LMFDB - Embedded newform 483.4.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,4,Mod(1,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("483.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	483.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:	$28.4979225328$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 34x^{5} + 7x^{4} + 295x^{3} + 84x^{2} - 524x - 288 $ x^7 - x^6 - 34x^5 + 7x^4 + 295x^3 + 84x^2 - 524*x - 288
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$1.60339$ of defining polynomial
Character	$\chi$	$=$	483.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.603389 q^{2} +3.00000 q^{3} -7.63592 q^{4} +14.1843 q^{5} +1.81017 q^{6} +7.00000 q^{7} -9.43454 q^{8} +9.00000 q^{9} +8.55866 q^{10} -54.0901 q^{11} -22.9078 q^{12} -81.7481 q^{13} +4.22372 q^{14} +42.5530 q^{15} +55.3947 q^{16} -21.9875 q^{17} +5.43050 q^{18} -124.995 q^{19} -108.310 q^{20} +21.0000 q^{21} -32.6373 q^{22} +23.0000 q^{23} -28.3036 q^{24} +76.1953 q^{25} -49.3259 q^{26} +27.0000 q^{27} -53.4515 q^{28} +69.8203 q^{29} +25.6760 q^{30} +147.223 q^{31} +108.901 q^{32} -162.270 q^{33} -13.2670 q^{34} +99.2903 q^{35} -68.7233 q^{36} -405.261 q^{37} -75.4208 q^{38} -245.244 q^{39} -133.823 q^{40} +378.089 q^{41} +12.6712 q^{42} +69.0245 q^{43} +413.027 q^{44} +127.659 q^{45} +13.8779 q^{46} -587.156 q^{47} +166.184 q^{48} +49.0000 q^{49} +45.9754 q^{50} -65.9625 q^{51} +624.222 q^{52} -380.189 q^{53} +16.2915 q^{54} -767.231 q^{55} -66.0418 q^{56} -374.986 q^{57} +42.1287 q^{58} +244.244 q^{59} -324.931 q^{60} -649.184 q^{61} +88.8327 q^{62} +63.0000 q^{63} -377.448 q^{64} -1159.54 q^{65} -97.9119 q^{66} -629.094 q^{67} +167.895 q^{68} +69.0000 q^{69} +59.9106 q^{70} +483.690 q^{71} -84.9108 q^{72} -682.062 q^{73} -244.530 q^{74} +228.586 q^{75} +954.456 q^{76} -378.630 q^{77} -147.978 q^{78} -691.752 q^{79} +785.737 q^{80} +81.0000 q^{81} +228.135 q^{82} +1194.52 q^{83} -160.354 q^{84} -311.878 q^{85} +41.6486 q^{86} +209.461 q^{87} +510.315 q^{88} +753.402 q^{89} +77.0280 q^{90} -572.237 q^{91} -175.626 q^{92} +441.669 q^{93} -354.283 q^{94} -1772.98 q^{95} +326.702 q^{96} +866.950 q^{97} +29.5660 q^{98} -486.810 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 6 q^{2} + 21 q^{3} + 18 q^{4} - 41 q^{5} - 18 q^{6} + 49 q^{7} - 33 q^{8} + 63 q^{9} + q^{10} - 126 q^{11} + 54 q^{12} - 87 q^{13} - 42 q^{14} - 123 q^{15} + 2 q^{16} - 204 q^{17} - 54 q^{18} - 286 q^{19}+ \cdots - 1134 q^{99}+O(q^{100}) $ 7 * q - 6 * q^2 + 21 * q^3 + 18 * q^4 - 41 * q^5 - 18 * q^6 + 49 * q^7 - 33 * q^8 + 63 * q^9 + q^10 - 126 * q^11 + 54 * q^12 - 87 * q^13 - 42 * q^14 - 123 * q^15 + 2 * q^16 - 204 * q^17 - 54 * q^18 - 286 * q^19 - 418 * q^20 + 147 * q^21 + 329 * q^22 + 161 * q^23 - 99 * q^24 + 440 * q^25 - 360 * q^26 + 189 * q^27 + 126 * q^28 - 329 * q^29 + 3 * q^30 + 296 * q^31 - 270 * q^32 - 378 * q^33 - 919 * q^34 - 287 * q^35 + 162 * q^36 - 691 * q^37 - 367 * q^38 - 261 * q^39 + 138 * q^40 - 343 * q^41 - 126 * q^42 - 171 * q^43 - 1279 * q^44 - 369 * q^45 - 138 * q^46 - 1403 * q^47 + 6 * q^48 + 343 * q^49 + 230 * q^50 - 612 * q^51 + 2157 * q^52 - 1024 * q^53 - 162 * q^54 - 158 * q^55 - 231 * q^56 - 858 * q^57 + 2608 * q^58 - 1388 * q^59 - 1254 * q^60 - 52 * q^61 - 309 * q^62 + 441 * q^63 - 187 * q^64 - 1067 * q^65 + 987 * q^66 - 1148 * q^67 + 1293 * q^68 + 483 * q^69 + 7 * q^70 - 1590 * q^71 - 297 * q^72 - 802 * q^73 - 878 * q^74 + 1320 * q^75 - 2505 * q^76 - 882 * q^77 - 1080 * q^78 + 618 * q^79 + 195 * q^80 + 567 * q^81 - 1040 * q^82 - 1818 * q^83 + 378 * q^84 - 1526 * q^85 + 1188 * q^86 - 987 * q^87 + 1664 * q^88 - 354 * q^89 + 9 * q^90 - 609 * q^91 + 414 * q^92 + 888 * q^93 + 663 * q^94 + 78 * q^95 - 810 * q^96 - 1575 * q^97 - 294 * q^98 - 1134 * 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 $

$2$	0.603389	0.213330	0.106665	−	0.994295i	$-0.465983\pi$
$2$	0.603389	0.213330	0.106665	+	0.994295i	$0.465983\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−7.63592	−0.954490
$5$	14.1843	1.26869	0.634343	−	0.773052i	$-0.281271\pi$
$5$	14.1843	1.26869	0.634343	+	0.773052i	$0.281271\pi$
$6$	1.81017	0.123166
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−9.43454	−0.416952
$9$	9.00000	0.333333
$10$	8.55866	0.270649
$11$	−54.0901	−1.48261	−0.741307	−	0.671166i	$-0.765794\pi$
$11$	−54.0901	−1.48261	−0.741307	+	0.671166i	$0.765794\pi$
$12$	−22.9078	−0.551075
$13$	−81.7481	−1.74407	−0.872033	−	0.489448i	$-0.837198\pi$
$13$	−81.7481	−1.74407	−0.872033	+	0.489448i	$0.837198\pi$
$14$	4.22372	0.0806312
$15$	42.5530	0.732476
$16$	55.3947	0.865542
$17$	−21.9875	−0.313691	−0.156846	−	0.987623i	$-0.550133\pi$
$17$	−21.9875	−0.313691	−0.156846	+	0.987623i	$0.550133\pi$
$18$	5.43050	0.0711100
$19$	−124.995	−1.50926	−0.754630	−	0.656151i	$-0.772183\pi$
$19$	−124.995	−1.50926	−0.754630	+	0.656151i	$0.772183\pi$
$20$	−108.310	−1.21095
$21$	21.0000	0.218218
$22$	−32.6373	−0.316286
$23$	23.0000	0.208514
$23$	23.0000	0.208514
$24$	−28.3036	−0.240727
$25$	76.1953	0.609562
$26$	−49.3259	−0.372062
$27$	27.0000	0.192450
$28$	−53.4515	−0.360763
$29$	69.8203	0.447079	0.223540	−	0.974695i	$-0.428239\pi$
$29$	69.8203	0.447079	0.223540	+	0.974695i	$0.428239\pi$
$30$	25.6760	0.156259
$31$	147.223	0.852969	0.426485	−	0.904495i	$-0.359752\pi$
$31$	147.223	0.852969	0.426485	+	0.904495i	$0.359752\pi$
$32$	108.901	0.601598
$33$	−162.270	−0.855988
$34$	−13.2670	−0.0669198
$35$	99.2903	0.479518
$36$	−68.7233	−0.318163
$37$	−405.261	−1.80066	−0.900330	−	0.435208i	$-0.856675\pi$
$37$	−405.261	−1.80066	−0.900330	+	0.435208i	$0.856675\pi$
$38$	−75.4208	−0.321970
$39$	−245.244	−1.00694
$40$	−133.823	−0.528980
$41$	378.089	1.44019	0.720093	−	0.693877i	$-0.244099\pi$
$41$	378.089	1.44019	0.720093	+	0.693877i	$0.244099\pi$
$42$	12.6712	0.0465524
$43$	69.0245	0.244794	0.122397	−	0.992481i	$-0.460942\pi$
$43$	69.0245	0.244794	0.122397	+	0.992481i	$0.460942\pi$
$44$	413.027	1.41514
$45$	127.659	0.422895
$46$	13.8779	0.0444824
$47$	−587.156	−1.82225	−0.911123	−	0.412135i	$-0.864783\pi$
$47$	−587.156	−1.82225	−0.911123	+	0.412135i	$0.864783\pi$
$48$	166.184	0.499721
$49$	49.0000	0.142857
$50$	45.9754	0.130038
$51$	−65.9625	−0.181110
$52$	624.222	1.66469
$53$	−380.189	−0.985340	−0.492670	−	0.870216i	$-0.663979\pi$
$53$	−380.189	−0.985340	−0.492670	+	0.870216i	$0.663979\pi$
$54$	16.2915	0.0410554
$55$	−767.231	−1.88097
$56$	−66.0418	−0.157593
$57$	−374.986	−0.871371
$58$	42.1287	0.0953754
$59$	244.244	0.538946	0.269473	−	0.963008i	$-0.413150\pi$
$59$	244.244	0.538946	0.269473	+	0.963008i	$0.413150\pi$
$60$	−324.931	−0.699141
$61$	−649.184	−1.36262	−0.681308	−	0.731997i	$-0.738588\pi$
$61$	−649.184	−1.36262	−0.681308	+	0.731997i	$0.738588\pi$
$62$	88.8327	0.181964
$63$	63.0000	0.125988
$64$	−377.448	−0.737203
$65$	−1159.54	−2.21267
$66$	−97.9119	−0.182608
$67$	−629.094	−1.14711	−0.573553	−	0.819168i	$-0.694435\pi$
$67$	−629.094	−1.14711	−0.573553	+	0.819168i	$0.694435\pi$
$68$	167.895	0.299415
$69$	69.0000	0.120386
$70$	59.9106	0.102296
$71$	483.690	0.808499	0.404249	−	0.914649i	$-0.367533\pi$
$71$	483.690	0.808499	0.404249	+	0.914649i	$0.367533\pi$
$72$	−84.9108	−0.138984
$73$	−682.062	−1.09355	−0.546776	−	0.837279i	$-0.684145\pi$
$73$	−682.062	−1.09355	−0.546776	+	0.837279i	$0.684145\pi$
$74$	−244.530	−0.384135
$75$	228.586	0.351931
$76$	954.456	1.44057
$77$	−378.630	−0.560376
$78$	−147.978	−0.214810
$79$	−691.752	−0.985166	−0.492583	−	0.870265i	$-0.663947\pi$
$79$	−691.752	−0.985166	−0.492583	+	0.870265i	$0.663947\pi$
$80$	785.737	1.09810
$81$	81.0000	0.111111
$82$	228.135	0.307235
$83$	1194.52	1.57970	0.789850	−	0.613300i	$-0.210158\pi$
$83$	1194.52	1.57970	0.789850	+	0.613300i	$0.210158\pi$
$84$	−160.354	−0.208287
$85$	−311.878	−0.397976
$86$	41.6486	0.0522219
$87$	209.461	0.258121
$88$	510.315	0.618179
$89$	753.402	0.897309	0.448654	−	0.893705i	$-0.351903\pi$
$89$	753.402	0.897309	0.448654	+	0.893705i	$0.351903\pi$
$90$	77.0280	0.0902162
$91$	−572.237	−0.659195
$92$	−175.626	−0.199025
$93$	441.669	0.492462
$94$	−354.283	−0.388740
$95$	−1772.98	−1.91478
$96$	326.702	0.347333
$97$	866.950	0.907478	0.453739	−	0.891135i	$-0.350090\pi$
$97$	866.950	0.907478	0.453739	+	0.891135i	$0.350090\pi$
$98$	29.5660	0.0304757
$99$	−486.810	−0.494205
$100$	−581.821	−0.581821
$101$	−9.31804	−0.00918000	−0.00459000	−	0.999989i	$-0.501461\pi$
$101$	−9.31804	−0.00918000	−0.00459000	+	0.999989i	$0.501461\pi$
$102$	−39.8010	−0.0386362
$103$	815.806	0.780425	0.390212	−	0.920725i	$-0.372402\pi$
$103$	815.806	0.780425	0.390212	+	0.920725i	$0.372402\pi$
$104$	771.256	0.727191
$105$	297.871	0.276850
$106$	−229.402	−0.210203
$107$	−1087.40	−0.982454	−0.491227	−	0.871031i	$-0.663452\pi$
$107$	−1087.40	−0.982454	−0.491227	+	0.871031i	$0.663452\pi$
$108$	−206.170	−0.183692
$109$	1939.64	1.70444	0.852218	−	0.523187i	$-0.175257\pi$
$109$	1939.64	1.70444	0.852218	+	0.523187i	$0.175257\pi$
$110$	−462.939	−0.401268
$111$	−1215.78	−1.03961
$112$	387.763	0.327144
$113$	−1381.90	−1.15042	−0.575212	−	0.818004i	$-0.695080\pi$
$113$	−1381.90	−1.15042	−0.575212	+	0.818004i	$0.695080\pi$
$114$	−226.263	−0.185890
$115$	326.240	0.264539
$116$	−533.142	−0.426733
$117$	−735.733	−0.581355
$118$	147.374	0.114973
$119$	−153.913	−0.118564
$120$	−401.468	−0.305407
$121$	1594.73	1.19815
$122$	−391.710	−0.290687
$123$	1134.27	0.831492
$124$	−1124.18	−0.814151
$125$	−692.262	−0.495342
$126$	38.0135	0.0268771
$127$	1331.57	0.930377	0.465189	−	0.885212i	$-0.345987\pi$
$127$	1331.57	0.930377	0.465189	+	0.885212i	$0.345987\pi$
$128$	−1098.95	−0.758865
$129$	207.074	0.141332
$130$	−699.655	−0.472029
$131$	−551.454	−0.367792	−0.183896	−	0.982946i	$-0.558871\pi$
$131$	−551.454	−0.367792	−0.183896	+	0.982946i	$0.558871\pi$
$132$	1239.08	0.817032
$133$	−874.968	−0.570446
$134$	−379.588	−0.244712
$135$	382.977	0.244159
$136$	207.442	0.130794
$137$	−1760.44	−1.09785	−0.548923	−	0.835873i	$-0.684962\pi$
$137$	−1760.44	−1.09785	−0.548923	+	0.835873i	$0.684962\pi$
$138$	41.6338	0.0256819
$139$	−215.134	−0.131277	−0.0656384	−	0.997843i	$-0.520908\pi$
$139$	−215.134	−0.131277	−0.0656384	+	0.997843i	$0.520908\pi$
$140$	−758.173	−0.457695
$141$	−1761.47	−1.05207
$142$	291.853	0.172477
$143$	4421.76	2.58578
$144$	498.552	0.288514
$145$	990.354	0.567203
$146$	−411.549	−0.233288
$147$	147.000	0.0824786
$148$	3094.54	1.71871
$149$	453.292	0.249229	0.124614	−	0.992205i	$-0.460231\pi$
$149$	453.292	0.249229	0.124614	+	0.992205i	$0.460231\pi$
$150$	137.926	0.0750775
$151$	3226.97	1.73912	0.869560	−	0.493827i	$-0.164403\pi$
$151$	3226.97	1.73912	0.869560	+	0.493827i	$0.164403\pi$
$152$	1179.27	0.629288
$153$	−197.888	−0.104564
$154$	−228.461	−0.119545
$155$	2088.26	1.08215
$156$	1872.67	0.961111
$157$	−336.553	−0.171082	−0.0855408	−	0.996335i	$-0.527262\pi$
$157$	−336.553	−0.171082	−0.0855408	+	0.996335i	$0.527262\pi$
$158$	−417.395	−0.210166
$159$	−1140.57	−0.568886
$160$	1544.69	0.763238
$161$	161.000	0.0788110
$162$	48.8745	0.0237033
$163$	−446.286	−0.214453	−0.107226	−	0.994235i	$-0.534197\pi$
$163$	−446.286	−0.214453	−0.107226	+	0.994235i	$0.534197\pi$
$164$	−2887.06	−1.37464
$165$	−2301.69	−1.08598
$166$	720.757	0.336998
$167$	−153.063	−0.0709244	−0.0354622	−	0.999371i	$-0.511290\pi$
$167$	−153.063	−0.0709244	−0.0354622	+	0.999371i	$0.511290\pi$
$168$	−198.125	−0.0909863
$169$	4485.76	2.04176
$170$	−188.184	−0.0849002
$171$	−1124.96	−0.503086
$172$	−527.066	−0.233654
$173$	−3130.16	−1.37562	−0.687808	−	0.725893i	$-0.741427\pi$
$173$	−3130.16	−1.37562	−0.687808	+	0.725893i	$0.741427\pi$
$174$	126.386	0.0550650
$175$	533.367	0.230393
$176$	−2996.30	−1.28327
$177$	732.732	0.311161
$178$	454.594	0.191423
$179$	−2316.34	−0.967214	−0.483607	−	0.875285i	$-0.660674\pi$
$179$	−2316.34	−0.967214	−0.483607	+	0.875285i	$0.660674\pi$
$180$	−974.794	−0.403649
$181$	−2417.71	−0.992855	−0.496428	−	0.868078i	$-0.665355\pi$
$181$	−2417.71	−0.992855	−0.496428	+	0.868078i	$0.665355\pi$
$182$	−345.281	−0.140626
$183$	−1947.55	−0.786706
$184$	−216.994	−0.0869404
$185$	−5748.35	−2.28447
$186$	266.498	0.105057
$187$	1189.31	0.465084
$188$	4483.48	1.73932
$189$	189.000	0.0727393
$190$	−1069.79	−0.408479
$191$	1065.57	0.403675	0.201837	−	0.979419i	$-0.435309\pi$
$191$	1065.57	0.403675	0.201837	+	0.979419i	$0.435309\pi$
$192$	−1132.34	−0.425624
$193$	−1004.80	−0.374751	−0.187376	−	0.982288i	$-0.559998\pi$
$193$	−1004.80	−0.374751	−0.187376	+	0.982288i	$0.559998\pi$
$194$	523.108	0.193592
$195$	−3478.63	−1.27749
$196$	−374.160	−0.136356
$197$	−1587.77	−0.574232	−0.287116	−	0.957896i	$-0.592697\pi$
$197$	−1587.77	−0.574232	−0.287116	+	0.957896i	$0.592697\pi$
$198$	−293.736	−0.105429
$199$	2826.24	1.00677	0.503385	−	0.864062i	$-0.332088\pi$
$199$	2826.24	1.00677	0.503385	+	0.864062i	$0.332088\pi$
$200$	−718.867	−0.254158
$201$	−1887.28	−0.662282
$202$	−5.62240	−0.00195837
$203$	488.742	0.168980
$204$	503.685	0.172868
$205$	5362.95	1.82714
$206$	492.248	0.166488
$207$	207.000	0.0695048
$208$	−4528.41	−1.50956
$209$	6761.01	2.23765
$210$	179.732	0.0590604
$211$	986.699	0.321930	0.160965	−	0.986960i	$-0.448539\pi$
$211$	986.699	0.321930	0.160965	+	0.986960i	$0.448539\pi$
$212$	2903.10	0.940497
$213$	1451.07	0.466787
$214$	−656.123	−0.209587
$215$	979.067	0.310567
$216$	−254.732	−0.0802424
$217$	1030.56	0.322392
$218$	1170.35	0.363607
$219$	−2046.19	−0.631363
$220$	5858.52	1.79537
$221$	1797.44	0.547098
$222$	−733.589	−0.221780
$223$	−1976.46	−0.593515	−0.296757	−	0.954953i	$-0.595905\pi$
$223$	−1976.46	−0.593515	−0.296757	+	0.954953i	$0.595905\pi$
$224$	762.306	0.227383
$225$	685.758	0.203187
$226$	−833.821	−0.245420
$227$	2372.50	0.693692	0.346846	−	0.937922i	$-0.387253\pi$
$227$	2372.50	0.693692	0.346846	+	0.937922i	$0.387253\pi$
$228$	2863.37	0.831715
$229$	2745.79	0.792343	0.396172	−	0.918176i	$-0.370339\pi$
$229$	2745.79	0.792343	0.396172	+	0.918176i	$0.370339\pi$
$230$	196.849	0.0564342
$231$	−1135.89	−0.323533
$232$	−658.722	−0.186410
$233$	4522.44	1.27157	0.635783	−	0.771868i	$-0.280677\pi$
$233$	4522.44	1.27157	0.635783	+	0.771868i	$0.280677\pi$
$234$	−443.933	−0.124021
$235$	−8328.42	−2.31186
$236$	−1865.03	−0.514419
$237$	−2075.25	−0.568786
$238$	−92.8691	−0.0252933
$239$	1247.82	0.337718	0.168859	−	0.985640i	$-0.445992\pi$
$239$	1247.82	0.337718	0.168859	+	0.985640i	$0.445992\pi$
$240$	2357.21	0.633989
$241$	3896.15	1.04138	0.520691	−	0.853745i	$-0.325674\pi$
$241$	3896.15	1.04138	0.520691	+	0.853745i	$0.325674\pi$
$242$	962.244	0.255601
$243$	243.000	0.0641500
$244$	4957.12	1.30060
$245$	695.032	0.181241
$246$	684.404	0.177382
$247$	10218.1	2.63225
$248$	−1388.98	−0.355647
$249$	3583.55	0.912040
$250$	−417.703	−0.105671
$251$	−3633.08	−0.913618	−0.456809	−	0.889565i	$-0.651008\pi$
$251$	−3633.08	−0.913618	−0.456809	+	0.889565i	$0.651008\pi$
$252$	−481.063	−0.120254
$253$	−1244.07	−0.309147
$254$	803.455	0.198477
$255$	−935.635	−0.229771
$256$	2356.49	0.575314
$257$	−4699.97	−1.14076	−0.570382	−	0.821380i	$-0.693205\pi$
$257$	−4699.97	−1.14076	−0.570382	+	0.821380i	$0.693205\pi$
$258$	124.946	0.0301503
$259$	−2836.82	−0.680586
$260$	8854.18	2.11197
$261$	628.382	0.149026
$262$	−332.741	−0.0784610
$263$	3367.46	0.789531	0.394766	−	0.918782i	$-0.370826\pi$
$263$	3367.46	0.789531	0.394766	+	0.918782i	$0.370826\pi$
$264$	1530.94	0.356906
$265$	−5392.73	−1.25009
$266$	−527.946	−0.121693
$267$	2260.21	0.518061
$268$	4803.72	1.09490
$269$	4885.24	1.10728	0.553640	−	0.832756i	$-0.313238\pi$
$269$	4885.24	1.10728	0.553640	+	0.832756i	$0.313238\pi$
$270$	231.084	0.0520864
$271$	6245.54	1.39996	0.699981	−	0.714161i	$-0.253192\pi$
$271$	6245.54	1.39996	0.699981	+	0.714161i	$0.253192\pi$
$272$	−1217.99	−0.271513
$273$	−1716.71	−0.380586
$274$	−1062.23	−0.234203
$275$	−4121.41	−0.903746
$276$	−526.879	−0.114907
$277$	−5682.81	−1.23266	−0.616331	−	0.787488i	$-0.711381\pi$
$277$	−5682.81	−1.23266	−0.616331	+	0.787488i	$0.711381\pi$
$278$	−129.810	−0.0280053
$279$	1325.01	0.284323
$280$	−936.758	−0.199936
$281$	−4631.83	−0.983317	−0.491658	−	0.870788i	$-0.663609\pi$
$281$	−4631.83	−0.983317	−0.491658	+	0.870788i	$0.663609\pi$
$282$	−1062.85	−0.224439
$283$	−6153.43	−1.29252	−0.646261	−	0.763117i	$-0.723668\pi$
$283$	−6153.43	−1.29252	−0.646261	+	0.763117i	$0.723668\pi$
$284$	−3693.42	−0.771704
$285$	−5318.93	−1.10550
$286$	2668.04	0.551624
$287$	2646.63	0.544339
$288$	980.107	0.200533
$289$	−4429.55	−0.901598
$290$	597.568	0.121001
$291$	2600.85	0.523933
$292$	5208.17	1.04379
$293$	3086.91	0.615492	0.307746	−	0.951468i	$-0.400425\pi$
$293$	3086.91	0.615492	0.307746	+	0.951468i	$0.400425\pi$
$294$	88.6981	0.0175952
$295$	3464.44	0.683753
$296$	3823.45	0.750788
$297$	−1460.43	−0.285329
$298$	273.511	0.0531680
$299$	−1880.21	−0.363663
$300$	−1745.46	−0.335915
$301$	483.172	0.0925235
$302$	1947.12	0.371007
$303$	−27.9541	−0.00530007
$304$	−6924.09	−1.30633
$305$	−9208.25	−1.72873
$306$	−119.403	−0.0223066
$307$	6372.69	1.18472	0.592360	−	0.805674i	$-0.298196\pi$
$307$	6372.69	1.18472	0.592360	+	0.805674i	$0.298196\pi$
$308$	2891.19	0.534873
$309$	2447.42	0.450578
$310$	1260.03	0.230855
$311$	7391.72	1.34774	0.673868	−	0.738852i	$-0.264632\pi$
$311$	7391.72	1.34774	0.673868	+	0.738852i	$0.264632\pi$
$312$	2313.77	0.419844
$313$	4519.92	0.816233	0.408116	−	0.912930i	$-0.366186\pi$
$313$	4519.92	0.816233	0.408116	+	0.912930i	$0.366186\pi$
$314$	−203.072	−0.0364969
$315$	893.613	0.159839
$316$	5282.16	0.940332
$317$	451.006	0.0799086	0.0399543	−	0.999202i	$-0.487279\pi$
$317$	451.006	0.0799086	0.0399543	+	0.999202i	$0.487279\pi$
$318$	−688.205	−0.121361
$319$	−3776.58	−0.662846
$320$	−5353.85	−0.935279
$321$	−3262.19	−0.567220
$322$	97.1455	0.0168128
$323$	2748.34	0.473442
$324$	−618.510	−0.106054
$325$	−6228.82	−1.06312
$326$	−269.284	−0.0457492
$327$	5818.91	0.984056
$328$	−3567.10	−0.600488
$329$	−4110.09	−0.688744
$330$	−1388.82	−0.231672
$331$	−1670.05	−0.277324	−0.138662	−	0.990340i	$-0.544280\pi$
$331$	−1670.05	−0.277324	−0.138662	+	0.990340i	$0.544280\pi$
$332$	−9121.23	−1.50781
$333$	−3647.35	−0.600220
$334$	−92.3565	−0.0151303
$335$	−8923.28	−1.45532
$336$	1163.29	0.188877
$337$	−2666.41	−0.431005	−0.215502	−	0.976503i	$-0.569139\pi$
$337$	−2666.41	−0.431005	−0.215502	+	0.976503i	$0.569139\pi$
$338$	2706.65	0.435570
$339$	−4145.69	−0.664198
$340$	2381.48	0.379864
$341$	−7963.30	−1.26463
$342$	−678.788	−0.107323
$343$	343.000	0.0539949
$344$	−651.215	−0.102067
$345$	978.719	0.152732
$346$	−1888.70	−0.293460
$347$	1266.30	0.195904	0.0979521	−	0.995191i	$-0.468771\pi$
$347$	1266.30	0.195904	0.0979521	+	0.995191i	$0.468771\pi$
$348$	−1599.43	−0.246374
$349$	−3024.43	−0.463879	−0.231940	−	0.972730i	$-0.574507\pi$
$349$	−3024.43	−0.463879	−0.231940	+	0.972730i	$0.574507\pi$
$350$	321.828	0.0491497
$351$	−2207.20	−0.335646
$352$	−5890.45	−0.891938
$353$	8262.39	1.24579	0.622893	−	0.782307i	$-0.285957\pi$
$353$	8262.39	1.24579	0.622893	+	0.782307i	$0.285957\pi$
$354$	442.122	0.0663800
$355$	6860.82	1.02573
$356$	−5752.92	−0.856472
$357$	−461.738	−0.0684531
$358$	−1397.65	−0.206336
$359$	−2905.91	−0.427209	−0.213604	−	0.976920i	$-0.568520\pi$
$359$	−2905.91	−0.427209	−0.213604	+	0.976920i	$0.568520\pi$
$360$	−1204.40	−0.176327
$361$	8764.87	1.27786
$362$	−1458.82	−0.211806
$363$	4784.20	0.691751
$364$	4369.56	0.629195
$365$	−9674.60	−1.38737
$366$	−1175.13	−0.167828
$367$	−3694.32	−0.525454	−0.262727	−	0.964870i	$-0.584622\pi$
$367$	−3694.32	−0.525454	−0.262727	+	0.964870i	$0.584622\pi$
$368$	1274.08	0.180478
$369$	3402.80	0.480062
$370$	−3468.49	−0.487346
$371$	−2661.32	−0.372423
$372$	−3372.55	−0.470050
$373$	6549.73	0.909202	0.454601	−	0.890695i	$-0.349782\pi$
$373$	6549.73	0.909202	0.454601	+	0.890695i	$0.349782\pi$
$374$	717.613	0.0992163
$375$	−2076.79	−0.285986
$376$	5539.55	0.759788
$377$	−5707.68	−0.779735
$378$	114.040	0.0155175
$379$	−11360.6	−1.53972	−0.769859	−	0.638214i	$-0.779674\pi$
$379$	−11360.6	−1.53972	−0.769859	+	0.638214i	$0.779674\pi$
$380$	13538.3	1.82763
$381$	3994.72	0.537154
$382$	642.952	0.0861160
$383$	−4375.72	−0.583784	−0.291892	−	0.956451i	$-0.594285\pi$
$383$	−4375.72	−0.583784	−0.291892	+	0.956451i	$0.594285\pi$
$384$	−3296.86	−0.438131
$385$	−5370.62	−0.710941
$386$	−606.284	−0.0799457
$387$	621.221	0.0815980
$388$	−6619.96	−0.866179
$389$	−5896.58	−0.768556	−0.384278	−	0.923217i	$-0.625550\pi$
$389$	−5896.58	−0.768556	−0.384278	+	0.923217i	$0.625550\pi$
$390$	−2098.96	−0.272526
$391$	−505.713	−0.0654092
$392$	−462.292	−0.0595645
$393$	−1654.36	−0.212345
$394$	−958.041	−0.122501
$395$	−9812.04	−1.24987
$396$	3717.25	0.471714
$397$	−3746.72	−0.473659	−0.236829	−	0.971551i	$-0.576108\pi$
$397$	−3746.72	−0.473659	−0.236829	+	0.971551i	$0.576108\pi$
$398$	1705.32	0.214774
$399$	−2624.91	−0.329347
$400$	4220.81	0.527602
$401$	−10558.0	−1.31482	−0.657408	−	0.753535i	$-0.728347\pi$
$401$	−10558.0	−1.31482	−0.657408	+	0.753535i	$0.728347\pi$
$402$	−1138.76	−0.141285
$403$	−12035.2	−1.48763
$404$	71.1518	0.00876222
$405$	1148.93	0.140965
$406$	294.901	0.0360485
$407$	21920.6	2.66969
$408$	622.326	0.0755140
$409$	−8252.08	−0.997651	−0.498825	−	0.866702i	$-0.666235\pi$
$409$	−8252.08	−0.997651	−0.498825	+	0.866702i	$0.666235\pi$
$410$	3235.94	0.389785
$411$	−5281.33	−0.633841
$412$	−6229.43	−0.744908
$413$	1709.71	0.203703
$414$	124.901	0.0148275
$415$	16943.4	2.00414
$416$	−8902.44	−1.04923
$417$	−645.403	−0.0757927
$418$	4079.52	0.477358
$419$	5243.24	0.611334	0.305667	−	0.952138i	$-0.401121\pi$
$419$	5243.24	0.611334	0.305667	+	0.952138i	$0.401121\pi$
$420$	−2274.52	−0.264250
$421$	3110.23	0.360055	0.180028	−	0.983662i	$-0.442381\pi$
$421$	3110.23	0.360055	0.180028	+	0.983662i	$0.442381\pi$
$422$	595.363	0.0686773
$423$	−5284.41	−0.607415
$424$	3586.91	0.410839
$425$	−1675.35	−0.191215
$426$	875.559	0.0995797
$427$	−4544.29	−0.515020
$428$	8303.28	0.937743
$429$	13265.3	1.49290
$430$	590.758	0.0662532
$431$	4385.42	0.490111	0.245056	−	0.969509i	$-0.421194\pi$
$431$	4385.42	0.490111	0.245056	+	0.969509i	$0.421194\pi$
$432$	1495.66	0.166574
$433$	92.3908	0.0102541	0.00512704	−	0.999987i	$-0.498368\pi$
$433$	92.3908	0.0102541	0.00512704	+	0.999987i	$0.498368\pi$
$434$	621.829	0.0687759
$435$	2971.06	0.327475
$436$	−14810.9	−1.62687
$437$	−2874.90	−0.314702
$438$	−1234.65	−0.134689
$439$	−14579.3	−1.58504	−0.792521	−	0.609845i	$-0.791232\pi$
$439$	−14579.3	−1.58504	−0.792521	+	0.609845i	$0.791232\pi$
$440$	7238.47	0.784274
$441$	441.000	0.0476190
$442$	1084.55	0.116713
$443$	−7912.94	−0.848657	−0.424328	−	0.905508i	$-0.639490\pi$
$443$	−7912.94	−0.848657	−0.424328	+	0.905508i	$0.639490\pi$
$444$	9283.62	0.992299
$445$	10686.5	1.13840
$446$	−1192.58	−0.126615
$447$	1359.87	0.143892
$448$	−2642.14	−0.278637
$449$	−13924.9	−1.46360	−0.731801	−	0.681518i	$-0.761320\pi$
$449$	−13924.9	−1.46360	−0.731801	+	0.681518i	$0.761320\pi$
$450$	413.778	0.0433460
$451$	−20450.9	−2.13524
$452$	10552.1	1.09807
$453$	9680.91	1.00408
$454$	1431.54	0.147985
$455$	−8116.80	−0.836311
$456$	3537.82	0.363320
$457$	19101.0	1.95516	0.977580	−	0.210563i	$-0.0675297\pi$
$457$	19101.0	1.95516	0.977580	+	0.210563i	$0.0675297\pi$
$458$	1656.78	0.169031
$459$	−593.663	−0.0603699
$460$	−2491.14	−0.252500
$461$	−11891.0	−1.20134	−0.600671	−	0.799496i	$-0.705100\pi$
$461$	−11891.0	−1.20134	−0.600671	+	0.799496i	$0.705100\pi$
$462$	−685.384	−0.0690193
$463$	16951.8	1.70154	0.850772	−	0.525534i	$-0.176135\pi$
$463$	16951.8	1.70154	0.850772	+	0.525534i	$0.176135\pi$
$464$	3867.67	0.386966
$465$	6264.78	0.624779
$466$	2728.79	0.271263
$467$	−15664.2	−1.55215	−0.776074	−	0.630642i	$-0.782791\pi$
$467$	−15664.2	−1.55215	−0.776074	+	0.630642i	$0.782791\pi$
$468$	5618.00	0.554898
$469$	−4403.66	−0.433565
$470$	−5025.27	−0.493188
$471$	−1009.66	−0.0987741
$472$	−2304.33	−0.224715
$473$	−3733.54	−0.362935
$474$	−1252.18	−0.121339
$475$	−9524.07	−0.919988
$476$	1175.26	0.113168
$477$	−3421.70	−0.328447
$478$	752.919	0.0720454
$479$	−19766.2	−1.88547	−0.942737	−	0.333536i	$-0.891758\pi$
$479$	−19766.2	−1.88547	−0.942737	+	0.333536i	$0.891758\pi$
$480$	4634.06	0.440656
$481$	33129.3	3.14047
$482$	2350.89	0.222158
$483$	483.000	0.0455016
$484$	−12177.3	−1.14362
$485$	12297.1	1.15130
$486$	146.623	0.0136851
$487$	−4451.57	−0.414209	−0.207105	−	0.978319i	$-0.566404\pi$
$487$	−4451.57	−0.414209	−0.207105	+	0.978319i	$0.566404\pi$
$488$	6124.75	0.568145
$489$	−1338.86	−0.123814
$490$	419.375	0.0386641
$491$	15243.7	1.40110	0.700550	−	0.713603i	$-0.252938\pi$
$491$	15243.7	1.40110	0.700550	+	0.713603i	$0.252938\pi$
$492$	−8661.18	−0.793651
$493$	−1535.17	−0.140245
$494$	6165.51	0.561537
$495$	−6905.08	−0.626991
$496$	8155.38	0.738281
$497$	3385.83	0.305584
$498$	2162.27	0.194566
$499$	−15477.3	−1.38850	−0.694249	−	0.719734i	$-0.744264\pi$
$499$	−15477.3	−1.38850	−0.694249	+	0.719734i	$0.744264\pi$
$500$	5286.06	0.472800
$501$	−459.189	−0.0409482
$502$	−2192.16	−0.194902
$503$	17141.3	1.51947	0.759736	−	0.650231i	$-0.225328\pi$
$503$	17141.3	1.51947	0.759736	+	0.650231i	$0.225328\pi$
$504$	−594.376	−0.0525310
$505$	−132.170	−0.0116465
$506$	−750.658	−0.0659503
$507$	13457.3	1.17881
$508$	−10167.8	−0.888036
$509$	−20411.7	−1.77747	−0.888735	−	0.458422i	$-0.848415\pi$
$509$	−20411.7	−1.77747	−0.888735	+	0.458422i	$0.848415\pi$
$510$	−564.551	−0.0490171
$511$	−4774.44	−0.413324
$512$	10213.5	0.881597
$513$	−3374.88	−0.290457
$514$	−2835.91	−0.243359
$515$	11571.7	0.990113
$516$	−1581.20	−0.134900
$517$	31759.3	2.70169
$518$	−1711.71	−0.145189
$519$	−9390.48	−0.794212
$520$	10939.7	0.922576
$521$	−12356.9	−1.03909	−0.519545	−	0.854443i	$-0.673899\pi$
$521$	−12356.9	−1.03909	−0.519545	+	0.854443i	$0.673899\pi$
$522$	379.159	0.0317918
$523$	2699.59	0.225707	0.112853	−	0.993612i	$-0.464001\pi$
$523$	2699.59	0.225707	0.112853	+	0.993612i	$0.464001\pi$
$524$	4210.86	0.351054
$525$	1600.10	0.133017
$526$	2031.89	0.168431
$527$	−3237.07	−0.267569
$528$	−8988.90	−0.740894
$529$	529.000	0.0434783
$530$	−3253.91	−0.266681
$531$	2198.19	0.179649
$532$	6681.19	0.544486
$533$	−30908.1	−2.51178
$534$	1363.78	0.110518
$535$	−15424.0	−1.24643
$536$	5935.21	0.478288
$537$	−6949.02	−0.558421
$538$	2947.70	0.236216
$539$	−2650.41	−0.211802
$540$	−2924.38	−0.233047
$541$	18420.4	1.46387	0.731937	−	0.681372i	$-0.238616\pi$
$541$	18420.4	1.46387	0.731937	+	0.681372i	$0.238616\pi$
$542$	3768.49	0.298654
$543$	−7253.12	−0.573225
$544$	−2394.46	−0.188716
$545$	27512.4	2.16239
$546$	−1035.84	−0.0811905
$547$	7118.81	0.556451	0.278225	−	0.960516i	$-0.410254\pi$
$547$	7118.81	0.556451	0.278225	+	0.960516i	$0.410254\pi$
$548$	13442.6	1.04788
$549$	−5842.66	−0.454205
$550$	−2486.81	−0.192796
$551$	−8727.22	−0.674759
$552$	−650.983	−0.0501951
$553$	−4842.26	−0.372358
$554$	−3428.94	−0.262964
$555$	−17245.1	−1.31894
$556$	1642.75	0.125302
$557$	−7298.25	−0.555183	−0.277591	−	0.960699i	$-0.589536\pi$
$557$	−7298.25	−0.555183	−0.277591	+	0.960699i	$0.589536\pi$
$558$	799.495	0.0606547
$559$	−5642.63	−0.426937
$560$	5500.16	0.415043
$561$	3567.92	0.268516
$562$	−2794.80	−0.209771
$563$	7198.40	0.538857	0.269429	−	0.963020i	$-0.413165\pi$
$563$	7198.40	0.538857	0.269429	+	0.963020i	$0.413165\pi$
$564$	13450.4	1.00419
$565$	−19601.3	−1.45953
$566$	−3712.91	−0.275734
$567$	567.000	0.0419961
$568$	−4563.39	−0.337105
$569$	−16000.9	−1.17890	−0.589448	−	0.807807i	$-0.700655\pi$
$569$	−16000.9	−1.17890	−0.589448	+	0.807807i	$0.700655\pi$
$570$	−3209.38	−0.235836
$571$	13286.1	0.973738	0.486869	−	0.873475i	$-0.338139\pi$
$571$	13286.1	0.973738	0.486869	+	0.873475i	$0.338139\pi$
$572$	−33764.2	−2.46810
$573$	3196.71	0.233062
$574$	1596.94	0.116124
$575$	1752.49	0.127103
$576$	−3397.03	−0.245734
$577$	1482.52	0.106964	0.0534820	−	0.998569i	$-0.482968\pi$
$577$	1482.52	0.106964	0.0534820	+	0.998569i	$0.482968\pi$
$578$	−2672.74	−0.192338
$579$	−3014.40	−0.216363
$580$	−7562.27	−0.541390
$581$	8361.61	0.597071
$582$	1569.32	0.111771
$583$	20564.5	1.46088
$584$	6434.94	0.455958
$585$	−10435.9	−0.737557
$586$	1862.61	0.131303
$587$	13872.4	0.975428	0.487714	−	0.873003i	$-0.337831\pi$
$587$	13872.4	0.975428	0.487714	+	0.873003i	$0.337831\pi$
$588$	−1122.48	−0.0787250
$589$	−18402.2	−1.28735
$590$	2090.40	0.145865
$591$	−4763.30	−0.331533
$592$	−22449.3	−1.55855
$593$	19467.7	1.34813	0.674066	−	0.738671i	$-0.264546\pi$
$593$	19467.7	1.34813	0.674066	+	0.738671i	$0.264546\pi$
$594$	−881.208	−0.0608693
$595$	−2183.15	−0.150421
$596$	−3461.30	−0.237887
$597$	8478.73	0.581259
$598$	−1134.50	−0.0775802
$599$	−11829.3	−0.806899	−0.403449	−	0.915002i	$-0.632189\pi$
$599$	−11829.3	−0.806899	−0.403449	+	0.915002i	$0.632189\pi$
$600$	−2156.60	−0.146738
$601$	4207.26	0.285554	0.142777	−	0.989755i	$-0.454397\pi$
$601$	4207.26	0.285554	0.142777	+	0.989755i	$0.454397\pi$
$602$	291.540	0.0197380
$603$	−5661.85	−0.382369
$604$	−24640.9	−1.65997
$605$	22620.2	1.52007
$606$	−16.8672	−0.00113067
$607$	−28961.6	−1.93659	−0.968297	−	0.249800i	$-0.919635\pi$
$607$	−28961.6	−1.93659	−0.968297	+	0.249800i	$0.919635\pi$
$608$	−13612.1	−0.907967
$609$	1466.23	0.0975607
$610$	−5556.15	−0.368790
$611$	47998.9	3.17812
$612$	1511.05	0.0998052
$613$	−1784.35	−0.117568	−0.0587842	−	0.998271i	$-0.518722\pi$
$613$	−1784.35	−0.117568	−0.0587842	+	0.998271i	$0.518722\pi$
$614$	3845.21	0.252736
$615$	16088.8	1.05490
$616$	3572.20	0.233650
$617$	−14302.8	−0.933240	−0.466620	−	0.884458i	$-0.654528\pi$
$617$	−14302.8	−0.933240	−0.466620	+	0.884458i	$0.654528\pi$
$618$	1476.74	0.0961219
$619$	−15576.2	−1.01141	−0.505704	−	0.862707i	$-0.668767\pi$
$619$	−15576.2	−1.01141	−0.505704	+	0.862707i	$0.668767\pi$
$620$	−15945.8	−1.03290
$621$	621.000	0.0401286
$622$	4460.08	0.287513
$623$	5273.81	0.339151
$624$	−13585.2	−0.871546
$625$	−19343.7	−1.23800
$626$	2727.27	0.174127
$627$	20283.0	1.29191
$628$	2569.89	0.163296
$629$	8910.67	0.564852
$630$	539.196	0.0340985
$631$	18453.7	1.16423	0.582115	−	0.813107i	$-0.302225\pi$
$631$	18453.7	1.16423	0.582115	+	0.813107i	$0.302225\pi$
$632$	6526.36	0.410767
$633$	2960.10	0.185866
$634$	272.132	0.0170469
$635$	18887.5	1.18036
$636$	8709.29	0.542996
$637$	−4005.66	−0.249152
$638$	−2278.75	−0.141405
$639$	4353.21	0.269500
$640$	−15587.9	−0.962761
$641$	6450.82	0.397492	0.198746	−	0.980051i	$-0.436313\pi$
$641$	6450.82	0.397492	0.198746	+	0.980051i	$0.436313\pi$
$642$	−1968.37	−0.121005
$643$	−27521.3	−1.68793	−0.843963	−	0.536402i	$-0.819783\pi$
$643$	−27521.3	−1.68793	−0.843963	+	0.536402i	$0.819783\pi$
$644$	−1229.38	−0.0752244
$645$	2937.20	0.179306
$646$	1658.32	0.100999
$647$	−22240.1	−1.35139	−0.675695	−	0.737181i	$-0.736156\pi$
$647$	−22240.1	−1.35139	−0.675695	+	0.737181i	$0.736156\pi$
$648$	−764.197	−0.0463279
$649$	−13211.2	−0.799050
$650$	−3758.40	−0.226795
$651$	3091.68	0.186133
$652$	3407.80	0.204693
$653$	−4904.89	−0.293940	−0.146970	−	0.989141i	$-0.546952\pi$
$653$	−4904.89	−0.293940	−0.146970	+	0.989141i	$0.546952\pi$
$654$	3511.06	0.209929
$655$	−7822.00	−0.466612
$656$	20944.1	1.24654
$657$	−6138.56	−0.364518
$658$	−2479.98	−0.146930
$659$	25697.5	1.51902	0.759509	−	0.650496i	$-0.225439\pi$
$659$	25697.5	1.51902	0.759509	+	0.650496i	$0.225439\pi$
$660$	17575.6	1.03656
$661$	13531.0	0.796208	0.398104	−	0.917340i	$-0.369668\pi$
$661$	13531.0	0.796208	0.398104	+	0.917340i	$0.369668\pi$
$662$	−1007.69	−0.0591616
$663$	5392.31	0.315867
$664$	−11269.7	−0.658658
$665$	−12410.8	−0.723717
$666$	−2200.77	−0.128045
$667$	1605.87	0.0932225
$668$	1168.78	0.0676967
$669$	−5929.39	−0.342666
$670$	−5384.21	−0.310463
$671$	35114.4	2.02023
$672$	2286.92	0.131279
$673$	21523.8	1.23281	0.616405	−	0.787430i	$-0.288589\pi$
$673$	21523.8	1.23281	0.616405	+	0.787430i	$0.288589\pi$
$674$	−1608.88	−0.0919463
$675$	2057.27	0.117310
$676$	−34252.9	−1.94884
$677$	−1412.30	−0.0801761	−0.0400880	−	0.999196i	$-0.512764\pi$
$677$	−1412.30	−0.0801761	−0.0400880	+	0.999196i	$0.512764\pi$
$678$	−2501.46	−0.141693
$679$	6068.65	0.342995
$680$	2942.43	0.165937
$681$	7117.49	0.400503
$682$	−4804.97	−0.269783
$683$	−10486.2	−0.587473	−0.293736	−	0.955886i	$-0.594899\pi$
$683$	−10486.2	−0.587473	−0.293736	+	0.955886i	$0.594899\pi$
$684$	8590.10	0.480191
$685$	−24970.7	−1.39282
$686$	206.962	0.0115187
$687$	8237.36	0.457460
$688$	3823.59	0.211880
$689$	31079.8	1.71850
$690$	590.548	0.0325823
$691$	13193.9	0.726364	0.363182	−	0.931718i	$-0.381690\pi$
$691$	13193.9	0.726364	0.363182	+	0.931718i	$0.381690\pi$
$692$	23901.6	1.31301
$693$	−3407.67	−0.186792
$694$	764.073	0.0417923
$695$	−3051.54	−0.166549
$696$	−1976.17	−0.107624
$697$	−8313.25	−0.451774
$698$	−1824.90	−0.0989594
$699$	13567.3	0.734139
$700$	−4072.75	−0.219908
$701$	20492.7	1.10414	0.552069	−	0.833799i	$-0.313839\pi$
$701$	20492.7	1.10414	0.552069	+	0.833799i	$0.313839\pi$
$702$	−1331.80	−0.0716033
$703$	50655.7	2.71766
$704$	20416.2	1.09299
$705$	−24985.3	−1.33475
$706$	4985.43	0.265764
$707$	−65.2263	−0.00346971
$708$	−5595.08	−0.297000
$709$	−2523.08	−0.133648	−0.0668238	−	0.997765i	$-0.521287\pi$
$709$	−2523.08	−0.133648	−0.0668238	+	0.997765i	$0.521287\pi$
$710$	4139.74	0.218819
$711$	−6225.76	−0.328389
$712$	−7108.00	−0.374134
$713$	3386.13	0.177856
$714$	−278.607	−0.0146031
$715$	62719.7	3.28054
$716$	17687.4	0.923197
$717$	3743.45	0.194982
$718$	−1753.39	−0.0911365
$719$	−3712.53	−0.192565	−0.0962824	−	0.995354i	$-0.530695\pi$
$719$	−3712.53	−0.192565	−0.0962824	+	0.995354i	$0.530695\pi$
$720$	7071.63	0.366033
$721$	5710.64	0.294973
$722$	5288.62	0.272607
$723$	11688.4	0.601242
$724$	18461.4	0.947671
$725$	5319.98	0.272523
$726$	2886.73	0.147571
$727$	33483.3	1.70815	0.854077	−	0.520147i	$-0.174123\pi$
$727$	33483.3	1.70815	0.854077	+	0.520147i	$0.174123\pi$
$728$	5398.79	0.274852
$729$	729.000	0.0370370
$730$	−5837.54	−0.295969
$731$	−1517.68	−0.0767898
$732$	14871.4	0.750904
$733$	−31775.3	−1.60116	−0.800578	−	0.599228i	$-0.795474\pi$
$733$	−31775.3	−1.60116	−0.800578	+	0.599228i	$0.795474\pi$
$734$	−2229.11	−0.112095
$735$	2085.10	0.104639
$736$	2504.72	0.125442
$737$	34027.7	1.70072
$738$	2053.21	0.102412
$739$	542.031	0.0269810	0.0134905	−	0.999909i	$-0.495706\pi$
$739$	542.031	0.0269810	0.0134905	+	0.999909i	$0.495706\pi$
$740$	43894.0	2.18051
$741$	30654.4	1.51973
$742$	−1605.81	−0.0794491
$743$	−3638.58	−0.179659	−0.0898294	−	0.995957i	$-0.528632\pi$
$743$	−3638.58	−0.179659	−0.0898294	+	0.995957i	$0.528632\pi$
$744$	−4166.94	−0.205333
$745$	6429.64	0.316193
$746$	3952.03	0.193960
$747$	10750.6	0.526567
$748$	−9081.45	−0.443918
$749$	−7611.78	−0.371333
$750$	−1253.11	−0.0610094
$751$	−37163.6	−1.80575	−0.902875	−	0.429904i	$-0.858548\pi$
$751$	−37163.6	−1.80575	−0.902875	+	0.429904i	$0.858548\pi$
$752$	−32525.3	−1.57723
$753$	−10899.3	−0.527478
$754$	−3443.95	−0.166341
$755$	45772.4	2.20640
$756$	−1443.19	−0.0694290
$757$	−83.9416	−0.00403027	−0.00201513	−	0.999998i	$-0.500641\pi$
$757$	−83.9416	−0.00403027	−0.00201513	+	0.999998i	$0.500641\pi$
$758$	−6854.84	−0.328468
$759$	−3732.21	−0.178486
$760$	16727.2	0.798368
$761$	−8416.02	−0.400894	−0.200447	−	0.979705i	$-0.564239\pi$
$761$	−8416.02	−0.400894	−0.200447	+	0.979705i	$0.564239\pi$
$762$	2410.37	0.114591
$763$	13577.5	0.644216
$764$	−8136.60	−0.385304
$765$	−2806.90	−0.132659
$766$	−2640.26	−0.124539
$767$	−19966.5	−0.939958
$768$	7069.46	0.332158
$769$	12701.8	0.595629	0.297815	−	0.954624i	$-0.403742\pi$
$769$	12701.8	0.595629	0.297815	+	0.954624i	$0.403742\pi$
$770$	−3240.57	−0.151665
$771$	−14099.9	−0.658620
$772$	7672.57	0.357697
$773$	−37101.5	−1.72632	−0.863162	−	0.504926i	$-0.831520\pi$
$773$	−37101.5	−1.72632	−0.863162	+	0.504926i	$0.831520\pi$
$774$	374.838	0.0174073
$775$	11217.7	0.519938
$776$	−8179.27	−0.378375
$777$	−8510.47	−0.392936
$778$	−3557.93	−0.163956
$779$	−47259.5	−2.17362
$780$	26562.5	1.21935
$781$	−26162.8	−1.19869
$782$	−305.141	−0.0139537
$783$	1885.15	0.0860404
$784$	2714.34	0.123649
$785$	−4773.77	−0.217049
$786$	−998.222	−0.0452995
$787$	−17097.2	−0.774397	−0.387198	−	0.921996i	$-0.626557\pi$
$787$	−17097.2	−0.774397	−0.387198	+	0.921996i	$0.626557\pi$
$788$	12124.1	0.548099
$789$	10102.4	0.455836
$790$	−5920.47	−0.266634
$791$	−9673.28	−0.434819
$792$	4592.83	0.206060
$793$	53069.6	2.37649
$794$	−2260.73	−0.101046
$795$	−16178.2	−0.721738
$796$	−21581.0	−0.960952
$797$	−26134.9	−1.16154	−0.580769	−	0.814068i	$-0.697248\pi$
$797$	−26134.9	−1.16154	−0.580769	+	0.814068i	$0.697248\pi$
$798$	−1583.84	−0.0702597
$799$	12910.1	0.571623
$800$	8297.73	0.366711
$801$	6780.62	0.299103
$802$	−6370.57	−0.280490
$803$	36892.8	1.62132
$804$	14411.1	0.632142
$805$	2283.68	0.0999864
$806$	−7261.91	−0.317357
$807$	14655.7	0.639289
$808$	87.9114	0.00382761
$809$	8968.52	0.389761	0.194880	−	0.980827i	$-0.437568\pi$
$809$	8968.52	0.389761	0.194880	+	0.980827i	$0.437568\pi$
$810$	693.252	0.0300721
$811$	7565.97	0.327592	0.163796	−	0.986494i	$-0.447626\pi$
$811$	7565.97	0.327592	0.163796	+	0.986494i	$0.447626\pi$
$812$	−3732.00	−0.161290
$813$	18736.6	0.808268
$814$	13226.6	0.569524
$815$	−6330.26	−0.272073
$816$	−3653.97	−0.156758
$817$	−8627.76	−0.369458
$818$	−4979.21	−0.212829
$819$	−5150.13	−0.219732
$820$	−40951.0	−1.74399
$821$	−31947.2	−1.35806	−0.679029	−	0.734112i	$-0.737599\pi$
$821$	−31947.2	−1.35806	−0.679029	+	0.734112i	$0.737599\pi$
$822$	−3186.69	−0.135217
$823$	−19163.4	−0.811660	−0.405830	−	0.913949i	$-0.633017\pi$
$823$	−19163.4	−0.811660	−0.405830	+	0.913949i	$0.633017\pi$
$824$	−7696.75	−0.325399
$825$	−12364.2	−0.521778
$826$	1031.62	0.0434559
$827$	−27083.7	−1.13880	−0.569402	−	0.822059i	$-0.692825\pi$
$827$	−27083.7	−1.13880	−0.569402	+	0.822059i	$0.692825\pi$
$828$	−1580.64	−0.0663417
$829$	11972.2	0.501583	0.250792	−	0.968041i	$-0.419309\pi$
$829$	11972.2	0.501583	0.250792	+	0.968041i	$0.419309\pi$
$830$	10223.5	0.427544
$831$	−17048.4	−0.711677
$832$	30855.7	1.28573
$833$	−1077.39	−0.0448131
$834$	−389.429	−0.0161689
$835$	−2171.10	−0.0899808
$836$	−51626.6	−2.13582
$837$	3975.02	0.164154
$838$	3163.71	0.130416
$839$	−23637.9	−0.972672	−0.486336	−	0.873772i	$-0.661667\pi$
$839$	−23637.9	−0.972672	−0.486336	+	0.873772i	$0.661667\pi$
$840$	−2810.27	−0.115433
$841$	−19514.1	−0.800120
$842$	1876.68	0.0768106
$843$	−13895.5	−0.567718
$844$	−7534.36	−0.307279
$845$	63627.5	2.59036
$846$	−3188.55	−0.129580
$847$	11163.1	0.452857
$848$	−21060.5	−0.852853
$849$	−18460.3	−0.746238
$850$	−1010.88	−0.0407918
$851$	−9320.99	−0.375464
$852$	−11080.3	−0.445544
$853$	−36296.6	−1.45694	−0.728472	−	0.685076i	$-0.759769\pi$
$853$	−36296.6	−1.45694	−0.728472	+	0.685076i	$0.759769\pi$
$854$	−2741.97	−0.109869
$855$	−15956.8	−0.638258
$856$	10259.1	0.409636
$857$	−6915.23	−0.275636	−0.137818	−	0.990458i	$-0.544009\pi$
$857$	−6915.23	−0.275636	−0.137818	+	0.990458i	$0.544009\pi$
$858$	8004.12	0.318480
$859$	34428.1	1.36749	0.683744	−	0.729722i	$-0.260350\pi$
$859$	34428.1	1.36749	0.683744	+	0.729722i	$0.260350\pi$
$860$	−7476.08	−0.296433
$861$	7939.88	0.314274
$862$	2646.11	0.104556
$863$	−5921.26	−0.233560	−0.116780	−	0.993158i	$-0.537257\pi$
$863$	−5921.26	−0.233560	−0.116780	+	0.993158i	$0.537257\pi$
$864$	2940.32	0.115778
$865$	−44399.2	−1.74522
$866$	55.7476	0.00218750
$867$	−13288.6	−0.520538
$868$	−7869.29	−0.307720
$869$	37416.9	1.46062
$870$	1792.70	0.0698602
$871$	51427.3	2.00063
$872$	−18299.6	−0.710667
$873$	7802.55	0.302493
$874$	−1734.68	−0.0671355
$875$	−4845.83	−0.187222
$876$	15624.5	0.602630
$877$	−10273.2	−0.395553	−0.197777	−	0.980247i	$-0.563372\pi$
$877$	−10273.2	−0.395553	−0.197777	+	0.980247i	$0.563372\pi$
$878$	−8797.00	−0.338137
$879$	9260.73	0.355355
$880$	−42500.5	−1.62806
$881$	−12323.5	−0.471272	−0.235636	−	0.971841i	$-0.575717\pi$
$881$	−12323.5	−0.471272	−0.235636	+	0.971841i	$0.575717\pi$
$882$	266.094	0.0101586
$883$	47000.6	1.79128	0.895638	−	0.444785i	$-0.146720\pi$
$883$	47000.6	1.79128	0.895638	+	0.444785i	$0.146720\pi$
$884$	−13725.1	−0.522200
$885$	10393.3	0.394765
$886$	−4774.57	−0.181044
$887$	−6934.21	−0.262489	−0.131245	−	0.991350i	$-0.541897\pi$
$887$	−6934.21	−0.262489	−0.131245	+	0.991350i	$0.541897\pi$
$888$	11470.3	0.433468
$889$	9321.00	0.351650
$890$	6448.11	0.242855
$891$	−4381.29	−0.164735
$892$	15092.1	0.566504
$893$	73391.9	2.75024
$894$	820.533	0.0306966
$895$	−32855.7	−1.22709
$896$	−7692.68	−0.286824
$897$	−5640.62	−0.209961
$898$	−8402.13	−0.312230
$899$	10279.2	0.381345
$900$	−5236.39	−0.193940
$901$	8359.42	0.309093
$902$	−12339.8	−0.455511
$903$	1449.52	0.0534184
$904$	13037.6	0.479671
$905$	−34293.6	−1.25962
$906$	5841.35	0.214201
$907$	−8064.65	−0.295240	−0.147620	−	0.989044i	$-0.547161\pi$
$907$	−8064.65	−0.295240	−0.147620	+	0.989044i	$0.547161\pi$
$908$	−18116.2	−0.662122
$909$	−83.8624	−0.00306000
$910$	−4897.58	−0.178410
$911$	22965.8	0.835224	0.417612	−	0.908625i	$-0.362867\pi$
$911$	22965.8	0.835224	0.417612	+	0.908625i	$0.362867\pi$
$912$	−20772.3	−0.754208
$913$	−64611.4	−2.34209
$914$	11525.3	0.417095
$915$	−27624.7	−0.998083
$916$	−20966.6	−0.756284
$917$	−3860.17	−0.139012
$918$	−358.209	−0.0128787
$919$	37634.5	1.35087	0.675434	−	0.737420i	$-0.263956\pi$
$919$	37634.5	1.35087	0.675434	+	0.737420i	$0.263956\pi$
$920$	−3077.92	−0.110300
$921$	19118.1	0.683998
$922$	−7174.89	−0.256282
$923$	−39540.7	−1.41007
$924$	8673.58	0.308809
$925$	−30879.0	−1.09761
$926$	10228.5	0.362991
$927$	7342.25	0.260142
$928$	7603.48	0.268962
$929$	−31422.4	−1.10972	−0.554862	−	0.831942i	$-0.687229\pi$
$929$	−31422.4	−1.10972	−0.554862	+	0.831942i	$0.687229\pi$
$930$	3780.10	0.133284
$931$	−6124.78	−0.215608
$932$	−34533.0	−1.21370
$933$	22175.2	0.778116
$934$	−9451.60	−0.331120
$935$	16869.5	0.590045
$936$	6941.30	0.242397
$937$	−40978.8	−1.42873	−0.714365	−	0.699773i	$-0.753284\pi$
$937$	−40978.8	−1.42873	−0.714365	+	0.699773i	$0.753284\pi$
$938$	−2657.12	−0.0924925
$939$	13559.8	0.471252
$940$	63595.2	2.20664
$941$	−4219.91	−0.146190	−0.0730952	−	0.997325i	$-0.523288\pi$
$941$	−4219.91	−0.146190	−0.0730952	+	0.997325i	$0.523288\pi$
$942$	−609.216	−0.0210715
$943$	8696.06	0.300300
$944$	13529.8	0.466481
$945$	2680.84	0.0922833
$946$	−2252.78	−0.0774250
$947$	48823.7	1.67535	0.837676	−	0.546168i	$-0.183914\pi$
$947$	48823.7	1.67535	0.837676	+	0.546168i	$0.183914\pi$
$948$	15846.5	0.542901
$949$	55757.3	1.90723
$950$	−5746.71	−0.196261
$951$	1353.02	0.0461352
$952$	1452.09	0.0494355
$953$	−28119.5	−0.955802	−0.477901	−	0.878414i	$-0.658602\pi$
$953$	−28119.5	−0.955802	−0.477901	+	0.878414i	$0.658602\pi$
$954$	−2064.62	−0.0700675
$955$	15114.4	0.512136
$956$	−9528.24	−0.322349
$957$	−11329.7	−0.382695
$958$	−11926.7	−0.402228
$959$	−12323.1	−0.414947
$960$	−16061.5	−0.539983
$961$	−8116.36	−0.272443
$962$	19989.8	0.669956
$963$	−9786.57	−0.327485
$964$	−29750.7	−0.993989
$965$	−14252.4	−0.475442
$966$	291.437	0.00970685
$967$	−31001.4	−1.03096	−0.515481	−	0.856901i	$-0.672387\pi$
$967$	−31001.4	−1.03096	−0.515481	+	0.856901i	$0.672387\pi$
$968$	−15045.6	−0.499569
$969$	8245.02	0.273342
$970$	7419.93	0.245608
$971$	−18525.0	−0.612252	−0.306126	−	0.951991i	$-0.599033\pi$
$971$	−18525.0	−0.612252	−0.306126	+	0.951991i	$0.599033\pi$
$972$	−1855.53	−0.0612306
$973$	−1505.94	−0.0496179
$974$	−2686.03	−0.0883633
$975$	−18686.5	−0.613791
$976$	−35961.4	−1.17940
$977$	−17405.9	−0.569972	−0.284986	−	0.958532i	$-0.591989\pi$
$977$	−17405.9	−0.569972	−0.284986	+	0.958532i	$0.591989\pi$
$978$	−807.851	−0.0264133
$979$	−40751.6	−1.33036
$980$	−5307.21	−0.172993
$981$	17456.7	0.568145
$982$	9197.90	0.298897
$983$	24936.0	0.809089	0.404545	−	0.914518i	$-0.367430\pi$
$983$	24936.0	0.809089	0.404545	+	0.914518i	$0.367430\pi$
$984$	−10701.3	−0.346692
$985$	−22521.4	−0.728520
$986$	−926.306	−0.0299185
$987$	−12330.3	−0.397647
$988$	−78025.0	−2.51245
$989$	1587.56	0.0510431
$990$	−4166.45	−0.133756
$991$	−11576.2	−0.371070	−0.185535	−	0.982638i	$-0.559402\pi$
$991$	−11576.2	−0.371070	−0.185535	+	0.982638i	$0.559402\pi$
$992$	16032.7	0.513144
$993$	−5010.16	−0.160113
$994$	2042.97	0.0651902
$995$	40088.4	1.27727
$996$	−27363.7	−0.870534
$997$	8899.71	0.282705	0.141352	−	0.989959i	$-0.454855\pi$
$997$	8899.71	0.282705	0.141352	+	0.989959i	$0.454855\pi$
$998$	−9338.85	−0.296209
$999$	−10942.0	−0.346537

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.4.a.c.1.5	✓	7
3.2	odd	2		1449.4.a.h.1.3		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.4.a.c.1.5	✓	7	1.1	even	1	trivial
1449.4.a.h.1.3		7	3.2	odd	2

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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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	483.a (trivial)

\(f(q)\)	\(=\)	\(q+0.603389 q^{2} +3.00000 q^{3} -7.63592 q^{4} +14.1843 q^{5} +1.81017 q^{6} +7.00000 q^{7} -9.43454 q^{8} +9.00000 q^{9} +8.55866 q^{10} -54.0901 q^{11} -22.9078 q^{12} -81.7481 q^{13} +4.22372 q^{14} +42.5530 q^{15} +55.3947 q^{16} -21.9875 q^{17} +5.43050 q^{18} -124.995 q^{19} -108.310 q^{20} +21.0000 q^{21} -32.6373 q^{22} +23.0000 q^{23} -28.3036 q^{24} +76.1953 q^{25} -49.3259 q^{26} +27.0000 q^{27} -53.4515 q^{28} +69.8203 q^{29} +25.6760 q^{30} +147.223 q^{31} +108.901 q^{32} -162.270 q^{33} -13.2670 q^{34} +99.2903 q^{35} -68.7233 q^{36} -405.261 q^{37} -75.4208 q^{38} -245.244 q^{39} -133.823 q^{40} +378.089 q^{41} +12.6712 q^{42} +69.0245 q^{43} +413.027 q^{44} +127.659 q^{45} +13.8779 q^{46} -587.156 q^{47} +166.184 q^{48} +49.0000 q^{49} +45.9754 q^{50} -65.9625 q^{51} +624.222 q^{52} -380.189 q^{53} +16.2915 q^{54} -767.231 q^{55} -66.0418 q^{56} -374.986 q^{57} +42.1287 q^{58} +244.244 q^{59} -324.931 q^{60} -649.184 q^{61} +88.8327 q^{62} +63.0000 q^{63} -377.448 q^{64} -1159.54 q^{65} -97.9119 q^{66} -629.094 q^{67} +167.895 q^{68} +69.0000 q^{69} +59.9106 q^{70} +483.690 q^{71} -84.9108 q^{72} -682.062 q^{73} -244.530 q^{74} +228.586 q^{75} +954.456 q^{76} -378.630 q^{77} -147.978 q^{78} -691.752 q^{79} +785.737 q^{80} +81.0000 q^{81} +228.135 q^{82} +1194.52 q^{83} -160.354 q^{84} -311.878 q^{85} +41.6486 q^{86} +209.461 q^{87} +510.315 q^{88} +753.402 q^{89} +77.0280 q^{90} -572.237 q^{91} -175.626 q^{92} +441.669 q^{93} -354.283 q^{94} -1772.98 q^{95} +326.702 q^{96} +866.950 q^{97} +29.5660 q^{98} -486.810 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 6 q^{2} + 21 q^{3} + 18 q^{4} - 41 q^{5} - 18 q^{6} + 49 q^{7} - 33 q^{8} + 63 q^{9} + q^{10} - 126 q^{11} + 54 q^{12} - 87 q^{13} - 42 q^{14} - 123 q^{15} + 2 q^{16} - 204 q^{17} - 54 q^{18} - 286 q^{19}+ \cdots - 1134 q^{99}+O(q^{100}) \) 7 * q - 6 * q^2 + 21 * q^3 + 18 * q^4 - 41 * q^5 - 18 * q^6 + 49 * q^7 - 33 * q^8 + 63 * q^9 + q^10 - 126 * q^11 + 54 * q^12 - 87 * q^13 - 42 * q^14 - 123 * q^15 + 2 * q^16 - 204 * q^17 - 54 * q^18 - 286 * q^19 - 418 * q^20 + 147 * q^21 + 329 * q^22 + 161 * q^23 - 99 * q^24 + 440 * q^25 - 360 * q^26 + 189 * q^27 + 126 * q^28 - 329 * q^29 + 3 * q^30 + 296 * q^31 - 270 * q^32 - 378 * q^33 - 919 * q^34 - 287 * q^35 + 162 * q^36 - 691 * q^37 - 367 * q^38 - 261 * q^39 + 138 * q^40 - 343 * q^41 - 126 * q^42 - 171 * q^43 - 1279 * q^44 - 369 * q^45 - 138 * q^46 - 1403 * q^47 + 6 * q^48 + 343 * q^49 + 230 * q^50 - 612 * q^51 + 2157 * q^52 - 1024 * q^53 - 162 * q^54 - 158 * q^55 - 231 * q^56 - 858 * q^57 + 2608 * q^58 - 1388 * q^59 - 1254 * q^60 - 52 * q^61 - 309 * q^62 + 441 * q^63 - 187 * q^64 - 1067 * q^65 + 987 * q^66 - 1148 * q^67 + 1293 * q^68 + 483 * q^69 + 7 * q^70 - 1590 * q^71 - 297 * q^72 - 802 * q^73 - 878 * q^74 + 1320 * q^75 - 2505 * q^76 - 882 * q^77 - 1080 * q^78 + 618 * q^79 + 195 * q^80 + 567 * q^81 - 1040 * q^82 - 1818 * q^83 + 378 * q^84 - 1526 * q^85 + 1188 * q^86 - 987 * q^87 + 1664 * q^88 - 354 * q^89 + 9 * q^90 - 609 * q^91 + 414 * q^92 + 888 * q^93 + 663 * q^94 + 78 * q^95 - 810 * q^96 - 1575 * q^97 - 294 * q^98 - 1134 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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