12665.1	−0.402920
$997$	−2663.81	−0.0846175	−0.0423087	−	0.999105i	$-0.513471\pi$
$997$	−2663.81	−0.0846175	−0.0423087	+	0.999105i	$0.513471\pi$
$998$	1321.15	0.0419041
$999$	8811.59	0.279065

Twists

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

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

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -6.24264 q^{3} +4.00000 q^{4} +12.2426 q^{5} +12.4853 q^{6} +7.00000 q^{7} -8.00000 q^{8} +11.9706 q^{9} -24.4853 q^{10} +46.9706 q^{11} -24.9706 q^{12} +38.8284 q^{13} -14.0000 q^{14} -76.4264 q^{15} +16.0000 q^{16} -77.4386 q^{17} -23.9411 q^{18} -42.2843 q^{19} +48.9706 q^{20} -43.6985 q^{21} -93.9411 q^{22} +23.0000 q^{23} +49.9411 q^{24} +24.8823 q^{25} -77.6569 q^{26} +93.8234 q^{27} +28.0000 q^{28} -105.456 q^{29} +152.853 q^{30} -57.1787 q^{31} -32.0000 q^{32} -293.220 q^{33} +154.877 q^{34} +85.6985 q^{35} +47.8823 q^{36} +93.9167 q^{37} +84.5685 q^{38} -242.392 q^{39} -97.9411 q^{40} +8.41212 q^{41} +87.3970 q^{42} +413.186 q^{43} +187.882 q^{44} +146.551 q^{45} -46.0000 q^{46} +539.453 q^{47} -99.8823 q^{48} +49.0000 q^{49} -49.7645 q^{50} +483.421 q^{51} +155.314 q^{52} +414.818 q^{53} -187.647 q^{54} +575.044 q^{55} -56.0000 q^{56} +263.966 q^{57} +210.912 q^{58} +55.9197 q^{59} -305.706 q^{60} +538.316 q^{61} +114.357 q^{62} +83.7939 q^{63} +64.0000 q^{64} +475.362 q^{65} +586.441 q^{66} +73.6670 q^{67} -309.754 q^{68} -143.581 q^{69} -171.397 q^{70} -213.200 q^{71} -95.7645 q^{72} -653.024 q^{73} -187.833 q^{74} -155.331 q^{75} -169.137 q^{76} +328.794 q^{77} +484.784 q^{78} +437.759 q^{79} +195.882 q^{80} -908.911 q^{81} -16.8242 q^{82} +507.200 q^{83} -174.794 q^{84} -948.053 q^{85} -826.372 q^{86} +658.323 q^{87} -375.765 q^{88} -871.153 q^{89} -293.103 q^{90} +271.799 q^{91} +92.0000 q^{92} +356.946 q^{93} -1078.91 q^{94} -517.671 q^{95} +199.765 q^{96} +284.482 q^{97} -98.0000 q^{98} +562.264 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 4 q^{2} - 4 q^{3} + 8 q^{4} + 16 q^{5} + 8 q^{6} + 14 q^{7} - 16 q^{8} - 10 q^{9} - 32 q^{10} + 60 q^{11} - 16 q^{12} + 72 q^{13} - 28 q^{14} - 68 q^{15} + 32 q^{16} + 12 q^{17} + 20 q^{18} - 28 q^{19}+ \cdots + 276 q^{99}+O(q^{100}) \) 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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