LMFDB - Embedded newform 529.4.a.m.1.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [529,4,Mod(1,529)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(529, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([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("529.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 529 = 23^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	529.a (trivial)

Newform invariants

comment:select newform

sage:traces = [25,0,-1,80,-51] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$31.2120103930$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 23)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	529.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+3.60724 q^{2} +7.96546 q^{3} +5.01217 q^{4} -17.8878 q^{5} +28.7333 q^{6} -17.9996 q^{7} -10.7778 q^{8} +36.4486 q^{9} -64.5257 q^{10} +24.9879 q^{11} +39.9242 q^{12} -54.6945 q^{13} -64.9288 q^{14} -142.485 q^{15} -78.9755 q^{16} -53.5185 q^{17} +131.479 q^{18} -17.2819 q^{19} -89.6569 q^{20} -143.375 q^{21} +90.1372 q^{22} -85.8504 q^{24} +194.975 q^{25} -197.296 q^{26} +75.2625 q^{27} -90.2169 q^{28} -84.7276 q^{29} -513.977 q^{30} +104.354 q^{31} -198.661 q^{32} +199.040 q^{33} -193.054 q^{34} +321.974 q^{35} +182.687 q^{36} +190.380 q^{37} -62.3398 q^{38} -435.667 q^{39} +192.792 q^{40} -111.494 q^{41} -517.188 q^{42} +291.169 q^{43} +125.243 q^{44} -651.987 q^{45} -504.689 q^{47} -629.077 q^{48} -19.0152 q^{49} +703.322 q^{50} -426.300 q^{51} -274.138 q^{52} +54.5628 q^{53} +271.490 q^{54} -446.979 q^{55} +193.996 q^{56} -137.658 q^{57} -305.633 q^{58} +301.679 q^{59} -714.159 q^{60} -834.342 q^{61} +376.430 q^{62} -656.060 q^{63} -84.8130 q^{64} +978.367 q^{65} +717.985 q^{66} +4.71109 q^{67} -268.244 q^{68} +1161.44 q^{70} +921.618 q^{71} -392.837 q^{72} +252.652 q^{73} +686.747 q^{74} +1553.07 q^{75} -86.6196 q^{76} -449.771 q^{77} -1571.56 q^{78} +249.708 q^{79} +1412.70 q^{80} -384.611 q^{81} -402.185 q^{82} -985.034 q^{83} -718.619 q^{84} +957.331 q^{85} +1050.32 q^{86} -674.895 q^{87} -269.315 q^{88} +146.652 q^{89} -2351.87 q^{90} +984.478 q^{91} +831.228 q^{93} -1820.53 q^{94} +309.135 q^{95} -1582.43 q^{96} -72.7164 q^{97} -68.5923 q^{98} +910.773 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19}+ \cdots - 7317 q^{99}+O(q^{100}) $ 25 * q - q^3 + 80 * q^4 - 51 * q^5 + 86 * q^6 - 73 * q^7 + 3 * q^8 + 166 * q^9 - 139 * q^10 - 221 * q^11 - 191 * q^12 - 27 * q^13 - 372 * q^14 - 310 * q^15 + 152 * q^16 - 365 * q^17 - 538 * q^18 - 405 * q^19 - 578 * q^20 - 352 * q^21 - 155 * q^22 + 803 * q^24 + 90 * q^25 - 850 * q^26 + 368 * q^27 - 459 * q^28 + 175 * q^29 - 893 * q^30 + 287 * q^31 + 164 * q^32 - 1020 * q^33 - 335 * q^34 + 462 * q^35 - 1092 * q^36 - 471 * q^37 - 810 * q^38 - 822 * q^39 - 1405 * q^40 - 73 * q^41 - 556 * q^42 - 901 * q^43 - 2073 * q^44 - 1384 * q^45 + 1452 * q^47 - 4028 * q^48 - 1092 * q^49 + 364 * q^50 - 2214 * q^51 + 1287 * q^52 - 2071 * q^53 + 2052 * q^54 + 1006 * q^55 - 4879 * q^56 - 418 * q^57 + 2796 * q^58 - 2713 * q^59 - 2805 * q^60 - 1225 * q^61 - 2852 * q^62 - 4003 * q^63 + 217 * q^64 - 2030 * q^65 - 2933 * q^66 - 767 * q^67 - 4175 * q^68 + 4851 * q^70 - 1683 * q^71 - 5265 * q^72 + 2203 * q^73 - 3089 * q^74 + 2333 * q^75 - 5252 * q^76 + 2760 * q^77 - 692 * q^78 - 5425 * q^79 - 4689 * q^80 + 1929 * q^81 - 2725 * q^82 - 5425 * q^83 - 4317 * q^84 - 912 * q^85 - 4359 * q^86 - 4404 * q^87 - 2610 * q^88 - 4933 * q^89 - 2695 * q^90 - 3619 * q^91 + 6375 * q^93 - 5117 * q^94 - 1338 * q^95 + 20 * q^96 - 2085 * q^97 + 5951 * q^98 - 7317 * 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 $

$2$	3.60724	1.27535	0.637676	−	0.770305i	$-0.279896\pi$
$2$	3.60724	1.27535	0.637676	+	0.770305i	$0.279896\pi$
$3$	7.96546	1.53295	0.766477	−	0.642272i	$-0.222008\pi$
$3$	7.96546	1.53295	0.766477	+	0.642272i	$0.222008\pi$
$4$	5.01217	0.626521
$5$	−17.8878	−1.59994	−0.799969	−	0.600041i	$-0.795151\pi$
$5$	−17.8878	−1.59994	−0.799969	+	0.600041i	$0.795151\pi$
$6$	28.7333	1.95506
$7$	−17.9996	−0.971886	−0.485943	−	0.873991i	$-0.661524\pi$
$7$	−17.9996	−0.971886	−0.485943	+	0.873991i	$0.661524\pi$
$8$	−10.7778	−0.476317
$9$	36.4486	1.34995
$10$	−64.5257	−2.04048
$11$	24.9879	0.684921	0.342460	−	0.939532i	$-0.388740\pi$
$11$	24.9879	0.684921	0.342460	+	0.939532i	$0.388740\pi$
$12$	39.9242	0.960428
$13$	−54.6945	−1.16689	−0.583443	−	0.812154i	$-0.698295\pi$
$13$	−54.6945	−1.16689	−0.583443	+	0.812154i	$0.698295\pi$
$14$	−64.9288	−1.23950
$15$	−142.485	−2.45263
$16$	−78.9755	−1.23399
$17$	−53.5185	−0.763538	−0.381769	−	0.924258i	$-0.624685\pi$
$17$	−53.5185	−0.763538	−0.381769	+	0.924258i	$0.624685\pi$
$18$	131.479	1.72166
$19$	−17.2819	−0.208670	−0.104335	−	0.994542i	$-0.533271\pi$
$19$	−17.2819	−0.208670	−0.104335	+	0.994542i	$0.533271\pi$
$20$	−89.6569	−1.00239
$21$	−143.375	−1.48986
$22$	90.1372	0.873515
$23$	0	0
$23$	0	0
$24$	−85.8504	−0.730172
$25$	194.975	1.55980
$26$	−197.296	−1.48819
$27$	75.2625	0.536455
$28$	−90.2169	−0.608907
$29$	−84.7276	−0.542535	−0.271268	−	0.962504i	$-0.587443\pi$
$29$	−84.7276	−0.542535	−0.271268	+	0.962504i	$0.587443\pi$
$30$	−513.977	−3.12797
$31$	104.354	0.604598	0.302299	−	0.953213i	$-0.402246\pi$
$31$	104.354	0.604598	0.302299	+	0.953213i	$0.402246\pi$
$32$	−198.661	−1.09746
$33$	199.040	1.04995
$34$	−193.054	−0.973779
$35$	321.974	1.55496
$36$	182.687	0.845771
$37$	190.380	0.845901	0.422951	−	0.906153i	$-0.360994\pi$
$37$	190.380	0.845901	0.422951	+	0.906153i	$0.360994\pi$
$38$	−62.3398	−0.266128
$39$	−435.667	−1.78878
$40$	192.792	0.762078
$41$	−111.494	−0.424693	−0.212347	−	0.977194i	$-0.568111\pi$
$41$	−111.494	−0.424693	−0.212347	+	0.977194i	$0.568111\pi$
$42$	−517.188	−1.90009
$43$	291.169	1.03263	0.516313	−	0.856400i	$-0.327304\pi$
$43$	291.169	1.03263	0.516313	+	0.856400i	$0.327304\pi$
$44$	125.243	0.429117
$45$	−651.987	−2.15983
$46$	0	0
$47$	−504.689	−1.56631	−0.783154	−	0.621828i	$-0.786390\pi$
$47$	−504.689	−1.56631	−0.783154	+	0.621828i	$0.786390\pi$
$48$	−629.077	−1.89165
$49$	−19.0152	−0.0554378
$50$	703.322	1.98929
$51$	−426.300	−1.17047
$52$	−274.138	−0.731079
$53$	54.5628	0.141411	0.0707054	−	0.997497i	$-0.477475\pi$
$53$	54.5628	0.141411	0.0707054	+	0.997497i	$0.477475\pi$
$54$	271.490	0.684168
$55$	−446.979	−1.09583
$56$	193.996	0.462926
$57$	−137.658	−0.319882
$58$	−305.633	−0.691923
$59$	301.679	0.665683	0.332841	−	0.942983i	$-0.391993\pi$
$59$	301.679	0.665683	0.332841	+	0.942983i	$0.391993\pi$
$60$	−714.159	−1.53662
$61$	−834.342	−1.75126	−0.875628	−	0.482987i	$-0.839552\pi$
$61$	−834.342	−1.75126	−0.875628	+	0.482987i	$0.839552\pi$
$62$	376.430	0.771074
$63$	−656.060	−1.31200
$64$	−84.8130	−0.165650
$65$	978.367	1.86695
$66$	717.985	1.33906
$67$	4.71109	0.00859032	0.00429516	−	0.999991i	$-0.498633\pi$
$67$	4.71109	0.00859032	0.00429516	+	0.999991i	$0.498633\pi$
$68$	−268.244	−0.478373
$69$	0	0
$70$	1161.44	1.98312
$71$	921.618	1.54051	0.770253	−	0.637738i	$-0.220130\pi$
$71$	921.618	1.54051	0.770253	+	0.637738i	$0.220130\pi$
$72$	−392.837	−0.643004
$73$	252.652	0.405077	0.202539	−	0.979274i	$-0.435081\pi$
$73$	252.652	0.405077	0.202539	+	0.979274i	$0.435081\pi$
$74$	686.747	1.07882
$75$	1553.07	2.39110
$76$	−86.6196	−0.130736
$77$	−449.771	−0.665665
$78$	−1571.56	−2.28133
$79$	249.708	0.355624	0.177812	−	0.984064i	$-0.443098\pi$
$79$	249.708	0.355624	0.177812	+	0.984064i	$0.443098\pi$
$80$	1412.70	1.97431
$81$	−384.611	−0.527588
$82$	−402.185	−0.541633
$83$	−985.034	−1.30267	−0.651335	−	0.758791i	$-0.725791\pi$
$83$	−985.034	−1.30267	−0.651335	+	0.758791i	$0.725791\pi$
$84$	−718.619	−0.933426
$85$	957.331	1.22161
$86$	1050.32	1.31696
$87$	−674.895	−0.831682
$88$	−269.315	−0.326239
$89$	146.652	0.174664	0.0873321	−	0.996179i	$-0.472166\pi$
$89$	146.652	0.174664	0.0873321	+	0.996179i	$0.472166\pi$
$90$	−2351.87	−2.75455
$91$	984.478	1.13408
$92$	0	0
$93$	831.228	0.926820
$94$	−1820.53	−1.99759
$95$	309.135	0.333859
$96$	−1582.43	−1.68235
$97$	−72.7164	−0.0761158	−0.0380579	−	0.999276i	$-0.512117\pi$
$97$	−72.7164	−0.0761158	−0.0380579	+	0.999276i	$0.512117\pi$
$98$	−68.5923	−0.0707027
$99$	910.773	0.924608
$100$	977.248	0.977248
$101$	1355.03	1.33496	0.667479	−	0.744628i	$-0.267373\pi$
$101$	1355.03	1.33496	0.667479	+	0.744628i	$0.267373\pi$
$102$	−1537.76	−1.49276
$103$	171.710	0.164263	0.0821315	−	0.996622i	$-0.473827\pi$
$103$	171.710	0.164263	0.0821315	+	0.996622i	$0.473827\pi$
$104$	589.488	0.555808
$105$	2564.67	2.38368
$106$	196.821	0.180348
$107$	414.272	0.374291	0.187146	−	0.982332i	$-0.440076\pi$
$107$	414.272	0.374291	0.187146	+	0.982332i	$0.440076\pi$
$108$	377.228	0.336100
$109$	−1177.76	−1.03494	−0.517471	−	0.855701i	$-0.673126\pi$
$109$	−1177.76	−1.03494	−0.517471	+	0.855701i	$0.673126\pi$
$110$	−1612.36	−1.39757
$111$	1516.47	1.29673
$112$	1421.53	1.19930
$113$	−466.361	−0.388244	−0.194122	−	0.980977i	$-0.562186\pi$
$113$	−466.361	−0.388244	−0.194122	+	0.980977i	$0.562186\pi$
$114$	−496.565	−0.407961
$115$	0	0
$116$	−424.669	−0.339910
$117$	−1993.54	−1.57524
$118$	1088.23	0.848979
$119$	963.311	0.742072
$120$	1535.68	1.16823
$121$	−706.606	−0.530884
$122$	−3009.67	−2.23347
$123$	−888.101	−0.651036
$124$	523.039	0.378793
$125$	−1251.71	−0.895647
$126$	−2366.56	−1.67326
$127$	−1895.72	−1.32455	−0.662274	−	0.749262i	$-0.730408\pi$
$127$	−1895.72	−1.32455	−0.662274	+	0.749262i	$0.730408\pi$
$128$	1283.35	0.886194
$129$	2319.30	1.58297
$130$	3529.20	2.38101
$131$	−706.426	−0.471150	−0.235575	−	0.971856i	$-0.575697\pi$
$131$	−706.426	−0.471150	−0.235575	+	0.971856i	$0.575697\pi$
$132$	997.622	0.657817
$133$	311.066	0.202803
$134$	16.9940	0.0109557
$135$	−1346.28	−0.858294
$136$	576.813	0.363686
$137$	2636.94	1.64444	0.822221	−	0.569168i	$-0.192735\pi$
$137$	2636.94	1.64444	0.822221	+	0.569168i	$0.192735\pi$
$138$	0	0
$139$	630.323	0.384628	0.192314	−	0.981333i	$-0.438401\pi$
$139$	630.323	0.384628	0.192314	+	0.981333i	$0.438401\pi$
$140$	1613.79	0.974213
$141$	−4020.08	−2.40108
$142$	3324.50	1.96469
$143$	−1366.70	−0.799225
$144$	−2878.55	−1.66583
$145$	1515.60	0.868023
$146$	911.374	0.516616
$147$	−151.465	−0.0849837
$148$	954.218	0.529975
$149$	−1942.42	−1.06798	−0.533992	−	0.845489i	$-0.679309\pi$
$149$	−1942.42	−1.06798	−0.533992	+	0.845489i	$0.679309\pi$
$150$	5602.28	3.04950
$151$	−735.965	−0.396636	−0.198318	−	0.980138i	$-0.563548\pi$
$151$	−735.965	−0.396636	−0.198318	+	0.980138i	$0.563548\pi$
$152$	186.261	0.0993931
$153$	−1950.68	−1.03074
$154$	−1622.43	−0.848956
$155$	−1866.67	−0.967319
$156$	−2183.64	−1.12071
$157$	792.880	0.403049	0.201525	−	0.979483i	$-0.435410\pi$
$157$	792.880	0.403049	0.201525	+	0.979483i	$0.435410\pi$
$158$	900.755	0.453546
$159$	434.618	0.216776
$160$	3553.62	1.75586
$161$	0	0
$162$	−1387.38	−0.672860
$163$	146.251	0.0702776	0.0351388	−	0.999382i	$-0.488813\pi$
$163$	146.251	0.0702776	0.0351388	+	0.999382i	$0.488813\pi$
$164$	−558.826	−0.266079
$165$	−3560.40	−1.67986
$166$	−3553.25	−1.66136
$167$	−1180.93	−0.547203	−0.273602	−	0.961843i	$-0.588215\pi$
$167$	−1180.93	−0.547203	−0.273602	+	0.961843i	$0.588215\pi$
$168$	1545.27	0.709644
$169$	794.489	0.361625
$170$	3453.32	1.55799
$171$	−629.900	−0.281694
$172$	1459.39	0.646961
$173$	−4113.54	−1.80779	−0.903893	−	0.427759i	$-0.859303\pi$
$173$	−4113.54	−1.80779	−0.903893	+	0.427759i	$0.859303\pi$
$174$	−2434.51	−1.06069
$175$	−3509.47	−1.51595
$176$	−1973.43	−0.845187
$177$	2403.01	1.02046
$178$	529.010	0.222758
$179$	2382.51	0.994845	0.497422	−	0.867509i	$-0.334280\pi$
$179$	2382.51	0.994845	0.497422	+	0.867509i	$0.334280\pi$
$180$	−3267.87	−1.35318
$181$	−3456.31	−1.41937	−0.709685	−	0.704520i	$-0.751163\pi$
$181$	−3456.31	−1.41937	−0.709685	+	0.704520i	$0.751163\pi$
$182$	3551.25	1.44635
$183$	−6645.92	−2.68459
$184$	0	0
$185$	−3405.50	−1.35339
$186$	2998.44	1.18202
$187$	−1337.31	−0.522963
$188$	−2529.58	−0.981324
$189$	−1354.69	−0.521373
$190$	1115.12	0.425788
$191$	−1924.97	−0.729247	−0.364623	−	0.931155i	$-0.618802\pi$
$191$	−1924.97	−0.729247	−0.364623	+	0.931155i	$0.618802\pi$
$192$	−675.575	−0.253934
$193$	−1186.63	−0.442566	−0.221283	−	0.975210i	$-0.571024\pi$
$193$	−1186.63	−0.442566	−0.221283	+	0.975210i	$0.571024\pi$
$194$	−262.305	−0.0970744
$195$	7793.15	2.86194
$196$	−95.3073	−0.0347330
$197$	−3099.74	−1.12105	−0.560526	−	0.828137i	$-0.689401\pi$
$197$	−3099.74	−1.12105	−0.560526	+	0.828137i	$0.689401\pi$
$198$	3285.38	1.17920
$199$	−161.324	−0.0574671	−0.0287336	−	0.999587i	$-0.509147\pi$
$199$	−161.324	−0.0574671	−0.0287336	+	0.999587i	$0.509147\pi$
$200$	−2101.41	−0.742960
$201$	37.5260	0.0131686
$202$	4887.93	1.70254
$203$	1525.06	0.527282
$204$	−2136.69	−0.733323
$205$	1994.39	0.679483
$206$	619.399	0.209493
$207$	0	0
$208$	4319.53	1.43993
$209$	−431.837	−0.142922
$210$	9251.38	3.04003
$211$	5461.25	1.78184	0.890919	−	0.454162i	$-0.150061\pi$
$211$	5461.25	1.78184	0.890919	+	0.454162i	$0.150061\pi$
$212$	273.478	0.0885968
$213$	7341.12	2.36153
$214$	1494.38	0.477353
$215$	−5208.39	−1.65214
$216$	−811.166	−0.255523
$217$	−1878.33	−0.587600
$218$	−4248.45	−1.31991
$219$	2012.49	0.620965
$220$	−2240.34	−0.686561
$221$	2927.17	0.890962
$222$	5470.26	1.65378
$223$	3162.82	0.949768	0.474884	−	0.880048i	$-0.342490\pi$
$223$	3162.82	0.949768	0.474884	+	0.880048i	$0.342490\pi$
$224$	3575.81	1.06660
$225$	7106.57	2.10565
$226$	−1682.28	−0.495147
$227$	−165.443	−0.0483737	−0.0241868	−	0.999707i	$-0.507700\pi$
$227$	−165.443	−0.0483737	−0.0241868	+	0.999707i	$0.507700\pi$
$228$	−689.965	−0.200412
$229$	−3260.79	−0.940958	−0.470479	−	0.882411i	$-0.655919\pi$
$229$	−3260.79	−0.940958	−0.470479	+	0.882411i	$0.655919\pi$
$230$	0	0
$231$	−3582.64	−1.02043
$232$	913.180	0.258419
$233$	844.980	0.237581	0.118791	−	0.992919i	$-0.462098\pi$
$233$	844.980	0.237581	0.118791	+	0.992919i	$0.462098\pi$
$234$	−7191.17	−2.00898
$235$	9027.80	2.50599
$236$	1512.07	0.417064
$237$	1989.04	0.545155
$238$	3474.89	0.946402
$239$	−293.669	−0.0794807	−0.0397404	−	0.999210i	$-0.512653\pi$
$239$	−293.669	−0.0794807	−0.0397404	+	0.999210i	$0.512653\pi$
$240$	11252.8	3.02653
$241$	−2903.22	−0.775986	−0.387993	−	0.921662i	$-0.626832\pi$
$241$	−2903.22	−0.775986	−0.387993	+	0.921662i	$0.626832\pi$
$242$	−2548.90	−0.677063
$243$	−5095.70	−1.34522
$244$	−4181.86	−1.09720
$245$	340.141	0.0886971
$246$	−3203.59	−0.830299
$247$	945.223	0.243494
$248$	−1124.71	−0.287980
$249$	−7846.25	−1.99693
$250$	−4515.20	−1.14226
$251$	−2016.97	−0.507211	−0.253606	−	0.967308i	$-0.581617\pi$
$251$	−2016.97	−0.507211	−0.253606	+	0.967308i	$0.581617\pi$
$252$	−3288.28	−0.821993
$253$	0	0
$254$	−6838.30	−1.68926
$255$	7625.59	1.87268
$256$	5307.84	1.29586
$257$	−3725.70	−0.904290	−0.452145	−	0.891944i	$-0.649341\pi$
$257$	−3725.70	−0.904290	−0.452145	+	0.891944i	$0.649341\pi$
$258$	8366.26	2.01884
$259$	−3426.77	−0.822119
$260$	4903.74	1.16968
$261$	−3088.20	−0.732395
$262$	−2548.25	−0.600882
$263$	7530.22	1.76553	0.882763	−	0.469818i	$-0.155681\pi$
$263$	7530.22	1.76553	0.882763	+	0.469818i	$0.155681\pi$
$264$	−2145.22	−0.500110
$265$	−976.011	−0.226249
$266$	1122.09	0.258646
$267$	1168.15	0.267752
$268$	23.6128	0.00538201
$269$	−8722.82	−1.97710	−0.988549	−	0.150898i	$-0.951784\pi$
$269$	−8722.82	−1.97710	−0.988549	+	0.150898i	$0.951784\pi$
$270$	−4856.37	−1.09463
$271$	−2580.89	−0.578516	−0.289258	−	0.957251i	$-0.593409\pi$
$271$	−2580.89	−0.578516	−0.289258	+	0.957251i	$0.593409\pi$
$272$	4226.65	0.942200
$273$	7841.82	1.73849
$274$	9512.05	2.09724
$275$	4872.02	1.06834
$276$	0	0
$277$	7990.19	1.73316	0.866578	−	0.499042i	$-0.166315\pi$
$277$	7990.19	1.73316	0.866578	+	0.499042i	$0.166315\pi$
$278$	2273.73	0.490536
$279$	3803.56	0.816176
$280$	−3470.18	−0.740653
$281$	−6584.26	−1.39781	−0.698904	−	0.715215i	$-0.746329\pi$
$281$	−6584.26	−1.39781	−0.698904	+	0.715215i	$0.746329\pi$
$282$	−14501.4	−3.06222
$283$	4735.87	0.994764	0.497382	−	0.867532i	$-0.334295\pi$
$283$	4735.87	0.994764	0.497382	+	0.867532i	$0.334295\pi$
$284$	4619.30	0.965159
$285$	2462.41	0.511791
$286$	−4930.01	−1.01929
$287$	2006.84	0.412754
$288$	−7240.91	−1.48151
$289$	−2048.77	−0.417010
$290$	5467.11	1.10703
$291$	−579.220	−0.116682
$292$	1266.33	0.253789
$293$	5678.18	1.13216	0.566080	−	0.824351i	$-0.308459\pi$
$293$	5678.18	1.13216	0.566080	+	0.824351i	$0.308459\pi$
$294$	−546.369	−0.108384
$295$	−5396.39	−1.06505
$296$	−2051.89	−0.402917
$297$	1880.65	0.367429
$298$	−7006.79	−1.36206
$299$	0	0
$300$	7784.23	1.49808
$301$	−5240.92	−1.00359
$302$	−2654.80	−0.505850
$303$	10793.5	2.04643
$304$	1364.84	0.257497
$305$	14924.6	2.80190
$306$	−7036.55	−1.31455
$307$	−2537.04	−0.471649	−0.235825	−	0.971796i	$-0.575779\pi$
$307$	−2537.04	−0.471649	−0.235825	+	0.971796i	$0.575779\pi$
$308$	−2254.33	−0.417053
$309$	1367.75	0.251808
$310$	−6733.52	−1.23367
$311$	5513.84	1.00534	0.502670	−	0.864478i	$-0.332351\pi$
$311$	5513.84	1.00534	0.502670	+	0.864478i	$0.332351\pi$
$312$	4695.54	0.852028
$313$	−6355.70	−1.14775	−0.573875	−	0.818943i	$-0.694560\pi$
$313$	−6355.70	−1.14775	−0.573875	+	0.818943i	$0.694560\pi$
$314$	2860.11	0.514029
$315$	11735.5	2.09911
$316$	1251.58	0.222806
$317$	−7190.62	−1.27402	−0.637012	−	0.770854i	$-0.719830\pi$
$317$	−7190.62	−1.27402	−0.637012	+	0.770854i	$0.719830\pi$
$318$	1567.77	0.276466
$319$	−2117.16	−0.371594
$320$	1517.12	0.265030
$321$	3299.87	0.573771
$322$	0	0
$323$	924.900	0.159328
$324$	−1927.74	−0.330545
$325$	−10664.1	−1.82011
$326$	527.561	0.0896286
$327$	−9381.38	−1.58652
$328$	1201.66	0.202289
$329$	9084.19	1.52227
$330$	−12843.2	−2.14241
$331$	10164.5	1.68789	0.843945	−	0.536429i	$-0.180227\pi$
$331$	10164.5	1.68789	0.843945	+	0.536429i	$0.180227\pi$
$332$	−4937.16	−0.816149
$333$	6939.10	1.14192
$334$	−4259.89	−0.697877
$335$	−84.2713	−0.0137440
$336$	11323.1	1.83847
$337$	−8047.79	−1.30086	−0.650432	−	0.759565i	$-0.725412\pi$
$337$	−8047.79	−1.30086	−0.650432	+	0.759565i	$0.725412\pi$
$338$	2865.91	0.461198
$339$	−3714.78	−0.595160
$340$	4798.30	0.765366
$341$	2607.58	0.414101
$342$	−2272.20	−0.359259
$343$	6516.12	1.02577
$344$	−3138.17	−0.491857
$345$	0	0
$346$	−14838.5	−2.30556
$347$	1710.23	0.264581	0.132291	−	0.991211i	$-0.457767\pi$
$347$	1710.23	0.264581	0.132291	+	0.991211i	$0.457767\pi$
$348$	−3382.69	−0.521066
$349$	−3859.21	−0.591916	−0.295958	−	0.955201i	$-0.595639\pi$
$349$	−3859.21	−0.591916	−0.295958	+	0.955201i	$0.595639\pi$
$350$	−12659.5	−1.93337
$351$	−4116.45	−0.625982
$352$	−4964.11	−0.751671
$353$	7692.33	1.15983	0.579917	−	0.814676i	$-0.303085\pi$
$353$	7692.33	1.15983	0.579917	+	0.814676i	$0.303085\pi$
$354$	8668.24	1.30145
$355$	−16485.8	−2.46471
$356$	735.046	0.109431
$357$	7673.22	1.13756
$358$	8594.28	1.26878
$359$	−8290.75	−1.21885	−0.609427	−	0.792842i	$-0.708601\pi$
$359$	−8290.75	−1.21885	−0.609427	+	0.792842i	$0.708601\pi$
$360$	7027.00	1.02877
$361$	−6560.34	−0.956457
$362$	−12467.7	−1.81019
$363$	−5628.44	−0.813820
$364$	4934.37	0.710525
$365$	−4519.39	−0.648098
$366$	−23973.4	−3.42380
$367$	12121.9	1.72414	0.862071	−	0.506787i	$-0.169167\pi$
$367$	12121.9	1.72414	0.862071	+	0.506787i	$0.169167\pi$
$368$	0	0
$369$	−4063.80	−0.573314
$370$	−12284.4	−1.72605
$371$	−982.107	−0.137435
$372$	4166.25	0.580672
$373$	7792.45	1.08171	0.540855	−	0.841116i	$-0.318101\pi$
$373$	7792.45	1.08171	0.540855	+	0.841116i	$0.318101\pi$
$374$	−4824.01	−0.666962
$375$	−9970.41	−1.37299
$376$	5439.45	0.746059
$377$	4634.14	0.633077
$378$	−4886.70	−0.664934
$379$	7384.19	1.00079	0.500396	−	0.865796i	$-0.333188\pi$
$379$	7384.19	1.00079	0.500396	+	0.865796i	$0.333188\pi$
$380$	1549.44	0.209170
$381$	−15100.3	−2.03047
$382$	−6943.83	−0.930045
$383$	6643.95	0.886397	0.443199	−	0.896423i	$-0.353844\pi$
$383$	6643.95	0.886397	0.443199	+	0.896423i	$0.353844\pi$
$384$	10222.4	1.35850
$385$	8045.44	1.06502
$386$	−4280.44	−0.564427
$387$	10612.7	1.39399
$388$	−364.467	−0.0476882
$389$	−11183.0	−1.45759	−0.728795	−	0.684732i	$-0.759919\pi$
$389$	−11183.0	−1.45759	−0.728795	+	0.684732i	$0.759919\pi$
$390$	28111.7	3.64998
$391$	0	0
$392$	204.942	0.0264060
$393$	−5627.01	−0.722252
$394$	−11181.5	−1.42973
$395$	−4466.73	−0.568976
$396$	4564.95	0.579286
$397$	−10640.0	−1.34510	−0.672552	−	0.740050i	$-0.734802\pi$
$397$	−10640.0	−1.34510	−0.672552	+	0.740050i	$0.734802\pi$
$398$	−581.934	−0.0732908
$399$	2477.79	0.310888
$400$	−15398.3	−1.92478
$401$	−1399.46	−0.174278	−0.0871390	−	0.996196i	$-0.527772\pi$
$401$	−1399.46	−0.174278	−0.0871390	+	0.996196i	$0.527772\pi$
$402$	135.365	0.0167945
$403$	−5707.59	−0.705497
$404$	6791.65	0.836379
$405$	6879.87	0.844108
$406$	5501.26	0.672470
$407$	4757.20	0.579375
$408$	4594.58	0.557514
$409$	14465.1	1.74879	0.874394	−	0.485217i	$-0.161260\pi$
$409$	14465.1	1.74879	0.874394	+	0.485217i	$0.161260\pi$
$410$	7194.23	0.866580
$411$	21004.4	2.52085
$412$	860.639	0.102914
$413$	−5430.10	−0.646967
$414$	0	0
$415$	17620.1	2.08419
$416$	10865.7	1.28061
$417$	5020.81	0.589617
$418$	−1557.74	−0.182276
$419$	85.7506	0.00999806	0.00499903	−	0.999988i	$-0.498409\pi$
$419$	85.7506	0.00999806	0.00499903	+	0.999988i	$0.498409\pi$
$420$	12854.6	1.49342
$421$	−14663.2	−1.69749	−0.848744	−	0.528804i	$-0.822641\pi$
$421$	−14663.2	−1.69749	−0.848744	+	0.528804i	$0.822641\pi$
$422$	19700.0	2.27247
$423$	−18395.2	−2.11443
$424$	−588.068	−0.0673564
$425$	−10434.8	−1.19097
$426$	26481.2	3.01177
$427$	15017.8	1.70202
$428$	2076.40	0.234501
$429$	−10886.4	−1.22518
$430$	−18787.9	−2.10705
$431$	−2322.02	−0.259508	−0.129754	−	0.991546i	$-0.541419\pi$
$431$	−2322.02	−0.259508	−0.129754	+	0.991546i	$0.541419\pi$
$432$	−5943.90	−0.661981
$433$	8099.49	0.898929	0.449465	−	0.893298i	$-0.351615\pi$
$433$	8099.49	0.898929	0.449465	+	0.893298i	$0.351615\pi$
$434$	−6775.57	−0.749396
$435$	12072.4	1.33064
$436$	−5903.12	−0.648413
$437$	0	0
$438$	7259.52	0.791948
$439$	−5179.17	−0.563071	−0.281536	−	0.959551i	$-0.590844\pi$
$439$	−5179.17	−0.563071	−0.281536	+	0.959551i	$0.590844\pi$
$440$	4817.47	0.521963
$441$	−693.077	−0.0748382
$442$	10559.0	1.13629
$443$	−2338.11	−0.250760	−0.125380	−	0.992109i	$-0.540015\pi$
$443$	−2338.11	−0.250760	−0.125380	+	0.992109i	$0.540015\pi$
$444$	7600.79	0.812427
$445$	−2623.30	−0.279452
$446$	11409.1	1.21129
$447$	−15472.3	−1.63717
$448$	1526.60	0.160993
$449$	−3256.35	−0.342264	−0.171132	−	0.985248i	$-0.554743\pi$
$449$	−3256.35	−0.342264	−0.171132	+	0.985248i	$0.554743\pi$
$450$	25635.1	2.68544
$451$	−2786.00	−0.290881
$452$	−2337.48	−0.243243
$453$	−5862.30	−0.608024
$454$	−596.792	−0.0616935
$455$	−17610.2	−1.81446
$456$	1483.65	0.152365
$457$	−11038.7	−1.12991	−0.564957	−	0.825120i	$-0.691107\pi$
$457$	−11038.7	−1.12991	−0.564957	+	0.825120i	$0.691107\pi$
$458$	−11762.5	−1.20005
$459$	−4027.94	−0.409604
$460$	0	0
$461$	−2802.25	−0.283110	−0.141555	−	0.989930i	$-0.545210\pi$
$461$	−2802.25	−0.283110	−0.141555	+	0.989930i	$0.545210\pi$
$462$	−12923.4	−1.30141
$463$	11084.4	1.11260	0.556300	−	0.830981i	$-0.312220\pi$
$463$	11084.4	1.11260	0.556300	+	0.830981i	$0.312220\pi$
$464$	6691.41	0.669485
$465$	−14868.9	−1.48286
$466$	3048.04	0.303000
$467$	2673.91	0.264955	0.132478	−	0.991186i	$-0.457707\pi$
$467$	2673.91	0.264955	0.132478	+	0.991186i	$0.457707\pi$
$468$	−9991.95	−0.986919
$469$	−84.7976	−0.00834881
$470$	32565.4	3.19602
$471$	6315.66	0.617856
$472$	−3251.44	−0.317076
$473$	7275.70	0.707266
$474$	7174.93	0.695265
$475$	−3369.53	−0.325484
$476$	4828.27	0.464923
$477$	1988.74	0.190897
$478$	−1059.34	−0.101366
$479$	−14809.7	−1.41268	−0.706339	−	0.707873i	$-0.749655\pi$
$479$	−14809.7	−1.41268	−0.706339	+	0.707873i	$0.749655\pi$
$480$	28306.2	2.69166
$481$	−10412.8	−0.987071
$482$	−10472.6	−0.989655
$483$	0	0
$484$	−3541.63	−0.332610
$485$	1300.74	0.121781
$486$	−18381.4	−1.71563
$487$	646.489	0.0601545	0.0300772	−	0.999548i	$-0.490425\pi$
$487$	646.489	0.0601545	0.0300772	+	0.999548i	$0.490425\pi$
$488$	8992.39	0.834153
$489$	1164.96	0.107732
$490$	1226.97	0.113120
$491$	−5608.33	−0.515480	−0.257740	−	0.966214i	$-0.582978\pi$
$491$	−5608.33	−0.515480	−0.257740	+	0.966214i	$0.582978\pi$
$492$	−4451.31	−0.407887
$493$	4534.50	0.414246
$494$	3409.64	0.310541
$495$	−16291.8	−1.47931
$496$	−8241.41	−0.746069
$497$	−16588.7	−1.49720
$498$	−28303.3	−2.54679
$499$	16920.8	1.51799	0.758997	−	0.651095i	$-0.225690\pi$
$499$	16920.8	1.51799	0.758997	+	0.651095i	$0.225690\pi$
$500$	−6273.75	−0.561142
$501$	−9406.64	−0.838838
$502$	−7275.69	−0.646872
$503$	7925.06	0.702507	0.351254	−	0.936280i	$-0.385756\pi$
$503$	7925.06	0.702507	0.351254	+	0.936280i	$0.385756\pi$
$504$	7070.90	0.624926
$505$	−24238.6	−2.13585
$506$	0	0
$507$	6328.48	0.554354
$508$	−9501.64	−0.829857
$509$	12791.2	1.11387	0.556936	−	0.830556i	$-0.311977\pi$
$509$	12791.2	1.11387	0.556936	+	0.830556i	$0.311977\pi$
$510$	27507.3	2.38832
$511$	−4547.62	−0.393689
$512$	8879.87	0.766482
$513$	−1300.68	−0.111942
$514$	−13439.5	−1.15329
$515$	−3071.52	−0.262811
$516$	11624.7	0.991762
$517$	−12611.1	−1.07280
$518$	−12361.2	−1.04849
$519$	−32766.3	−2.77125
$520$	−10544.7	−0.889258
$521$	−12897.1	−1.08451	−0.542257	−	0.840213i	$-0.682430\pi$
$521$	−12897.1	−1.08451	−0.542257	+	0.840213i	$0.682430\pi$
$522$	−11139.9	−0.934061
$523$	−13529.3	−1.13116	−0.565579	−	0.824694i	$-0.691347\pi$
$523$	−13529.3	−1.13116	−0.565579	+	0.824694i	$0.691347\pi$
$524$	−3540.72	−0.295186
$525$	−27954.6	−2.32388
$526$	27163.3	2.25167
$527$	−5584.87	−0.461633
$528$	−15719.3	−1.29563
$529$	0	0
$530$	−3520.70	−0.288546
$531$	10995.8	0.898637
$532$	1559.12	0.127061
$533$	6098.11	0.495569
$534$	4213.81	0.341478
$535$	−7410.43	−0.598843
$536$	−50.7753	−0.00409171
$537$	18977.8	1.52505
$538$	−31465.3	−2.52150
$539$	−475.149	−0.0379705
$540$	−6747.80	−0.537739
$541$	1452.70	0.115446	0.0577230	−	0.998333i	$-0.481616\pi$
$541$	1452.70	0.115446	0.0577230	+	0.998333i	$0.481616\pi$
$542$	−9309.89	−0.737812
$543$	−27531.1	−2.17583
$544$	10632.0	0.837950
$545$	21067.5	1.65584
$546$	28287.3	2.21719
$547$	11532.8	0.901475	0.450738	−	0.892656i	$-0.351161\pi$
$547$	11532.8	0.901475	0.450738	+	0.892656i	$0.351161\pi$
$548$	13216.8	1.03028
$549$	−30410.6	−2.36410
$550$	17574.5	1.36251
$551$	1464.25	0.113211
$552$	0	0
$553$	−4494.63	−0.345626
$554$	28822.5	2.21038
$555$	−27126.3	−2.07468
$556$	3159.28	0.240977
$557$	−7753.70	−0.589829	−0.294914	−	0.955524i	$-0.595291\pi$
$557$	−7753.70	−0.589829	−0.294914	+	0.955524i	$0.595291\pi$
$558$	13720.3	1.04091
$559$	−15925.4	−1.20496
$560$	−25428.0	−1.91881
$561$	−10652.3	−0.801678
$562$	−23751.0	−1.78270
$563$	−6929.35	−0.518716	−0.259358	−	0.965781i	$-0.583511\pi$
$563$	−6929.35	−0.518716	−0.259358	+	0.965781i	$0.583511\pi$
$564$	−20149.3	−1.50432
$565$	8342.20	0.621166
$566$	17083.4	1.26867
$567$	6922.84	0.512755
$568$	−9933.04	−0.733769
$569$	−5737.87	−0.422749	−0.211374	−	0.977405i	$-0.567794\pi$
$569$	−5737.87	−0.422749	−0.211374	+	0.977405i	$0.567794\pi$
$570$	8882.49	0.652713
$571$	−12377.9	−0.907179	−0.453590	−	0.891211i	$-0.649857\pi$
$571$	−12377.9	−0.907179	−0.453590	+	0.891211i	$0.649857\pi$
$572$	−6850.13	−0.500731
$573$	−15333.3	−1.11790
$574$	7239.17	0.526406
$575$	0	0
$576$	−3091.32	−0.223620
$577$	−336.552	−0.0242822	−0.0121411	−	0.999926i	$-0.503865\pi$
$577$	−336.552	−0.0242822	−0.0121411	+	0.999926i	$0.503865\pi$
$578$	−7390.40	−0.531834
$579$	−9452.03	−0.678433
$580$	7596.42	0.543834
$581$	17730.2	1.26605
$582$	−2089.38	−0.148811
$583$	1363.41	0.0968552
$584$	−2723.03	−0.192945
$585$	35660.1	2.52028
$586$	20482.5	1.44390
$587$	−21603.9	−1.51906	−0.759530	−	0.650473i	$-0.774571\pi$
$587$	−21603.9	−1.51906	−0.759530	+	0.650473i	$0.774571\pi$
$588$	−759.166	−0.0532440
$589$	−1803.43	−0.126161
$590$	−19466.1	−1.35831
$591$	−24690.8	−1.71852
$592$	−15035.4	−1.04384
$593$	−1374.31	−0.0951706	−0.0475853	−	0.998867i	$-0.515153\pi$
$593$	−1374.31	−0.0951706	−0.0475853	+	0.998867i	$0.515153\pi$
$594$	6783.96	0.468601
$595$	−17231.6	−1.18727
$596$	−9735.76	−0.669114
$597$	−1285.02	−0.0880945
$598$	0	0
$599$	−4773.99	−0.325643	−0.162821	−	0.986656i	$-0.552059\pi$
$599$	−4773.99	−0.325643	−0.162821	+	0.986656i	$0.552059\pi$
$600$	−16738.7	−1.13892
$601$	−931.036	−0.0631909	−0.0315955	−	0.999501i	$-0.510059\pi$
$601$	−931.036	−0.0631909	−0.0315955	+	0.999501i	$0.510059\pi$
$602$	−18905.3	−1.27993
$603$	171.713	0.0115965
$604$	−3688.78	−0.248501
$605$	12639.7	0.849381
$606$	38934.6	2.60992
$607$	5599.19	0.374406	0.187203	−	0.982321i	$-0.440058\pi$
$607$	5599.19	0.374406	0.187203	+	0.982321i	$0.440058\pi$
$608$	3433.23	0.229006
$609$	12147.8	0.808300
$610$	53836.5	3.57341
$611$	27603.7	1.82770
$612$	−9777.11	−0.645778
$613$	3560.82	0.234617	0.117308	−	0.993096i	$-0.462573\pi$
$613$	3560.82	0.234617	0.117308	+	0.993096i	$0.462573\pi$
$614$	−9151.69	−0.601518
$615$	15886.2	1.04162
$616$	4847.56	0.317068
$617$	14730.8	0.961167	0.480584	−	0.876949i	$-0.340425\pi$
$617$	14730.8	0.961167	0.480584	+	0.876949i	$0.340425\pi$
$618$	4933.80	0.321143
$619$	27103.3	1.75989	0.879945	−	0.475076i	$-0.157579\pi$
$619$	27103.3	1.75989	0.879945	+	0.475076i	$0.157579\pi$
$620$	−9356.05	−0.606045
$621$	0	0
$622$	19889.7	1.28216
$623$	−2639.68	−0.169754
$624$	34407.0	2.20735
$625$	−1981.58	−0.126821
$626$	−22926.5	−1.46378
$627$	−3439.78	−0.219094
$628$	3974.05	0.252519
$629$	−10188.9	−0.645878
$630$	42332.7	2.67710
$631$	12462.3	0.786238	0.393119	−	0.919488i	$-0.371396\pi$
$631$	12462.3	0.786238	0.393119	+	0.919488i	$0.371396\pi$
$632$	−2691.30	−0.169390
$633$	43501.4	2.73148
$634$	−25938.3	−1.62483
$635$	33910.3	2.11919
$636$	2178.38	0.135815
$637$	1040.03	0.0646897
$638$	−7637.11	−0.473913
$639$	33591.7	2.07960
$640$	−22956.3	−1.41786
$641$	8849.87	0.545318	0.272659	−	0.962111i	$-0.412097\pi$
$641$	8849.87	0.545318	0.272659	+	0.962111i	$0.412097\pi$
$642$	11903.4	0.731760
$643$	25367.3	1.55581	0.777906	−	0.628380i	$-0.216282\pi$
$643$	25367.3	1.55581	0.777906	+	0.628380i	$0.216282\pi$
$644$	0	0
$645$	−41487.2	−2.53265
$646$	3336.33	0.203199
$647$	25619.6	1.55674	0.778371	−	0.627805i	$-0.216046\pi$
$647$	25619.6	1.55674	0.778371	+	0.627805i	$0.216046\pi$
$648$	4145.27	0.251299
$649$	7538.32	0.455940
$650$	−38467.8	−2.32128
$651$	−14961.7	−0.900764
$652$	733.033	0.0440304
$653$	5631.72	0.337498	0.168749	−	0.985659i	$-0.446027\pi$
$653$	5631.72	0.337498	0.168749	+	0.985659i	$0.446027\pi$
$654$	−33840.9	−2.02337
$655$	12636.4	0.753811
$656$	8805.29	0.524069
$657$	9208.80	0.546833
$658$	32768.8	1.94143
$659$	7120.69	0.420915	0.210457	−	0.977603i	$-0.432505\pi$
$659$	7120.69	0.420915	0.210457	+	0.977603i	$0.432505\pi$
$660$	−17845.3	−1.05247
$661$	24152.7	1.42123	0.710613	−	0.703583i	$-0.248418\pi$
$661$	24152.7	1.42123	0.710613	+	0.703583i	$0.248418\pi$
$662$	36665.8	2.15265
$663$	23316.3	1.36580
$664$	10616.5	0.620484
$665$	−5564.31	−0.324473
$666$	25031.0	1.45635
$667$	0	0
$668$	−5919.01	−0.342834
$669$	25193.4	1.45595
$670$	−303.986	−0.0175284
$671$	−20848.4	−1.19947
$672$	28483.0	1.63505
$673$	−5852.26	−0.335198	−0.167599	−	0.985855i	$-0.553601\pi$
$673$	−5852.26	−0.335198	−0.167599	+	0.985855i	$0.553601\pi$
$674$	−29030.3	−1.65906
$675$	14674.3	0.836763
$676$	3982.11	0.226565
$677$	−24338.0	−1.38166	−0.690832	−	0.723015i	$-0.742756\pi$
$677$	−24338.0	−1.38166	−0.690832	+	0.723015i	$0.742756\pi$
$678$	−13400.1	−0.759038
$679$	1308.87	0.0739759
$680$	−10317.9	−0.581875
$681$	−1317.83	−0.0741547
$682$	9406.18	0.528125
$683$	8464.54	0.474212	0.237106	−	0.971484i	$-0.423801\pi$
$683$	8464.54	0.474212	0.237106	+	0.971484i	$0.423801\pi$
$684$	−3157.16	−0.176487
$685$	−47169.1	−2.63101
$686$	23505.2	1.30821
$687$	−25973.7	−1.44245
$688$	−22995.2	−1.27425
$689$	−2984.28	−0.165010
$690$	0	0
$691$	−2234.24	−0.123002	−0.0615011	−	0.998107i	$-0.519589\pi$
$691$	−2234.24	−0.123002	−0.0615011	+	0.998107i	$0.519589\pi$
$692$	−20617.8	−1.13262
$693$	−16393.5	−0.898613
$694$	6169.19	0.337434
$695$	−11275.1	−0.615381
$696$	7273.90	0.396144
$697$	5966.99	0.324270
$698$	−13921.1	−0.754901
$699$	6730.66	0.364201
$700$	−17590.1	−0.949774
$701$	−13502.0	−0.727479	−0.363739	−	0.931501i	$-0.618500\pi$
$701$	−13502.0	−0.727479	−0.363739	+	0.931501i	$0.618500\pi$
$702$	−14849.0	−0.798347
$703$	−3290.13	−0.176514
$704$	−2119.30	−0.113457
$705$	71910.6	3.84157
$706$	27748.1	1.47919
$707$	−24390.0	−1.29743
$708$	12044.3	0.639340
$709$	12150.5	0.643612	0.321806	−	0.946806i	$-0.395710\pi$
$709$	12150.5	0.643612	0.321806	+	0.946806i	$0.395710\pi$
$710$	−59468.1	−3.14338
$711$	9101.49	0.480074
$712$	−1580.59	−0.0831956
$713$	0	0
$714$	27679.1	1.45079
$715$	24447.3	1.27871
$716$	11941.5	0.623291
$717$	−2339.21	−0.121840
$718$	−29906.7	−1.55447
$719$	−19023.2	−0.986712	−0.493356	−	0.869827i	$-0.664230\pi$
$719$	−19023.2	−0.986712	−0.493356	+	0.869827i	$0.664230\pi$
$720$	51491.0	2.66522
$721$	−3090.71	−0.159645
$722$	−23664.7	−1.21982
$723$	−23125.5	−1.18955
$724$	−17323.6	−0.889264
$725$	−16519.8	−0.846247
$726$	−20303.1	−1.03791
$727$	5323.19	0.271563	0.135781	−	0.990739i	$-0.456646\pi$
$727$	5323.19	0.271563	0.135781	+	0.990739i	$0.456646\pi$
$728$	−10610.5	−0.540182
$729$	−30205.1	−1.53458
$730$	−16302.5	−0.826553
$731$	−15582.9	−0.788448
$732$	−33310.5	−1.68195
$733$	27879.3	1.40484	0.702420	−	0.711763i	$-0.252103\pi$
$733$	27879.3	1.40484	0.702420	+	0.711763i	$0.252103\pi$
$734$	43726.7	2.19889
$735$	2709.38	0.135969
$736$	0	0
$737$	117.720	0.00588369
$738$	−14659.1	−0.731177
$739$	−3163.82	−0.157487	−0.0787437	−	0.996895i	$-0.525091\pi$
$739$	−3163.82	−0.157487	−0.0787437	+	0.996895i	$0.525091\pi$
$740$	−17068.9	−0.847927
$741$	7529.14	0.373266
$742$	−3542.69	−0.175278
$743$	−15214.0	−0.751208	−0.375604	−	0.926780i	$-0.622565\pi$
$743$	−15214.0	−0.751208	−0.375604	+	0.926780i	$0.622565\pi$
$744$	−8958.83	−0.441460
$745$	34745.8	1.70871
$746$	28109.2	1.37956
$747$	−35903.1	−1.75854
$748$	−6702.84	−0.327647
$749$	−7456.72	−0.363768
$750$	−35965.6	−1.75104
$751$	−23732.0	−1.15312	−0.576560	−	0.817055i	$-0.695605\pi$
$751$	−23732.0	−1.15312	−0.576560	+	0.817055i	$0.695605\pi$
$752$	39858.1	1.93281
$753$	−16066.1	−0.777532
$754$	16716.4	0.807396
$755$	13164.8	0.634592
$756$	−6789.95	−0.326651
$757$	−30642.3	−1.47122	−0.735609	−	0.677407i	$-0.763104\pi$
$757$	−30642.3	−1.47122	−0.735609	+	0.677407i	$0.763104\pi$
$758$	26636.5	1.27636
$759$	0	0
$760$	−3331.81	−0.159023
$761$	6637.64	0.316182	0.158091	−	0.987425i	$-0.449466\pi$
$761$	6637.64	0.316182	0.158091	+	0.987425i	$0.449466\pi$
$762$	−54470.2	−2.58956
$763$	21199.1	1.00585
$764$	−9648.28	−0.456888
$765$	34893.4	1.64912
$766$	23966.3	1.13047
$767$	−16500.2	−0.776776
$768$	42279.4	1.98649
$769$	25832.8	1.21138	0.605692	−	0.795699i	$-0.292896\pi$
$769$	25832.8	1.21138	0.605692	+	0.795699i	$0.292896\pi$
$770$	29021.8	1.35828
$771$	−29676.9	−1.38624
$772$	−5947.57	−0.277277
$773$	20840.7	0.969713	0.484856	−	0.874594i	$-0.338872\pi$
$773$	20840.7	0.969713	0.484856	+	0.874594i	$0.338872\pi$
$774$	38282.6	1.77783
$775$	20346.4	0.943052
$776$	783.725	0.0362553
$777$	−27295.8	−1.26027
$778$	−40339.9	−1.85894
$779$	1926.82	0.0886208
$780$	39060.6	1.79307
$781$	23029.3	1.05512
$782$	0	0
$783$	−6376.82	−0.291046
$784$	1501.73	0.0684099
$785$	−14182.9	−0.644854
$786$	−20298.0	−0.921125
$787$	15519.8	0.702948	0.351474	−	0.936198i	$-0.385681\pi$
$787$	15519.8	0.702948	0.351474	+	0.936198i	$0.385681\pi$
$788$	−15536.4	−0.702362
$789$	59981.7	2.70647
$790$	−16112.6	−0.725645
$791$	8394.30	0.377329
$792$	−9816.16	−0.440406
$793$	45633.9	2.04352
$794$	−38381.0	−1.71548
$795$	−7774.38	−0.346829
$796$	−808.583	−0.0360044
$797$	4581.96	0.203640	0.101820	−	0.994803i	$-0.467533\pi$
$797$	4581.96	0.203640	0.101820	+	0.994803i	$0.467533\pi$
$798$	8937.97	0.396492
$799$	27010.2	1.19594
$800$	−38733.9	−1.71181
$801$	5345.27	0.235788
$802$	−5048.17	−0.222266
$803$	6313.23	0.277446
$804$	188.087	0.00825038
$805$	0	0
$806$	−20588.6	−0.899756
$807$	−69481.3	−3.03080
$808$	−14604.3	−0.635864
$809$	−24783.3	−1.07705	−0.538526	−	0.842609i	$-0.681019\pi$
$809$	−24783.3	−1.07705	−0.538526	+	0.842609i	$0.681019\pi$
$810$	24817.3	1.07653
$811$	−5141.97	−0.222638	−0.111319	−	0.993785i	$-0.535507\pi$
$811$	−5141.97	−0.222638	−0.111319	+	0.993785i	$0.535507\pi$
$812$	7643.86	0.330353
$813$	−20558.0	−0.886839
$814$	17160.4	0.738907
$815$	−2616.11	−0.112440
$816$	33667.2	1.44435
$817$	−5031.94	−0.215478
$818$	52179.1	2.23032
$819$	35882.9	1.53095
$820$	9996.20	0.425710
$821$	−288.654	−0.0122705	−0.00613526	−	0.999981i	$-0.501953\pi$
$821$	−288.654	−0.0122705	−0.00613526	+	0.999981i	$0.501953\pi$
$822$	75767.9	3.21498
$823$	28522.8	1.20807	0.604035	−	0.796958i	$-0.293559\pi$
$823$	28522.8	1.20807	0.604035	+	0.796958i	$0.293559\pi$
$824$	−1850.66	−0.0782413
$825$	38807.9	1.63772
$826$	−19587.7	−0.825111
$827$	−30103.4	−1.26578	−0.632889	−	0.774243i	$-0.718131\pi$
$827$	−30103.4	−1.26578	−0.632889	+	0.774243i	$0.718131\pi$
$828$	0	0
$829$	40724.8	1.70619	0.853095	−	0.521756i	$-0.174723\pi$
$829$	40724.8	1.70619	0.853095	+	0.521756i	$0.174723\pi$
$830$	63560.0	2.65807
$831$	63645.6	2.65685
$832$	4638.81	0.193295
$833$	1017.66	0.0423289
$834$	18111.3	0.751969
$835$	21124.3	0.875492
$836$	−2164.44	−0.0895439
$837$	7853.94	0.324339
$838$	309.323	0.0127510
$839$	−35857.6	−1.47549	−0.737747	−	0.675077i	$-0.764110\pi$
$839$	−35857.6	−1.47549	−0.737747	+	0.675077i	$0.764110\pi$
$840$	−27641.6	−1.13539
$841$	−17210.2	−0.705655
$842$	−52893.8	−2.16489
$843$	−52446.7	−2.14278
$844$	27372.7	1.11636
$845$	−14211.7	−0.578577
$846$	−66355.9	−2.69665
$847$	12718.6	0.515958
$848$	−4309.12	−0.174500
$849$	37723.4	1.52493
$850$	−37640.7	−1.51890
$851$	0	0
$852$	36794.9	1.47954
$853$	−6769.13	−0.271712	−0.135856	−	0.990729i	$-0.543379\pi$
$853$	−6769.13	−0.271712	−0.135856	+	0.990729i	$0.543379\pi$
$854$	54172.8	2.17067
$855$	11267.6	0.450693
$856$	−4464.95	−0.178281
$857$	−11441.8	−0.456060	−0.228030	−	0.973654i	$-0.573228\pi$
$857$	−11441.8	−0.456060	−0.228030	+	0.973654i	$0.573228\pi$
$858$	−39269.8	−1.56253
$859$	11667.5	0.463433	0.231717	−	0.972783i	$-0.425566\pi$
$859$	11667.5	0.463433	0.231717	+	0.972783i	$0.425566\pi$
$860$	−26105.3	−1.03510
$861$	15985.4	0.632732
$862$	−8376.08	−0.330963
$863$	24351.0	0.960506	0.480253	−	0.877130i	$-0.340545\pi$
$863$	24351.0	0.960506	0.480253	+	0.877130i	$0.340545\pi$
$864$	−14951.7	−0.588736
$865$	73582.4	2.89234
$866$	29216.8	1.14645
$867$	−16319.4	−0.639257
$868$	−9414.49	−0.368144
$869$	6239.66	0.243574
$870$	43548.1	1.69703
$871$	−257.671	−0.0100239
$872$	12693.7	0.492961
$873$	−2650.41	−0.102752
$874$	0	0
$875$	22530.2	0.870467
$876$	10086.9	0.389047
$877$	27991.1	1.07776	0.538878	−	0.842384i	$-0.318848\pi$
$877$	27991.1	1.07776	0.538878	+	0.842384i	$0.318848\pi$
$878$	−18682.5	−0.718114
$879$	45229.3	1.73555
$880$	35300.4	1.35225
$881$	8327.99	0.318476	0.159238	−	0.987240i	$-0.449096\pi$
$881$	8327.99	0.318476	0.159238	+	0.987240i	$0.449096\pi$
$882$	−2500.09	−0.0954450
$883$	−34929.3	−1.33122	−0.665608	−	0.746302i	$-0.731828\pi$
$883$	−34929.3	−1.33122	−0.665608	+	0.746302i	$0.731828\pi$
$884$	14671.5	0.558207
$885$	−42984.7	−1.63267
$886$	−8434.11	−0.319808
$887$	29292.1	1.10883	0.554416	−	0.832240i	$-0.312942\pi$
$887$	29292.1	1.10883	0.554416	+	0.832240i	$0.312942\pi$
$888$	−16344.2	−0.617653
$889$	34122.1	1.28731
$890$	−9462.85	−0.356399
$891$	−9610.62	−0.361356
$892$	15852.6	0.595050
$893$	8721.96	0.326841
$894$	−55812.3	−2.08797
$895$	−42618.0	−1.59169
$896$	−23099.7	−0.861280
$897$	0	0
$898$	−11746.4	−0.436507
$899$	−8841.66	−0.328016
$900$	35619.3	1.31923
$901$	−2920.12	−0.107973
$902$	−10049.8	−0.370976
$903$	−41746.4	−1.53846
$904$	5026.36	0.184927
$905$	61826.0	2.27090
$906$	−21146.7	−0.775445
$907$	48915.0	1.79074	0.895368	−	0.445327i	$-0.146913\pi$
$907$	48915.0	1.79074	0.895368	+	0.445327i	$0.146913\pi$
$908$	−829.227	−0.0303071
$909$	49389.1	1.80212
$910$	−63524.2	−2.31407
$911$	−36674.2	−1.33378	−0.666888	−	0.745158i	$-0.732374\pi$
$911$	−36674.2	−1.33378	−0.666888	+	0.745158i	$0.732374\pi$
$912$	10871.6	0.394731
$913$	−24613.9	−0.892225
$914$	−39819.4	−1.44104
$915$	118881.	4.29518
$916$	−16343.6	−0.589530
$917$	12715.4	0.457904
$918$	−14529.7	−0.522389
$919$	18591.9	0.667345	0.333673	−	0.942689i	$-0.391712\pi$
$919$	18591.9	0.667345	0.333673	+	0.942689i	$0.391712\pi$
$920$	0	0
$921$	−20208.7	−0.723017
$922$	−10108.4	−0.361065
$923$	−50407.4	−1.79760
$924$	−17956.8	−0.639323
$925$	37119.4	1.31944
$926$	39983.9	1.41896
$927$	6258.59	0.221747
$928$	16832.1	0.595409
$929$	−1425.50	−0.0503434	−0.0251717	−	0.999683i	$-0.508013\pi$
$929$	−1425.50	−0.0503434	−0.0251717	+	0.999683i	$0.508013\pi$
$930$	−53635.6	−1.89116
$931$	328.618	0.0115682
$932$	4235.18	0.148850
$933$	43920.3	1.54114
$934$	9645.45	0.337911
$935$	23921.7	0.836708
$936$	21486.0	0.750312
$937$	−12145.8	−0.423465	−0.211733	−	0.977328i	$-0.567911\pi$
$937$	−12145.8	−0.423465	−0.211733	+	0.977328i	$0.567911\pi$
$938$	−305.885	−0.0106477
$939$	−50626.1	−1.75945
$940$	45248.8	1.57006
$941$	−9805.30	−0.339685	−0.169843	−	0.985471i	$-0.554326\pi$
$941$	−9805.30	−0.339685	−0.169843	+	0.985471i	$0.554326\pi$
$942$	22782.1	0.787983
$943$	0	0
$944$	−23825.3	−0.821447
$945$	24232.6	0.834164
$946$	26245.2	0.902013
$947$	−18463.8	−0.633571	−0.316786	−	0.948497i	$-0.602604\pi$
$947$	−18463.8	−0.633571	−0.316786	+	0.948497i	$0.602604\pi$
$948$	9969.38	0.341551
$949$	−13818.7	−0.472679
$950$	−12154.7	−0.415106
$951$	−57276.6	−1.95302
$952$	−10382.4	−0.353461
$953$	−44610.8	−1.51635	−0.758177	−	0.652048i	$-0.773910\pi$
$953$	−44610.8	−1.51635	−0.758177	+	0.652048i	$0.773910\pi$
$954$	7173.85	0.243461
$955$	34433.6	1.16675
$956$	−1471.92	−0.0497963
$957$	−16864.2	−0.569636
$958$	−53422.2	−1.80166
$959$	−47463.7	−1.59821
$960$	12084.6	0.406279
$961$	−18901.2	−0.634462
$962$	−37561.3	−1.25886
$963$	15099.6	0.505274
$964$	−14551.4	−0.486171
$965$	21226.2	0.708078
$966$	0	0
$967$	17717.8	0.589211	0.294606	−	0.955619i	$-0.404812\pi$
$967$	17717.8	0.589211	0.294606	+	0.955619i	$0.404812\pi$
$968$	7615.68	0.252869
$969$	7367.25	0.244242
$970$	4692.08	0.155313
$971$	12761.2	0.421757	0.210879	−	0.977512i	$-0.432368\pi$
$971$	12761.2	0.421757	0.210879	+	0.977512i	$0.432368\pi$
$972$	−25540.5	−0.842810
$973$	−11345.5	−0.373815
$974$	2332.04	0.0767181
$975$	−84944.3	−2.79015
$976$	65892.6	2.16104
$977$	58418.8	1.91298	0.956490	−	0.291765i	$-0.0942426\pi$
$977$	58418.8	1.91298	0.956490	+	0.291765i	$0.0942426\pi$
$978$	4202.27	0.137397
$979$	3664.53	0.119631
$980$	1704.84	0.0555706
$981$	−42927.6	−1.39712
$982$	−20230.6	−0.657418
$983$	−53539.3	−1.73717	−0.868585	−	0.495540i	$-0.834970\pi$
$983$	−53539.3	−1.73717	−0.868585	+	0.495540i	$0.834970\pi$
$984$	9571.80	0.310099
$985$	55447.6	1.79361
$986$	16357.0	0.528310
$987$	72359.8	2.33357
$988$	4737.61	0.152554
$989$	0	0
$990$	−58768.3	−1.88665
$991$	−30861.6	−0.989255	−0.494628	−	0.869105i	$-0.664696\pi$
$991$	−30861.6	−0.989255	−0.494628	+	0.869105i	$0.664696\pi$
$992$	−20731.1	−0.663520
$993$	80965.0	2.58746
$994$	−59839.5	−1.90945
$995$	2885.74	0.0919438
$996$	−39326.7	−1.25112
$997$	−17788.1	−0.565050	−0.282525	−	0.959260i	$-0.591172\pi$
$997$	−17788.1	−0.565050	−0.282525	+	0.959260i	$0.591172\pi$
$998$	61037.3	1.93597
$999$	14328.5	0.453788

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.4.a.m.1.20		25
23.11	odd	22		23.4.c.a.6.4	yes	50
23.21	odd	22		23.4.c.a.4.4	✓	50
23.22	odd	2		529.4.a.n.1.20		25
69.11	even	22		207.4.i.a.190.2		50
69.44	even	22		207.4.i.a.73.2		50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.c.a.4.4	✓	50	23.21	odd	22
23.4.c.a.6.4	yes	50	23.11	odd	22
207.4.i.a.73.2		50	69.44	even	22
207.4.i.a.190.2		50	69.11	even	22
529.4.a.m.1.20		25	1.1	even	1	trivial
529.4.a.n.1.20		25	23.22	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 529 = 23^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	529.a (trivial)

\(f(q)\)	\(=\)	\(q+3.60724 q^{2} +7.96546 q^{3} +5.01217 q^{4} -17.8878 q^{5} +28.7333 q^{6} -17.9996 q^{7} -10.7778 q^{8} +36.4486 q^{9} -64.5257 q^{10} +24.9879 q^{11} +39.9242 q^{12} -54.6945 q^{13} -64.9288 q^{14} -142.485 q^{15} -78.9755 q^{16} -53.5185 q^{17} +131.479 q^{18} -17.2819 q^{19} -89.6569 q^{20} -143.375 q^{21} +90.1372 q^{22} -85.8504 q^{24} +194.975 q^{25} -197.296 q^{26} +75.2625 q^{27} -90.2169 q^{28} -84.7276 q^{29} -513.977 q^{30} +104.354 q^{31} -198.661 q^{32} +199.040 q^{33} -193.054 q^{34} +321.974 q^{35} +182.687 q^{36} +190.380 q^{37} -62.3398 q^{38} -435.667 q^{39} +192.792 q^{40} -111.494 q^{41} -517.188 q^{42} +291.169 q^{43} +125.243 q^{44} -651.987 q^{45} -504.689 q^{47} -629.077 q^{48} -19.0152 q^{49} +703.322 q^{50} -426.300 q^{51} -274.138 q^{52} +54.5628 q^{53} +271.490 q^{54} -446.979 q^{55} +193.996 q^{56} -137.658 q^{57} -305.633 q^{58} +301.679 q^{59} -714.159 q^{60} -834.342 q^{61} +376.430 q^{62} -656.060 q^{63} -84.8130 q^{64} +978.367 q^{65} +717.985 q^{66} +4.71109 q^{67} -268.244 q^{68} +1161.44 q^{70} +921.618 q^{71} -392.837 q^{72} +252.652 q^{73} +686.747 q^{74} +1553.07 q^{75} -86.6196 q^{76} -449.771 q^{77} -1571.56 q^{78} +249.708 q^{79} +1412.70 q^{80} -384.611 q^{81} -402.185 q^{82} -985.034 q^{83} -718.619 q^{84} +957.331 q^{85} +1050.32 q^{86} -674.895 q^{87} -269.315 q^{88} +146.652 q^{89} -2351.87 q^{90} +984.478 q^{91} +831.228 q^{93} -1820.53 q^{94} +309.135 q^{95} -1582.43 q^{96} -72.7164 q^{97} -68.5923 q^{98} +910.773 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19}+ \cdots - 7317 q^{99}+O(q^{100}) \) 25 * q - q^3 + 80 * q^4 - 51 * q^5 + 86 * q^6 - 73 * q^7 + 3 * q^8 + 166 * q^9 - 139 * q^10 - 221 * q^11 - 191 * q^12 - 27 * q^13 - 372 * q^14 - 310 * q^15 + 152 * q^16 - 365 * q^17 - 538 * q^18 - 405 * q^19 - 578 * q^20 - 352 * q^21 - 155 * q^22 + 803 * q^24 + 90 * q^25 - 850 * q^26 + 368 * q^27 - 459 * q^28 + 175 * q^29 - 893 * q^30 + 287 * q^31 + 164 * q^32 - 1020 * q^33 - 335 * q^34 + 462 * q^35 - 1092 * q^36 - 471 * q^37 - 810 * q^38 - 822 * q^39 - 1405 * q^40 - 73 * q^41 - 556 * q^42 - 901 * q^43 - 2073 * q^44 - 1384 * q^45 + 1452 * q^47 - 4028 * q^48 - 1092 * q^49 + 364 * q^50 - 2214 * q^51 + 1287 * q^52 - 2071 * q^53 + 2052 * q^54 + 1006 * q^55 - 4879 * q^56 - 418 * q^57 + 2796 * q^58 - 2713 * q^59 - 2805 * q^60 - 1225 * q^61 - 2852 * q^62 - 4003 * q^63 + 217 * q^64 - 2030 * q^65 - 2933 * q^66 - 767 * q^67 - 4175 * q^68 + 4851 * q^70 - 1683 * q^71 - 5265 * q^72 + 2203 * q^73 - 3089 * q^74 + 2333 * q^75 - 5252 * q^76 + 2760 * q^77 - 692 * q^78 - 5425 * q^79 - 4689 * q^80 + 1929 * q^81 - 2725 * q^82 - 5425 * q^83 - 4317 * q^84 - 912 * q^85 - 4359 * q^86 - 4404 * q^87 - 2610 * q^88 - 4933 * q^89 - 2695 * q^90 - 3619 * q^91 + 6375 * q^93 - 5117 * q^94 - 1338 * q^95 + 20 * q^96 - 2085 * q^97 + 5951 * q^98 - 7317 * q^99

Introduction

L-functions

Modular forms

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Database

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