LMFDB - Embedded newform 529.4.a.m.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [529,4,Mod(1,529)]

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

lf = mfeigenbasis(mf)

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")

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

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			1.19
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)

$f(q)$	$=$	\(q+2.60332 q^{2} -3.42880 q^{3} -1.22274 q^{4} +15.6832 q^{5} -8.92624 q^{6} +5.94573 q^{7} -24.0097 q^{8} -15.2434 q^{9} +40.8282 q^{10} +21.8696 q^{11} +4.19253 q^{12} -34.3301 q^{13} +15.4786 q^{14} -53.7743 q^{15} -52.7230 q^{16} -129.408 q^{17} -39.6833 q^{18} +27.9061 q^{19} -19.1764 q^{20} -20.3867 q^{21} +56.9335 q^{22} +82.3244 q^{24} +120.961 q^{25} -89.3721 q^{26} +144.844 q^{27} -7.27009 q^{28} +12.5587 q^{29} -139.992 q^{30} +15.7988 q^{31} +54.8232 q^{32} -74.9864 q^{33} -336.891 q^{34} +93.2477 q^{35} +18.6387 q^{36} +236.142 q^{37} +72.6483 q^{38} +117.711 q^{39} -376.548 q^{40} -377.108 q^{41} -53.0730 q^{42} -474.145 q^{43} -26.7409 q^{44} -239.064 q^{45} -547.089 q^{47} +180.776 q^{48} -307.648 q^{49} +314.900 q^{50} +443.715 q^{51} +41.9768 q^{52} -463.871 q^{53} +377.074 q^{54} +342.984 q^{55} -142.755 q^{56} -95.6842 q^{57} +32.6943 q^{58} -597.203 q^{59} +65.7521 q^{60} -277.251 q^{61} +41.1292 q^{62} -90.6328 q^{63} +564.506 q^{64} -538.404 q^{65} -195.213 q^{66} +171.626 q^{67} +158.233 q^{68} +242.753 q^{70} +227.710 q^{71} +365.989 q^{72} +932.242 q^{73} +614.754 q^{74} -414.751 q^{75} -34.1219 q^{76} +130.031 q^{77} +306.439 q^{78} -234.256 q^{79} -826.862 q^{80} -85.0692 q^{81} -981.731 q^{82} -912.812 q^{83} +24.9276 q^{84} -2029.53 q^{85} -1234.35 q^{86} -43.0612 q^{87} -525.083 q^{88} +689.993 q^{89} -622.359 q^{90} -204.117 q^{91} -54.1708 q^{93} -1424.25 q^{94} +437.655 q^{95} -187.977 q^{96} -86.1031 q^{97} -800.906 q^{98} -333.366 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.60332	0.920411	0.460206	−	0.887812i	$-0.347776\pi$
$2$	2.60332	0.920411	0.460206	+	0.887812i	$0.347776\pi$
$3$	−3.42880	−0.659872	−0.329936	−	0.944003i	$-0.607027\pi$
$3$	−3.42880	−0.659872	−0.329936	+	0.944003i	$0.607027\pi$
$4$	−1.22274	−0.152843
$5$	15.6832	1.40274	0.701372	−	0.712796i	$-0.252571\pi$
$5$	15.6832	1.40274	0.701372	+	0.712796i	$0.252571\pi$
$6$	−8.92624	−0.607354
$7$	5.94573	0.321039	0.160520	−	0.987033i	$-0.448683\pi$
$7$	5.94573	0.321039	0.160520	+	0.987033i	$0.448683\pi$
$8$	−24.0097	−1.06109
$9$	−15.2434	−0.564569
$10$	40.8282	1.29110
$11$	21.8696	0.599449	0.299724	−	0.954026i	$-0.403105\pi$
$11$	21.8696	0.599449	0.299724	+	0.954026i	$0.403105\pi$
$12$	4.19253	0.100857
$13$	−34.3301	−0.732419	−0.366210	−	0.930532i	$-0.619345\pi$
$13$	−34.3301	−0.732419	−0.366210	+	0.930532i	$0.619345\pi$
$14$	15.4786	0.295488
$15$	−53.7743	−0.925631
$16$	−52.7230	−0.823796
$17$	−129.408	−1.84624	−0.923122	−	0.384507i	$-0.874372\pi$
$17$	−129.408	−1.84624	−0.923122	+	0.384507i	$0.874372\pi$
$18$	−39.6833	−0.519636
$19$	27.9061	0.336952	0.168476	−	0.985706i	$-0.446115\pi$
$19$	27.9061	0.336952	0.168476	+	0.985706i	$0.446115\pi$
$20$	−19.1764	−0.214399
$21$	−20.3867	−0.211845
$22$	56.9335	0.551740
$23$	0	0
$23$	0	0
$24$	82.3244	0.700183
$25$	120.961	0.967690
$26$	−89.3721	−0.674127
$27$	144.844	1.03242
$28$	−7.27009	−0.0490685
$29$	12.5587	0.0804169	0.0402085	−	0.999191i	$-0.487198\pi$
$29$	12.5587	0.0804169	0.0402085	+	0.999191i	$0.487198\pi$
$30$	−139.992	−0.851962
$31$	15.7988	0.0915336	0.0457668	−	0.998952i	$-0.485427\pi$
$31$	15.7988	0.0915336	0.0457668	+	0.998952i	$0.485427\pi$
$32$	54.8232	0.302858
$33$	−74.9864	−0.395560
$34$	−336.891	−1.69930
$35$	93.2477	0.450336
$36$	18.6387	0.0862903
$37$	236.142	1.04923	0.524616	−	0.851339i	$-0.324209\pi$
$37$	236.142	1.04923	0.524616	+	0.851339i	$0.324209\pi$
$38$	72.6483	0.310135
$39$	117.711	0.483303
$40$	−376.548	−1.48844
$41$	−377.108	−1.43645	−0.718224	−	0.695812i	$-0.755045\pi$
$41$	−377.108	−1.43645	−0.718224	+	0.695812i	$0.755045\pi$
$42$	−53.0730	−0.194984
$43$	−474.145	−1.68155	−0.840773	−	0.541388i	$-0.817899\pi$
$43$	−474.145	−1.68155	−0.840773	+	0.541388i	$0.817899\pi$
$44$	−26.7409	−0.0916214
$45$	−239.064	−0.791946
$46$	0	0
$47$	−547.089	−1.69790	−0.848948	−	0.528476i	$-0.822764\pi$
$47$	−547.089	−1.69790	−0.848948	+	0.528476i	$0.822764\pi$
$48$	180.776	0.543600
$49$	−307.648	−0.896934
$50$	314.900	0.890673
$51$	443.715	1.21829
$52$	41.9768	0.111945
$53$	−463.871	−1.20222	−0.601109	−	0.799167i	$-0.705274\pi$
$53$	−463.871	−1.20222	−0.601109	+	0.799167i	$0.705274\pi$
$54$	377.074	0.950247
$55$	342.984	0.840873
$56$	−142.755	−0.340651
$57$	−95.6842	−0.222345
$58$	32.6943	0.0740167
$59$	−597.203	−1.31778	−0.658891	−	0.752238i	$-0.728974\pi$
$59$	−597.203	−1.31778	−0.658891	+	0.752238i	$0.728974\pi$
$60$	65.7521	0.141476
$61$	−277.251	−0.581939	−0.290970	−	0.956732i	$-0.593978\pi$
$61$	−277.251	−0.581939	−0.290970	+	0.956732i	$0.593978\pi$
$62$	41.1292	0.0842486
$63$	−90.6328	−0.181249
$64$	564.506	1.10255
$65$	−538.404	−1.02740
$66$	−195.213	−0.364078
$67$	171.626	0.312947	0.156474	−	0.987682i	$-0.449987\pi$
$67$	171.626	0.312947	0.156474	+	0.987682i	$0.449987\pi$
$68$	158.233	0.282185
$69$	0	0
$70$	242.753	0.414494
$71$	227.710	0.380623	0.190311	−	0.981724i	$-0.439050\pi$
$71$	227.710	0.380623	0.190311	+	0.981724i	$0.439050\pi$
$72$	365.989	0.599058
$73$	932.242	1.49467	0.747333	−	0.664449i	$-0.231334\pi$
$73$	932.242	1.49467	0.747333	+	0.664449i	$0.231334\pi$
$74$	614.754	0.965725
$75$	−414.751	−0.638552
$76$	−34.1219	−0.0515007
$77$	130.031	0.192446
$78$	306.439	0.444838
$79$	−234.256	−0.333618	−0.166809	−	0.985989i	$-0.553346\pi$
$79$	−234.256	−0.333618	−0.166809	+	0.985989i	$0.553346\pi$
$80$	−826.862	−1.15558
$81$	−85.0692	−0.116693
$82$	−981.731	−1.32212
$83$	−912.812	−1.20716	−0.603579	−	0.797303i	$-0.706259\pi$
$83$	−912.812	−1.20716	−0.603579	+	0.797303i	$0.706259\pi$
$84$	24.9276	0.0323789
$85$	−2029.53	−2.58981
$86$	−1234.35	−1.54771
$87$	−43.0612	−0.0530649
$88$	−525.083	−0.636069
$89$	689.993	0.821788	0.410894	−	0.911683i	$-0.365217\pi$
$89$	689.993	0.821788	0.410894	+	0.911683i	$0.365217\pi$
$90$	−622.359	−0.728916
$91$	−204.117	−0.235135
$92$	0	0
$93$	−54.1708	−0.0604005
$94$	−1424.25	−1.56276
$95$	437.655	0.472658
$96$	−187.977	−0.199848
$97$	−86.1031	−0.0901283	−0.0450642	−	0.998984i	$-0.514349\pi$
$97$	−86.1031	−0.0901283	−0.0450642	+	0.998984i	$0.514349\pi$
$98$	−800.906	−0.825548
$99$	−333.366	−0.338430
$100$	−147.904	−0.147904
$101$	484.282	0.477108	0.238554	−	0.971129i	$-0.423327\pi$
$101$	484.282	0.477108	0.238554	+	0.971129i	$0.423327\pi$
$102$	1155.13	1.12132
$103$	126.788	0.121289	0.0606444	−	0.998159i	$-0.480684\pi$
$103$	126.788	0.121289	0.0606444	+	0.998159i	$0.480684\pi$
$104$	824.255	0.777162
$105$	−319.727	−0.297164
$106$	−1207.60	−1.10654
$107$	1897.81	1.71465	0.857327	−	0.514772i	$-0.172123\pi$
$107$	1897.81	1.71465	0.857327	+	0.514772i	$0.172123\pi$
$108$	−177.107	−0.157797
$109$	854.420	0.750813	0.375406	−	0.926860i	$-0.377503\pi$
$109$	854.420	0.750813	0.375406	+	0.926860i	$0.377503\pi$
$110$	892.897	0.773949
$111$	−809.684	−0.692359
$112$	−313.476	−0.264471
$113$	−568.874	−0.473586	−0.236793	−	0.971560i	$-0.576096\pi$
$113$	−568.874	−0.473586	−0.236793	+	0.971560i	$0.576096\pi$
$114$	−249.096	−0.204649
$115$	0	0
$116$	−15.3560	−0.0122911
$117$	523.306	0.413501
$118$	−1554.71	−1.21290
$119$	−769.427	−0.592717
$120$	1291.11	0.982178
$121$	−852.720	−0.640661
$122$	−721.771	−0.535623
$123$	1293.03	0.947871
$124$	−19.3178	−0.0139903
$125$	−63.3402	−0.0453225
$126$	−235.946	−0.166823
$127$	1064.51	0.743779	0.371890	−	0.928277i	$-0.378710\pi$
$127$	1064.51	0.743779	0.371890	+	0.928277i	$0.378710\pi$
$128$	1031.00	0.711942
$129$	1625.75	1.10960
$130$	−1401.64	−0.945628
$131$	714.292	0.476396	0.238198	−	0.971217i	$-0.423443\pi$
$131$	714.292	0.476396	0.238198	+	0.971217i	$0.423443\pi$
$132$	91.6891	0.0604584
$133$	165.922	0.108175
$134$	446.797	0.288040
$135$	2271.61	1.44821
$136$	3107.06	1.95903
$137$	−442.264	−0.275804	−0.137902	−	0.990446i	$-0.544036\pi$
$137$	−442.264	−0.275804	−0.137902	+	0.990446i	$0.544036\pi$
$138$	0	0
$139$	−1903.69	−1.16164	−0.580822	−	0.814030i	$-0.697269\pi$
$139$	−1903.69	−1.16164	−0.580822	+	0.814030i	$0.697269\pi$
$140$	−114.018	−0.0688305
$141$	1875.86	1.12039
$142$	592.802	0.350330
$143$	−750.786	−0.439048
$144$	803.675	0.465090
$145$	196.960	0.112804
$146$	2426.92	1.37571
$147$	1054.86	0.591862
$148$	−288.741	−0.160367
$149$	−421.281	−0.231629	−0.115814	−	0.993271i	$-0.536948\pi$
$149$	−421.281	−0.231629	−0.115814	+	0.993271i	$0.536948\pi$
$150$	−1079.73	−0.587730
$151$	883.890	0.476357	0.238179	−	0.971221i	$-0.423450\pi$
$151$	883.890	0.476357	0.238179	+	0.971221i	$0.423450\pi$
$152$	−670.017	−0.357536
$153$	1972.62	1.04233
$154$	338.511	0.177130
$155$	247.775	0.128398
$156$	−143.930	−0.0738693
$157$	2255.69	1.14665	0.573325	−	0.819328i	$-0.305653\pi$
$157$	2255.69	1.14665	0.573325	+	0.819328i	$0.305653\pi$
$158$	−609.842	−0.307066
$159$	1590.52	0.793311
$160$	859.800	0.424832
$161$	0	0
$162$	−221.462	−0.107406
$163$	116.912	0.0561794	0.0280897	−	0.999605i	$-0.491058\pi$
$163$	116.912	0.0561794	0.0280897	+	0.999605i	$0.491058\pi$
$164$	461.106	0.219551
$165$	−1176.02	−0.554869
$166$	−2376.34	−1.11108
$167$	1476.71	0.684261	0.342130	−	0.939652i	$-0.388852\pi$
$167$	1476.71	0.684261	0.342130	+	0.939652i	$0.388852\pi$
$168$	489.478	0.224786
$169$	−1018.45	−0.463562
$170$	−5283.52	−2.38369
$171$	−425.382	−0.190233
$172$	579.757	0.257012
$173$	474.255	0.208421	0.104211	−	0.994555i	$-0.466768\pi$
$173$	474.255	0.208421	0.104211	+	0.994555i	$0.466768\pi$
$174$	−112.102	−0.0488415
$175$	719.203	0.310666
$176$	−1153.03	−0.493824
$177$	2047.69	0.869568
$178$	1796.27	0.756383
$179$	−2236.70	−0.933958	−0.466979	−	0.884268i	$-0.654658\pi$
$179$	−2236.70	−0.933958	−0.466979	+	0.884268i	$0.654658\pi$
$180$	292.314	0.121043
$181$	−2842.81	−1.16743	−0.583714	−	0.811959i	$-0.698401\pi$
$181$	−2842.81	−1.16743	−0.583714	+	0.811959i	$0.698401\pi$
$182$	−531.382	−0.216421
$183$	950.635	0.384005
$184$	0	0
$185$	3703.46	1.47180
$186$	−141.024	−0.0555933
$187$	−2830.11	−1.10673
$188$	668.948	0.259511
$189$	861.202	0.331446
$190$	1139.35	0.435039
$191$	434.402	0.164567	0.0822833	−	0.996609i	$-0.473779\pi$
$191$	434.402	0.164567	0.0822833	+	0.996609i	$0.473779\pi$
$192$	−1935.58	−0.727542
$193$	3237.50	1.20746	0.603732	−	0.797188i	$-0.293680\pi$
$193$	3237.50	1.20746	0.603732	+	0.797188i	$0.293680\pi$
$194$	−224.154	−0.0829551
$195$	1846.08	0.677950
$196$	376.175	0.137090
$197$	3216.72	1.16336	0.581680	−	0.813417i	$-0.302395\pi$
$197$	3216.72	1.16336	0.581680	+	0.813417i	$0.302395\pi$
$198$	−867.858	−0.311495
$199$	−597.892	−0.212982	−0.106491	−	0.994314i	$-0.533962\pi$
$199$	−597.892	−0.212982	−0.106491	+	0.994314i	$0.533962\pi$
$200$	−2904.25	−1.02681
$201$	−588.471	−0.206505
$202$	1260.74	0.439136
$203$	74.6706	0.0258170
$204$	−542.549	−0.186206
$205$	−5914.24	−2.01497
$206$	330.068	0.111636
$207$	0	0
$208$	1809.98	0.603364
$209$	610.295	0.201986
$210$	−832.352	−0.273513
$211$	−4564.34	−1.48921	−0.744603	−	0.667508i	$-0.767361\pi$
$211$	−4564.34	−1.48921	−0.744603	+	0.667508i	$0.767361\pi$
$212$	567.195	0.183750
$213$	−780.772	−0.251162
$214$	4940.60	1.57819
$215$	−7436.09	−2.35878
$216$	−3477.66	−1.09549
$217$	93.9352	0.0293859
$218$	2224.33	0.691057
$219$	−3196.47	−0.986289
$220$	−419.382	−0.128521
$221$	4442.60	1.35222
$222$	−2107.86	−0.637255
$223$	3745.20	1.12465	0.562325	−	0.826916i	$-0.309907\pi$
$223$	3745.20	1.12465	0.562325	+	0.826916i	$0.309907\pi$
$224$	325.964	0.0972293
$225$	−1843.86	−0.546328
$226$	−1480.96	−0.435894
$227$	3325.66	0.972386	0.486193	−	0.873852i	$-0.338385\pi$
$227$	3325.66	0.972386	0.486193	+	0.873852i	$0.338385\pi$
$228$	116.997	0.0339839
$229$	−1285.35	−0.370909	−0.185454	−	0.982653i	$-0.559376\pi$
$229$	−1285.35	−0.370909	−0.185454	+	0.982653i	$0.559376\pi$
$230$	0	0
$231$	−445.849	−0.126990
$232$	−301.531	−0.0853296
$233$	5568.58	1.56571	0.782854	−	0.622205i	$-0.213763\pi$
$233$	5568.58	1.56571	0.782854	+	0.622205i	$0.213763\pi$
$234$	1362.33	0.380591
$235$	−8580.08	−2.38171
$236$	730.225	0.201413
$237$	803.215	0.220145
$238$	−2003.06	−0.545543
$239$	1031.31	0.279120	0.139560	−	0.990214i	$-0.455431\pi$
$239$	1031.31	0.279120	0.139560	+	0.990214i	$0.455431\pi$
$240$	2835.14	0.762532
$241$	3263.41	0.872261	0.436130	−	0.899884i	$-0.356349\pi$
$241$	3263.41	0.872261	0.436130	+	0.899884i	$0.356349\pi$
$242$	−2219.90	−0.589672
$243$	−3619.10	−0.955413
$244$	339.006	0.0889452
$245$	−4824.90	−1.25817
$246$	3366.16	0.872432
$247$	−958.017	−0.246790
$248$	−379.324	−0.0971254
$249$	3129.85	0.796570
$250$	−164.895	−0.0417154
$251$	−3361.89	−0.845422	−0.422711	−	0.906265i	$-0.638921\pi$
$251$	−3361.89	−0.845422	−0.422711	+	0.906265i	$0.638921\pi$
$252$	110.821	0.0277025
$253$	0	0
$254$	2771.26	0.684583
$255$	6958.85	1.70894
$256$	−1832.02	−0.447271
$257$	1274.74	0.309401	0.154701	−	0.987961i	$-0.450559\pi$
$257$	1274.74	0.309401	0.154701	+	0.987961i	$0.450559\pi$
$258$	4232.33	1.02129
$259$	1404.04	0.336844
$260$	658.329	0.157030
$261$	−191.437	−0.0454009
$262$	1859.53	0.438481
$263$	−5238.38	−1.22818	−0.614092	−	0.789234i	$-0.710478\pi$
$263$	−5238.38	−1.22818	−0.614092	+	0.789234i	$0.710478\pi$
$264$	1800.40	0.419724
$265$	−7274.96	−1.68640
$266$	431.947	0.0995653
$267$	−2365.85	−0.542275
$268$	−209.854	−0.0478317
$269$	6289.31	1.42552	0.712762	−	0.701406i	$-0.247444\pi$
$269$	6289.31	1.42552	0.712762	+	0.701406i	$0.247444\pi$
$270$	5913.72	1.33295
$271$	−491.262	−0.110118	−0.0550591	−	0.998483i	$-0.517535\pi$
$271$	−491.262	−0.110118	−0.0550591	+	0.998483i	$0.517535\pi$
$272$	6822.80	1.52093
$273$	699.876	0.155159
$274$	−1151.35	−0.253853
$275$	2645.38	0.580081
$276$	0	0
$277$	−4007.70	−0.869312	−0.434656	−	0.900597i	$-0.643130\pi$
$277$	−4007.70	−0.869312	−0.434656	+	0.900597i	$0.643130\pi$
$278$	−4955.90	−1.06919
$279$	−240.826	−0.0516770
$280$	−2238.85	−0.477846
$281$	−1618.61	−0.343623	−0.171811	−	0.985130i	$-0.554962\pi$
$281$	−1618.61	−0.343623	−0.171811	+	0.985130i	$0.554962\pi$
$282$	4883.45	1.03122
$283$	−3706.89	−0.778628	−0.389314	−	0.921105i	$-0.627288\pi$
$283$	−3706.89	−0.778628	−0.389314	+	0.921105i	$0.627288\pi$
$284$	−278.431	−0.0581754
$285$	−1500.63	−0.311893
$286$	−1954.53	−0.404105
$287$	−2242.18	−0.461156
$288$	−835.689	−0.170984
$289$	11833.5	2.40862
$290$	512.749	0.103826
$291$	295.230	0.0594732
$292$	−1139.89	−0.228449
$293$	5022.03	1.00133	0.500666	−	0.865641i	$-0.333088\pi$
$293$	5022.03	1.00133	0.500666	+	0.865641i	$0.333088\pi$
$294$	2746.14	0.544756
$295$	−9366.02	−1.84851
$296$	−5669.71	−1.11333
$297$	3167.68	0.618880
$298$	−1096.73	−0.213194
$299$	0	0
$300$	507.134	0.0975980
$301$	−2819.14	−0.539842
$302$	2301.04	0.438444
$303$	−1660.51	−0.314830
$304$	−1471.29	−0.277580
$305$	−4348.16	−0.816312
$306$	5135.35	0.959375
$307$	4428.94	0.823365	0.411682	−	0.911327i	$-0.364941\pi$
$307$	4428.94	0.823365	0.411682	+	0.911327i	$0.364941\pi$
$308$	−158.994	−0.0294140
$309$	−434.729	−0.0800351
$310$	645.036	0.118179
$311$	9184.68	1.67465	0.837324	−	0.546707i	$-0.184119\pi$
$311$	9184.68	1.67465	0.837324	+	0.546707i	$0.184119\pi$
$312$	−2826.20	−0.512828
$313$	2491.75	0.449975	0.224987	−	0.974362i	$-0.427766\pi$
$313$	2491.75	0.449975	0.224987	+	0.974362i	$0.427766\pi$
$314$	5872.29	1.05539
$315$	−1421.41	−0.254245
$316$	286.434	0.0509911
$317$	−4985.51	−0.883326	−0.441663	−	0.897181i	$-0.645611\pi$
$317$	−4985.51	−0.883326	−0.441663	+	0.897181i	$0.645611\pi$
$318$	4140.63	0.730172
$319$	274.654	0.0482058
$320$	8853.23	1.54660
$321$	−6507.20	−1.13145
$322$	0	0
$323$	−3611.28	−0.622096
$324$	104.018	0.0178357
$325$	−4152.61	−0.708755
$326$	304.359	0.0517082
$327$	−2929.63	−0.495440
$328$	9054.25	1.52420
$329$	−3252.84	−0.545091
$330$	−3061.56	−0.510707
$331$	−6285.44	−1.04374	−0.521872	−	0.853024i	$-0.674766\pi$
$331$	−6285.44	−1.04374	−0.521872	+	0.853024i	$0.674766\pi$
$332$	1116.13	0.184505
$333$	−3599.60	−0.592364
$334$	3844.35	0.629802
$335$	2691.64	0.438985
$336$	1074.85	0.174517
$337$	3218.22	0.520201	0.260100	−	0.965582i	$-0.416244\pi$
$337$	3218.22	0.520201	0.260100	+	0.965582i	$0.416244\pi$
$338$	−2651.34	−0.426668
$339$	1950.55	0.312506
$340$	2481.59	0.395833
$341$	345.513	0.0548697
$342$	−1107.40	−0.175092
$343$	−3868.58	−0.608990
$344$	11384.1	1.78427
$345$	0	0
$346$	1234.64	0.191834
$347$	−7884.61	−1.21979	−0.609897	−	0.792481i	$-0.708789\pi$
$347$	−7884.61	−1.21979	−0.609897	+	0.792481i	$0.708789\pi$
$348$	52.6527	0.00811058
$349$	−442.238	−0.0678294	−0.0339147	−	0.999425i	$-0.510797\pi$
$349$	−442.238	−0.0678294	−0.0339147	+	0.999425i	$0.510797\pi$
$350$	1872.31	0.285941
$351$	−4972.50	−0.756161
$352$	1198.96	0.181548
$353$	4656.00	0.702022	0.351011	−	0.936371i	$-0.385838\pi$
$353$	4656.00	0.702022	0.351011	+	0.936371i	$0.385838\pi$
$354$	5330.77	0.800360
$355$	3571.21	0.533916
$356$	−843.684	−0.125604
$357$	2638.21	0.391117
$358$	−5822.83	−0.859626
$359$	−8680.80	−1.27620	−0.638099	−	0.769954i	$-0.720279\pi$
$359$	−8680.80	−1.27620	−0.638099	+	0.769954i	$0.720279\pi$
$360$	5739.86	0.840325
$361$	−6080.25	−0.886463
$362$	−7400.74	−1.07451
$363$	2923.80	0.422754
$364$	249.583	0.0359387
$365$	14620.5	2.09663
$366$	2474.80	0.353443
$367$	−5699.85	−0.810708	−0.405354	−	0.914160i	$-0.632852\pi$
$367$	−5699.85	−0.810708	−0.405354	+	0.914160i	$0.632852\pi$
$368$	0	0
$369$	5748.39	0.810974
$370$	9641.27	1.35466
$371$	−2758.05	−0.385959
$372$	66.2369	0.00923178
$373$	7369.50	1.02300	0.511499	−	0.859284i	$-0.329090\pi$
$373$	7369.50	1.02300	0.511499	+	0.859284i	$0.329090\pi$
$374$	−7367.68	−1.01865
$375$	217.181	0.0299071
$376$	13135.4	1.80162
$377$	−431.141	−0.0588989
$378$	2241.98	0.305066
$379$	7818.94	1.05972	0.529858	−	0.848087i	$-0.322245\pi$
$379$	7818.94	1.05972	0.529858	+	0.848087i	$0.322245\pi$
$380$	−535.139	−0.0722423
$381$	−3649.99	−0.490799
$382$	1130.89	0.151469
$383$	−7704.70	−1.02792	−0.513958	−	0.857816i	$-0.671821\pi$
$383$	−7704.70	−1.02792	−0.513958	+	0.857816i	$0.671821\pi$
$384$	−3535.10	−0.469791
$385$	2039.29	0.269953
$386$	8428.24	1.11136
$387$	7227.56	0.949348
$388$	105.282	0.0137755
$389$	4432.04	0.577669	0.288835	−	0.957379i	$-0.406732\pi$
$389$	4432.04	0.577669	0.288835	+	0.957379i	$0.406732\pi$
$390$	4805.92	0.623993
$391$	0	0
$392$	7386.55	0.951727
$393$	−2449.16	−0.314361
$394$	8374.15	1.07077
$395$	−3673.87	−0.467981
$396$	407.621	0.0517266
$397$	−9138.14	−1.15524	−0.577620	−	0.816306i	$-0.696018\pi$
$397$	−9138.14	−1.15524	−0.577620	+	0.816306i	$0.696018\pi$
$398$	−1556.50	−0.196031
$399$	−568.912	−0.0713815
$400$	−6377.44	−0.797180
$401$	4004.40	0.498679	0.249340	−	0.968416i	$-0.419786\pi$
$401$	4004.40	0.498679	0.249340	+	0.968416i	$0.419786\pi$
$402$	−1531.98	−0.190070
$403$	−542.373	−0.0670410
$404$	−592.152	−0.0729225
$405$	−1334.15	−0.163690
$406$	194.391	0.0237622
$407$	5164.34	0.628961
$408$	−10653.5	−1.29271
$409$	1921.28	0.232277	0.116139	−	0.993233i	$-0.462948\pi$
$409$	1921.28	0.232277	0.116139	+	0.993233i	$0.462948\pi$
$410$	−15396.6	−1.85460
$411$	1516.43	0.181995
$412$	−155.028	−0.0185381
$413$	−3550.80	−0.423060
$414$	0	0
$415$	−14315.8	−1.69333
$416$	−1882.08	−0.221819
$417$	6527.35	0.766537
$418$	1588.79	0.185910
$419$	−1310.02	−0.152741	−0.0763707	−	0.997079i	$-0.524333\pi$
$419$	−1310.02	−0.152741	−0.0763707	+	0.997079i	$0.524333\pi$
$420$	390.944	0.0454193
$421$	−3328.69	−0.385346	−0.192673	−	0.981263i	$-0.561716\pi$
$421$	−3328.69	−0.385346	−0.192673	+	0.981263i	$0.561716\pi$
$422$	−11882.4	−1.37068
$423$	8339.47	0.958579
$424$	11137.4	1.27566
$425$	−15653.4	−1.78659
$426$	−2032.60	−0.231173
$427$	−1648.46	−0.186825
$428$	−2320.53	−0.262073
$429$	2574.29	0.289715
$430$	−19358.5	−2.17105
$431$	−15684.7	−1.75291	−0.876455	−	0.481484i	$-0.840098\pi$
$431$	−15684.7	−1.75291	−0.876455	+	0.481484i	$0.840098\pi$
$432$	−7636.60	−0.850500
$433$	−9340.59	−1.03667	−0.518337	−	0.855176i	$-0.673449\pi$
$433$	−9340.59	−1.03667	−0.518337	+	0.855176i	$0.673449\pi$
$434$	244.543	0.0270471
$435$	−675.335	−0.0744364
$436$	−1044.73	−0.114756
$437$	0	0
$438$	−8321.42	−0.907791
$439$	1975.05	0.214724	0.107362	−	0.994220i	$-0.465760\pi$
$439$	1975.05	0.214724	0.107362	+	0.994220i	$0.465760\pi$
$440$	−8234.96	−0.892242
$441$	4689.59	0.506381
$442$	11565.5	1.24460
$443$	−13052.2	−1.39984	−0.699921	−	0.714220i	$-0.746781\pi$
$443$	−13052.2	−1.39984	−0.699921	+	0.714220i	$0.746781\pi$
$444$	990.035	0.105822
$445$	10821.3	1.15276
$446$	9749.93	1.03514
$447$	1444.48	0.152845
$448$	3356.40	0.353962
$449$	2939.49	0.308960	0.154480	−	0.987996i	$-0.450630\pi$
$449$	2939.49	0.308960	0.154480	+	0.987996i	$0.450630\pi$
$450$	−4800.14	−0.502846
$451$	−8247.20	−0.861077
$452$	695.586	0.0723842
$453$	−3030.68	−0.314335
$454$	8657.74	0.894995
$455$	−3201.20	−0.329834
$456$	2297.35	0.235928
$457$	−4861.32	−0.497600	−0.248800	−	0.968555i	$-0.580036\pi$
$457$	−4861.32	−0.497600	−0.248800	+	0.968555i	$0.580036\pi$
$458$	−3346.17	−0.341389
$459$	−18744.0	−1.90609
$460$	0	0
$461$	5249.19	0.530323	0.265162	−	0.964204i	$-0.414575\pi$
$461$	5249.19	0.530323	0.265162	+	0.964204i	$0.414575\pi$
$462$	−1160.69	−0.116883
$463$	−4118.23	−0.413370	−0.206685	−	0.978407i	$-0.566268\pi$
$463$	−4118.23	−0.413370	−0.206685	+	0.978407i	$0.566268\pi$
$464$	−662.132	−0.0662472
$465$	−849.568	−0.0847264
$466$	14496.8	1.44110
$467$	−14796.9	−1.46620	−0.733102	−	0.680119i	$-0.761928\pi$
$467$	−14796.9	−1.46620	−0.733102	+	0.680119i	$0.761928\pi$
$468$	−639.868	−0.0632006
$469$	1020.44	0.100468
$470$	−22336.7	−2.19216
$471$	−7734.32	−0.756642
$472$	14338.7	1.39829
$473$	−10369.4	−1.00800
$474$	2091.02	0.202624
$475$	3375.55	0.326065
$476$	940.811	0.0905924
$477$	7070.95	0.678735
$478$	2684.82	0.256906
$479$	4413.40	0.420988	0.210494	−	0.977595i	$-0.432493\pi$
$479$	4413.40	0.420988	0.210494	+	0.977595i	$0.432493\pi$
$480$	−2948.08	−0.280335
$481$	−8106.79	−0.768478
$482$	8495.69	0.802839
$483$	0	0
$484$	1042.66	0.0979204
$485$	−1350.37	−0.126427
$486$	−9421.66	−0.879373
$487$	14084.6	1.31054	0.655271	−	0.755394i	$-0.272555\pi$
$487$	14084.6	1.31054	0.655271	+	0.755394i	$0.272555\pi$
$488$	6656.71	0.617490
$489$	−400.867	−0.0370712
$490$	−12560.7	−1.15803
$491$	5563.44	0.511354	0.255677	−	0.966762i	$-0.417702\pi$
$491$	5563.44	0.511354	0.255677	+	0.966762i	$0.417702\pi$
$492$	−1581.04	−0.144875
$493$	−1625.20	−0.148469
$494$	−2494.02	−0.227149
$495$	−5228.24	−0.474731
$496$	−832.958	−0.0754051
$497$	1353.90	0.122195
$498$	8147.98	0.733172
$499$	7594.26	0.681294	0.340647	−	0.940191i	$-0.389354\pi$
$499$	7594.26	0.681294	0.340647	+	0.940191i	$0.389354\pi$
$500$	77.4487	0.00692722
$501$	−5063.35	−0.451525
$502$	−8752.07	−0.778136
$503$	−13930.3	−1.23483	−0.617416	−	0.786637i	$-0.711820\pi$
$503$	−13930.3	−1.23483	−0.617416	+	0.786637i	$0.711820\pi$
$504$	2176.07	0.192321
$505$	7595.07	0.669260
$506$	0	0
$507$	3492.04	0.305892
$508$	−1301.62	−0.113681
$509$	5608.05	0.488355	0.244177	−	0.969731i	$-0.421482\pi$
$509$	5608.05	0.488355	0.244177	+	0.969731i	$0.421482\pi$
$510$	18116.1	1.57293
$511$	5542.86	0.479846
$512$	−13017.3	−1.12362
$513$	4042.02	0.347875
$514$	3318.55	0.284777
$515$	1988.43	0.170137
$516$	−1987.87	−0.169595
$517$	−11964.6	−1.01780
$518$	3655.16	0.310035
$519$	−1626.12	−0.137532
$520$	12926.9	1.09016
$521$	−8852.27	−0.744386	−0.372193	−	0.928155i	$-0.621394\pi$
$521$	−8852.27	−0.744386	−0.372193	+	0.928155i	$0.621394\pi$
$522$	−498.370	−0.0417875
$523$	−19350.8	−1.61788	−0.808942	−	0.587889i	$-0.799959\pi$
$523$	−19350.8	−1.61788	−0.808942	+	0.587889i	$0.799959\pi$
$524$	−873.394	−0.0728137
$525$	−2466.00	−0.205000
$526$	−13637.2	−1.13044
$527$	−2044.49	−0.168993
$528$	3953.51	0.325860
$529$	0	0
$530$	−18939.0	−1.55219
$531$	9103.37	0.743979
$532$	−202.880	−0.0165337
$533$	12946.1	1.05208
$534$	−6159.05	−0.499116
$535$	29763.6	2.40522
$536$	−4120.69	−0.332065
$537$	7669.18	0.616293
$538$	16373.1	1.31207
$539$	−6728.15	−0.537666
$540$	−2777.59	−0.221349
$541$	−13429.0	−1.06721	−0.533603	−	0.845735i	$-0.679162\pi$
$541$	−13429.0	−1.06721	−0.533603	+	0.845735i	$0.679162\pi$
$542$	−1278.91	−0.101354
$543$	9747.42	0.770353
$544$	−7094.58	−0.559150
$545$	13400.0	1.05320
$546$	1822.00	0.142810
$547$	15088.1	1.17938	0.589689	−	0.807631i	$-0.299250\pi$
$547$	15088.1	1.17938	0.589689	+	0.807631i	$0.299250\pi$
$548$	540.774	0.0421546
$549$	4226.23	0.328545
$550$	6886.75	0.533913
$551$	350.464	0.0270967
$552$	0	0
$553$	−1392.82	−0.107104
$554$	−10433.3	−0.800125
$555$	−12698.4	−0.971202
$556$	2327.72	0.177549
$557$	7951.43	0.604871	0.302435	−	0.953170i	$-0.402200\pi$
$557$	7951.43	0.604871	0.302435	+	0.953170i	$0.402200\pi$
$558$	−626.947	−0.0475641
$559$	16277.4	1.23160
$560$	−4916.30	−0.370985
$561$	9703.88	0.730300
$562$	−4213.75	−0.316274
$563$	−3042.56	−0.227759	−0.113880	−	0.993495i	$-0.536328\pi$
$563$	−3042.56	−0.227759	−0.113880	+	0.993495i	$0.536328\pi$
$564$	−2293.69	−0.171244
$565$	−8921.74	−0.664320
$566$	−9650.21	−0.716658
$567$	−505.798	−0.0374630
$568$	−5467.26	−0.403875
$569$	−11726.3	−0.863960	−0.431980	−	0.901883i	$-0.642185\pi$
$569$	−11726.3	−0.863960	−0.431980	+	0.901883i	$0.642185\pi$
$570$	−3906.61	−0.287070
$571$	−4489.41	−0.329030	−0.164515	−	0.986375i	$-0.552606\pi$
$571$	−4489.41	−0.329030	−0.164515	+	0.986375i	$0.552606\pi$
$572$	918.017	0.0671053
$573$	−1489.48	−0.108593
$574$	−5837.10	−0.424453
$575$	0	0
$576$	−8604.97	−0.622466
$577$	20073.7	1.44831	0.724157	−	0.689635i	$-0.242229\pi$
$577$	20073.7	1.44831	0.724157	+	0.689635i	$0.242229\pi$
$578$	30806.5	2.21692
$579$	−11100.7	−0.796771
$580$	−240.831	−0.0172413
$581$	−5427.33	−0.387545
$582$	768.577	0.0547398
$583$	−10144.7	−0.720669
$584$	−22382.9	−1.58598
$585$	8207.08	0.580036
$586$	13073.9	0.921637
$587$	−9497.04	−0.667776	−0.333888	−	0.942613i	$-0.608361\pi$
$587$	−9497.04	−0.667776	−0.333888	+	0.942613i	$0.608361\pi$
$588$	−1289.83	−0.0904618
$589$	440.882	0.0308425
$590$	−24382.7	−1.70139
$591$	−11029.5	−0.767669
$592$	−12450.1	−0.864353
$593$	−12599.4	−0.872502	−0.436251	−	0.899825i	$-0.643694\pi$
$593$	−12599.4	−0.872502	−0.436251	+	0.899825i	$0.643694\pi$
$594$	8246.47	0.569624
$595$	−12067.0	−0.831429
$596$	515.117	0.0354027
$597$	2050.05	0.140541
$598$	0	0
$599$	5827.00	0.397471	0.198735	−	0.980053i	$-0.436317\pi$
$599$	5827.00	0.397471	0.198735	+	0.980053i	$0.436317\pi$
$600$	9958.07	0.677561
$601$	−24199.0	−1.64243	−0.821213	−	0.570622i	$-0.806702\pi$
$601$	−24199.0	−1.64243	−0.821213	+	0.570622i	$0.806702\pi$
$602$	−7339.11	−0.496876
$603$	−2616.16	−0.176680
$604$	−1080.77	−0.0728077
$605$	−13373.3	−0.898683
$606$	−4322.82	−0.289773
$607$	−2390.33	−0.159836	−0.0799181	−	0.996801i	$-0.525466\pi$
$607$	−2390.33	−0.159836	−0.0799181	+	0.996801i	$0.525466\pi$
$608$	1529.90	0.102049
$609$	−256.030	−0.0170359
$610$	−11319.6	−0.751342
$611$	18781.6	1.24357
$612$	−2412.00	−0.159313
$613$	22277.9	1.46786	0.733928	−	0.679227i	$-0.237685\pi$
$613$	22277.9	1.46786	0.733928	+	0.679227i	$0.237685\pi$
$614$	11529.9	0.757835
$615$	20278.7	1.32962
$616$	−3122.00	−0.204203
$617$	4096.57	0.267296	0.133648	−	0.991029i	$-0.457331\pi$
$617$	4096.57	0.267296	0.133648	+	0.991029i	$0.457331\pi$
$618$	−1131.74	−0.0736652
$619$	−12215.0	−0.793153	−0.396576	−	0.918002i	$-0.629802\pi$
$619$	−12215.0	−0.793153	−0.396576	+	0.918002i	$0.629802\pi$
$620$	−302.964	−0.0196247
$621$	0	0
$622$	23910.6	1.54137
$623$	4102.51	0.263826
$624$	−6206.06	−0.398143
$625$	−16113.5	−1.03127
$626$	6486.82	0.414162
$627$	−2092.58	−0.133285
$628$	−2758.13	−0.175257
$629$	−30558.8	−1.93714
$630$	−3700.38	−0.234010
$631$	28283.5	1.78439	0.892195	−	0.451650i	$-0.149164\pi$
$631$	28283.5	1.78439	0.892195	+	0.451650i	$0.149164\pi$
$632$	5624.41	0.353999
$633$	15650.2	0.982685
$634$	−12978.9	−0.813024
$635$	16694.9	1.04333
$636$	−1944.79	−0.121252
$637$	10561.6	0.656932
$638$	715.011	0.0443692
$639$	−3471.07	−0.214888
$640$	16169.4	0.998672
$641$	11965.2	0.737278	0.368639	−	0.929573i	$-0.379824\pi$
$641$	11965.2	0.737278	0.368639	+	0.929573i	$0.379824\pi$
$642$	−16940.3	−1.04140
$643$	−2342.99	−0.143699	−0.0718495	−	0.997415i	$-0.522890\pi$
$643$	−2342.99	−0.143699	−0.0718495	+	0.997415i	$0.522890\pi$
$644$	0	0
$645$	25496.8	1.55649
$646$	−9401.31	−0.572584
$647$	6345.14	0.385553	0.192777	−	0.981243i	$-0.438251\pi$
$647$	6345.14	0.385553	0.192777	+	0.981243i	$0.438251\pi$
$648$	2042.49	0.123822
$649$	−13060.6	−0.789943
$650$	−10810.6	−0.652346
$651$	−322.084	−0.0193909
$652$	−142.953	−0.00858662
$653$	−2844.49	−0.170465	−0.0852324	−	0.996361i	$-0.527163\pi$
$653$	−2844.49	−0.170465	−0.0852324	+	0.996361i	$0.527163\pi$
$654$	−7626.76	−0.456009
$655$	11202.3	0.668262
$656$	19882.2	1.18334
$657$	−14210.5	−0.843842
$658$	−8468.17	−0.501708
$659$	−18420.2	−1.08885	−0.544423	−	0.838811i	$-0.683251\pi$
$659$	−18420.2	−1.08885	−0.544423	+	0.838811i	$0.683251\pi$
$660$	1437.97	0.0848076
$661$	−1288.07	−0.0757944	−0.0378972	−	0.999282i	$-0.512066\pi$
$661$	−1288.07	−0.0757944	−0.0378972	+	0.999282i	$0.512066\pi$
$662$	−16363.0	−0.960674
$663$	−15232.8	−0.892295
$664$	21916.4	1.28090
$665$	2602.18	0.151742
$666$	−9370.91	−0.545218
$667$	0	0
$668$	−1805.64	−0.104584
$669$	−12841.5	−0.742125
$670$	7007.19	0.404047
$671$	−6063.36	−0.348843
$672$	−1117.66	−0.0641589
$673$	−14596.4	−0.836031	−0.418016	−	0.908440i	$-0.637274\pi$
$673$	−14596.4	−0.836031	−0.418016	+	0.908440i	$0.637274\pi$
$674$	8378.05	0.478799
$675$	17520.5	0.999058
$676$	1245.30	0.0708521
$677$	−5126.00	−0.291002	−0.145501	−	0.989358i	$-0.546479\pi$
$677$	−5126.00	−0.291002	−0.145501	+	0.989358i	$0.546479\pi$
$678$	5077.91	0.287634
$679$	−511.946	−0.0289347
$680$	48728.5	2.74802
$681$	−11403.0	−0.641650
$682$	899.480	0.0505027
$683$	−35023.3	−1.96212	−0.981062	−	0.193692i	$-0.937954\pi$
$683$	−35023.3	−1.96212	−0.981062	+	0.193692i	$0.937954\pi$
$684$	520.133	0.0290757
$685$	−6936.09	−0.386882
$686$	−10071.1	−0.560521
$687$	4407.19	0.244752
$688$	24998.3	1.38525
$689$	15924.7	0.880528
$690$	0	0
$691$	−21001.1	−1.15618	−0.578090	−	0.815973i	$-0.696202\pi$
$691$	−21001.1	−1.15618	−0.578090	+	0.815973i	$0.696202\pi$
$692$	−579.891	−0.0318557
$693$	−1982.11	−0.108649
$694$	−20526.1	−1.12271
$695$	−29855.8	−1.62949
$696$	1033.89	0.0563066
$697$	48800.9	2.65203
$698$	−1151.29	−0.0624309
$699$	−19093.5	−1.03317
$700$	−879.399	−0.0474831
$701$	6818.71	0.367388	0.183694	−	0.982983i	$-0.441194\pi$
$701$	6818.71	0.367388	0.183694	+	0.982983i	$0.441194\pi$
$702$	−12945.0	−0.695979
$703$	6589.81	0.353541
$704$	12345.5	0.660923
$705$	29419.3	1.57163
$706$	12121.0	0.646149
$707$	2879.41	0.153170
$708$	−2503.79	−0.132907
$709$	36207.0	1.91789	0.958945	−	0.283592i	$-0.0915260\pi$
$709$	36207.0	1.91789	0.958945	+	0.283592i	$0.0915260\pi$
$710$	9297.00	0.491423
$711$	3570.84	0.188350
$712$	−16566.5	−0.871991
$713$	0	0
$714$	6868.09	0.359989
$715$	−11774.7	−0.615872
$716$	2734.90	0.142749
$717$	−3536.15	−0.184184
$718$	−22598.9	−1.17463
$719$	34307.2	1.77947	0.889736	−	0.456475i	$-0.150888\pi$
$719$	34307.2	1.77947	0.889736	+	0.456475i	$0.150888\pi$
$720$	12604.2	0.652402
$721$	753.844	0.0389384
$722$	−15828.8	−0.815911
$723$	−11189.6	−0.575580
$724$	3476.03	0.178433
$725$	1519.12	0.0778187
$726$	7611.58	0.389108
$727$	1831.18	0.0934178	0.0467089	−	0.998909i	$-0.485127\pi$
$727$	1831.18	0.0934178	0.0467089	+	0.998909i	$0.485127\pi$
$728$	4900.80	0.249500
$729$	14706.0	0.747143
$730$	38061.8	1.92977
$731$	61358.4	3.10454
$732$	−1162.38	−0.0586924
$733$	8437.85	0.425183	0.212591	−	0.977141i	$-0.431810\pi$
$733$	8437.85	0.425183	0.212591	+	0.977141i	$0.431810\pi$
$734$	−14838.5	−0.746185
$735$	16543.6	0.830230
$736$	0	0
$737$	3753.40	0.187596
$738$	14964.9	0.746429
$739$	6052.18	0.301262	0.150631	−	0.988590i	$-0.451869\pi$
$739$	6052.18	0.301262	0.150631	+	0.988590i	$0.451869\pi$
$740$	−4528.37	−0.224954
$741$	3284.85	0.162850
$742$	−7180.08	−0.355241
$743$	−17865.8	−0.882142	−0.441071	−	0.897472i	$-0.645401\pi$
$743$	−17865.8	−0.882142	−0.441071	+	0.897472i	$0.645401\pi$
$744$	1300.62	0.0640903
$745$	−6607.01	−0.324915
$746$	19185.1	0.941579
$747$	13914.3	0.681524
$748$	3460.50	0.169156
$749$	11283.8	0.550471
$750$	565.390	0.0275268
$751$	−17492.6	−0.849952	−0.424976	−	0.905205i	$-0.639718\pi$
$751$	−17492.6	−0.849952	−0.424976	+	0.905205i	$0.639718\pi$
$752$	28844.1	1.39872
$753$	11527.2	0.557870
$754$	−1122.40	−0.0542112
$755$	13862.2	0.668207
$756$	−1053.03	−0.0506591
$757$	36349.6	1.74524	0.872621	−	0.488398i	$-0.162419\pi$
$757$	36349.6	1.74524	0.872621	+	0.488398i	$0.162419\pi$
$758$	20355.2	0.975374
$759$	0	0
$760$	−10508.0	−0.501532
$761$	−22731.3	−1.08280	−0.541398	−	0.840766i	$-0.682105\pi$
$761$	−22731.3	−1.08280	−0.541398	+	0.840766i	$0.682105\pi$
$762$	−9502.07	−0.451737
$763$	5080.15	0.241040
$764$	−531.161	−0.0251528
$765$	30936.9	1.46213
$766$	−20057.8	−0.946105
$767$	20502.0	0.965169
$768$	6281.63	0.295142
$769$	−20618.2	−0.966855	−0.483428	−	0.875384i	$-0.660608\pi$
$769$	−20618.2	−0.966855	−0.483428	+	0.875384i	$0.660608\pi$
$770$	5308.92	0.248468
$771$	−4370.83	−0.204165
$772$	−3958.63	−0.184552
$773$	−24258.7	−1.12875	−0.564376	−	0.825518i	$-0.690883\pi$
$773$	−24258.7	−1.12875	−0.564376	+	0.825518i	$0.690883\pi$
$774$	18815.6	0.873791
$775$	1911.04	0.0885762
$776$	2067.31	0.0956342
$777$	−4814.16	−0.222274
$778$	11538.0	0.531693
$779$	−10523.6	−0.484014
$780$	−2257.28	−0.103620
$781$	4979.93	0.228164
$782$	0	0
$783$	1819.05	0.0830237
$784$	16220.1	0.738891
$785$	35376.4	1.60846
$786$	−6375.94	−0.289341
$787$	9995.13	0.452717	0.226358	−	0.974044i	$-0.427318\pi$
$787$	9995.13	0.452717	0.226358	+	0.974044i	$0.427318\pi$
$788$	−3933.22	−0.177811
$789$	17961.3	0.810445
$790$	−9564.24	−0.430735
$791$	−3382.37	−0.152040
$792$	8004.03	0.359105
$793$	9518.03	0.426223
$794$	−23789.5	−1.06330
$795$	24944.4	1.11281
$796$	731.068	0.0325528
$797$	1482.34	0.0658812	0.0329406	−	0.999457i	$-0.489513\pi$
$797$	1482.34	0.0658812	0.0329406	+	0.999457i	$0.489513\pi$
$798$	−1481.06	−0.0657004
$799$	70797.9	3.13473
$800$	6631.48	0.293073
$801$	−10517.8	−0.463956
$802$	10424.7	0.458990
$803$	20387.8	0.895976
$804$	719.548	0.0315628
$805$	0	0
$806$	−1411.97	−0.0617053
$807$	−21564.7	−0.940663
$808$	−11627.5	−0.506254
$809$	−36583.1	−1.58985	−0.794927	−	0.606705i	$-0.792491\pi$
$809$	−36583.1	−1.58985	−0.794927	+	0.606705i	$0.792491\pi$
$810$	−3473.23	−0.150663
$811$	−10066.0	−0.435840	−0.217920	−	0.975967i	$-0.569927\pi$
$811$	−10066.0	−0.435840	−0.217920	+	0.975967i	$0.569927\pi$
$812$	−91.3028	−0.00394594
$813$	1684.44	0.0726640
$814$	13444.4	0.578903
$815$	1833.55	0.0788054
$816$	−23394.0	−1.00362
$817$	−13231.5	−0.566600
$818$	5001.71	0.213790
$819$	3111.43	0.132750
$820$	7231.59	0.307973
$821$	16365.4	0.695684	0.347842	−	0.937553i	$-0.386914\pi$
$821$	16365.4	0.695684	0.347842	+	0.937553i	$0.386914\pi$
$822$	3947.75	0.167511
$823$	−21157.8	−0.896128	−0.448064	−	0.894001i	$-0.647886\pi$
$823$	−21157.8	−0.896128	−0.448064	+	0.894001i	$0.647886\pi$
$824$	−3044.13	−0.128698
$825$	−9070.45	−0.382779
$826$	−9243.86	−0.389389
$827$	−7331.71	−0.308281	−0.154141	−	0.988049i	$-0.549261\pi$
$827$	−7331.71	−0.308281	−0.154141	+	0.988049i	$0.549261\pi$
$828$	0	0
$829$	3353.85	0.140511	0.0702557	−	0.997529i	$-0.477618\pi$
$829$	3353.85	0.140511	0.0702557	+	0.997529i	$0.477618\pi$
$830$	−37268.5	−1.55856
$831$	13741.6	0.573635
$832$	−19379.5	−0.807529
$833$	39812.3	1.65596
$834$	16992.8	0.705529
$835$	23159.5	0.959843
$836$	−746.233	−0.0308720
$837$	2288.35	0.0945007
$838$	−3410.40	−0.140585
$839$	47363.4	1.94895	0.974474	−	0.224502i	$-0.0720754\pi$
$839$	47363.4	1.94895	0.974474	+	0.224502i	$0.0720754\pi$
$840$	7676.57	0.315317
$841$	−24231.3	−0.993533
$842$	−8665.65	−0.354677
$843$	5549.87	0.226747
$844$	5581.01	0.227614
$845$	−15972.4	−0.650259
$846$	21710.3	0.882287
$847$	−5070.04	−0.205677
$848$	24456.7	0.990383
$849$	12710.2	0.513795
$850$	−40750.8	−1.64440
$851$	0	0
$852$	954.682	0.0383883
$853$	19153.0	0.768800	0.384400	−	0.923167i	$-0.374408\pi$
$853$	19153.0	0.768800	0.384400	+	0.923167i	$0.374408\pi$
$854$	−4291.45	−0.171956
$855$	−6671.33	−0.266848
$856$	−45565.8	−1.81940
$857$	−6136.91	−0.244612	−0.122306	−	0.992492i	$-0.539029\pi$
$857$	−6136.91	−0.244612	−0.122306	+	0.992492i	$0.539029\pi$
$858$	6701.69	0.266657
$859$	−30060.1	−1.19399	−0.596995	−	0.802245i	$-0.703639\pi$
$859$	−30060.1	−1.19399	−0.596995	+	0.802245i	$0.703639\pi$
$860$	9092.42	0.360522
$861$	7687.98	0.304304
$862$	−40832.2	−1.61340
$863$	42666.1	1.68293	0.841466	−	0.540309i	$-0.181693\pi$
$863$	42666.1	1.68293	0.841466	+	0.540309i	$0.181693\pi$
$864$	7940.80	0.312675
$865$	7437.81	0.292362
$866$	−24316.5	−0.954167
$867$	−40574.8	−1.58938
$868$	−114.858	−0.00449142
$869$	−5123.08	−0.199987
$870$	−1758.11	−0.0685122
$871$	−5891.94	−0.229209
$872$	−20514.4	−0.796680
$873$	1312.50	0.0508836
$874$	0	0
$875$	−376.603	−0.0145503
$876$	3908.45	0.150747
$877$	3581.50	0.137901	0.0689503	−	0.997620i	$-0.478035\pi$
$877$	3581.50	0.137901	0.0689503	+	0.997620i	$0.478035\pi$
$878$	5141.68	0.197635
$879$	−17219.5	−0.660751
$880$	−18083.2	−0.692708
$881$	−26861.6	−1.02723	−0.513616	−	0.858020i	$-0.671694\pi$
$881$	−26861.6	−1.02723	−0.513616	+	0.858020i	$0.671694\pi$
$882$	12208.5	0.466079
$883$	11078.7	0.422227	0.211114	−	0.977462i	$-0.432291\pi$
$883$	11078.7	0.422227	0.211114	+	0.977462i	$0.432291\pi$
$884$	−5432.16	−0.206678
$885$	32114.2	1.21978
$886$	−33979.1	−1.28843
$887$	4079.22	0.154416	0.0772078	−	0.997015i	$-0.475399\pi$
$887$	4079.22	0.154416	0.0772078	+	0.997015i	$0.475399\pi$
$888$	19440.3	0.734655
$889$	6329.28	0.238782
$890$	28171.2	1.06101
$891$	−1860.43	−0.0699515
$892$	−4579.41	−0.171895
$893$	−15267.1	−0.572110
$894$	3760.45	0.140680
$895$	−35078.5	−1.31010
$896$	6130.06	0.228561
$897$	0	0
$898$	7652.41	0.284370
$899$	198.412	0.00736086
$900$	2254.56	0.0835022
$901$	60028.8	2.21959
$902$	−21470.1	−0.792545
$903$	9666.24	0.356226
$904$	13658.5	0.502517
$905$	−44584.2	−1.63760
$906$	−7889.81	−0.289317
$907$	−5619.99	−0.205743	−0.102871	−	0.994695i	$-0.532803\pi$
$907$	−5619.99	−0.205743	−0.102871	+	0.994695i	$0.532803\pi$
$908$	−4066.42	−0.148622
$909$	−7382.09	−0.269360
$910$	−8333.74	−0.303583
$911$	−15003.0	−0.545635	−0.272817	−	0.962066i	$-0.587955\pi$
$911$	−15003.0	−0.545635	−0.272817	+	0.962066i	$0.587955\pi$
$912$	5044.75	0.183167
$913$	−19962.8	−0.723630
$914$	−12655.6	−0.457997
$915$	14909.0	0.538661
$916$	1571.65	0.0566907
$917$	4246.98	0.152942
$918$	−48796.6	−1.75439
$919$	11481.3	0.412114	0.206057	−	0.978540i	$-0.433937\pi$
$919$	11481.3	0.412114	0.206057	+	0.978540i	$0.433937\pi$
$920$	0	0
$921$	−15185.9	−0.543316
$922$	13665.3	0.488116
$923$	−7817.31	−0.278775
$924$	545.158	0.0194095
$925$	28564.1	1.01533
$926$	−10721.1	−0.380471
$927$	−1932.67	−0.0684759
$928$	688.507	0.0243549
$929$	−44831.9	−1.58330	−0.791651	−	0.610974i	$-0.790778\pi$
$929$	−44831.9	−1.58330	−0.791651	+	0.610974i	$0.790778\pi$
$930$	−2211.70	−0.0779832
$931$	−8585.25	−0.302224
$932$	−6808.94	−0.239307
$933$	−31492.4	−1.10505
$934$	−38520.9	−1.34951
$935$	−44385.1	−1.55246
$936$	−12564.4	−0.438762
$937$	−922.732	−0.0321711	−0.0160856	−	0.999871i	$-0.505120\pi$
$937$	−922.732	−0.0321711	−0.0160856	+	0.999871i	$0.505120\pi$
$938$	2656.53	0.0924721
$939$	−8543.70	−0.296926
$940$	10491.2	0.364028
$941$	−7858.15	−0.272230	−0.136115	−	0.990693i	$-0.543462\pi$
$941$	−7858.15	−0.272230	−0.136115	+	0.990693i	$0.543462\pi$
$942$	−20134.9	−0.696422
$943$	0	0
$944$	31486.3	1.08558
$945$	13506.4	0.464933
$946$	−26994.8	−0.927775
$947$	9843.50	0.337773	0.168886	−	0.985636i	$-0.445983\pi$
$947$	9843.50	0.337773	0.168886	+	0.985636i	$0.445983\pi$
$948$	−982.124	−0.0336476
$949$	−32003.9	−1.09472
$950$	8787.63	0.300114
$951$	17094.3	0.582882
$952$	18473.7	0.628925
$953$	−38484.7	−1.30812	−0.654062	−	0.756441i	$-0.726936\pi$
$953$	−38484.7	−1.30812	−0.654062	+	0.756441i	$0.726936\pi$
$954$	18407.9	0.624716
$955$	6812.79	0.230845
$956$	−1261.02	−0.0426615
$957$	−941.732	−0.0318097
$958$	11489.5	0.387483
$959$	−2629.58	−0.0885438
$960$	−30355.9	−1.02056
$961$	−29541.4	−0.991622
$962$	−21104.5	−0.707316
$963$	−28929.0	−0.968041
$964$	−3990.31	−0.133319
$965$	50774.2	1.69376
$966$	0	0
$967$	27609.5	0.918161	0.459081	−	0.888395i	$-0.348179\pi$
$967$	27609.5	0.918161	0.459081	+	0.888395i	$0.348179\pi$
$968$	20473.6	0.679799
$969$	12382.3	0.410504
$970$	−3515.44	−0.116365
$971$	14590.6	0.482219	0.241109	−	0.970498i	$-0.422489\pi$
$971$	14590.6	0.482219	0.241109	+	0.970498i	$0.422489\pi$
$972$	4425.22	0.146028
$973$	−11318.8	−0.372933
$974$	36666.6	1.20624
$975$	14238.4	0.467687
$976$	14617.5	0.479399
$977$	−36031.7	−1.17990	−0.589948	−	0.807442i	$-0.700852\pi$
$977$	−36031.7	−1.17990	−0.589948	+	0.807442i	$0.700852\pi$
$978$	−1043.58	−0.0341208
$979$	15089.9	0.492620
$980$	5899.60	0.192302
$981$	−13024.2	−0.423885
$982$	14483.4	0.470656
$983$	−60342.6	−1.95791	−0.978957	−	0.204069i	$-0.934583\pi$
$983$	−60342.6	−1.95791	−0.978957	+	0.204069i	$0.934583\pi$
$984$	−31045.2	−1.00578
$985$	50448.4	1.63190
$986$	−4230.91	−0.136653
$987$	11153.3	0.359690
$988$	1171.41	0.0377201
$989$	0	0
$990$	−13610.8	−0.436948
$991$	−19939.8	−0.639162	−0.319581	−	0.947559i	$-0.603542\pi$
$991$	−19939.8	−0.639162	−0.319581	+	0.947559i	$0.603542\pi$
$992$	866.139	0.0277217
$993$	21551.5	0.688738
$994$	3524.64	0.112469
$995$	−9376.84	−0.298760
$996$	−3826.99	−0.121750
$997$	−38178.9	−1.21278	−0.606388	−	0.795169i	$-0.707382\pi$
$997$	−38178.9	−1.21278	−0.606388	+	0.795169i	$0.707382\pi$
$998$	19770.3	0.627071
$999$	34203.8	1.08324

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.4.a.m.1.19		25
23.15	odd	22		23.4.c.a.18.2	yes	50
23.20	odd	22		23.4.c.a.9.2	✓	50
23.22	odd	2		529.4.a.n.1.19		25
69.20	even	22		207.4.i.a.55.4		50
69.38	even	22		207.4.i.a.64.4		50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.c.a.9.2	✓	50	23.20	odd	22
23.4.c.a.18.2	yes	50	23.15	odd	22
207.4.i.a.55.4		50	69.20	even	22
207.4.i.a.64.4		50	69.38	even	22
529.4.a.m.1.19		25	1.1	even	1	trivial
529.4.a.n.1.19		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)

\(f(q)\)	\(=\)	\(q+2.60332 q^{2} -3.42880 q^{3} -1.22274 q^{4} +15.6832 q^{5} -8.92624 q^{6} +5.94573 q^{7} -24.0097 q^{8} -15.2434 q^{9} +40.8282 q^{10} +21.8696 q^{11} +4.19253 q^{12} -34.3301 q^{13} +15.4786 q^{14} -53.7743 q^{15} -52.7230 q^{16} -129.408 q^{17} -39.6833 q^{18} +27.9061 q^{19} -19.1764 q^{20} -20.3867 q^{21} +56.9335 q^{22} +82.3244 q^{24} +120.961 q^{25} -89.3721 q^{26} +144.844 q^{27} -7.27009 q^{28} +12.5587 q^{29} -139.992 q^{30} +15.7988 q^{31} +54.8232 q^{32} -74.9864 q^{33} -336.891 q^{34} +93.2477 q^{35} +18.6387 q^{36} +236.142 q^{37} +72.6483 q^{38} +117.711 q^{39} -376.548 q^{40} -377.108 q^{41} -53.0730 q^{42} -474.145 q^{43} -26.7409 q^{44} -239.064 q^{45} -547.089 q^{47} +180.776 q^{48} -307.648 q^{49} +314.900 q^{50} +443.715 q^{51} +41.9768 q^{52} -463.871 q^{53} +377.074 q^{54} +342.984 q^{55} -142.755 q^{56} -95.6842 q^{57} +32.6943 q^{58} -597.203 q^{59} +65.7521 q^{60} -277.251 q^{61} +41.1292 q^{62} -90.6328 q^{63} +564.506 q^{64} -538.404 q^{65} -195.213 q^{66} +171.626 q^{67} +158.233 q^{68} +242.753 q^{70} +227.710 q^{71} +365.989 q^{72} +932.242 q^{73} +614.754 q^{74} -414.751 q^{75} -34.1219 q^{76} +130.031 q^{77} +306.439 q^{78} -234.256 q^{79} -826.862 q^{80} -85.0692 q^{81} -981.731 q^{82} -912.812 q^{83} +24.9276 q^{84} -2029.53 q^{85} -1234.35 q^{86} -43.0612 q^{87} -525.083 q^{88} +689.993 q^{89} -622.359 q^{90} -204.117 q^{91} -54.1708 q^{93} -1424.25 q^{94} +437.655 q^{95} -187.977 q^{96} -86.1031 q^{97} -800.906 q^{98} -333.366 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19}+ \cdots - 7317 q^{99}+O(q^{100}) \) 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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