LMFDB - Embedded newform 197.4.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,4,Mod(1,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, 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("197.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	197.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:	$11.6233762711$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	197.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-5.48735 q^{2} +9.71574 q^{3} +22.1111 q^{4} +4.58132 q^{5} -53.3137 q^{6} +25.8976 q^{7} -77.4324 q^{8} +67.3955 q^{9} -25.1393 q^{10} +39.0976 q^{11} +214.825 q^{12} +45.9957 q^{13} -142.109 q^{14} +44.5109 q^{15} +248.010 q^{16} -98.6487 q^{17} -369.823 q^{18} -75.0279 q^{19} +101.298 q^{20} +251.614 q^{21} -214.542 q^{22} -30.0829 q^{23} -752.312 q^{24} -104.012 q^{25} -252.395 q^{26} +392.472 q^{27} +572.622 q^{28} -202.560 q^{29} -244.247 q^{30} -191.875 q^{31} -741.462 q^{32} +379.862 q^{33} +541.320 q^{34} +118.645 q^{35} +1490.19 q^{36} +74.7942 q^{37} +411.705 q^{38} +446.882 q^{39} -354.742 q^{40} -106.106 q^{41} -1380.69 q^{42} +42.6517 q^{43} +864.490 q^{44} +308.760 q^{45} +165.075 q^{46} -319.877 q^{47} +2409.60 q^{48} +327.684 q^{49} +570.748 q^{50} -958.445 q^{51} +1017.01 q^{52} +26.4730 q^{53} -2153.64 q^{54} +179.119 q^{55} -2005.31 q^{56} -728.952 q^{57} +1111.52 q^{58} +57.5083 q^{59} +984.182 q^{60} -196.769 q^{61} +1052.89 q^{62} +1745.38 q^{63} +2084.58 q^{64} +210.721 q^{65} -2084.44 q^{66} +22.2964 q^{67} -2181.23 q^{68} -292.277 q^{69} -651.047 q^{70} +907.055 q^{71} -5218.60 q^{72} +8.84591 q^{73} -410.422 q^{74} -1010.55 q^{75} -1658.95 q^{76} +1012.53 q^{77} -2452.20 q^{78} -156.887 q^{79} +1136.21 q^{80} +1993.48 q^{81} +582.242 q^{82} -572.777 q^{83} +5563.45 q^{84} -451.941 q^{85} -234.045 q^{86} -1968.02 q^{87} -3027.42 q^{88} +1076.89 q^{89} -1694.28 q^{90} +1191.18 q^{91} -665.164 q^{92} -1864.21 q^{93} +1755.28 q^{94} -343.727 q^{95} -7203.85 q^{96} +875.835 q^{97} -1798.12 q^{98} +2635.01 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q + 4 q^{2} + 32 q^{3} + 128 q^{4} + 29 q^{5} + 36 q^{6} + 122 q^{7} + 27 q^{8} + 287 q^{9} + 127 q^{10} + 98 q^{11} + 256 q^{12} + 193 q^{13} + 113 q^{14} + 194 q^{15} + 672 q^{16} + 124 q^{17} + 61 q^{18}+ \cdots + 1940 q^{99}+O(q^{100}) $ 27 * q + 4 * q^2 + 32 * q^3 + 128 * q^4 + 29 * q^5 + 36 * q^6 + 122 * q^7 + 27 * q^8 + 287 * q^9 + 127 * q^10 + 98 * q^11 + 256 * q^12 + 193 * q^13 + 113 * q^14 + 194 * q^15 + 672 * q^16 + 124 * q^17 + 61 * q^18 + 535 * q^19 + 279 * q^20 + 188 * q^21 + 165 * q^22 + 344 * q^23 + 165 * q^24 + 910 * q^25 - 44 * q^26 + 1382 * q^27 + 1038 * q^28 + 346 * q^29 + 115 * q^30 + 599 * q^31 + 100 * q^32 + 794 * q^33 + 886 * q^34 + 12 * q^35 + 1714 * q^36 + 1428 * q^37 + 1108 * q^38 + 568 * q^39 + 1206 * q^40 + 549 * q^41 + 355 * q^42 + 2091 * q^43 + 586 * q^44 + 1167 * q^45 + 469 * q^46 + 1270 * q^47 + 2258 * q^48 + 2165 * q^49 - 353 * q^50 - 128 * q^51 + 1000 * q^52 - 208 * q^53 - 2945 * q^54 + 810 * q^55 - 5592 * q^56 - 1006 * q^57 + 287 * q^58 + 603 * q^59 - 2211 * q^60 - 314 * q^61 - 1347 * q^62 + 2416 * q^63 + 5 * q^64 - 1958 * q^65 - 8706 * q^66 + 4372 * q^67 - 6709 * q^68 - 306 * q^69 - 4329 * q^70 - 871 * q^71 - 7589 * q^72 + 942 * q^73 - 5237 * q^74 - 1530 * q^75 - 2470 * q^76 - 1868 * q^77 - 10179 * q^78 - 197 * q^79 - 1882 * q^80 + 1083 * q^81 - 961 * q^82 - 799 * q^83 - 3140 * q^84 - 1444 * q^85 - 7066 * q^86 - 794 * q^87 - 2409 * q^88 - 572 * q^89 - 10939 * q^90 + 3872 * q^91 - 6154 * q^92 - 1506 * q^93 + 1231 * q^94 - 756 * q^95 - 10975 * q^96 + 6335 * q^97 - 5330 * q^98 + 1940 * 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 $

$2$	−5.48735	−1.94007	−0.970036	−	0.242960i	$-0.921882\pi$
$2$	−5.48735	−1.94007	−0.970036	+	0.242960i	$0.921882\pi$
$3$	9.71574	1.86979	0.934897	−	0.354919i	$-0.115491\pi$
$3$	9.71574	1.86979	0.934897	+	0.354919i	$0.115491\pi$
$4$	22.1111	2.76388
$5$	4.58132	0.409765	0.204883	−	0.978787i	$-0.434319\pi$
$5$	4.58132	0.409765	0.204883	+	0.978787i	$0.434319\pi$
$6$	−53.3137	−3.62754
$7$	25.8976	1.39834	0.699168	−	0.714957i	$-0.253554\pi$
$7$	25.8976	1.39834	0.699168	+	0.714957i	$0.253554\pi$
$8$	−77.4324	−3.42206
$9$	67.3955	2.49613
$10$	−25.1393	−0.794975
$11$	39.0976	1.07167	0.535835	−	0.844323i	$-0.319997\pi$
$11$	39.0976	1.07167	0.535835	+	0.844323i	$0.319997\pi$
$12$	214.825	5.16789
$13$	45.9957	0.981300	0.490650	−	0.871357i	$-0.336759\pi$
$13$	45.9957	0.981300	0.490650	+	0.871357i	$0.336759\pi$
$14$	−142.109	−2.71287
$15$	44.5109	0.766177
$16$	248.010	3.87516
$17$	−98.6487	−1.40740	−0.703701	−	0.710496i	$-0.748470\pi$
$17$	−98.6487	−1.40740	−0.703701	+	0.710496i	$0.748470\pi$
$18$	−369.823	−4.84268
$19$	−75.0279	−0.905926	−0.452963	−	0.891529i	$-0.649633\pi$
$19$	−75.0279	−0.905926	−0.452963	+	0.891529i	$0.649633\pi$
$20$	101.298	1.13254
$21$	251.614	2.61460
$22$	−214.542	−2.07912
$23$	−30.0829	−0.272727	−0.136363	−	0.990659i	$-0.543541\pi$
$23$	−30.0829	−0.272727	−0.136363	+	0.990659i	$0.543541\pi$
$24$	−752.312	−6.39855
$25$	−104.012	−0.832092
$26$	−252.395	−1.90379
$27$	392.472	2.79746
$28$	572.622	3.86484
$29$	−202.560	−1.29705	−0.648526	−	0.761193i	$-0.724614\pi$
$29$	−202.560	−1.29705	−0.648526	+	0.761193i	$0.724614\pi$
$30$	−244.247	−1.48644
$31$	−191.875	−1.11167	−0.555836	−	0.831292i	$-0.687602\pi$
$31$	−191.875	−1.11167	−0.555836	+	0.831292i	$0.687602\pi$
$32$	−741.462	−4.09604
$33$	379.862	2.00380
$34$	541.320	2.73046
$35$	118.645	0.572990
$36$	1490.19	6.89901
$37$	74.7942	0.332327	0.166163	−	0.986098i	$-0.446862\pi$
$37$	74.7942	0.332327	0.166163	+	0.986098i	$0.446862\pi$
$38$	411.705	1.75756
$39$	446.882	1.83483
$40$	−354.742	−1.40224
$41$	−106.106	−0.404171	−0.202085	−	0.979368i	$-0.564772\pi$
$41$	−106.106	−0.404171	−0.202085	+	0.979368i	$0.564772\pi$
$42$	−1380.69	−5.07252
$43$	42.6517	0.151263	0.0756317	−	0.997136i	$-0.475903\pi$
$43$	42.6517	0.151263	0.0756317	+	0.997136i	$0.475903\pi$
$44$	864.490	2.96197
$45$	308.760	1.02283
$46$	165.075	0.529110
$47$	−319.877	−0.992742	−0.496371	−	0.868110i	$-0.665334\pi$
$47$	−319.877	−0.992742	−0.496371	+	0.868110i	$0.665334\pi$
$48$	2409.60	7.24576
$49$	327.684	0.955346
$50$	570.748	1.61432
$51$	−958.445	−2.63155
$52$	1017.01	2.71220
$53$	26.4730	0.0686104	0.0343052	−	0.999411i	$-0.489078\pi$
$53$	26.4730	0.0686104	0.0343052	+	0.999411i	$0.489078\pi$
$54$	−2153.64	−5.42727
$55$	179.119	0.439133
$56$	−2005.31	−4.78519
$57$	−728.952	−1.69389
$58$	1111.52	2.51637
$59$	57.5083	0.126897	0.0634487	−	0.997985i	$-0.479790\pi$
$59$	57.5083	0.126897	0.0634487	+	0.997985i	$0.479790\pi$
$60$	984.182	2.11762
$61$	−196.769	−0.413010	−0.206505	−	0.978446i	$-0.566209\pi$
$61$	−196.769	−0.413010	−0.206505	+	0.978446i	$0.566209\pi$
$62$	1052.89	2.15673
$63$	1745.38	3.49043
$64$	2084.58	4.07145
$65$	210.721	0.402103
$66$	−2084.44	−3.88752
$67$	22.2964	0.0406558	0.0203279	−	0.999793i	$-0.493529\pi$
$67$	22.2964	0.0406558	0.0203279	+	0.999793i	$0.493529\pi$
$68$	−2181.23	−3.88989
$69$	−292.277	−0.509943
$70$	−651.047	−1.11164
$71$	907.055	1.51616	0.758082	−	0.652159i	$-0.226137\pi$
$71$	907.055	1.51616	0.758082	+	0.652159i	$0.226137\pi$
$72$	−5218.60	−8.54191
$73$	8.84591	0.0141827	0.00709134	−	0.999975i	$-0.497743\pi$
$73$	8.84591	0.0141827	0.00709134	+	0.999975i	$0.497743\pi$
$74$	−410.422	−0.644738
$75$	−1010.55	−1.55584
$76$	−1658.95	−2.50387
$77$	1012.53	1.49856
$78$	−2452.20	−3.55970
$79$	−156.887	−0.223432	−0.111716	−	0.993740i	$-0.535635\pi$
$79$	−156.887	−0.223432	−0.111716	+	0.993740i	$0.535635\pi$
$80$	1136.21	1.58791
$81$	1993.48	2.73454
$82$	582.242	0.784120
$83$	−572.777	−0.757475	−0.378738	−	0.925504i	$-0.623642\pi$
$83$	−572.777	−0.757475	−0.378738	+	0.925504i	$0.623642\pi$
$84$	5563.45	7.22645
$85$	−451.941	−0.576704
$86$	−234.045	−0.293462
$87$	−1968.02	−2.42522
$88$	−3027.42	−3.66732
$89$	1076.89	1.28258	0.641291	−	0.767298i	$-0.278399\pi$
$89$	1076.89	1.28258	0.641291	+	0.767298i	$0.278399\pi$
$90$	−1694.28	−1.98436
$91$	1191.18	1.37219
$92$	−665.164	−0.753785
$93$	−1864.21	−2.07860
$94$	1755.28	1.92599
$95$	−343.727	−0.371217
$96$	−7203.85	−7.65875
$97$	875.835	0.916779	0.458389	−	0.888751i	$-0.348427\pi$
$97$	875.835	0.916779	0.458389	+	0.888751i	$0.348427\pi$
$98$	−1798.12	−1.85344
$99$	2635.01	2.67503
$100$	−2299.81	−2.29981
$101$	486.190	0.478987	0.239494	−	0.970898i	$-0.423019\pi$
$101$	486.190	0.478987	0.239494	+	0.970898i	$0.423019\pi$
$102$	5259.33	5.10540
$103$	−37.9860	−0.0363386	−0.0181693	−	0.999835i	$-0.505784\pi$
$103$	−37.9860	−0.0363386	−0.0181693	+	0.999835i	$0.505784\pi$
$104$	−3561.55	−3.35807
$105$	1152.72	1.07137
$106$	−145.267	−0.133109
$107$	−1414.93	−1.27838	−0.639189	−	0.769049i	$-0.720730\pi$
$107$	−1414.93	−1.27838	−0.639189	+	0.769049i	$0.720730\pi$
$108$	8677.98	7.73184
$109$	558.404	0.490692	0.245346	−	0.969436i	$-0.421098\pi$
$109$	558.404	0.490692	0.245346	+	0.969436i	$0.421098\pi$
$110$	−982.887	−0.851951
$111$	726.681	0.621383
$112$	6422.86	5.41878
$113$	670.769	0.558413	0.279207	−	0.960231i	$-0.409929\pi$
$113$	670.769	0.558413	0.279207	+	0.960231i	$0.409929\pi$
$114$	4000.02	3.28628
$115$	−137.819	−0.111754
$116$	−4478.82	−3.58490
$117$	3099.90	2.44945
$118$	−315.569	−0.246190
$119$	−2554.76	−1.96802
$120$	−3446.58	−2.62190
$121$	197.624	0.148478
$122$	1079.74	0.801270
$123$	−1030.90	−0.755716
$124$	−4242.57	−3.07253
$125$	−1049.17	−0.750728
$126$	−9577.52	−6.77169
$127$	1278.84	0.893533	0.446767	−	0.894651i	$-0.352575\pi$
$127$	1278.84	0.893533	0.446767	+	0.894651i	$0.352575\pi$
$128$	−5507.14	−3.80287
$129$	414.393	0.282832
$130$	−1156.30	−0.780109
$131$	−2611.02	−1.74142	−0.870711	−	0.491795i	$-0.836341\pi$
$131$	−2611.02	−1.74142	−0.870711	+	0.491795i	$0.836341\pi$
$132$	8399.15	5.53828
$133$	−1943.04	−1.26679
$134$	−122.348	−0.0788753
$135$	1798.04	1.14630
$136$	7638.60	4.81621
$137$	−64.3621	−0.0401374	−0.0200687	−	0.999799i	$-0.506388\pi$
$137$	−64.3621	−0.0401374	−0.0200687	+	0.999799i	$0.506388\pi$
$138$	1603.83	0.989326
$139$	−1239.34	−0.756255	−0.378127	−	0.925754i	$-0.623432\pi$
$139$	−1239.34	−0.756255	−0.378127	+	0.925754i	$0.623432\pi$
$140$	2623.36	1.58368
$141$	−3107.84	−1.85622
$142$	−4977.33	−2.94147
$143$	1798.32	1.05163
$144$	16714.8	9.67291
$145$	−927.992	−0.531487
$146$	−48.5406	−0.0275154
$147$	3183.69	1.78630
$148$	1653.78	0.918512
$149$	2128.19	1.17012	0.585059	−	0.810990i	$-0.301071\pi$
$149$	2128.19	1.17012	0.585059	+	0.810990i	$0.301071\pi$
$150$	5545.24	3.01845
$151$	−2060.52	−1.11048	−0.555240	−	0.831690i	$-0.687374\pi$
$151$	−2060.52	−1.11048	−0.555240	+	0.831690i	$0.687374\pi$
$152$	5809.59	3.10013
$153$	−6648.48	−3.51306
$154$	−5556.13	−2.90731
$155$	−879.042	−0.455525
$156$	9881.03	5.07125
$157$	−273.582	−0.139071	−0.0695356	−	0.997579i	$-0.522152\pi$
$157$	−273.582	−0.139071	−0.0695356	+	0.997579i	$0.522152\pi$
$158$	860.893	0.433475
$159$	257.205	0.128287
$160$	−3396.87	−1.67841
$161$	−779.073	−0.381364
$162$	−10938.9	−5.30521
$163$	3634.97	1.74670	0.873352	−	0.487089i	$-0.161941\pi$
$163$	3634.97	1.74670	0.873352	+	0.487089i	$0.161941\pi$
$164$	−2346.12	−1.11708
$165$	1740.27	0.821089
$166$	3143.03	1.46956
$167$	−178.178	−0.0825620	−0.0412810	−	0.999148i	$-0.513144\pi$
$167$	−178.178	−0.0825620	−0.0412810	+	0.999148i	$0.513144\pi$
$168$	−19483.1	−8.94732
$169$	−81.3980	−0.0370496
$170$	2479.96	1.11885
$171$	−5056.55	−2.26131
$172$	943.075	0.418074
$173$	4514.91	1.98417	0.992086	−	0.125557i	$-0.0400719\pi$
$173$	4514.91	1.98417	0.992086	+	0.125557i	$0.0400719\pi$
$174$	10799.2	4.70510
$175$	−2693.65	−1.16355
$176$	9696.61	4.15290
$177$	558.736	0.237272
$178$	−5909.26	−2.48830
$179$	554.379	0.231487	0.115744	−	0.993279i	$-0.463075\pi$
$179$	554.379	0.231487	0.115744	+	0.993279i	$0.463075\pi$
$180$	6827.02	2.82698
$181$	−4328.20	−1.77742	−0.888709	−	0.458472i	$-0.848397\pi$
$181$	−4328.20	−1.77742	−0.888709	+	0.458472i	$0.848397\pi$
$182$	−6536.40	−2.66215
$183$	−1911.75	−0.772244
$184$	2329.39	0.933287
$185$	342.656	0.136176
$186$	10229.6	4.03263
$187$	−3856.93	−1.50827
$188$	−7072.82	−2.74382
$189$	10164.1	3.91179
$190$	1886.15	0.720188
$191$	−3521.02	−1.33388	−0.666942	−	0.745110i	$-0.732397\pi$
$191$	−3521.02	−1.33388	−0.666942	+	0.745110i	$0.732397\pi$
$192$	20253.2	7.61277
$193$	1222.02	0.455767	0.227883	−	0.973688i	$-0.426820\pi$
$193$	1222.02	0.455767	0.227883	+	0.973688i	$0.426820\pi$
$194$	−4806.01	−1.77862
$195$	2047.31	0.751850
$196$	7245.43	2.64046
$197$	−197.000	−0.0712470
$197$	−197.000	−0.0712470
$198$	−14459.2	−5.18975
$199$	−1241.22	−0.442151	−0.221075	−	0.975257i	$-0.570957\pi$
$199$	−1241.22	−0.442151	−0.221075	+	0.975257i	$0.570957\pi$
$200$	8053.86	2.84747
$201$	216.626	0.0760180
$202$	−2667.90	−0.929270
$203$	−5245.81	−1.81371
$204$	−21192.2	−7.27330
$205$	−486.106	−0.165615
$206$	208.443	0.0704995
$207$	−2027.45	−0.680762
$208$	11407.4	3.80270
$209$	−2933.41	−0.970854
$210$	−6325.40	−2.07854
$211$	−2158.56	−0.704272	−0.352136	−	0.935949i	$-0.614544\pi$
$211$	−2158.56	−0.704272	−0.352136	+	0.935949i	$0.614544\pi$
$212$	585.347	0.189631
$213$	8812.71	2.83492
$214$	7764.23	2.48015
$215$	195.401	0.0619825
$216$	−30390.1	−9.57307
$217$	−4969.11	−1.55449
$218$	−3064.16	−0.951978
$219$	85.9445	0.0265187
$220$	3960.50	1.21371
$221$	−4537.41	−1.38108
$222$	−3987.55	−1.20553
$223$	4189.73	1.25814	0.629069	−	0.777349i	$-0.283436\pi$
$223$	4189.73	1.25814	0.629069	+	0.777349i	$0.283436\pi$
$224$	−19202.1	−5.72764
$225$	−7009.91	−2.07701
$226$	−3680.75	−1.08336
$227$	4287.90	1.25374	0.626868	−	0.779126i	$-0.284337\pi$
$227$	4287.90	1.25374	0.626868	+	0.779126i	$0.284337\pi$
$228$	−16117.9	−4.68173
$229$	4026.47	1.16191	0.580954	−	0.813936i	$-0.302680\pi$
$229$	4026.47	1.16191	0.580954	+	0.813936i	$0.302680\pi$
$230$	756.263	0.216811
$231$	9837.50	2.80199
$232$	15684.7	4.43859
$233$	1412.30	0.397094	0.198547	−	0.980091i	$-0.436378\pi$
$233$	1412.30	0.397094	0.198547	+	0.980091i	$0.436378\pi$
$234$	−17010.3	−4.75212
$235$	−1465.46	−0.406791
$236$	1271.57	0.350729
$237$	−1524.27	−0.417772
$238$	14018.9	3.81810
$239$	474.159	0.128330	0.0641649	−	0.997939i	$-0.479562\pi$
$239$	474.159	0.128330	0.0641649	+	0.997939i	$0.479562\pi$
$240$	11039.2	2.96906
$241$	1530.14	0.408983	0.204491	−	0.978868i	$-0.434446\pi$
$241$	1530.14	0.408983	0.204491	+	0.978868i	$0.434446\pi$
$242$	−1084.43	−0.288057
$243$	8771.37	2.31557
$244$	−4350.76	−1.14151
$245$	1501.22	0.391467
$246$	5656.91	1.46614
$247$	−3450.96	−0.888985
$248$	14857.4	3.80421
$249$	−5564.95	−1.41632
$250$	5757.19	1.45647
$251$	3748.78	0.942712	0.471356	−	0.881943i	$-0.343765\pi$
$251$	3748.78	0.942712	0.471356	+	0.881943i	$0.343765\pi$
$252$	38592.2	9.64714
$253$	−1176.17	−0.292273
$254$	−7017.45	−1.73352
$255$	−4390.94	−1.07832
$256$	13543.0	3.30639
$257$	7597.48	1.84404	0.922019	−	0.387144i	$-0.126538\pi$
$257$	7597.48	1.84404	0.922019	+	0.387144i	$0.126538\pi$
$258$	−2273.92	−0.548714
$259$	1936.99	0.464705
$260$	4659.26	1.11136
$261$	−13651.7	−3.23761
$262$	14327.6	3.37848
$263$	−1561.63	−0.366138	−0.183069	−	0.983100i	$-0.558603\pi$
$263$	−1561.63	−0.366138	−0.183069	+	0.983100i	$0.558603\pi$
$264$	−29413.6	−6.85713
$265$	121.281	0.0281142
$266$	10662.1	2.45766
$267$	10462.7	2.39816
$268$	492.997	0.112368
$269$	−2266.19	−0.513651	−0.256826	−	0.966458i	$-0.582677\pi$
$269$	−2266.19	−0.513651	−0.256826	+	0.966458i	$0.582677\pi$
$270$	−9866.48	−2.22391
$271$	−2692.36	−0.603503	−0.301751	−	0.953387i	$-0.597571\pi$
$271$	−2692.36	−0.603503	−0.301751	+	0.953387i	$0.597571\pi$
$272$	−24465.9	−5.45391
$273$	11573.1	2.56571
$274$	353.177	0.0778694
$275$	−4066.60	−0.891729
$276$	−6462.56	−1.40942
$277$	−6346.61	−1.37664	−0.688322	−	0.725405i	$-0.741653\pi$
$277$	−6346.61	−1.37664	−0.688322	+	0.725405i	$0.741653\pi$
$278$	6800.69	1.46719
$279$	−12931.6	−2.77488
$280$	−9186.95	−1.96081
$281$	7780.13	1.65169	0.825843	−	0.563900i	$-0.190700\pi$
$281$	7780.13	1.65169	0.825843	+	0.563900i	$0.190700\pi$
$282$	17053.8	3.60121
$283$	4755.19	0.998822	0.499411	−	0.866365i	$-0.333550\pi$
$283$	4755.19	0.998822	0.499411	+	0.866365i	$0.333550\pi$
$284$	20056.0	4.19050
$285$	−3339.56	−0.694099
$286$	−9868.03	−2.04024
$287$	−2747.89	−0.565167
$288$	−49971.2	−10.2242
$289$	4818.57	0.980780
$290$	5092.22	1.03112
$291$	8509.38	1.71419
$292$	195.592	0.0391992
$293$	−880.143	−0.175490	−0.0877449	−	0.996143i	$-0.527966\pi$
$293$	−880.143	−0.175490	−0.0877449	+	0.996143i	$0.527966\pi$
$294$	−17470.0	−3.46555
$295$	263.464	0.0519982
$296$	−5791.49	−1.13724
$297$	15344.7	2.99795
$298$	−11678.1	−2.27012
$299$	−1383.68	−0.267627
$300$	−22344.3	−4.30016
$301$	1104.58	0.211517
$302$	11306.8	2.15441
$303$	4723.70	0.895608
$304$	−18607.7	−3.51061
$305$	−901.459	−0.169237
$306$	36482.6	6.81559
$307$	10077.0	1.87336	0.936682	−	0.350181i	$-0.113880\pi$
$307$	10077.0	1.87336	0.936682	+	0.350181i	$0.113880\pi$
$308$	22388.2	4.14183
$309$	−369.062	−0.0679457
$310$	4823.62	0.883751
$311$	−589.544	−0.107492	−0.0537459	−	0.998555i	$-0.517116\pi$
$311$	−589.544	−0.107492	−0.0537459	+	0.998555i	$0.517116\pi$
$312$	−34603.1	−6.27890
$313$	−1228.86	−0.221914	−0.110957	−	0.993825i	$-0.535392\pi$
$313$	−1228.86	−0.221914	−0.110957	+	0.993825i	$0.535392\pi$
$314$	1501.24	0.269808
$315$	7996.14	1.43026
$316$	−3468.93	−0.617540
$317$	−4467.39	−0.791525	−0.395763	−	0.918353i	$-0.629520\pi$
$317$	−4467.39	−0.791525	−0.395763	+	0.918353i	$0.629520\pi$
$318$	−1411.38	−0.248887
$319$	−7919.62	−1.39001
$320$	9550.12	1.66834
$321$	−13747.1	−2.39031
$322$	4275.05	0.739874
$323$	7401.41	1.27500
$324$	44077.9	7.55795
$325$	−4784.08	−0.816533
$326$	−19946.4	−3.38873
$327$	5425.31	0.917493
$328$	8216.05	1.38310
$329$	−8284.04	−1.38819
$330$	−9549.47	−1.59297
$331$	−10943.6	−1.81727	−0.908635	−	0.417591i	$-0.862875\pi$
$331$	−10943.6	−1.81727	−0.908635	+	0.417591i	$0.862875\pi$
$332$	−12664.7	−2.09357
$333$	5040.79	0.829531
$334$	977.728	0.160176
$335$	102.147	0.0166593
$336$	62402.8	10.1320
$337$	−9992.98	−1.61529	−0.807644	−	0.589670i	$-0.799258\pi$
$337$	−9992.98	−1.61529	−0.807644	+	0.589670i	$0.799258\pi$
$338$	446.660	0.0718789
$339$	6517.02	1.04412
$340$	−9992.89	−1.59394
$341$	−7501.87	−1.19135
$342$	27747.1	4.38710
$343$	−396.659	−0.0624420
$344$	−3302.62	−0.517633
$345$	−1339.02	−0.208957
$346$	−24774.9	−3.84944
$347$	11844.5	1.83240	0.916202	−	0.400718i	$-0.131239\pi$
$347$	11844.5	1.83240	0.916202	+	0.400718i	$0.131239\pi$
$348$	−43515.0	−6.70302
$349$	6913.74	1.06041	0.530207	−	0.847868i	$-0.322114\pi$
$349$	6913.74	1.06041	0.530207	+	0.847868i	$0.322114\pi$
$350$	14781.0	2.25736
$351$	18052.0	2.74515
$352$	−28989.4	−4.38960
$353$	12217.6	1.84215	0.921076	−	0.389382i	$-0.127311\pi$
$353$	12217.6	1.84215	0.921076	+	0.389382i	$0.127311\pi$
$354$	−3065.98	−0.460325
$355$	4155.51	0.621271
$356$	23811.1	3.54490
$357$	−24821.4	−3.67980
$358$	−3042.08	−0.449103
$359$	−2573.76	−0.378378	−0.189189	−	0.981941i	$-0.560586\pi$
$359$	−2573.76	−0.378378	−0.189189	+	0.981941i	$0.560586\pi$
$360$	−23908.0	−3.50018
$361$	−1229.81	−0.179299
$362$	23750.4	3.44832
$363$	1920.06	0.277623
$364$	26338.2	3.79257
$365$	40.5259	0.00581157
$366$	10490.5	1.49821
$367$	7202.97	1.02450	0.512251	−	0.858836i	$-0.328812\pi$
$367$	7202.97	1.02450	0.512251	+	0.858836i	$0.328812\pi$
$368$	−7460.87	−1.05686
$369$	−7151.08	−1.00886
$370$	−1880.27	−0.264191
$371$	685.587	0.0959405
$372$	−41219.7	−5.74500
$373$	−10255.9	−1.42367	−0.711836	−	0.702346i	$-0.752136\pi$
$373$	−10255.9	−1.42367	−0.711836	+	0.702346i	$0.752136\pi$
$374$	21164.3	2.92616
$375$	−10193.5	−1.40371
$376$	24768.9	3.39722
$377$	−9316.89	−1.27280
$378$	−55773.9	−7.58915
$379$	−1008.26	−0.136651	−0.0683254	−	0.997663i	$-0.521766\pi$
$379$	−1008.26	−0.136651	−0.0683254	+	0.997663i	$0.521766\pi$
$380$	−7600.16	−1.02600
$381$	12424.9	1.67072
$382$	19321.1	2.58783
$383$	−12891.0	−1.71984	−0.859921	−	0.510428i	$-0.829487\pi$
$383$	−12891.0	−1.71984	−0.859921	+	0.510428i	$0.829487\pi$
$384$	−53505.9	−7.11058
$385$	4638.73	0.614056
$386$	−6705.66	−0.884220
$387$	2874.54	0.377573
$388$	19365.6	2.53387
$389$	−14490.8	−1.88872	−0.944362	−	0.328908i	$-0.893319\pi$
$389$	−14490.8	−1.88872	−0.944362	+	0.328908i	$0.893319\pi$
$390$	−11234.3	−1.45864
$391$	2967.64	0.383836
$392$	−25373.3	−3.26925
$393$	−25368.0	−3.25610
$394$	1081.01	0.138224
$395$	−718.748	−0.0915548
$396$	58262.8	7.39347
$397$	−11352.4	−1.43516	−0.717580	−	0.696477i	$-0.754750\pi$
$397$	−11352.4	−1.43516	−0.717580	+	0.696477i	$0.754750\pi$
$398$	6811.03	0.857805
$399$	−18878.1	−2.36864
$400$	−25795.9	−3.22449
$401$	1027.11	0.127909	0.0639546	−	0.997953i	$-0.479629\pi$
$401$	1027.11	0.127909	0.0639546	+	0.997953i	$0.479629\pi$
$402$	−1188.70	−0.147481
$403$	−8825.44	−1.09088
$404$	10750.2	1.32386
$405$	9132.76	1.12052
$406$	28785.6	3.51874
$407$	2924.27	0.356145
$408$	74214.7	9.00533
$409$	7555.90	0.913485	0.456742	−	0.889599i	$-0.349016\pi$
$409$	7555.90	0.913485	0.456742	+	0.889599i	$0.349016\pi$
$410$	2667.43	0.321305
$411$	−625.325	−0.0750487
$412$	−839.911	−0.100436
$413$	1489.33	0.177445
$414$	11125.4	1.32073
$415$	−2624.07	−0.310387
$416$	−34104.0	−4.01944
$417$	−12041.1	−1.41404
$418$	16096.7	1.88353
$419$	−1952.80	−0.227686	−0.113843	−	0.993499i	$-0.536316\pi$
$419$	−1952.80	−0.227686	−0.113843	+	0.993499i	$0.536316\pi$
$420$	25487.9	2.96115
$421$	−14305.3	−1.65605	−0.828026	−	0.560689i	$-0.810536\pi$
$421$	−14305.3	−1.65605	−0.828026	+	0.560689i	$0.810536\pi$
$422$	11844.8	1.36634
$423$	−21558.3	−2.47802
$424$	−2049.87	−0.234789
$425$	10260.6	1.17109
$426$	−48358.5	−5.49994
$427$	−5095.82	−0.577527
$428$	−31285.6	−3.53329
$429$	17472.0	1.96633
$430$	−1072.23	−0.120251
$431$	12560.7	1.40378	0.701890	−	0.712285i	$-0.252340\pi$
$431$	12560.7	1.40378	0.701890	+	0.712285i	$0.252340\pi$
$432$	97337.2	10.8406
$433$	13084.4	1.45219	0.726093	−	0.687597i	$-0.241334\pi$
$433$	13084.4	1.45219	0.726093	+	0.687597i	$0.241334\pi$
$434$	27267.2	3.01583
$435$	−9016.13	−0.993771
$436$	12346.9	1.35621
$437$	2257.06	0.247070
$438$	−471.608	−0.0514482
$439$	−3928.93	−0.427147	−0.213574	−	0.976927i	$-0.568510\pi$
$439$	−3928.93	−0.427147	−0.213574	+	0.976927i	$0.568510\pi$
$440$	−13869.6	−1.50274
$441$	22084.4	2.38467
$442$	24898.4	2.67940
$443$	12445.3	1.33475	0.667377	−	0.744720i	$-0.267417\pi$
$443$	12445.3	1.33475	0.667377	+	0.744720i	$0.267417\pi$
$444$	16067.7	1.71743
$445$	4933.56	0.525557
$446$	−22990.5	−2.44088
$447$	20676.9	2.18788
$448$	53985.5	5.69325
$449$	14248.8	1.49764	0.748822	−	0.662771i	$-0.230620\pi$
$449$	14248.8	1.49764	0.748822	+	0.662771i	$0.230620\pi$
$450$	38465.9	4.02955
$451$	−4148.50	−0.433138
$452$	14831.4	1.54339
$453$	−20019.4	−2.07637
$454$	−23529.2	−2.43234
$455$	5457.15	0.562275
$456$	56444.4	5.79661
$457$	−12248.9	−1.25379	−0.626895	−	0.779104i	$-0.715674\pi$
$457$	−12248.9	−1.25379	−0.626895	+	0.779104i	$0.715674\pi$
$458$	−22094.7	−2.25419
$459$	−38716.9	−3.93715
$460$	−3047.33	−0.308875
$461$	−3292.23	−0.332612	−0.166306	−	0.986074i	$-0.553184\pi$
$461$	−3292.23	−0.332612	−0.166306	+	0.986074i	$0.553184\pi$
$462$	−53981.9	−5.43607
$463$	8135.92	0.816649	0.408324	−	0.912837i	$-0.366113\pi$
$463$	8135.92	0.816649	0.408324	+	0.912837i	$0.366113\pi$
$464$	−50237.0	−5.02628
$465$	−8540.54	−0.851738
$466$	−7749.80	−0.770391
$467$	1453.16	0.143992	0.0719960	−	0.997405i	$-0.477063\pi$
$467$	1453.16	0.143992	0.0719960	+	0.997405i	$0.477063\pi$
$468$	68542.1	6.77000
$469$	577.423	0.0568505
$470$	8041.49	0.789205
$471$	−2658.05	−0.260035
$472$	−4453.01	−0.434250
$473$	1667.58	0.162105
$474$	8364.21	0.810509
$475$	7803.77	0.753814
$476$	−56488.5	−5.43938
$477$	1784.17	0.171261
$478$	−2601.88	−0.248969
$479$	13876.3	1.32364	0.661819	−	0.749664i	$-0.269785\pi$
$479$	13876.3	1.32364	0.661819	+	0.749664i	$0.269785\pi$
$480$	−33003.1	−3.13829
$481$	3440.21	0.326112
$482$	−8396.41	−0.793457
$483$	−7569.27	−0.713072
$484$	4369.67	0.410375
$485$	4012.47	0.375664
$486$	−48131.6	−4.49237
$487$	12578.8	1.17043	0.585217	−	0.810877i	$-0.301009\pi$
$487$	12578.8	1.17043	0.585217	+	0.810877i	$0.301009\pi$
$488$	15236.3	1.41335
$489$	35316.4	3.26598
$490$	−8237.73	−0.759475
$491$	−2569.11	−0.236135	−0.118067	−	0.993006i	$-0.537670\pi$
$491$	−2569.11	−0.236135	−0.118067	+	0.993006i	$0.537670\pi$
$492$	−22794.3	−2.08871
$493$	19982.3	1.82547
$494$	18936.6	1.72470
$495$	12071.8	1.09613
$496$	−47587.1	−4.30791
$497$	23490.5	2.12011
$498$	30536.9	2.74777
$499$	−17056.0	−1.53013	−0.765063	−	0.643955i	$-0.777292\pi$
$499$	−17056.0	−1.53013	−0.765063	+	0.643955i	$0.777292\pi$
$500$	−23198.3	−2.07492
$501$	−1731.13	−0.154374
$502$	−20570.9	−1.82893
$503$	−10615.3	−0.940982	−0.470491	−	0.882405i	$-0.655923\pi$
$503$	−10615.3	−0.940982	−0.470491	+	0.882405i	$0.655923\pi$
$504$	−135149.	−11.9445
$505$	2227.39	0.196272
$506$	6454.06	0.567031
$507$	−790.841	−0.0692751
$508$	28276.5	2.46962
$509$	−5037.53	−0.438673	−0.219337	−	0.975649i	$-0.570389\pi$
$509$	−5037.53	−0.438673	−0.219337	+	0.975649i	$0.570389\pi$
$510$	24094.6	2.09202
$511$	229.087	0.0198322
$512$	−30258.0	−2.61177
$513$	−29446.4	−2.53429
$514$	−41690.1	−3.57757
$515$	−174.026	−0.0148903
$516$	9162.67	0.781713
$517$	−12506.4	−1.06389
$518$	−10628.9	−0.901561
$519$	43865.6	3.71000
$520$	−16316.6	−1.37602
$521$	−1861.14	−0.156503	−0.0782515	−	0.996934i	$-0.524934\pi$
$521$	−1861.14	−0.156503	−0.0782515	+	0.996934i	$0.524934\pi$
$522$	74911.5	6.28120
$523$	13844.0	1.15747	0.578735	−	0.815516i	$-0.303547\pi$
$523$	13844.0	1.15747	0.578735	+	0.815516i	$0.303547\pi$
$524$	−57732.5	−4.81308
$525$	−26170.7	−2.17559
$526$	8569.23	0.710335
$527$	18928.3	1.56457
$528$	94209.8	7.76506
$529$	−11262.0	−0.925620
$530$	−665.514	−0.0545435
$531$	3875.80	0.316753
$532$	−42962.7	−3.50126
$533$	−4880.42	−0.396613
$534$	−57412.8	−4.65261
$535$	−6482.24	−0.523835
$536$	−1726.46	−0.139127
$537$	5386.20	0.432834
$538$	12435.4	0.996521
$539$	12811.6	1.02382
$540$	39756.6	3.16824
$541$	−4942.80	−0.392805	−0.196402	−	0.980523i	$-0.562926\pi$
$541$	−4942.80	−0.392805	−0.196402	+	0.980523i	$0.562926\pi$
$542$	14773.9	1.17084
$543$	−42051.6	−3.32341
$544$	73144.3	5.76477
$545$	2558.23	0.201069
$546$	−63506.0	−4.97766
$547$	17213.0	1.34547	0.672736	−	0.739882i	$-0.265119\pi$
$547$	17213.0	1.34547	0.672736	+	0.739882i	$0.265119\pi$
$548$	−1423.11	−0.110935
$549$	−13261.3	−1.03093
$550$	22314.9	1.73002
$551$	15197.7	1.17503
$552$	22631.7	1.74506
$553$	−4062.99	−0.312433
$554$	34826.1	2.67079
$555$	3329.15	0.254621
$556$	−27403.1	−2.09020
$557$	−3401.71	−0.258770	−0.129385	−	0.991594i	$-0.541300\pi$
$557$	−3401.71	−0.258770	−0.129385	+	0.991594i	$0.541300\pi$
$558$	70960.0	5.38347
$559$	1961.80	0.148435
$560$	29425.2	2.22043
$561$	−37472.9	−2.82016
$562$	−42692.3	−3.20439
$563$	18952.8	1.41877	0.709383	−	0.704823i	$-0.248974\pi$
$563$	18952.8	1.41877	0.709383	+	0.704823i	$0.248974\pi$
$564$	−68717.7	−5.13038
$565$	3073.01	0.228818
$566$	−26093.4	−1.93779
$567$	51626.3	3.82381
$568$	−70235.4	−5.18840
$569$	12963.5	0.955111	0.477556	−	0.878602i	$-0.341523\pi$
$569$	12963.5	0.955111	0.477556	+	0.878602i	$0.341523\pi$
$570$	18325.3	1.34660
$571$	8754.34	0.641607	0.320804	−	0.947146i	$-0.396047\pi$
$571$	8754.34	0.641607	0.320804	+	0.947146i	$0.396047\pi$
$572$	39762.8	2.90658
$573$	−34209.3	−2.49409
$574$	15078.6	1.09646
$575$	3128.97	0.226934
$576$	140491.	10.1629
$577$	−15463.4	−1.11568	−0.557841	−	0.829948i	$-0.688370\pi$
$577$	−15463.4	−1.11568	−0.557841	+	0.829948i	$0.688370\pi$
$578$	−26441.2	−1.90278
$579$	11872.8	0.852190
$580$	−20518.9	−1.46897
$581$	−14833.5	−1.05921
$582$	−46694.0	−3.32565
$583$	1035.03	0.0735278
$584$	−684.960	−0.0485340
$585$	14201.6	1.00370
$586$	4829.66	0.340463
$587$	6494.94	0.456686	0.228343	−	0.973581i	$-0.426669\pi$
$587$	6494.94	0.456686	0.228343	+	0.973581i	$0.426669\pi$
$588$	70394.7	4.93712
$589$	14396.0	1.00709
$590$	−1445.72	−0.100880
$591$	−1914.00	−0.133217
$592$	18549.7	1.28782
$593$	−18159.7	−1.25755	−0.628775	−	0.777587i	$-0.716443\pi$
$593$	−18159.7	−1.25755	−0.628775	+	0.777587i	$0.716443\pi$
$594$	−84202.0	−5.81625
$595$	−11704.2	−0.806427
$596$	47056.4	3.23407
$597$	−12059.4	−0.826731
$598$	7592.76	0.519216
$599$	13682.4	0.933301	0.466650	−	0.884442i	$-0.345461\pi$
$599$	13682.4	0.933301	0.466650	+	0.884442i	$0.345461\pi$
$600$	78249.2	5.32418
$601$	−59.3950	−0.00403124	−0.00201562	−	0.999998i	$-0.500642\pi$
$601$	−59.3950	−0.00403124	−0.00201562	+	0.999998i	$0.500642\pi$
$602$	−6061.20	−0.410359
$603$	1502.68	0.101482
$604$	−45560.2	−3.06924
$605$	905.377	0.0608410
$606$	−25920.6	−1.73754
$607$	5149.73	0.344351	0.172176	−	0.985066i	$-0.444920\pi$
$607$	5149.73	0.344351	0.172176	+	0.985066i	$0.444920\pi$
$608$	55630.3	3.71070
$609$	−50966.9	−3.39127
$610$	4946.62	0.328333
$611$	−14713.0	−0.974178
$612$	−147005.	−9.70968
$613$	4241.19	0.279445	0.139723	−	0.990191i	$-0.455379\pi$
$613$	4241.19	0.279445	0.139723	+	0.990191i	$0.455379\pi$
$614$	−55295.9	−3.63446
$615$	−4722.88	−0.309666
$616$	−78402.8	−5.12815
$617$	50.5962	0.00330134	0.00165067	−	0.999999i	$-0.499475\pi$
$617$	50.5962	0.00330134	0.00165067	+	0.999999i	$0.499475\pi$
$618$	2025.17	0.131820
$619$	9294.78	0.603536	0.301768	−	0.953381i	$-0.402423\pi$
$619$	9294.78	0.603536	0.301768	+	0.953381i	$0.402423\pi$
$620$	−19436.6	−1.25902
$621$	−11806.7	−0.762942
$622$	3235.03	0.208542
$623$	27888.7	1.79348
$624$	110831.	7.11026
$625$	8194.85	0.524470
$626$	6743.17	0.430529
$627$	−28500.3	−1.81530
$628$	−6049.18	−0.384377
$629$	−7378.35	−0.467717
$630$	−43877.6	−2.77480
$631$	−3923.91	−0.247557	−0.123778	−	0.992310i	$-0.539501\pi$
$631$	−3923.91	−0.247557	−0.123778	+	0.992310i	$0.539501\pi$
$632$	12148.1	0.764598
$633$	−20972.0	−1.31684
$634$	24514.1	1.53562
$635$	5858.77	0.366139
$636$	5687.08	0.354571
$637$	15072.0	0.937481
$638$	43457.8	2.69672
$639$	61131.5	3.78454
$640$	−25229.9	−1.55828
$641$	−6408.80	−0.394902	−0.197451	−	0.980313i	$-0.563266\pi$
$641$	−6408.80	−0.394902	−0.197451	+	0.980313i	$0.563266\pi$
$642$	75435.2	4.63737
$643$	−24786.7	−1.52020	−0.760101	−	0.649805i	$-0.774851\pi$
$643$	−24786.7	−1.52020	−0.760101	+	0.649805i	$0.774851\pi$
$644$	−17226.1	−1.05404
$645$	1898.47	0.115895
$646$	−40614.2	−2.47360
$647$	593.492	0.0360627	0.0180313	−	0.999837i	$-0.494260\pi$
$647$	593.492	0.0360627	0.0180313	+	0.999837i	$0.494260\pi$
$648$	−154360.	−9.35776
$649$	2248.44	0.135992
$650$	26251.9	1.58413
$651$	−48278.5	−2.90658
$652$	80373.1	4.82769
$653$	−20458.1	−1.22601	−0.613007	−	0.790078i	$-0.710040\pi$
$653$	−20458.1	−1.22601	−0.613007	+	0.790078i	$0.710040\pi$
$654$	−29770.6	−1.78000
$655$	−11961.9	−0.713574
$656$	−26315.4	−1.56623
$657$	596.175	0.0354018
$658$	45457.5	2.69319
$659$	−13664.6	−0.807733	−0.403867	−	0.914818i	$-0.632334\pi$
$659$	−13664.6	−0.807733	−0.403867	+	0.914818i	$0.632334\pi$
$660$	38479.2	2.26939
$661$	−6478.49	−0.381217	−0.190608	−	0.981666i	$-0.561046\pi$
$661$	−6478.49	−0.381217	−0.190608	+	0.981666i	$0.561046\pi$
$662$	60051.6	3.52564
$663$	−44084.3	−2.58234
$664$	44351.5	2.59213
$665$	−8901.68	−0.519086
$666$	−27660.6	−1.60935
$667$	6093.59	0.353741
$668$	−3939.71	−0.228192
$669$	40706.3	2.35246
$670$	−560.516	−0.0323203
$671$	−7693.18	−0.442611
$672$	−186562.	−10.7095
$673$	10808.2	0.619058	0.309529	−	0.950890i	$-0.399829\pi$
$673$	10808.2	0.619058	0.309529	+	0.950890i	$0.399829\pi$
$674$	54835.0	3.13378
$675$	−40821.7	−2.32774
$676$	−1799.80	−0.102401
$677$	−15465.6	−0.877976	−0.438988	−	0.898493i	$-0.644663\pi$
$677$	−15465.6	−0.877976	−0.438988	+	0.898493i	$0.644663\pi$
$678$	−35761.2	−2.02566
$679$	22682.0	1.28197
$680$	34994.9	1.97352
$681$	41660.1	2.34423
$682$	41165.4	2.31130
$683$	437.676	0.0245201	0.0122600	−	0.999925i	$-0.496097\pi$
$683$	437.676	0.0245201	0.0122600	+	0.999925i	$0.496097\pi$
$684$	−111806.	−6.24999
$685$	−294.863	−0.0164469
$686$	2176.61	0.121142
$687$	39120.2	2.17253
$688$	10578.1	0.586170
$689$	1217.65	0.0673274
$690$	7347.65	0.405392
$691$	22092.1	1.21624	0.608120	−	0.793845i	$-0.291924\pi$
$691$	22092.1	1.21624	0.608120	+	0.793845i	$0.291924\pi$
$692$	99829.3	5.48402
$693$	68240.2	3.74059
$694$	−64994.7	−3.55500
$695$	−5677.81	−0.309887
$696$	152389.	8.29924
$697$	10467.2	0.568830
$698$	−37938.2	−2.05728
$699$	13721.5	0.742484
$700$	−59559.3	−3.21590
$701$	13838.5	0.745611	0.372806	−	0.927909i	$-0.378396\pi$
$701$	13838.5	0.745611	0.372806	+	0.927909i	$0.378396\pi$
$702$	−99057.9	−5.32578
$703$	−5611.65	−0.301063
$704$	81502.1	4.36325
$705$	−14238.0	−0.760616
$706$	−67042.6	−3.57391
$707$	12591.1	0.669786
$708$	12354.2	0.655792
$709$	33305.0	1.76417	0.882083	−	0.471093i	$-0.156140\pi$
$709$	33305.0	1.76417	0.882083	+	0.471093i	$0.156140\pi$
$710$	−22802.7	−1.20531
$711$	−10573.5	−0.557716
$712$	−83385.9	−4.38907
$713$	5772.17	0.303183
$714$	136204.	7.13907
$715$	8238.68	0.430922
$716$	12257.9	0.639804
$717$	4606.81	0.239950
$718$	14123.1	0.734081
$719$	−26824.6	−1.39136	−0.695680	−	0.718352i	$-0.744897\pi$
$719$	−26824.6	−1.39136	−0.695680	+	0.718352i	$0.744897\pi$
$720$	76575.7	3.96362
$721$	−983.745	−0.0508136
$722$	6748.41	0.347853
$723$	14866.4	0.764714
$724$	−95701.1	−4.91257
$725$	21068.6	1.07927
$726$	−10536.1	−0.538608
$727$	7270.17	0.370888	0.185444	−	0.982655i	$-0.440628\pi$
$727$	7270.17	0.370888	0.185444	+	0.982655i	$0.440628\pi$
$728$	−92235.5	−4.69571
$729$	31396.3	1.59510
$730$	−222.380	−0.0112749
$731$	−4207.54	−0.212888
$732$	−42270.8	−2.13439
$733$	−19506.7	−0.982941	−0.491471	−	0.870894i	$-0.663541\pi$
$733$	−19506.7	−0.982941	−0.491471	+	0.870894i	$0.663541\pi$
$734$	−39525.2	−1.98761
$735$	14585.5	0.731964
$736$	22305.3	1.11710
$737$	871.737	0.0435696
$738$	39240.5	1.95727
$739$	−36165.4	−1.80023	−0.900113	−	0.435657i	$-0.856516\pi$
$739$	−36165.4	−1.80023	−0.900113	+	0.435657i	$0.856516\pi$
$740$	7576.48	0.376374
$741$	−33528.6	−1.66222
$742$	−3762.06	−0.186132
$743$	−2240.83	−0.110643	−0.0553217	−	0.998469i	$-0.517618\pi$
$743$	−2240.83	−0.110643	−0.0553217	+	0.998469i	$0.517618\pi$
$744$	144350.	7.11309
$745$	9749.89	0.479474
$746$	56277.7	2.76203
$747$	−38602.6	−1.89076
$748$	−85280.8	−4.16868
$749$	−36643.3	−1.78760
$750$	55935.3	2.72329
$751$	7397.98	0.359462	0.179731	−	0.983716i	$-0.442477\pi$
$751$	7397.98	0.359462	0.179731	+	0.983716i	$0.442477\pi$
$752$	−79332.9	−3.84704
$753$	36422.1	1.76268
$754$	51125.1	2.46932
$755$	−9439.88	−0.455036
$756$	224739.	10.8117
$757$	−32914.1	−1.58030	−0.790148	−	0.612916i	$-0.789996\pi$
$757$	−32914.1	−1.58030	−0.790148	+	0.612916i	$0.789996\pi$
$758$	5532.66	0.265113
$759$	−11427.4	−0.546491
$760$	26615.6	1.27033
$761$	264.654	0.0126067	0.00630336	−	0.999980i	$-0.497994\pi$
$761$	264.654	0.0126067	0.00630336	+	0.999980i	$0.497994\pi$
$762$	−68179.7	−3.24132
$763$	14461.3	0.686152
$764$	−77853.4	−3.68670
$765$	−30458.8	−1.43953
$766$	70737.5	3.33662
$767$	2645.13	0.124524
$768$	131580.	6.18227
$769$	−22322.4	−1.04677	−0.523385	−	0.852096i	$-0.675331\pi$
$769$	−22322.4	−1.04677	−0.523385	+	0.852096i	$0.675331\pi$
$770$	−25454.4	−1.19131
$771$	73815.2	3.44797
$772$	27020.2	1.25969
$773$	7389.03	0.343810	0.171905	−	0.985114i	$-0.445008\pi$
$773$	7389.03	0.343810	0.171905	+	0.985114i	$0.445008\pi$
$774$	−15773.6	−0.732520
$775$	19957.3	0.925014
$776$	−67817.9	−3.13727
$777$	18819.3	0.868902
$778$	79516.3	3.66426
$779$	7960.92	0.366149
$780$	45268.1	2.07802
$781$	35463.7	1.62483
$782$	−16284.5	−0.744670
$783$	−79499.3	−3.62845
$784$	81268.9	3.70212
$785$	−1253.36	−0.0569866
$786$	139203.	6.31707
$787$	−3551.31	−0.160852	−0.0804260	−	0.996761i	$-0.525628\pi$
$787$	−3551.31	−0.160852	−0.0804260	+	0.996761i	$0.525628\pi$
$788$	−4355.88	−0.196918
$789$	−15172.4	−0.684604
$790$	3944.02	0.177623
$791$	17371.3	0.780849
$792$	−204035.	−9.15411
$793$	−9050.50	−0.405287
$794$	62294.4	2.78431
$795$	1178.34	0.0525677
$796$	−27444.8	−1.22205
$797$	15446.4	0.686498	0.343249	−	0.939244i	$-0.388473\pi$
$797$	15446.4	0.686498	0.343249	+	0.939244i	$0.388473\pi$
$798$	103591.	4.59532
$799$	31555.5	1.39719
$800$	77120.6	3.40828
$801$	72577.4	3.20149
$802$	−5636.13	−0.248153
$803$	345.854	0.0151992
$804$	4789.83	0.210105
$805$	−3569.18	−0.156270
$806$	48428.3	2.11640
$807$	−22017.7	−0.960423
$808$	−37646.8	−1.63912
$809$	−2232.12	−0.0970052	−0.0485026	−	0.998823i	$-0.515445\pi$
$809$	−2232.12	−0.0970052	−0.0485026	+	0.998823i	$0.515445\pi$
$810$	−50114.7	−2.17389
$811$	−13499.9	−0.584519	−0.292259	−	0.956339i	$-0.594407\pi$
$811$	−13499.9	−0.584519	−0.292259	+	0.956339i	$0.594407\pi$
$812$	−115990.	−5.01289
$813$	−26158.3	−1.12843
$814$	−16046.5	−0.690947
$815$	16652.9	0.715739
$816$	−237704.	−10.1977
$817$	−3200.07	−0.137033
$818$	−41461.9	−1.77223
$819$	80279.9	3.42516
$820$	−10748.3	−0.457741
$821$	−25774.9	−1.09568	−0.547839	−	0.836584i	$-0.684549\pi$
$821$	−25774.9	−1.09568	−0.547839	+	0.836584i	$0.684549\pi$
$822$	3431.38	0.145600
$823$	−14459.2	−0.612415	−0.306207	−	0.951965i	$-0.599060\pi$
$823$	−14459.2	−0.612415	−0.306207	+	0.951965i	$0.599060\pi$
$824$	2941.35	0.124353
$825$	−39510.1	−1.66735
$826$	−8172.45	−0.344257
$827$	−233.479	−0.00981725	−0.00490863	−	0.999988i	$-0.501562\pi$
$827$	−233.479	−0.00981725	−0.00490863	+	0.999988i	$0.501562\pi$
$828$	−44829.1	−1.88155
$829$	12799.2	0.536228	0.268114	−	0.963387i	$-0.413600\pi$
$829$	12799.2	0.536228	0.268114	+	0.963387i	$0.413600\pi$
$830$	14399.2	0.602174
$831$	−61662.0	−2.57404
$832$	95881.7	3.99531
$833$	−32325.6	−1.34456
$834$	66073.8	2.74334
$835$	−816.292	−0.0338311
$836$	−64860.9	−2.68333
$837$	−75305.8	−3.10986
$838$	10715.7	0.441727
$839$	−32588.4	−1.34097	−0.670487	−	0.741922i	$-0.733915\pi$
$839$	−32588.4	−1.34097	−0.670487	+	0.741922i	$0.733915\pi$
$840$	−89258.0	−3.66630
$841$	16641.6	0.682341
$842$	78498.3	3.21286
$843$	75589.7	3.08831
$844$	−47728.0	−1.94652
$845$	−372.910	−0.0151816
$846$	118298.	4.80753
$847$	5117.97	0.207622
$848$	6565.59	0.265877
$849$	46200.2	1.86759
$850$	−56303.6	−2.27200
$851$	−2250.02	−0.0906344
$852$	194858.	7.83537
$853$	8289.79	0.332752	0.166376	−	0.986062i	$-0.446794\pi$
$853$	8289.79	0.332752	0.166376	+	0.986062i	$0.446794\pi$
$854$	27962.6	1.12045
$855$	−23165.6	−0.926606
$856$	109561.	4.37469
$857$	20182.2	0.804447	0.402224	−	0.915541i	$-0.368237\pi$
$857$	20182.2	0.804447	0.402224	+	0.915541i	$0.368237\pi$
$858$	−95875.1	−3.81483
$859$	−13077.3	−0.519433	−0.259717	−	0.965685i	$-0.583629\pi$
$859$	−13077.3	−0.519433	−0.259717	+	0.965685i	$0.583629\pi$
$860$	4320.52	0.171312
$861$	−26697.8	−1.05675
$862$	−68925.2	−2.72344
$863$	−35412.3	−1.39681	−0.698406	−	0.715702i	$-0.746107\pi$
$863$	−35412.3	−1.39681	−0.698406	+	0.715702i	$0.746107\pi$
$864$	−291003.	−11.4585
$865$	20684.2	0.813045
$866$	−71798.8	−2.81735
$867$	46816.0	1.83386
$868$	−109872.	−4.29643
$869$	−6133.90	−0.239446
$870$	49474.7	1.92799
$871$	1025.54	0.0398956
$872$	−43238.5	−1.67918
$873$	59027.4	2.28840
$874$	−12385.3	−0.479334
$875$	−27171.0	−1.04977
$876$	1900.32	0.0732945
$877$	44956.8	1.73100	0.865499	−	0.500911i	$-0.167002\pi$
$877$	44956.8	1.73100	0.865499	+	0.500911i	$0.167002\pi$
$878$	21559.4	0.828696
$879$	−8551.24	−0.328130
$880$	44423.3	1.70171
$881$	−11980.0	−0.458136	−0.229068	−	0.973410i	$-0.573568\pi$
$881$	−11980.0	−0.458136	−0.229068	+	0.973410i	$0.573568\pi$
$882$	−121185.	−4.62643
$883$	−18843.8	−0.718170	−0.359085	−	0.933305i	$-0.616911\pi$
$883$	−18843.8	−0.718170	−0.359085	+	0.933305i	$0.616911\pi$
$884$	−100327.	−3.81715
$885$	2559.74	0.0972259
$886$	−68292.0	−2.58952
$887$	41096.3	1.55567	0.777834	−	0.628470i	$-0.216319\pi$
$887$	41096.3	1.55567	0.777834	+	0.628470i	$0.216319\pi$
$888$	−56268.6	−2.12641
$889$	33118.8	1.24946
$890$	−27072.2	−1.01962
$891$	77940.3	2.93053
$892$	92639.3	3.47735
$893$	23999.7	0.899351
$894$	−113461.	−4.24465
$895$	2539.79	0.0948555
$896$	−142621.	−5.31769
$897$	−13443.5	−0.500407
$898$	−78188.2	−2.90554
$899$	38866.3	1.44190
$900$	−154997.	−5.74062
$901$	−2611.53	−0.0965624
$902$	22764.3	0.840319
$903$	10731.8	0.395494
$904$	−51939.3	−1.91092
$905$	−19828.8	−0.728324
$906$	109854.	4.02831
$907$	−3832.78	−0.140314	−0.0701572	−	0.997536i	$-0.522350\pi$
$907$	−3832.78	−0.140314	−0.0701572	+	0.997536i	$0.522350\pi$
$908$	94810.0	3.46518
$909$	32767.0	1.19562
$910$	−29945.3	−1.09085
$911$	−33480.1	−1.21761	−0.608807	−	0.793318i	$-0.708352\pi$
$911$	−33480.1	−1.21761	−0.608807	+	0.793318i	$0.708352\pi$
$912$	−180788.	−6.56412
$913$	−22394.2	−0.811764
$914$	67214.3	2.43244
$915$	−8758.34	−0.316439
$916$	89029.6	3.21138
$917$	−67619.2	−2.43509
$918$	212453.	7.63835
$919$	23969.6	0.860373	0.430186	−	0.902740i	$-0.358448\pi$
$919$	23969.6	0.860373	0.430186	+	0.902740i	$0.358448\pi$
$920$	10671.7	0.382429
$921$	97905.1	3.50281
$922$	18065.6	0.645292
$923$	41720.6	1.48781
$924$	217518.	7.74438
$925$	−7779.46	−0.276526
$926$	−44644.7	−1.58436
$927$	−2560.09	−0.0907058
$928$	150191.	5.31277
$929$	−11370.8	−0.401577	−0.200788	−	0.979635i	$-0.564350\pi$
$929$	−11370.8	−0.401577	−0.200788	+	0.979635i	$0.564350\pi$
$930$	46865.0	1.65243
$931$	−24585.4	−0.865472
$932$	31227.5	1.09752
$933$	−5727.85	−0.200988
$934$	−7974.01	−0.279355
$935$	−17669.8	−0.618037
$936$	−240033.	−8.38218
$937$	23154.3	0.807277	0.403638	−	0.914919i	$-0.367745\pi$
$937$	23154.3	0.807277	0.403638	+	0.914919i	$0.367745\pi$
$938$	−3168.52	−0.110294
$939$	−11939.2	−0.414933
$940$	−32402.8	−1.12432
$941$	−28651.4	−0.992571	−0.496286	−	0.868159i	$-0.665303\pi$
$941$	−28651.4	−0.992571	−0.496286	+	0.868159i	$0.665303\pi$
$942$	14585.6	0.504486
$943$	3191.98	0.110228
$944$	14262.7	0.491748
$945$	46564.9	1.60292
$946$	−9150.61	−0.314495
$947$	−2231.72	−0.0765799	−0.0382900	−	0.999267i	$-0.512191\pi$
$947$	−2231.72	−0.0765799	−0.0382900	+	0.999267i	$0.512191\pi$
$948$	−33703.2	−1.15467
$949$	406.874	0.0139175
$950$	−42822.1	−1.46245
$951$	−43404.0	−1.47999
$952$	197821.	6.73469
$953$	−1142.10	−0.0388207	−0.0194104	−	0.999812i	$-0.506179\pi$
$953$	−1142.10	−0.0388207	−0.0194104	+	0.999812i	$0.506179\pi$
$954$	−9790.35	−0.332258
$955$	−16130.9	−0.546579
$956$	10484.2	0.354688
$957$	−76944.9	−2.59904
$958$	−76143.9	−2.56795
$959$	−1666.82	−0.0561256
$960$	92786.5	3.11945
$961$	7025.20	0.235816
$962$	−18877.6	−0.632682
$963$	−95360.0	−3.19100
$964$	33833.0	1.13038
$965$	5598.46	0.186757
$966$	41535.3	1.38341
$967$	−5971.79	−0.198593	−0.0992967	−	0.995058i	$-0.531659\pi$
$967$	−5971.79	−0.198593	−0.0992967	+	0.995058i	$0.531659\pi$
$968$	−15302.5	−0.508099
$969$	71910.1	2.38399
$970$	−22017.9	−0.728816
$971$	−17316.9	−0.572322	−0.286161	−	0.958182i	$-0.592379\pi$
$971$	−17316.9	−0.572322	−0.286161	+	0.958182i	$0.592379\pi$
$972$	193944.	6.39996
$973$	−32095.9	−1.05750
$974$	−69024.5	−2.27073
$975$	−46480.9	−1.52675
$976$	−48800.6	−1.60048
$977$	31185.2	1.02119	0.510595	−	0.859821i	$-0.329425\pi$
$977$	31185.2	1.02119	0.510595	+	0.859821i	$0.329425\pi$
$978$	−193794.	−6.33624
$979$	42103.7	1.37450
$980$	33193.6	1.08197
$981$	37633.9	1.22483
$982$	14097.6	0.458119
$983$	−10114.5	−0.328182	−0.164091	−	0.986445i	$-0.552469\pi$
$983$	−10114.5	−0.328182	−0.164091	+	0.986445i	$0.552469\pi$
$984$	79825.0	2.58611
$985$	−902.519	−0.0291946
$986$	−109650.	−3.54155
$987$	−80485.5	−2.59563
$988$	−76304.4	−2.45705
$989$	−1283.09	−0.0412536
$990$	−66242.2	−2.12658
$991$	−40250.6	−1.29021	−0.645106	−	0.764093i	$-0.723187\pi$
$991$	−40250.6	−1.29021	−0.645106	+	0.764093i	$0.723187\pi$
$992$	142268.	4.55345
$993$	−106325.	−3.39792
$994$	−128901.	−4.11316
$995$	−5686.44	−0.181178
$996$	−123047.	−3.91455
$997$	23774.3	0.755207	0.377603	−	0.925967i	$-0.376748\pi$
$997$	23774.3	0.755207	0.377603	+	0.925967i	$0.376748\pi$
$998$	93592.5	2.96856
$999$	29354.7	0.929670

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.4.a.b.1.1	✓	27
3.2	odd	2		1773.4.a.d.1.27		27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.4.a.b.1.1	✓	27	1.1	even	1	trivial
1773.4.a.d.1.27		27	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	197.a (trivial)

\(f(q)\)	\(=\)	\(q-5.48735 q^{2} +9.71574 q^{3} +22.1111 q^{4} +4.58132 q^{5} -53.3137 q^{6} +25.8976 q^{7} -77.4324 q^{8} +67.3955 q^{9} -25.1393 q^{10} +39.0976 q^{11} +214.825 q^{12} +45.9957 q^{13} -142.109 q^{14} +44.5109 q^{15} +248.010 q^{16} -98.6487 q^{17} -369.823 q^{18} -75.0279 q^{19} +101.298 q^{20} +251.614 q^{21} -214.542 q^{22} -30.0829 q^{23} -752.312 q^{24} -104.012 q^{25} -252.395 q^{26} +392.472 q^{27} +572.622 q^{28} -202.560 q^{29} -244.247 q^{30} -191.875 q^{31} -741.462 q^{32} +379.862 q^{33} +541.320 q^{34} +118.645 q^{35} +1490.19 q^{36} +74.7942 q^{37} +411.705 q^{38} +446.882 q^{39} -354.742 q^{40} -106.106 q^{41} -1380.69 q^{42} +42.6517 q^{43} +864.490 q^{44} +308.760 q^{45} +165.075 q^{46} -319.877 q^{47} +2409.60 q^{48} +327.684 q^{49} +570.748 q^{50} -958.445 q^{51} +1017.01 q^{52} +26.4730 q^{53} -2153.64 q^{54} +179.119 q^{55} -2005.31 q^{56} -728.952 q^{57} +1111.52 q^{58} +57.5083 q^{59} +984.182 q^{60} -196.769 q^{61} +1052.89 q^{62} +1745.38 q^{63} +2084.58 q^{64} +210.721 q^{65} -2084.44 q^{66} +22.2964 q^{67} -2181.23 q^{68} -292.277 q^{69} -651.047 q^{70} +907.055 q^{71} -5218.60 q^{72} +8.84591 q^{73} -410.422 q^{74} -1010.55 q^{75} -1658.95 q^{76} +1012.53 q^{77} -2452.20 q^{78} -156.887 q^{79} +1136.21 q^{80} +1993.48 q^{81} +582.242 q^{82} -572.777 q^{83} +5563.45 q^{84} -451.941 q^{85} -234.045 q^{86} -1968.02 q^{87} -3027.42 q^{88} +1076.89 q^{89} -1694.28 q^{90} +1191.18 q^{91} -665.164 q^{92} -1864.21 q^{93} +1755.28 q^{94} -343.727 q^{95} -7203.85 q^{96} +875.835 q^{97} -1798.12 q^{98} +2635.01 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q + 4 q^{2} + 32 q^{3} + 128 q^{4} + 29 q^{5} + 36 q^{6} + 122 q^{7} + 27 q^{8} + 287 q^{9} + 127 q^{10} + 98 q^{11} + 256 q^{12} + 193 q^{13} + 113 q^{14} + 194 q^{15} + 672 q^{16} + 124 q^{17} + 61 q^{18}+ \cdots + 1940 q^{99}+O(q^{100}) \) 27 * q + 4 * q^2 + 32 * q^3 + 128 * q^4 + 29 * q^5 + 36 * q^6 + 122 * q^7 + 27 * q^8 + 287 * q^9 + 127 * q^10 + 98 * q^11 + 256 * q^12 + 193 * q^13 + 113 * q^14 + 194 * q^15 + 672 * q^16 + 124 * q^17 + 61 * q^18 + 535 * q^19 + 279 * q^20 + 188 * q^21 + 165 * q^22 + 344 * q^23 + 165 * q^24 + 910 * q^25 - 44 * q^26 + 1382 * q^27 + 1038 * q^28 + 346 * q^29 + 115 * q^30 + 599 * q^31 + 100 * q^32 + 794 * q^33 + 886 * q^34 + 12 * q^35 + 1714 * q^36 + 1428 * q^37 + 1108 * q^38 + 568 * q^39 + 1206 * q^40 + 549 * q^41 + 355 * q^42 + 2091 * q^43 + 586 * q^44 + 1167 * q^45 + 469 * q^46 + 1270 * q^47 + 2258 * q^48 + 2165 * q^49 - 353 * q^50 - 128 * q^51 + 1000 * q^52 - 208 * q^53 - 2945 * q^54 + 810 * q^55 - 5592 * q^56 - 1006 * q^57 + 287 * q^58 + 603 * q^59 - 2211 * q^60 - 314 * q^61 - 1347 * q^62 + 2416 * q^63 + 5 * q^64 - 1958 * q^65 - 8706 * q^66 + 4372 * q^67 - 6709 * q^68 - 306 * q^69 - 4329 * q^70 - 871 * q^71 - 7589 * q^72 + 942 * q^73 - 5237 * q^74 - 1530 * q^75 - 2470 * q^76 - 1868 * q^77 - 10179 * q^78 - 197 * q^79 - 1882 * q^80 + 1083 * q^81 - 961 * q^82 - 799 * q^83 - 3140 * q^84 - 1444 * q^85 - 7066 * q^86 - 794 * q^87 - 2409 * q^88 - 572 * q^89 - 10939 * q^90 + 3872 * q^91 - 6154 * q^92 - 1506 * q^93 + 1231 * q^94 - 756 * q^95 - 10975 * q^96 + 6335 * q^97 - 5330 * q^98 + 1940 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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