LMFDB - Embedded newform 2023.4.a.l.1.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2023,4,Mod(1,2023)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2023, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2023.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 2023 = 7 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2023.a (trivial)

Newform invariants

comment:select newform

sage:traces = [12,3,3,65,-12,-22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	yes
Analytic conductor:	$119.360863942$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 76 x^{10} + 195 x^{9} + 2126 x^{8} - 4299 x^{7} - 26508 x^{6} + 35641 x^{5} + \cdots + 17280 $ x^12 - 3x^11 - 76x^10 + 195x^9 + 2126x^8 - 4299x^7 - 26508x^6 + 35641x^5 + 137633x^4 - 72318x^3 - 196104x^2 - 42272*x + 17280
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$4.56003$ of defining polynomial
Character	$\chi$	$=$	2023.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+4.56003 q^{2} -5.59626 q^{3} +12.7939 q^{4} -16.5864 q^{5} -25.5191 q^{6} -7.00000 q^{7} +21.8602 q^{8} +4.31818 q^{9} -75.6344 q^{10} -54.2366 q^{11} -71.5978 q^{12} -39.7142 q^{13} -31.9202 q^{14} +92.8218 q^{15} -2.66795 q^{16} +19.6910 q^{18} -12.7918 q^{19} -212.204 q^{20} +39.1739 q^{21} -247.320 q^{22} -78.5231 q^{23} -122.335 q^{24} +150.108 q^{25} -181.098 q^{26} +126.933 q^{27} -89.5571 q^{28} -257.158 q^{29} +423.270 q^{30} -1.21010 q^{31} -187.047 q^{32} +303.522 q^{33} +116.105 q^{35} +55.2461 q^{36} -245.600 q^{37} -58.3308 q^{38} +222.251 q^{39} -362.581 q^{40} +145.374 q^{41} +178.634 q^{42} -502.036 q^{43} -693.895 q^{44} -71.6229 q^{45} -358.068 q^{46} -338.971 q^{47} +14.9305 q^{48} +49.0000 q^{49} +684.498 q^{50} -508.098 q^{52} +382.486 q^{53} +578.820 q^{54} +899.589 q^{55} -153.021 q^{56} +71.5861 q^{57} -1172.65 q^{58} -209.765 q^{59} +1187.55 q^{60} +512.323 q^{61} -5.51808 q^{62} -30.2272 q^{63} -831.597 q^{64} +658.714 q^{65} +1384.07 q^{66} +816.118 q^{67} +439.436 q^{69} +529.441 q^{70} -870.540 q^{71} +94.3960 q^{72} -271.000 q^{73} -1119.94 q^{74} -840.045 q^{75} -163.656 q^{76} +379.656 q^{77} +1013.47 q^{78} +683.406 q^{79} +44.2516 q^{80} -826.944 q^{81} +662.908 q^{82} +995.996 q^{83} +501.185 q^{84} -2289.30 q^{86} +1439.13 q^{87} -1185.62 q^{88} +998.273 q^{89} -326.603 q^{90} +277.999 q^{91} -1004.61 q^{92} +6.77203 q^{93} -1545.72 q^{94} +212.169 q^{95} +1046.77 q^{96} +107.199 q^{97} +223.441 q^{98} -234.203 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} + 3 q^{3} + 65 q^{4} - 12 q^{5} - 22 q^{6} - 84 q^{7} + 78 q^{8} + 233 q^{9} + 36 q^{10} + 4 q^{11} + 6 q^{12} + 98 q^{13} - 21 q^{14} - 196 q^{15} + 429 q^{16} + 603 q^{18} - 37 q^{19} + 54 q^{20}+ \cdots + 5140 q^{99}+O(q^{100}) $ 12 * q + 3 * q^2 + 3 * q^3 + 65 * q^4 - 12 * q^5 - 22 * q^6 - 84 * q^7 + 78 * q^8 + 233 * q^9 + 36 * q^10 + 4 * q^11 + 6 * q^12 + 98 * q^13 - 21 * q^14 - 196 * q^15 + 429 * q^16 + 603 * q^18 - 37 * q^19 + 54 * q^20 - 21 * q^21 + 70 * q^22 - 369 * q^23 - 652 * q^24 + 590 * q^25 + 638 * q^26 + 501 * q^27 - 455 * q^28 + 144 * q^29 - 160 * q^30 + 67 * q^31 + 417 * q^32 + 628 * q^33 + 84 * q^35 + 999 * q^36 - 345 * q^37 - 190 * q^38 + 6 * q^39 - 466 * q^40 - 156 * q^41 + 154 * q^42 - 763 * q^43 + 1046 * q^44 + 832 * q^45 - 395 * q^46 + 561 * q^47 + 532 * q^48 + 588 * q^49 + 1923 * q^50 + 3138 * q^52 + 1156 * q^53 - 1682 * q^54 - 156 * q^55 - 546 * q^56 - 501 * q^57 - 2305 * q^58 - 473 * q^59 - 1292 * q^60 + 1850 * q^61 + 202 * q^62 - 1631 * q^63 - 712 * q^64 + 1718 * q^65 + 2142 * q^66 - 834 * q^67 + 1316 * q^69 - 252 * q^70 - 3179 * q^71 + 2046 * q^72 + 1012 * q^73 - 2695 * q^74 - 3841 * q^75 + 3272 * q^76 - 28 * q^77 + 970 * q^78 - 3897 * q^79 - 1616 * q^80 + 3448 * q^81 + 4758 * q^82 + 675 * q^83 - 42 * q^84 + 77 * q^86 + 805 * q^87 + 5398 * q^88 + 4078 * q^89 + 13384 * q^90 - 686 * q^91 - 3393 * q^92 + 3671 * q^93 + 958 * q^94 - 4126 * q^95 - 2320 * q^96 + 1474 * q^97 + 147 * q^98 + 5140 * 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 $

$2$	4.56003	1.61221	0.806107	−	0.591770i	$-0.201571\pi$
$2$	4.56003	1.61221	0.806107	+	0.591770i	$0.201571\pi$
$3$	−5.59626	−1.07700	−0.538501	−	0.842625i	$-0.681009\pi$
$3$	−5.59626	−1.07700	−0.538501	+	0.842625i	$0.681009\pi$
$4$	12.7939	1.59923
$5$	−16.5864	−1.48353	−0.741766	−	0.670659i	$-0.766011\pi$
$5$	−16.5864	−1.48353	−0.741766	+	0.670659i	$0.766011\pi$
$6$	−25.5191	−1.73636
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	21.8602	0.966092
$9$	4.31818	0.159932
$10$	−75.6344	−2.39177
$11$	−54.2366	−1.48663	−0.743315	−	0.668941i	$-0.766748\pi$
$11$	−54.2366	−1.48663	−0.743315	+	0.668941i	$0.766748\pi$
$12$	−71.5978	−1.72238
$13$	−39.7142	−0.847287	−0.423643	−	0.905829i	$-0.639249\pi$
$13$	−39.7142	−0.847287	−0.423643	+	0.905829i	$0.639249\pi$
$14$	−31.9202	−0.609360
$15$	92.8218	1.59777
$16$	−2.66795	−0.0416867
$17$	0	0
$17$	0	0
$18$	19.6910	0.257845
$19$	−12.7918	−0.154454	−0.0772272	−	0.997014i	$-0.524607\pi$
$19$	−12.7918	−0.154454	−0.0772272	+	0.997014i	$0.524607\pi$
$20$	−212.204	−2.37251
$21$	39.1739	0.407068
$22$	−247.320	−2.39677
$23$	−78.5231	−0.711878	−0.355939	−	0.934509i	$-0.615839\pi$
$23$	−78.5231	−0.711878	−0.355939	+	0.934509i	$0.615839\pi$
$24$	−122.335	−1.04048
$25$	150.108	1.20087
$26$	−181.098	−1.36601
$27$	126.933	0.904754
$28$	−89.5571	−0.604453
$29$	−257.158	−1.64666	−0.823330	−	0.567563i	$-0.807886\pi$
$29$	−257.158	−1.64666	−0.823330	+	0.567563i	$0.807886\pi$
$30$	423.270	2.57594
$31$	−1.21010	−0.00701097	−0.00350548	−	0.999994i	$-0.501116\pi$
$31$	−1.21010	−0.00701097	−0.00350548	+	0.999994i	$0.501116\pi$
$32$	−187.047	−1.03330
$33$	303.522	1.60110
$34$	0	0
$35$	116.105	0.560722
$36$	55.2461	0.255769
$37$	−245.600	−1.09125	−0.545627	−	0.838028i	$-0.683709\pi$
$37$	−245.600	−1.09125	−0.545627	+	0.838028i	$0.683709\pi$
$38$	−58.3308	−0.249013
$39$	222.251	0.912529
$40$	−362.581	−1.43323
$41$	145.374	0.553745	0.276872	−	0.960907i	$-0.410702\pi$
$41$	145.374	0.553745	0.276872	+	0.960907i	$0.410702\pi$
$42$	178.634	0.656281
$43$	−502.036	−1.78046	−0.890229	−	0.455512i	$-0.849456\pi$
$43$	−502.036	−1.78046	−0.890229	+	0.455512i	$0.849456\pi$
$44$	−693.895	−2.37747
$45$	−71.6229	−0.237265
$46$	−358.068	−1.14770
$47$	−338.971	−1.05200	−0.525999	−	0.850485i	$-0.676309\pi$
$47$	−338.971	−1.05200	−0.525999	+	0.850485i	$0.676309\pi$
$48$	14.9305	0.0448966
$49$	49.0000	0.142857
$50$	684.498	1.93605
$51$	0	0
$52$	−508.098	−1.35501
$53$	382.486	0.991293	0.495647	−	0.868524i	$-0.334931\pi$
$53$	382.486	0.991293	0.495647	+	0.868524i	$0.334931\pi$
$54$	578.820	1.45866
$55$	899.589	2.20546
$56$	−153.021	−0.365148
$57$	71.5861	0.166348
$58$	−1172.65	−2.65477
$59$	−209.765	−0.462866	−0.231433	−	0.972851i	$-0.574341\pi$
$59$	−209.765	−0.462866	−0.231433	+	0.972851i	$0.574341\pi$
$60$	1187.55	2.55520
$61$	512.323	1.07535	0.537674	−	0.843153i	$-0.319303\pi$
$61$	512.323	1.07535	0.537674	+	0.843153i	$0.319303\pi$
$62$	−5.51808	−0.0113032
$63$	−30.2272	−0.0604488
$64$	−831.597	−1.62421
$65$	658.714	1.25698
$66$	1384.07	2.58132
$67$	816.118	1.48813	0.744065	−	0.668107i	$-0.232895\pi$
$67$	816.118	1.48813	0.744065	+	0.668107i	$0.232895\pi$
$68$	0	0
$69$	439.436	0.766694
$70$	529.441	0.904004
$71$	−870.540	−1.45513	−0.727564	−	0.686040i	$-0.759348\pi$
$71$	−870.540	−1.45513	−0.727564	+	0.686040i	$0.759348\pi$
$72$	94.3960	0.154509
$73$	−271.000	−0.434496	−0.217248	−	0.976116i	$-0.569708\pi$
$73$	−271.000	−0.434496	−0.217248	+	0.976116i	$0.569708\pi$
$74$	−1119.94	−1.75934
$75$	−840.045	−1.29333
$76$	−163.656	−0.247008
$77$	379.656	0.561894
$78$	1013.47	1.47119
$79$	683.406	0.973281	0.486640	−	0.873602i	$-0.338222\pi$
$79$	683.406	0.973281	0.486640	+	0.873602i	$0.338222\pi$
$80$	44.2516	0.0618435
$81$	−826.944	−1.13435
$82$	662.908	0.892755
$83$	995.996	1.31717	0.658583	−	0.752508i	$-0.271156\pi$
$83$	995.996	1.31717	0.658583	+	0.752508i	$0.271156\pi$
$84$	501.185	0.650997
$85$	0	0
$86$	−2289.30	−2.87048
$87$	1439.13	1.77345
$88$	−1185.62	−1.43622
$89$	998.273	1.18895	0.594476	−	0.804114i	$-0.297360\pi$
$89$	998.273	1.18895	0.594476	+	0.804114i	$0.297360\pi$
$90$	−326.603	−0.382521
$91$	277.999	0.320244
$92$	−1004.61	−1.13846
$93$	6.77203	0.00755082
$94$	−1545.72	−1.69605
$95$	212.169	0.229138
$96$	1046.77	1.11287
$97$	107.199	0.112210	0.0561052	−	0.998425i	$-0.482132\pi$
$97$	107.199	0.112210	0.0561052	+	0.998425i	$0.482132\pi$
$98$	223.441	0.230316
$99$	−234.203	−0.237760
$100$	1920.46	1.92046
$101$	−954.213	−0.940077	−0.470038	−	0.882646i	$-0.655760\pi$
$101$	−954.213	−0.940077	−0.470038	+	0.882646i	$0.655760\pi$
$102$	0	0
$103$	−1855.78	−1.77529	−0.887646	−	0.460527i	$-0.847660\pi$
$103$	−1855.78	−1.77529	−0.887646	+	0.460527i	$0.847660\pi$
$104$	−868.158	−0.818557
$105$	−649.753	−0.603899
$106$	1744.15	1.59818
$107$	1503.94	1.35879	0.679397	−	0.733770i	$-0.262241\pi$
$107$	1503.94	1.35879	0.679397	+	0.733770i	$0.262241\pi$
$108$	1623.97	1.44691
$109$	−1211.54	−1.06463	−0.532313	−	0.846548i	$-0.678677\pi$
$109$	−1211.54	−1.06463	−0.532313	+	0.846548i	$0.678677\pi$
$110$	4102.15	3.55568
$111$	1374.44	1.17528
$112$	18.6756	0.0157561
$113$	603.563	0.502464	0.251232	−	0.967927i	$-0.419164\pi$
$113$	603.563	0.502464	0.251232	+	0.967927i	$0.419164\pi$
$114$	326.435	0.268188
$115$	1302.41	1.05609
$116$	−3290.05	−2.63339
$117$	−171.493	−0.135509
$118$	−956.535	−0.746239
$119$	0	0
$120$	2029.10	1.54359
$121$	1610.61	1.21007
$122$	2336.21	1.73369
$123$	−813.549	−0.596384
$124$	−15.4818	−0.0112122
$125$	−416.453	−0.297990
$126$	−137.837	−0.0974563
$127$	−1725.70	−1.20576	−0.602879	−	0.797833i	$-0.705980\pi$
$127$	−1725.70	−1.20576	−0.602879	+	0.797833i	$0.705980\pi$
$128$	−2295.73	−1.58528
$129$	2809.52	1.91756
$130$	3003.76	2.02651
$131$	1200.04	0.800363	0.400181	−	0.916436i	$-0.368947\pi$
$131$	1200.04	0.800363	0.400181	+	0.916436i	$0.368947\pi$
$132$	3883.22	2.56054
$133$	89.5424	0.0583783
$134$	3721.52	2.39918
$135$	−2105.37	−1.34223
$136$	0	0
$137$	−289.928	−0.180805	−0.0904023	−	0.995905i	$-0.528815\pi$
$137$	−289.928	−0.180805	−0.0904023	+	0.995905i	$0.528815\pi$
$138$	2003.84	1.23607
$139$	2605.99	1.59019	0.795096	−	0.606483i	$-0.207420\pi$
$139$	2605.99	1.59019	0.795096	+	0.606483i	$0.207420\pi$
$140$	1485.43	0.896725
$141$	1896.97	1.13300
$142$	−3969.69	−2.34598
$143$	2153.96	1.25960
$144$	−11.5207	−0.00666705
$145$	4265.33	2.44287
$146$	−1235.77	−0.700500
$147$	−274.217	−0.153857
$148$	−3142.18	−1.74517
$149$	−311.829	−0.171450	−0.0857250	−	0.996319i	$-0.527321\pi$
$149$	−311.829	−0.171450	−0.0857250	+	0.996319i	$0.527321\pi$
$150$	−3830.63	−2.08513
$151$	−2966.52	−1.59876	−0.799378	−	0.600828i	$-0.794838\pi$
$151$	−2966.52	−1.59876	−0.799378	+	0.600828i	$0.794838\pi$
$152$	−279.630	−0.149217
$153$	0	0
$154$	1731.24	0.905893
$155$	20.0711	0.0104010
$156$	2843.45	1.45935
$157$	−2432.43	−1.23649	−0.618245	−	0.785985i	$-0.712156\pi$
$157$	−2432.43	−1.23649	−0.618245	+	0.785985i	$0.712156\pi$
$158$	3116.35	1.56914
$159$	−2140.49	−1.06762
$160$	3102.44	1.53293
$161$	549.662	0.269065
$162$	−3770.89	−1.82882
$163$	−2436.61	−1.17086	−0.585429	−	0.810724i	$-0.699074\pi$
$163$	−2436.61	−1.17086	−0.585429	+	0.810724i	$0.699074\pi$
$164$	1859.89	0.885567
$165$	−5034.34	−2.37529
$166$	4541.77	2.12355
$167$	−1825.85	−0.846041	−0.423021	−	0.906120i	$-0.639030\pi$
$167$	−1825.85	−0.846041	−0.423021	+	0.906120i	$0.639030\pi$
$168$	856.347	0.393265
$169$	−619.785	−0.282105
$170$	0	0
$171$	−55.2371	−0.0247023
$172$	−6422.98	−2.84737
$173$	−4268.75	−1.87600	−0.937998	−	0.346640i	$-0.887323\pi$
$173$	−4268.75	−1.87600	−0.937998	+	0.346640i	$0.887323\pi$
$174$	6562.46	2.85919
$175$	−1050.76	−0.453884
$176$	144.700	0.0619727
$177$	1173.90	0.498507
$178$	4552.15	1.91684
$179$	−1876.68	−0.783629	−0.391814	−	0.920044i	$-0.628152\pi$
$179$	−1876.68	−0.783629	−0.391814	+	0.920044i	$0.628152\pi$
$180$	−916.334	−0.379442
$181$	−3062.61	−1.25769	−0.628846	−	0.777530i	$-0.716472\pi$
$181$	−3062.61	−1.25769	−0.628846	+	0.777530i	$0.716472\pi$
$182$	1267.68	0.516302
$183$	−2867.10	−1.15815
$184$	−1716.53	−0.687740
$185$	4073.62	1.61891
$186$	30.8806	0.0121735
$187$	0	0
$188$	−4336.74	−1.68239
$189$	−888.534	−0.341965
$190$	967.497	0.369419
$191$	3686.99	1.39676	0.698381	−	0.715726i	$-0.253904\pi$
$191$	3686.99	1.39676	0.698381	+	0.715726i	$0.253904\pi$
$192$	4653.84	1.74928
$193$	2380.80	0.887949	0.443974	−	0.896040i	$-0.353568\pi$
$193$	2380.80	0.887949	0.443974	+	0.896040i	$0.353568\pi$
$194$	488.830	0.180907
$195$	−3686.34	−1.35377
$196$	626.899	0.228462
$197$	588.171	0.212718	0.106359	−	0.994328i	$-0.466081\pi$
$197$	588.171	0.212718	0.106359	+	0.994328i	$0.466081\pi$
$198$	−1067.97	−0.383321
$199$	−2563.36	−0.913125	−0.456562	−	0.889691i	$-0.650919\pi$
$199$	−2563.36	−0.913125	−0.456562	+	0.889691i	$0.650919\pi$
$200$	3281.39	1.16015
$201$	−4567.21	−1.60272
$202$	−4351.24	−1.51560
$203$	1800.11	0.622379
$204$	0	0
$205$	−2411.22	−0.821498
$206$	−8462.39	−2.86215
$207$	−339.076	−0.113852
$208$	105.955	0.0353206
$209$	693.782	0.229617
$210$	−2962.89	−0.973614
$211$	−4835.88	−1.57780	−0.788899	−	0.614522i	$-0.789349\pi$
$211$	−4835.88	−1.57780	−0.788899	+	0.614522i	$0.789349\pi$
$212$	4893.48	1.58531
$213$	4871.77	1.56717
$214$	6858.00	2.19067
$215$	8326.96	2.64137
$216$	2774.79	0.874076
$217$	8.47068	0.00264990
$218$	−5524.64	−1.71640
$219$	1516.59	0.467952
$220$	11509.2	3.52705
$221$	0	0
$222$	6267.50	1.89481
$223$	5637.03	1.69275	0.846375	−	0.532587i	$-0.178780\pi$
$223$	5637.03	1.69275	0.846375	+	0.532587i	$0.178780\pi$
$224$	1309.33	0.390551
$225$	648.193	0.192057
$226$	2752.26	0.810079
$227$	5351.53	1.56473	0.782365	−	0.622820i	$-0.214013\pi$
$227$	5351.53	1.56473	0.782365	+	0.622820i	$0.214013\pi$
$228$	915.863	0.266029
$229$	−1086.98	−0.313666	−0.156833	−	0.987625i	$-0.550128\pi$
$229$	−1086.98	−0.313666	−0.156833	+	0.987625i	$0.550128\pi$
$230$	5939.05	1.70265
$231$	−2124.66	−0.605160
$232$	−5621.53	−1.59082
$233$	4847.48	1.36296	0.681478	−	0.731838i	$-0.261337\pi$
$233$	4847.48	1.36296	0.681478	+	0.731838i	$0.261337\pi$
$234$	−782.012	−0.218469
$235$	5622.30	1.56067
$236$	−2683.71	−0.740231
$237$	−3824.52	−1.04822
$238$	0	0
$239$	−4769.07	−1.29073	−0.645367	−	0.763873i	$-0.723295\pi$
$239$	−4769.07	−1.29073	−0.645367	+	0.763873i	$0.723295\pi$
$240$	−247.644	−0.0666055
$241$	4414.19	1.17985	0.589923	−	0.807460i	$-0.299158\pi$
$241$	4414.19	1.17985	0.589923	+	0.807460i	$0.299158\pi$
$242$	7344.41	1.95089
$243$	1200.59	0.316947
$244$	6554.59	1.71973
$245$	−812.733	−0.211933
$246$	−3709.81	−0.961499
$247$	508.014	0.130867
$248$	−26.4529	−0.00677324
$249$	−5573.86	−1.41859
$250$	−1899.04	−0.480423
$251$	142.193	0.0357577	0.0178788	−	0.999840i	$-0.494309\pi$
$251$	142.193	0.0357577	0.0178788	+	0.999840i	$0.494309\pi$
$252$	−386.723	−0.0966717
$253$	4258.82	1.05830
$254$	−7869.25	−1.94394
$255$	0	0
$256$	−3815.82	−0.931596
$257$	482.480	0.117106	0.0585531	−	0.998284i	$-0.481351\pi$
$257$	482.480	0.117106	0.0585531	+	0.998284i	$0.481351\pi$
$258$	12811.5	3.09151
$259$	1719.20	0.412455
$260$	8427.50	2.01020
$261$	−1110.46	−0.263354
$262$	5472.19	1.29036
$263$	836.582	0.196144	0.0980720	−	0.995179i	$-0.468732\pi$
$263$	836.582	0.196144	0.0980720	+	0.995179i	$0.468732\pi$
$264$	6635.04	1.54681
$265$	−6344.06	−1.47061
$266$	408.316	0.0941182
$267$	−5586.60	−1.28050
$268$	10441.3	2.37987
$269$	53.7897	0.0121919	0.00609594	−	0.999981i	$-0.498060\pi$
$269$	53.7897	0.0121919	0.00609594	+	0.999981i	$0.498060\pi$
$270$	−9600.54	−2.16396
$271$	−1010.96	−0.226610	−0.113305	−	0.993560i	$-0.536144\pi$
$271$	−1010.96	−0.226610	−0.113305	+	0.993560i	$0.536144\pi$
$272$	0	0
$273$	−1555.76	−0.344904
$274$	−1322.08	−0.291496
$275$	−8141.35	−1.78524
$276$	5622.08	1.22612
$277$	−4711.43	−1.02196	−0.510979	−	0.859593i	$-0.670717\pi$
$277$	−4711.43	−1.02196	−0.510979	+	0.859593i	$0.670717\pi$
$278$	11883.4	2.56373
$279$	−5.22541	−0.00112128
$280$	2538.07	0.541709
$281$	1153.69	0.244924	0.122462	−	0.992473i	$-0.460921\pi$
$281$	1153.69	0.244924	0.122462	+	0.992473i	$0.460921\pi$
$282$	8650.23	1.82665
$283$	981.068	0.206072	0.103036	−	0.994678i	$-0.467144\pi$
$283$	981.068	0.206072	0.103036	+	0.994678i	$0.467144\pi$
$284$	−11137.6	−2.32709
$285$	−1187.35	−0.246782
$286$	9822.12	2.03075
$287$	−1017.62	−0.209296
$288$	−807.703	−0.165258
$289$	0	0
$290$	19450.0	3.93843
$291$	−599.913	−0.120851
$292$	−3467.14	−0.694860
$293$	−1407.45	−0.280628	−0.140314	−	0.990107i	$-0.544811\pi$
$293$	−1407.45	−0.280628	−0.140314	+	0.990107i	$0.544811\pi$
$294$	−1250.44	−0.248051
$295$	3479.25	0.686676
$296$	−5368.86	−1.05425
$297$	−6884.44	−1.34504
$298$	−1421.95	−0.276414
$299$	3118.48	0.603165
$300$	−10747.4	−2.06834
$301$	3514.25	0.672950
$302$	−13527.4	−2.57754
$303$	5340.03	1.01246
$304$	34.1277	0.00643868
$305$	−8497.59	−1.59531
$306$	0	0
$307$	−5085.93	−0.945502	−0.472751	−	0.881196i	$-0.656739\pi$
$307$	−5085.93	−0.945502	−0.472751	+	0.881196i	$0.656739\pi$
$308$	4857.27	0.898599
$309$	10385.4	1.91199
$310$	91.5250	0.0167686
$311$	807.820	0.147290	0.0736452	−	0.997285i	$-0.476537\pi$
$311$	807.820	0.147290	0.0736452	+	0.997285i	$0.476537\pi$
$312$	4858.44	0.881587
$313$	−875.988	−0.158191	−0.0790955	−	0.996867i	$-0.525203\pi$
$313$	−875.988	−0.158191	−0.0790955	+	0.996867i	$0.525203\pi$
$314$	−11092.0	−1.99349
$315$	501.360	0.0896776
$316$	8743.40	1.55650
$317$	165.917	0.0293970	0.0146985	−	0.999892i	$-0.495321\pi$
$317$	165.917	0.0293970	0.0146985	+	0.999892i	$0.495321\pi$
$318$	−9760.72	−1.72124
$319$	13947.4	2.44798
$320$	13793.2	2.40957
$321$	−8416.43	−1.46342
$322$	2506.47	0.433790
$323$	0	0
$324$	−10579.8	−1.81410
$325$	−5961.42	−1.01748
$326$	−11111.0	−1.88767
$327$	6780.08	1.14660
$328$	3177.89	0.534968
$329$	2372.79	0.397618
$330$	−22956.7	−3.82947
$331$	2365.15	0.392750	0.196375	−	0.980529i	$-0.437083\pi$
$331$	2365.15	0.392750	0.196375	+	0.980529i	$0.437083\pi$
$332$	12742.6	2.10646
$333$	−1060.54	−0.174527
$334$	−8325.95	−1.36400
$335$	−13536.5	−2.20769
$336$	−104.514	−0.0169693
$337$	3410.11	0.551218	0.275609	−	0.961270i	$-0.411120\pi$
$337$	3410.11	0.551218	0.275609	+	0.961270i	$0.411120\pi$
$338$	−2826.24	−0.454814
$339$	−3377.70	−0.541154
$340$	0	0
$341$	65.6315	0.0104227
$342$	−251.883	−0.0398253
$343$	−343.000	−0.0539949
$344$	−10974.6	−1.72009
$345$	−7288.65	−1.13741
$346$	−19465.6	−3.02451
$347$	−3520.52	−0.544644	−0.272322	−	0.962206i	$-0.587792\pi$
$347$	−3520.52	−0.544644	−0.272322	+	0.962206i	$0.587792\pi$
$348$	18412.0	2.83617
$349$	5445.52	0.835220	0.417610	−	0.908626i	$-0.362868\pi$
$349$	5445.52	0.835220	0.417610	+	0.908626i	$0.362868\pi$
$350$	−4791.48	−0.731759
$351$	−5041.06	−0.766586
$352$	10144.8	1.53614
$353$	−9491.22	−1.43107	−0.715534	−	0.698578i	$-0.753816\pi$
$353$	−9491.22	−1.43107	−0.715534	+	0.698578i	$0.753816\pi$
$354$	5353.02	0.803700
$355$	14439.1	2.15873
$356$	12771.8	1.90141
$357$	0	0
$358$	−8557.71	−1.26338
$359$	1.65708	0.000243613 0	0.000121807	−	1.00000i	$-0.499961\pi$
$359$	1.65708	0.000243613 0	0.000121807		1.00000i	$0.499961\pi$
$360$	−1565.69	−0.229220
$361$	−6695.37	−0.976144
$362$	−13965.6	−2.02767
$363$	−9013.37	−1.30325
$364$	3556.68	0.512145
$365$	4494.91	0.644588
$366$	−13074.0	−1.86719
$367$	−11612.5	−1.65168	−0.825841	−	0.563903i	$-0.809299\pi$
$367$	−11612.5	−1.65168	−0.825841	+	0.563903i	$0.809299\pi$
$368$	209.495	0.0296758
$369$	627.749	0.0885617
$370$	18575.8	2.61003
$371$	−2677.40	−0.374674
$372$	86.6404	0.0120755
$373$	−1767.69	−0.245381	−0.122691	−	0.992445i	$-0.539152\pi$
$373$	−1767.69	−0.245381	−0.122691	+	0.992445i	$0.539152\pi$
$374$	0	0
$375$	2330.58	0.320935
$376$	−7409.95	−1.01633
$377$	10212.8	1.39519
$378$	−4051.74	−0.551321
$379$	2360.62	0.319938	0.159969	−	0.987122i	$-0.448860\pi$
$379$	2360.62	0.319938	0.159969	+	0.987122i	$0.448860\pi$
$380$	2714.46	0.366445
$381$	9657.48	1.29860
$382$	16812.8	2.25188
$383$	1574.00	0.209994	0.104997	−	0.994473i	$-0.466517\pi$
$383$	1574.00	0.209994	0.104997	+	0.994473i	$0.466517\pi$
$384$	12847.5	1.70735
$385$	−6297.12	−0.833587
$386$	10856.5	1.43156
$387$	−2167.88	−0.284753
$388$	1371.49	0.179450
$389$	222.732	0.0290307	0.0145154	−	0.999895i	$-0.495379\pi$
$389$	222.732	0.0290307	0.0145154	+	0.999895i	$0.495379\pi$
$390$	−16809.8	−2.18256
$391$	0	0
$392$	1071.15	0.138013
$393$	−6715.71	−0.861992
$394$	2682.07	0.342947
$395$	−11335.2	−1.44389
$396$	−2996.36	−0.380234
$397$	−14387.6	−1.81888	−0.909439	−	0.415838i	$-0.863488\pi$
$397$	−14387.6	−1.81888	−0.909439	+	0.415838i	$0.863488\pi$
$398$	−11689.0	−1.47215
$399$	−501.103	−0.0628735
$400$	−400.480	−0.0500601
$401$	−9740.86	−1.21306	−0.606528	−	0.795062i	$-0.707438\pi$
$401$	−9740.86	−1.21306	−0.606528	+	0.795062i	$0.707438\pi$
$402$	−20826.6	−2.58393
$403$	48.0580	0.00594030
$404$	−12208.1	−1.50340
$405$	13716.0	1.68285
$406$	8208.55	1.00341
$407$	13320.5	1.62229
$408$	0	0
$409$	2221.61	0.268586	0.134293	−	0.990942i	$-0.457124\pi$
$409$	2221.61	0.268586	0.134293	+	0.990942i	$0.457124\pi$
$410$	−10995.2	−1.32443
$411$	1622.51	0.194727
$412$	−23742.5	−2.83910
$413$	1468.36	0.174947
$414$	−1546.20	−0.183554
$415$	−16520.0	−1.95406
$416$	7428.42	0.875501
$417$	−14583.8	−1.71264
$418$	3163.66	0.370191
$419$	−10989.1	−1.28127	−0.640634	−	0.767846i	$-0.721329\pi$
$419$	−10989.1	−1.28127	−0.640634	+	0.767846i	$0.721329\pi$
$420$	−8312.85	−0.965775
$421$	−1051.51	−0.121728	−0.0608639	−	0.998146i	$-0.519386\pi$
$421$	−1051.51	−0.121728	−0.0608639	+	0.998146i	$0.519386\pi$
$422$	−22051.7	−2.54375
$423$	−1463.73	−0.168249
$424$	8361.21	0.957680
$425$	0	0
$426$	22215.4	2.52662
$427$	−3586.26	−0.406443
$428$	19241.2	2.17303
$429$	−12054.1	−1.35659
$430$	37971.2	4.25845
$431$	−4772.07	−0.533323	−0.266662	−	0.963790i	$-0.585921\pi$
$431$	−4772.07	−0.533323	−0.266662	+	0.963790i	$0.585921\pi$
$432$	−338.652	−0.0377162
$433$	−5952.72	−0.660668	−0.330334	−	0.943864i	$-0.607161\pi$
$433$	−5952.72	−0.660668	−0.330334	+	0.943864i	$0.607161\pi$
$434$	38.6266	0.00427220
$435$	−23869.9	−2.63098
$436$	−15500.2	−1.70258
$437$	1004.45	0.109953
$438$	6915.69	0.754439
$439$	12310.8	1.33841	0.669206	−	0.743077i	$-0.266634\pi$
$439$	12310.8	1.33841	0.669206	+	0.743077i	$0.266634\pi$
$440$	19665.2	2.13068
$441$	211.591	0.0228475
$442$	0	0
$443$	2755.06	0.295478	0.147739	−	0.989026i	$-0.452800\pi$
$443$	2755.06	0.295478	0.147739	+	0.989026i	$0.452800\pi$
$444$	17584.4	1.87955
$445$	−16557.7	−1.76385
$446$	25705.0	2.72908
$447$	1745.08	0.184652
$448$	5821.18	0.613895
$449$	11322.3	1.19005	0.595023	−	0.803709i	$-0.297143\pi$
$449$	11322.3	1.19005	0.595023	+	0.803709i	$0.297143\pi$
$450$	2955.78	0.309637
$451$	−7884.56	−0.823214
$452$	7721.90	0.803557
$453$	16601.4	1.72186
$454$	24403.1	2.52268
$455$	−4611.00	−0.475092
$456$	1564.88	0.160707
$457$	13575.5	1.38958	0.694789	−	0.719214i	$-0.255498\pi$
$457$	13575.5	1.38958	0.694789	+	0.719214i	$0.255498\pi$
$458$	−4956.64	−0.505696
$459$	0	0
$460$	16662.9	1.68894
$461$	−2043.21	−0.206424	−0.103212	−	0.994659i	$-0.532912\pi$
$461$	−2043.21	−0.206424	−0.103212	+	0.994659i	$0.532912\pi$
$462$	−9688.49	−0.975648
$463$	−1921.91	−0.192913	−0.0964563	−	0.995337i	$-0.530751\pi$
$463$	−1921.91	−0.192913	−0.0964563	+	0.995337i	$0.530751\pi$
$464$	686.085	0.0686437
$465$	−112.323	−0.0112019
$466$	22104.6	2.19738
$467$	−3896.41	−0.386091	−0.193045	−	0.981190i	$-0.561836\pi$
$467$	−3896.41	−0.386091	−0.193045	+	0.981190i	$0.561836\pi$
$468$	−2194.05	−0.216710
$469$	−5712.83	−0.562460
$470$	25637.8	2.51614
$471$	13612.5	1.33170
$472$	−4585.50	−0.447171
$473$	27228.7	2.64689
$474$	−17439.9	−1.68996
$475$	−1920.15	−0.185479
$476$	0	0
$477$	1651.64	0.158540
$478$	−21747.1	−2.08094
$479$	−14443.9	−1.37779	−0.688894	−	0.724862i	$-0.741904\pi$
$479$	−14443.9	−1.37779	−0.688894	+	0.724862i	$0.741904\pi$
$480$	−17362.1	−1.65097
$481$	9753.81	0.924606
$482$	20128.8	1.90216
$483$	−3076.05	−0.289783
$484$	20605.9	1.93519
$485$	−1778.04	−0.166468
$486$	5474.74	0.510986
$487$	−6873.72	−0.639585	−0.319793	−	0.947488i	$-0.603613\pi$
$487$	−6873.72	−0.639585	−0.319793	+	0.947488i	$0.603613\pi$
$488$	11199.5	1.03889
$489$	13635.9	1.26102
$490$	−3706.09	−0.341681
$491$	6686.90	0.614614	0.307307	−	0.951610i	$-0.400572\pi$
$491$	6686.90	0.614614	0.307307	+	0.951610i	$0.400572\pi$
$492$	−10408.4	−0.953757
$493$	0	0
$494$	2316.56	0.210986
$495$	3884.58	0.352725
$496$	3.22848	0.000292264 0
$497$	6093.78	0.549987
$498$	−25417.0	−2.28707
$499$	−10506.3	−0.942540	−0.471270	−	0.881989i	$-0.656204\pi$
$499$	−10506.3	−0.942540	−0.471270	+	0.881989i	$0.656204\pi$
$500$	−5328.05	−0.476555
$501$	10218.0	0.911188
$502$	648.406	0.0576490
$503$	19541.7	1.73225	0.866124	−	0.499830i	$-0.166604\pi$
$503$	19541.7	1.73225	0.866124	+	0.499830i	$0.166604\pi$
$504$	−660.772	−0.0583991
$505$	15826.9	1.39463
$506$	19420.4	1.70621
$507$	3468.48	0.303828
$508$	−22078.4	−1.92829
$509$	−18409.4	−1.60310	−0.801552	−	0.597925i	$-0.795992\pi$
$509$	−18409.4	−1.60310	−0.801552	+	0.597925i	$0.795992\pi$
$510$	0	0
$511$	1897.00	0.164224
$512$	965.606	0.0833479
$513$	−1623.70	−0.139743
$514$	2200.12	0.188800
$515$	30780.6	2.63370
$516$	35944.7	3.06662
$517$	18384.6	1.56393
$518$	7839.61	0.664966
$519$	23889.1	2.02045
$520$	14399.6	1.21435
$521$	−12217.0	−1.02733	−0.513664	−	0.857992i	$-0.671712\pi$
$521$	−12217.0	−1.02733	−0.513664	+	0.857992i	$0.671712\pi$
$522$	−5063.71	−0.424583
$523$	−16501.8	−1.37968	−0.689841	−	0.723961i	$-0.742320\pi$
$523$	−16501.8	−1.37968	−0.689841	+	0.723961i	$0.742320\pi$
$524$	15353.1	1.27997
$525$	5880.31	0.488834
$526$	3814.84	0.316226
$527$	0	0
$528$	−809.781	−0.0667447
$529$	−6001.12	−0.493230
$530$	−28929.1	−2.37094
$531$	−905.803	−0.0740273
$532$	1145.59	0.0933604
$533$	−5773.39	−0.469181
$534$	−25475.0	−2.06444
$535$	−24944.9	−2.01581
$536$	17840.5	1.43767
$537$	10502.4	0.843970
$538$	245.282	0.0196559
$539$	−2657.59	−0.212376
$540$	−26935.8	−2.14654
$541$	−21274.4	−1.69068	−0.845339	−	0.534231i	$-0.820601\pi$
$541$	−21274.4	−1.69068	−0.845339	+	0.534231i	$0.820601\pi$
$542$	−4610.00	−0.365344
$543$	17139.2	1.35454
$544$	0	0
$545$	20095.0	1.57940
$546$	−7094.30	−0.556058
$547$	−19363.0	−1.51353	−0.756766	−	0.653686i	$-0.773222\pi$
$547$	−19363.0	−1.51353	−0.756766	+	0.653686i	$0.773222\pi$
$548$	−3709.30	−0.289149
$549$	2212.30	0.171983
$550$	−37124.8	−2.87819
$551$	3289.51	0.254334
$552$	9606.14	0.740697
$553$	−4783.84	−0.367866
$554$	−21484.3	−1.64761
$555$	−22797.0	−1.74357
$556$	33340.6	2.54309
$557$	−25595.2	−1.94705	−0.973523	−	0.228590i	$-0.926589\pi$
$557$	−25595.2	−1.94705	−0.973523	+	0.228590i	$0.926589\pi$
$558$	−23.8280	−0.00180774
$559$	19937.9	1.50856
$560$	−309.761	−0.0233746
$561$	0	0
$562$	5260.87	0.394869
$563$	−7344.93	−0.549826	−0.274913	−	0.961469i	$-0.588649\pi$
$563$	−7344.93	−0.549826	−0.274913	+	0.961469i	$0.588649\pi$
$564$	24269.6	1.81194
$565$	−10010.9	−0.745421
$566$	4473.70	0.332233
$567$	5788.61	0.428746
$568$	−19030.1	−1.40579
$569$	15128.8	1.11464	0.557321	−	0.830297i	$-0.311829\pi$
$569$	15128.8	1.11464	0.557321	+	0.830297i	$0.311829\pi$
$570$	−5414.37	−0.397865
$571$	−6451.42	−0.472826	−0.236413	−	0.971653i	$-0.575972\pi$
$571$	−6451.42	−0.472826	−0.236413	+	0.971653i	$0.575972\pi$
$572$	27557.5	2.01440
$573$	−20633.4	−1.50431
$574$	−4640.35	−0.337430
$575$	−11787.0	−0.854870
$576$	−3590.98	−0.259764
$577$	2081.11	0.150152	0.0750759	−	0.997178i	$-0.476080\pi$
$577$	2081.11	0.150152	0.0750759	+	0.997178i	$0.476080\pi$
$578$	0	0
$579$	−13323.6	−0.956322
$580$	54570.0	3.90672
$581$	−6971.97	−0.497842
$582$	−2735.62	−0.194837
$583$	−20744.7	−1.47369
$584$	−5924.11	−0.419763
$585$	2844.44	0.201031
$586$	−6418.01	−0.452433
$587$	−292.238	−0.0205485	−0.0102742	−	0.999947i	$-0.503270\pi$
$587$	−292.238	−0.0205485	−0.0102742	+	0.999947i	$0.503270\pi$
$588$	−3508.29	−0.246054
$589$	15.4793	0.00108287
$590$	15865.5	1.10707
$591$	−3291.56	−0.229097
$592$	655.248	0.0454908
$593$	22333.5	1.54659	0.773295	−	0.634046i	$-0.218607\pi$
$593$	22333.5	1.54659	0.773295	+	0.634046i	$0.218607\pi$
$594$	−31393.2	−2.16848
$595$	0	0
$596$	−3989.50	−0.274188
$597$	14345.2	0.983437
$598$	14220.4	0.972431
$599$	10247.1	0.698974	0.349487	−	0.936941i	$-0.386356\pi$
$599$	10247.1	0.698974	0.349487	+	0.936941i	$0.386356\pi$
$600$	−18363.5	−1.24948
$601$	19611.1	1.33103	0.665517	−	0.746382i	$-0.268211\pi$
$601$	19611.1	1.33103	0.665517	+	0.746382i	$0.268211\pi$
$602$	16025.1	1.08494
$603$	3524.14	0.238000
$604$	−37953.3	−2.55678
$605$	−26714.1	−1.79518
$606$	24350.7	1.63231
$607$	−8920.32	−0.596482	−0.298241	−	0.954491i	$-0.596400\pi$
$607$	−8920.32	−0.596482	−0.298241	+	0.954491i	$0.596400\pi$
$608$	2392.66	0.159598
$609$	−10073.9	−0.670303
$610$	−38749.2	−2.57199
$611$	13461.9	0.891345
$612$	0	0
$613$	993.762	0.0654774	0.0327387	−	0.999464i	$-0.489577\pi$
$613$	993.762	0.0654774	0.0327387	+	0.999464i	$0.489577\pi$
$614$	−23192.0	−1.52435
$615$	13493.8	0.884754
$616$	8299.34	0.542841
$617$	−9995.00	−0.652161	−0.326081	−	0.945342i	$-0.605728\pi$
$617$	−9995.00	−0.652161	−0.326081	+	0.945342i	$0.605728\pi$
$618$	47357.8	3.08254
$619$	54.6200	0.00354663	0.00177332	−	0.999998i	$-0.499436\pi$
$619$	54.6200	0.00354663	0.00177332	+	0.999998i	$0.499436\pi$
$620$	256.788	0.0166336
$621$	−9967.21	−0.644075
$622$	3683.68	0.237463
$623$	−6987.91	−0.449381
$624$	−592.954	−0.0380403
$625$	−11856.1	−0.758788
$626$	−3994.53	−0.255038
$627$	−3882.58	−0.247297
$628$	−31120.2	−1.97744
$629$	0	0
$630$	2286.22	0.144580
$631$	2876.31	0.181464	0.0907322	−	0.995875i	$-0.471079\pi$
$631$	2876.31	0.181464	0.0907322	+	0.995875i	$0.471079\pi$
$632$	14939.4	0.940278
$633$	27062.8	1.69929
$634$	756.588	0.0473943
$635$	28623.1	1.78878
$636$	−27385.2	−1.70738
$637$	−1945.99	−0.121041
$638$	63600.5	3.94666
$639$	−3759.14	−0.232722
$640$	38077.8	2.35181
$641$	−3787.11	−0.233357	−0.116679	−	0.993170i	$-0.537225\pi$
$641$	−3787.11	−0.233357	−0.116679	+	0.993170i	$0.537225\pi$
$642$	−38379.2	−2.35935
$643$	1452.27	0.0890700	0.0445350	−	0.999008i	$-0.485819\pi$
$643$	1452.27	0.0890700	0.0445350	+	0.999008i	$0.485819\pi$
$644$	7032.30	0.430297
$645$	−46599.9	−2.84476
$646$	0	0
$647$	−2230.55	−0.135536	−0.0677680	−	0.997701i	$-0.521588\pi$
$647$	−2230.55	−0.135536	−0.0677680	+	0.997701i	$0.521588\pi$
$648$	−18077.1	−1.09589
$649$	11376.9	0.688111
$650$	−27184.2	−1.64039
$651$	−47.4042	−0.00285394
$652$	−31173.6	−1.87247
$653$	9386.24	0.562499	0.281249	−	0.959635i	$-0.409251\pi$
$653$	9386.24	0.562499	0.281249	+	0.959635i	$0.409251\pi$
$654$	30917.4	1.84857
$655$	−19904.2	−1.18736
$656$	−387.849	−0.0230838
$657$	−1170.23	−0.0694899
$658$	10820.0	0.641045
$659$	−19498.6	−1.15259	−0.576294	−	0.817242i	$-0.695502\pi$
$659$	−19498.6	−1.15259	−0.576294	+	0.817242i	$0.695502\pi$
$660$	−64408.6	−3.79864
$661$	−31452.2	−1.85075	−0.925377	−	0.379049i	$-0.876251\pi$
$661$	−31452.2	−1.85075	−0.925377	+	0.379049i	$0.876251\pi$
$662$	10785.1	0.633196
$663$	0	0
$664$	21772.6	1.27250
$665$	−1485.18	−0.0866060
$666$	−4836.11	−0.281375
$667$	20192.9	1.17222
$668$	−23359.7	−1.35302
$669$	−31546.3	−1.82310
$670$	−61726.6	−3.55926
$671$	−27786.6	−1.59865
$672$	−7327.36	−0.420624
$673$	17176.7	0.983824	0.491912	−	0.870645i	$-0.336298\pi$
$673$	17176.7	0.983824	0.491912	+	0.870645i	$0.336298\pi$
$674$	15550.2	0.888681
$675$	19053.8	1.08649
$676$	−7929.44	−0.451152
$677$	−10960.6	−0.622228	−0.311114	−	0.950373i	$-0.600702\pi$
$677$	−10960.6	−0.622228	−0.311114	+	0.950373i	$0.600702\pi$
$678$	−15402.4	−0.872457
$679$	−750.392	−0.0424115
$680$	0	0
$681$	−29948.6	−1.68522
$682$	299.282	0.0168037
$683$	8739.75	0.489630	0.244815	−	0.969570i	$-0.421273\pi$
$683$	8739.75	0.489630	0.244815	+	0.969570i	$0.421273\pi$
$684$	−706.696	−0.0395047
$685$	4808.86	0.268229
$686$	−1564.09	−0.0870514
$687$	6083.01	0.337818
$688$	1339.40	0.0742214
$689$	−15190.1	−0.839910
$690$	−33236.5	−1.83376
$691$	−9458.53	−0.520723	−0.260361	−	0.965511i	$-0.583842\pi$
$691$	−9458.53	−0.520723	−0.260361	+	0.965511i	$0.583842\pi$
$692$	−54613.9	−3.00016
$693$	1639.42	0.0898650
$694$	−16053.7	−0.878083
$695$	−43223.9	−2.35910
$696$	31459.5	1.71332
$697$	0	0
$698$	24831.7	1.34655
$699$	−27127.8	−1.46791
$700$	−13443.2	−0.725867
$701$	27233.3	1.46732	0.733658	−	0.679518i	$-0.237811\pi$
$701$	27233.3	1.46732	0.733658	+	0.679518i	$0.237811\pi$
$702$	−22987.4	−1.23590
$703$	3141.66	0.168549
$704$	45103.0	2.41461
$705$	−31463.9	−1.68085
$706$	−43280.3	−2.30719
$707$	6679.49	0.355316
$708$	15018.7	0.797230
$709$	−5101.51	−0.270227	−0.135114	−	0.990830i	$-0.543140\pi$
$709$	−5101.51	−0.270227	−0.135114	+	0.990830i	$0.543140\pi$
$710$	65842.8	3.48033
$711$	2951.07	0.155659
$712$	21822.4	1.14864
$713$	95.0206	0.00499095
$714$	0	0
$715$	−35726.4	−1.86866
$716$	−24010.0	−1.25321
$717$	26689.0	1.39012
$718$	7.55632	0.000392757 0
$719$	16399.8	0.850636	0.425318	−	0.905044i	$-0.360162\pi$
$719$	16399.8	0.850636	0.425318	+	0.905044i	$0.360162\pi$
$720$	191.086	0.00989077
$721$	12990.4	0.670997
$722$	−30531.1	−1.57375
$723$	−24703.0	−1.27070
$724$	−39182.6	−2.01134
$725$	−38601.6	−1.97742
$726$	−41101.2	−2.10112
$727$	35224.3	1.79697	0.898486	−	0.439002i	$-0.144668\pi$
$727$	35224.3	1.79697	0.898486	+	0.439002i	$0.144668\pi$
$728$	6077.11	0.309385
$729$	15608.7	0.793002
$730$	20496.9	1.03921
$731$	0	0
$732$	−36681.2	−1.85215
$733$	24492.2	1.23416	0.617080	−	0.786901i	$-0.288316\pi$
$733$	24492.2	1.23416	0.617080	+	0.786901i	$0.288316\pi$
$734$	−52953.3	−2.66287
$735$	4548.27	0.228252
$736$	14687.5	0.735583
$737$	−44263.5	−2.21230
$738$	2862.55	0.142780
$739$	−15242.9	−0.758753	−0.379377	−	0.925242i	$-0.623862\pi$
$739$	−15242.9	−0.758753	−0.379377	+	0.925242i	$0.623862\pi$
$740$	52117.3	2.58902
$741$	−2842.98	−0.140944
$742$	−12209.0	−0.604054
$743$	39870.7	1.96866	0.984329	−	0.176341i	$-0.0564263\pi$
$743$	39870.7	1.96866	0.984329	+	0.176341i	$0.0564263\pi$
$744$	148.038	0.00729479
$745$	5172.12	0.254351
$746$	−8060.70	−0.395607
$747$	4300.89	0.210658
$748$	0	0
$749$	−10527.6	−0.513576
$750$	10627.5	0.517417
$751$	2654.53	0.128982	0.0644908	−	0.997918i	$-0.479458\pi$
$751$	2654.53	0.128982	0.0644908	+	0.997918i	$0.479458\pi$
$752$	904.355	0.0438543
$753$	−795.752	−0.0385111
$754$	46570.8	2.24935
$755$	49203.9	2.37180
$756$	−11367.8	−0.546882
$757$	−1010.67	−0.0485248	−0.0242624	−	0.999706i	$-0.507724\pi$
$757$	−1010.67	−0.0485248	−0.0242624	+	0.999706i	$0.507724\pi$
$758$	10764.5	0.515809
$759$	−23833.5	−1.13979
$760$	4638.05	0.221368
$761$	−332.507	−0.0158388	−0.00791942	−	0.999969i	$-0.502521\pi$
$761$	−332.507	−0.0158388	−0.00791942	+	0.999969i	$0.502521\pi$
$762$	44038.4	2.09362
$763$	8480.76	0.402391
$764$	47170.9	2.23375
$765$	0	0
$766$	7177.50	0.338556
$767$	8330.65	0.392180
$768$	21354.3	1.00333
$769$	30704.4	1.43983	0.719915	−	0.694062i	$-0.244181\pi$
$769$	30704.4	1.43983	0.719915	+	0.694062i	$0.244181\pi$
$770$	−28715.1	−1.34392
$771$	−2700.09	−0.126124
$772$	30459.7	1.42004
$773$	−8703.14	−0.404955	−0.202477	−	0.979287i	$-0.564899\pi$
$773$	−8703.14	−0.404955	−0.202477	+	0.979287i	$0.564899\pi$
$774$	−9885.59	−0.459083
$775$	−181.646	−0.00841923
$776$	2343.39	0.108405
$777$	−9621.11	−0.444215
$778$	1015.66	0.0468037
$779$	−1859.58	−0.0855283
$780$	−47162.5	−2.16499
$781$	47215.1	2.16324
$782$	0	0
$783$	−32642.0	−1.48982
$784$	−130.729	−0.00595524
$785$	40345.2	1.83437
$786$	−30623.8	−1.38972
$787$	−19895.2	−0.901128	−0.450564	−	0.892744i	$-0.648777\pi$
$787$	−19895.2	−0.901128	−0.450564	+	0.892744i	$0.648777\pi$
$788$	7524.97	0.340185
$789$	−4681.73	−0.211247
$790$	−51689.0	−2.32786
$791$	−4224.94	−0.189914
$792$	−5119.72	−0.229698
$793$	−20346.5	−0.911128
$794$	−65608.0	−2.93242
$795$	35503.1	1.58385
$796$	−32795.3	−1.46030
$797$	−16467.8	−0.731895	−0.365947	−	0.930636i	$-0.619255\pi$
$797$	−16467.8	−0.731895	−0.365947	+	0.930636i	$0.619255\pi$
$798$	−2285.04	−0.101365
$799$	0	0
$800$	−28077.3	−1.24085
$801$	4310.72	0.190152
$802$	−44418.6	−1.95570
$803$	14698.1	0.645935
$804$	−58432.3	−2.56312
$805$	−9116.90	−0.399166
$806$	219.146	0.00957703
$807$	−301.021	−0.0131307
$808$	−20859.3	−0.908200
$809$	2656.20	0.115435	0.0577175	−	0.998333i	$-0.481618\pi$
$809$	2656.20	0.115435	0.0577175	+	0.998333i	$0.481618\pi$
$810$	62545.4	2.71311
$811$	38641.9	1.67312	0.836560	−	0.547875i	$-0.184563\pi$
$811$	38641.9	1.67312	0.836560	+	0.547875i	$0.184563\pi$
$812$	23030.4	0.995329
$813$	5657.59	0.244059
$814$	60741.9	2.61548
$815$	40414.5	1.73700
$816$	0	0
$817$	6421.92	0.275000
$818$	10130.6	0.433018
$819$	1200.45	0.0512174
$820$	−30848.8	−1.31377
$821$	9005.92	0.382836	0.191418	−	0.981509i	$-0.438691\pi$
$821$	9005.92	0.382836	0.191418	+	0.981509i	$0.438691\pi$
$822$	7398.71	0.313941
$823$	−36800.9	−1.55869	−0.779343	−	0.626598i	$-0.784447\pi$
$823$	−36800.9	−1.55869	−0.779343	+	0.626598i	$0.784447\pi$
$824$	−40567.6	−1.71509
$825$	45561.2	1.92271
$826$	6695.75	0.282052
$827$	13301.3	0.559287	0.279644	−	0.960104i	$-0.409784\pi$
$827$	13301.3	0.559287	0.279644	+	0.960104i	$0.409784\pi$
$828$	−4338.10	−0.182077
$829$	−18299.1	−0.766651	−0.383326	−	0.923613i	$-0.625221\pi$
$829$	−18299.1	−0.766651	−0.383326	+	0.923613i	$0.625221\pi$
$830$	−75331.6	−3.15036
$831$	26366.4	1.10065
$832$	33026.2	1.37617
$833$	0	0
$834$	−66502.5	−2.76114
$835$	30284.3	1.25513
$836$	8876.15	0.367210
$837$	−153.602	−0.00634320
$838$	−50110.5	−2.06568
$839$	11672.3	0.480300	0.240150	−	0.970736i	$-0.422803\pi$
$839$	11672.3	0.480300	0.240150	+	0.970736i	$0.422803\pi$
$840$	−14203.7	−0.583421
$841$	41741.5	1.71149
$842$	−4794.91	−0.196251
$843$	−6456.37	−0.263783
$844$	−61869.6	−2.52327
$845$	10280.0	0.418512
$846$	−6674.67	−0.271253
$847$	−11274.2	−0.457364
$848$	−1020.45	−0.0413237
$849$	−5490.32	−0.221940
$850$	0	0
$851$	19285.3	0.776840
$852$	62328.8	2.50628
$853$	14306.3	0.574254	0.287127	−	0.957893i	$-0.407300\pi$
$853$	14306.3	0.574254	0.287127	+	0.957893i	$0.407300\pi$
$854$	−16353.5	−0.655274
$855$	916.184	0.0366466
$856$	32876.3	1.31272
$857$	41452.9	1.65228	0.826140	−	0.563465i	$-0.190532\pi$
$857$	41452.9	1.65228	0.826140	+	0.563465i	$0.190532\pi$
$858$	−54967.2	−2.18712
$859$	−12908.8	−0.512739	−0.256370	−	0.966579i	$-0.582526\pi$
$859$	−12908.8	−0.512739	−0.256370	+	0.966579i	$0.582526\pi$
$860$	106534.	4.22416
$861$	5694.84	0.225412
$862$	−21760.8	−0.859831
$863$	−2970.29	−0.117161	−0.0585804	−	0.998283i	$-0.518657\pi$
$863$	−2970.29	−0.117161	−0.0585804	+	0.998283i	$0.518657\pi$
$864$	−23742.6	−0.934882
$865$	70803.2	2.78310
$866$	−27144.6	−1.06514
$867$	0	0
$868$	108.373	0.00423780
$869$	−37065.6	−1.44691
$870$	−108847.	−4.24170
$871$	−32411.5	−1.26087
$872$	−26484.4	−1.02853
$873$	462.904	0.0179461
$874$	4580.32	0.177267
$875$	2915.17	0.112630
$876$	19403.0	0.748365
$877$	−35809.8	−1.37880	−0.689402	−	0.724379i	$-0.742126\pi$
$877$	−35809.8	−1.37880	−0.689402	+	0.724379i	$0.742126\pi$
$878$	56137.7	2.15781
$879$	7876.46	0.302237
$880$	−2400.05	−0.0919384
$881$	−1976.82	−0.0755969	−0.0377984	−	0.999285i	$-0.512034\pi$
$881$	−1976.82	−0.0755969	−0.0377984	+	0.999285i	$0.512034\pi$
$882$	964.859	0.0368350
$883$	−48132.0	−1.83440	−0.917198	−	0.398431i	$-0.869555\pi$
$883$	−48132.0	−1.83440	−0.917198	+	0.398431i	$0.869555\pi$
$884$	0	0
$885$	−19470.8	−0.739551
$886$	12563.1	0.476373
$887$	3448.67	0.130547	0.0652734	−	0.997867i	$-0.479208\pi$
$887$	3448.67	0.130547	0.0652734	+	0.997867i	$0.479208\pi$
$888$	30045.6	1.13543
$889$	12079.9	0.455733
$890$	−75503.7	−2.84370
$891$	44850.6	1.68637
$892$	72119.4	2.70710
$893$	4336.03	0.162486
$894$	7957.61	0.297698
$895$	31127.3	1.16254
$896$	16070.1	0.599179
$897$	−17451.8	−0.649610
$898$	51629.8	1.91861
$899$	311.187	0.0115447
$900$	8292.90	0.307144
$901$	0	0
$902$	−35953.8	−1.32720
$903$	−19666.7	−0.724768
$904$	13194.0	0.485426
$905$	50797.6	1.86582
$906$	75703.1	2.77601
$907$	−21771.1	−0.797019	−0.398509	−	0.917164i	$-0.630472\pi$
$907$	−21771.1	−0.797019	−0.398509	+	0.917164i	$0.630472\pi$
$908$	68466.8	2.50237
$909$	−4120.46	−0.150349
$910$	−21026.3	−0.765951
$911$	186.035	0.00676576	0.00338288	−	0.999994i	$-0.498923\pi$
$911$	186.035	0.00676576	0.00338288	+	0.999994i	$0.498923\pi$
$912$	−190.988	−0.00693447
$913$	−54019.4	−1.95814
$914$	61904.9	2.24030
$915$	47554.7	1.71815
$916$	−13906.6	−0.501624
$917$	−8400.25	−0.302509
$918$	0	0
$919$	19292.1	0.692477	0.346238	−	0.938147i	$-0.387459\pi$
$919$	19292.1	0.692477	0.346238	+	0.938147i	$0.387459\pi$
$920$	28471.0	1.02028
$921$	28462.2	1.01831
$922$	−9317.09	−0.332800
$923$	34572.8	1.23291
$924$	−27182.6	−0.967793
$925$	−36866.6	−1.31045
$926$	−8763.95	−0.311016
$927$	−8013.56	−0.283927
$928$	48100.8	1.70149
$929$	51848.3	1.83110	0.915548	−	0.402209i	$-0.131758\pi$
$929$	51848.3	1.83110	0.915548	+	0.402209i	$0.131758\pi$
$930$	−512.198	−0.0180598
$931$	−626.797	−0.0220649
$932$	62018.0	2.17968
$933$	−4520.78	−0.158632
$934$	−17767.7	−0.622461
$935$	0	0
$936$	−3748.86	−0.130914
$937$	19428.8	0.677388	0.338694	−	0.940897i	$-0.390015\pi$
$937$	19428.8	0.677388	0.338694	+	0.940897i	$0.390015\pi$
$938$	−26050.7	−0.906806
$939$	4902.26	0.170372
$940$	71930.9	2.49588
$941$	27279.2	0.945034	0.472517	−	0.881322i	$-0.343346\pi$
$941$	27279.2	0.945034	0.472517	+	0.881322i	$0.343346\pi$
$942$	62073.5	2.14699
$943$	−11415.2	−0.394199
$944$	559.642	0.0192953
$945$	14737.6	0.507316
$946$	124164.	4.26734
$947$	−28524.9	−0.978812	−0.489406	−	0.872056i	$-0.662786\pi$
$947$	−28524.9	−0.978812	−0.489406	+	0.872056i	$0.662786\pi$
$948$	−48930.4	−1.67636
$949$	10762.5	0.368142
$950$	−8755.93	−0.299032
$951$	−928.518	−0.0316606
$952$	0	0
$953$	47301.2	1.60780	0.803902	−	0.594761i	$-0.202753\pi$
$953$	47301.2	1.60780	0.803902	+	0.594761i	$0.202753\pi$
$954$	7531.54	0.255600
$955$	−61153.9	−2.07214
$956$	−61014.8	−2.06418
$957$	−78053.3	−2.63647
$958$	−65864.8	−2.22129
$959$	2029.50	0.0683377
$960$	−77190.3	−2.59511
$961$	−29789.5	−0.999951
$962$	44477.6	1.49066
$963$	6494.26	0.217315
$964$	56474.5	1.88685
$965$	−39488.9	−1.31730
$966$	−14026.9	−0.467192
$967$	1072.86	0.0356781	0.0178391	−	0.999841i	$-0.494321\pi$
$967$	1072.86	0.0356781	0.0178391	+	0.999841i	$0.494321\pi$
$968$	35208.1	1.16904
$969$	0	0
$970$	−8107.93	−0.268381
$971$	45369.2	1.49945	0.749725	−	0.661749i	$-0.230186\pi$
$971$	45369.2	1.49945	0.749725	+	0.661749i	$0.230186\pi$
$972$	15360.2	0.506872
$973$	−18241.9	−0.601036
$974$	−31344.4	−1.03115
$975$	33361.7	1.09582
$976$	−1366.85	−0.0448277
$977$	−17955.4	−0.587966	−0.293983	−	0.955811i	$-0.594981\pi$
$977$	−17955.4	−0.587966	−0.293983	+	0.955811i	$0.594981\pi$
$978$	62180.1	2.03303
$979$	−54142.9	−1.76753
$980$	−10398.0	−0.338930
$981$	−5231.63	−0.170268
$982$	30492.5	0.990890
$983$	−40761.1	−1.32256	−0.661281	−	0.750138i	$-0.729987\pi$
$983$	−40761.1	−1.32256	−0.661281	+	0.750138i	$0.729987\pi$
$984$	−17784.3	−0.576162
$985$	−9755.62	−0.315574
$986$	0	0
$987$	−13278.8	−0.428235
$988$	6499.47	0.209287
$989$	39421.4	1.26747
$990$	17713.8	0.568668
$991$	47753.6	1.53072	0.765359	−	0.643603i	$-0.222561\pi$
$991$	47753.6	1.53072	0.765359	+	0.643603i	$0.222561\pi$
$992$	226.345	0.00724443
$993$	−13236.0	−0.422992
$994$	27787.8	0.886696
$995$	42516.9	1.35465
$996$	−71311.2	−2.26866
$997$	29104.5	0.924522	0.462261	−	0.886744i	$-0.347038\pi$
$997$	29104.5	0.924522	0.462261	+	0.886744i	$0.347038\pi$
$998$	−47909.1	−1.51958
$999$	−31174.9	−0.987317

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2023.4.a.l.1.10	yes	12
17.16	even	2		2023.4.a.k.1.10	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2023.4.a.k.1.10	✓	12	17.16	even	2
2023.4.a.l.1.10	yes	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2023 = 7 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2023.a (trivial)

\(f(q)\)	\(=\)	\(q+4.56003 q^{2} -5.59626 q^{3} +12.7939 q^{4} -16.5864 q^{5} -25.5191 q^{6} -7.00000 q^{7} +21.8602 q^{8} +4.31818 q^{9} -75.6344 q^{10} -54.2366 q^{11} -71.5978 q^{12} -39.7142 q^{13} -31.9202 q^{14} +92.8218 q^{15} -2.66795 q^{16} +19.6910 q^{18} -12.7918 q^{19} -212.204 q^{20} +39.1739 q^{21} -247.320 q^{22} -78.5231 q^{23} -122.335 q^{24} +150.108 q^{25} -181.098 q^{26} +126.933 q^{27} -89.5571 q^{28} -257.158 q^{29} +423.270 q^{30} -1.21010 q^{31} -187.047 q^{32} +303.522 q^{33} +116.105 q^{35} +55.2461 q^{36} -245.600 q^{37} -58.3308 q^{38} +222.251 q^{39} -362.581 q^{40} +145.374 q^{41} +178.634 q^{42} -502.036 q^{43} -693.895 q^{44} -71.6229 q^{45} -358.068 q^{46} -338.971 q^{47} +14.9305 q^{48} +49.0000 q^{49} +684.498 q^{50} -508.098 q^{52} +382.486 q^{53} +578.820 q^{54} +899.589 q^{55} -153.021 q^{56} +71.5861 q^{57} -1172.65 q^{58} -209.765 q^{59} +1187.55 q^{60} +512.323 q^{61} -5.51808 q^{62} -30.2272 q^{63} -831.597 q^{64} +658.714 q^{65} +1384.07 q^{66} +816.118 q^{67} +439.436 q^{69} +529.441 q^{70} -870.540 q^{71} +94.3960 q^{72} -271.000 q^{73} -1119.94 q^{74} -840.045 q^{75} -163.656 q^{76} +379.656 q^{77} +1013.47 q^{78} +683.406 q^{79} +44.2516 q^{80} -826.944 q^{81} +662.908 q^{82} +995.996 q^{83} +501.185 q^{84} -2289.30 q^{86} +1439.13 q^{87} -1185.62 q^{88} +998.273 q^{89} -326.603 q^{90} +277.999 q^{91} -1004.61 q^{92} +6.77203 q^{93} -1545.72 q^{94} +212.169 q^{95} +1046.77 q^{96} +107.199 q^{97} +223.441 q^{98} -234.203 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} + 3 q^{3} + 65 q^{4} - 12 q^{5} - 22 q^{6} - 84 q^{7} + 78 q^{8} + 233 q^{9} + 36 q^{10} + 4 q^{11} + 6 q^{12} + 98 q^{13} - 21 q^{14} - 196 q^{15} + 429 q^{16} + 603 q^{18} - 37 q^{19} + 54 q^{20}+ \cdots + 5140 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 + 3 * q^3 + 65 * q^4 - 12 * q^5 - 22 * q^6 - 84 * q^7 + 78 * q^8 + 233 * q^9 + 36 * q^10 + 4 * q^11 + 6 * q^12 + 98 * q^13 - 21 * q^14 - 196 * q^15 + 429 * q^16 + 603 * q^18 - 37 * q^19 + 54 * q^20 - 21 * q^21 + 70 * q^22 - 369 * q^23 - 652 * q^24 + 590 * q^25 + 638 * q^26 + 501 * q^27 - 455 * q^28 + 144 * q^29 - 160 * q^30 + 67 * q^31 + 417 * q^32 + 628 * q^33 + 84 * q^35 + 999 * q^36 - 345 * q^37 - 190 * q^38 + 6 * q^39 - 466 * q^40 - 156 * q^41 + 154 * q^42 - 763 * q^43 + 1046 * q^44 + 832 * q^45 - 395 * q^46 + 561 * q^47 + 532 * q^48 + 588 * q^49 + 1923 * q^50 + 3138 * q^52 + 1156 * q^53 - 1682 * q^54 - 156 * q^55 - 546 * q^56 - 501 * q^57 - 2305 * q^58 - 473 * q^59 - 1292 * q^60 + 1850 * q^61 + 202 * q^62 - 1631 * q^63 - 712 * q^64 + 1718 * q^65 + 2142 * q^66 - 834 * q^67 + 1316 * q^69 - 252 * q^70 - 3179 * q^71 + 2046 * q^72 + 1012 * q^73 - 2695 * q^74 - 3841 * q^75 + 3272 * q^76 - 28 * q^77 + 970 * q^78 - 3897 * q^79 - 1616 * q^80 + 3448 * q^81 + 4758 * q^82 + 675 * q^83 - 42 * q^84 + 77 * q^86 + 805 * q^87 + 5398 * q^88 + 4078 * q^89 + 13384 * q^90 - 686 * q^91 - 3393 * q^92 + 3671 * q^93 + 958 * q^94 - 4126 * q^95 - 2320 * q^96 + 1474 * q^97 + 147 * q^98 + 5140 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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