LMFDB - Embedded newform 2303.4.a.h.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2303,4,Mod(1,2303)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2303, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2303.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 2303 = 7^{2} \cdot 47 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	2303.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:	$135.881398743$
Analytic rank:	$0$
Dimension:	$35$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	2303.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.07002 q^{2} +9.29307 q^{3} -3.71503 q^{4} +12.3025 q^{5} -19.2368 q^{6} +24.2503 q^{8} +59.3612 q^{9} +O(q^{10})$	\(q-2.07002 q^{2} +9.29307 q^{3} -3.71503 q^{4} +12.3025 q^{5} -19.2368 q^{6} +24.2503 q^{8} +59.3612 q^{9} -25.4663 q^{10} +65.1536 q^{11} -34.5240 q^{12} +8.15075 q^{13} +114.328 q^{15} -20.4784 q^{16} +3.31969 q^{17} -122.879 q^{18} +115.635 q^{19} -45.7040 q^{20} -134.869 q^{22} -56.7291 q^{23} +225.360 q^{24} +26.3504 q^{25} -16.8722 q^{26} +300.735 q^{27} +49.8317 q^{29} -236.660 q^{30} -8.65516 q^{31} -151.612 q^{32} +605.477 q^{33} -6.87183 q^{34} -220.528 q^{36} +14.4088 q^{37} -239.367 q^{38} +75.7455 q^{39} +298.338 q^{40} +84.4822 q^{41} +356.797 q^{43} -242.047 q^{44} +730.288 q^{45} +117.430 q^{46} +47.0000 q^{47} -190.307 q^{48} -54.5458 q^{50} +30.8502 q^{51} -30.2802 q^{52} -446.075 q^{53} -622.527 q^{54} +801.549 q^{55} +1074.61 q^{57} -103.153 q^{58} +442.839 q^{59} -424.730 q^{60} -93.0781 q^{61} +17.9163 q^{62} +477.666 q^{64} +100.274 q^{65} -1253.35 q^{66} +293.840 q^{67} -12.3328 q^{68} -527.188 q^{69} +697.751 q^{71} +1439.53 q^{72} -402.050 q^{73} -29.8265 q^{74} +244.876 q^{75} -429.589 q^{76} -156.794 q^{78} -1319.27 q^{79} -251.934 q^{80} +1192.00 q^{81} -174.880 q^{82} -791.185 q^{83} +40.8404 q^{85} -738.577 q^{86} +463.090 q^{87} +1580.00 q^{88} +244.376 q^{89} -1511.71 q^{90} +210.750 q^{92} -80.4330 q^{93} -97.2908 q^{94} +1422.60 q^{95} -1408.94 q^{96} -1766.48 q^{97} +3867.60 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9}+O(q^{10}) $ 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9	\( 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9} + 100 q^{10} + 40 q^{11} + 144 q^{12} + 328 q^{13} + 20 q^{15} + 643 q^{16} + 152 q^{17} + 51 q^{18} + 266 q^{19} + 1064 q^{20} - 168 q^{22} - 134 q^{23} + 288 q^{24} + 1137 q^{25} + 156 q^{26} + 672 q^{27} + 248 q^{29} - 216 q^{30} + 276 q^{31} + 347 q^{32} + 1056 q^{33} + 908 q^{34} + 909 q^{36} - 418 q^{37} + 164 q^{38} - 548 q^{39} + 1200 q^{40} + 918 q^{41} + 608 q^{43} + 1288 q^{44} + 876 q^{45} - 972 q^{46} + 1645 q^{47} + 1252 q^{48} - 367 q^{50} - 464 q^{51} + 3798 q^{52} - 218 q^{53} - 744 q^{54} + 1004 q^{55} - 436 q^{57} - 1270 q^{58} + 3760 q^{59} - 424 q^{60} + 956 q^{61} + 84 q^{62} + 2189 q^{64} - 596 q^{65} + 5500 q^{66} - 476 q^{67} + 256 q^{68} + 444 q^{69} + 852 q^{71} - 883 q^{72} + 6250 q^{73} + 1366 q^{74} - 2568 q^{75} + 1742 q^{76} - 1460 q^{78} + 632 q^{79} + 10124 q^{80} + 1267 q^{81} + 792 q^{82} + 796 q^{83} - 1228 q^{85} - 2864 q^{86} + 8360 q^{87} - 50 q^{88} + 908 q^{89} - 1858 q^{90} + 1696 q^{92} + 644 q^{93} + 235 q^{94} + 1320 q^{95} + 2688 q^{96} + 6184 q^{97} - 1812 q^{99}+O(q^{100}) \) 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9 + 100 * q^10 + 40 * q^11 + 144 * q^12 + 328 * q^13 + 20 * q^15 + 643 * q^16 + 152 * q^17 + 51 * q^18 + 266 * q^19 + 1064 * q^20 - 168 * q^22 - 134 * q^23 + 288 * q^24 + 1137 * q^25 + 156 * q^26 + 672 * q^27 + 248 * q^29 - 216 * q^30 + 276 * q^31 + 347 * q^32 + 1056 * q^33 + 908 * q^34 + 909 * q^36 - 418 * q^37 + 164 * q^38 - 548 * q^39 + 1200 * q^40 + 918 * q^41 + 608 * q^43 + 1288 * q^44 + 876 * q^45 - 972 * q^46 + 1645 * q^47 + 1252 * q^48 - 367 * q^50 - 464 * q^51 + 3798 * q^52 - 218 * q^53 - 744 * q^54 + 1004 * q^55 - 436 * q^57 - 1270 * q^58 + 3760 * q^59 - 424 * q^60 + 956 * q^61 + 84 * q^62 + 2189 * q^64 - 596 * q^65 + 5500 * q^66 - 476 * q^67 + 256 * q^68 + 444 * q^69 + 852 * q^71 - 883 * q^72 + 6250 * q^73 + 1366 * q^74 - 2568 * q^75 + 1742 * q^76 - 1460 * q^78 + 632 * q^79 + 10124 * q^80 + 1267 * q^81 + 792 * q^82 + 796 * q^83 - 1228 * q^85 - 2864 * q^86 + 8360 * q^87 - 50 * q^88 + 908 * q^89 - 1858 * q^90 + 1696 * q^92 + 644 * q^93 + 235 * q^94 + 1320 * q^95 + 2688 * q^96 + 6184 * q^97 - 1812 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.07002	−0.731862	−0.365931	−	0.930642i	$-0.619249\pi$
$2$	−2.07002	−0.731862	−0.365931	+	0.930642i	$0.619249\pi$
$3$	9.29307	1.78845	0.894226	−	0.447615i	$-0.147727\pi$
$3$	9.29307	1.78845	0.894226	+	0.447615i	$0.147727\pi$
$4$	−3.71503	−0.464378
$5$	12.3025	1.10037	0.550183	−	0.835044i	$-0.314558\pi$
$5$	12.3025	1.10037	0.550183	+	0.835044i	$0.314558\pi$
$6$	−19.2368	−1.30890
$7$	0	0
$7$	0	0
$8$	24.2503	1.07172
$9$	59.3612	2.19856
$10$	−25.4663	−0.805315
$11$	65.1536	1.78587	0.892934	−	0.450187i	$-0.148643\pi$
$11$	65.1536	1.78587	0.892934	+	0.450187i	$0.148643\pi$
$12$	−34.5240	−0.830519
$13$	8.15075	0.173893	0.0869465	−	0.996213i	$-0.472289\pi$
$13$	8.15075	0.173893	0.0869465	+	0.996213i	$0.472289\pi$
$14$	0	0
$15$	114.328	1.96795
$16$	−20.4784	−0.319974
$17$	3.31969	0.0473614	0.0236807	−	0.999720i	$-0.492461\pi$
$17$	3.31969	0.0473614	0.0236807	+	0.999720i	$0.492461\pi$
$18$	−122.879	−1.60904
$19$	115.635	1.39624	0.698121	−	0.715980i	$-0.254020\pi$
$19$	115.635	1.39624	0.698121	+	0.715980i	$0.254020\pi$
$20$	−45.7040	−0.510986
$21$	0	0
$22$	−134.869	−1.30701
$23$	−56.7291	−0.514298	−0.257149	−	0.966372i	$-0.582783\pi$
$23$	−56.7291	−0.514298	−0.257149	+	0.966372i	$0.582783\pi$
$24$	225.360	1.91672
$25$	26.3504	0.210803
$26$	−16.8722	−0.127266
$27$	300.735	2.14357
$28$	0	0
$29$	49.8317	0.319087	0.159543	−	0.987191i	$-0.448998\pi$
$29$	49.8317	0.319087	0.159543	+	0.987191i	$0.448998\pi$
$30$	−236.660	−1.44027
$31$	−8.65516	−0.0501456	−0.0250728	−	0.999686i	$-0.507982\pi$
$31$	−8.65516	−0.0501456	−0.0250728	+	0.999686i	$0.507982\pi$
$32$	−151.612	−0.837546
$33$	605.477	3.19394
$34$	−6.87183	−0.0346620
$35$	0	0
$36$	−220.528	−1.02097
$37$	14.4088	0.0640214	0.0320107	−	0.999488i	$-0.489809\pi$
$37$	14.4088	0.0640214	0.0320107	+	0.999488i	$0.489809\pi$
$38$	−239.367	−1.02186
$39$	75.7455	0.311000
$40$	298.338	1.17929
$41$	84.4822	0.321803	0.160901	−	0.986970i	$-0.448560\pi$
$41$	84.4822	0.321803	0.160901	+	0.986970i	$0.448560\pi$
$42$	0	0
$43$	356.797	1.26537	0.632687	−	0.774408i	$-0.281952\pi$
$43$	356.797	1.26537	0.632687	+	0.774408i	$0.281952\pi$
$44$	−242.047	−0.829319
$45$	730.288	2.41922
$46$	117.430	0.376395
$47$	47.0000	0.145865
$47$	47.0000	0.145865
$48$	−190.307	−0.572259
$49$	0	0
$50$	−54.5458	−0.154279
$51$	30.8502	0.0847037
$52$	−30.2802	−0.0807522
$53$	−446.075	−1.15610	−0.578048	−	0.816002i	$-0.696186\pi$
$53$	−446.075	−1.15610	−0.578048	+	0.816002i	$0.696186\pi$
$54$	−622.527	−1.56880
$55$	801.549	1.96511
$56$	0	0
$57$	1074.61	2.49711
$58$	−103.153	−0.233527
$59$	442.839	0.977166	0.488583	−	0.872517i	$-0.337514\pi$
$59$	442.839	0.977166	0.488583	+	0.872517i	$0.337514\pi$
$60$	−424.730	−0.913874
$61$	−93.0781	−0.195368	−0.0976838	−	0.995217i	$-0.531143\pi$
$61$	−93.0781	−0.195368	−0.0976838	+	0.995217i	$0.531143\pi$
$62$	17.9163	0.0366996
$63$	0	0
$64$	477.666	0.932942
$65$	100.274	0.191346
$66$	−1253.35	−2.33752
$67$	293.840	0.535795	0.267897	−	0.963447i	$-0.413671\pi$
$67$	293.840	0.535795	0.267897	+	0.963447i	$0.413671\pi$
$68$	−12.3328	−0.0219936
$69$	−527.188	−0.919797
$70$	0	0
$71$	697.751	1.16631	0.583153	−	0.812362i	$-0.301819\pi$
$71$	697.751	1.16631	0.583153	+	0.812362i	$0.301819\pi$
$72$	1439.53	2.35625
$73$	−402.050	−0.644609	−0.322304	−	0.946636i	$-0.604457\pi$
$73$	−402.050	−0.644609	−0.322304	+	0.946636i	$0.604457\pi$
$74$	−29.8265	−0.0468548
$75$	244.876	0.377012
$76$	−429.589	−0.648385
$77$	0	0
$78$	−156.794	−0.227609
$79$	−1319.27	−1.87885	−0.939425	−	0.342753i	$-0.888640\pi$
$79$	−1319.27	−1.87885	−0.939425	+	0.342753i	$0.888640\pi$
$80$	−251.934	−0.352088
$81$	1192.00	1.63512
$82$	−174.880	−0.235515
$83$	−791.185	−1.04631	−0.523155	−	0.852237i	$-0.675245\pi$
$83$	−791.185	−1.04631	−0.523155	+	0.852237i	$0.675245\pi$
$84$	0	0
$85$	40.8404	0.0521149
$86$	−738.577	−0.926079
$87$	463.090	0.570672
$88$	1580.00	1.91396
$89$	244.376	0.291054	0.145527	−	0.989354i	$-0.453512\pi$
$89$	244.376	0.291054	0.145527	+	0.989354i	$0.453512\pi$
$90$	−1511.71	−1.77054
$91$	0	0
$92$	210.750	0.238829
$93$	−80.4330	−0.0896830
$94$	−97.2908	−0.106753
$95$	1422.60	1.53638
$96$	−1408.94	−1.49791
$97$	−1766.48	−1.84906	−0.924528	−	0.381113i	$-0.875541\pi$
$97$	−1766.48	−1.84906	−0.924528	+	0.381113i	$0.875541\pi$
$98$	0	0
$99$	3867.60	3.92634
$100$	−97.8925	−0.0978925
$101$	−120.887	−0.119096	−0.0595480	−	0.998225i	$-0.518966\pi$
$101$	−120.887	−0.119096	−0.0595480	+	0.998225i	$0.518966\pi$
$102$	−63.8604	−0.0619914
$103$	312.456	0.298905	0.149452	−	0.988769i	$-0.452249\pi$
$103$	312.456	0.298905	0.149452	+	0.988769i	$0.452249\pi$
$104$	197.658	0.186365
$105$	0	0
$106$	923.383	0.846103
$107$	−1655.60	−1.49582	−0.747910	−	0.663800i	$-0.768943\pi$
$107$	−1655.60	−1.49582	−0.747910	+	0.663800i	$0.768943\pi$
$108$	−1117.24	−0.995429
$109$	−314.168	−0.276072	−0.138036	−	0.990427i	$-0.544079\pi$
$109$	−314.168	−0.276072	−0.138036	+	0.990427i	$0.544079\pi$
$110$	−1659.22	−1.43819
$111$	133.902	0.114499
$112$	0	0
$113$	−387.987	−0.322998	−0.161499	−	0.986873i	$-0.551633\pi$
$113$	−387.987	−0.322998	−0.161499	+	0.986873i	$0.551633\pi$
$114$	−2224.46	−1.82754
$115$	−697.908	−0.565915
$116$	−185.126	−0.148177
$117$	483.838	0.382315
$118$	−916.685	−0.715150
$119$	0	0
$120$	2772.48	2.10910
$121$	2913.99	2.18933
$122$	192.673	0.142982
$123$	785.100	0.575529
$124$	32.1542	0.0232865
$125$	−1213.63	−0.868404
$126$	0	0
$127$	−2129.85	−1.48814	−0.744071	−	0.668101i	$-0.767108\pi$
$127$	−2129.85	−1.48814	−0.744071	+	0.668101i	$0.767108\pi$
$128$	224.118	0.154761
$129$	3315.74	2.26306
$130$	−207.569	−0.140039
$131$	504.372	0.336391	0.168195	−	0.985754i	$-0.446206\pi$
$131$	504.372	0.336391	0.168195	+	0.985754i	$0.446206\pi$
$132$	−2249.36	−1.48320
$133$	0	0
$134$	−608.254	−0.392128
$135$	3699.78	2.35871
$136$	80.5036	0.0507583
$137$	−1915.76	−1.19471	−0.597353	−	0.801978i	$-0.703781\pi$
$137$	−1915.76	−1.19471	−0.597353	+	0.801978i	$0.703781\pi$
$138$	1091.29	0.673164
$139$	−2914.75	−1.77860	−0.889301	−	0.457322i	$-0.848809\pi$
$139$	−2914.75	−1.77860	−0.889301	+	0.457322i	$0.848809\pi$
$140$	0	0
$141$	436.774	0.260873
$142$	−1444.36	−0.853575
$143$	531.050	0.310550
$144$	−1215.62	−0.703483
$145$	613.052	0.351112
$146$	832.251	0.471764
$147$	0	0
$148$	−53.5291	−0.0297302
$149$	−1227.51	−0.674909	−0.337455	−	0.941342i	$-0.609566\pi$
$149$	−1227.51	−0.674909	−0.337455	+	0.941342i	$0.609566\pi$
$150$	−506.898	−0.275921
$151$	3246.50	1.74965	0.874824	−	0.484442i	$-0.160977\pi$
$151$	3246.50	1.74965	0.874824	+	0.484442i	$0.160977\pi$
$152$	2804.20	1.49638
$153$	197.061	0.104127
$154$	0	0
$155$	−106.480	−0.0551784
$156$	−281.397	−0.144421
$157$	2600.19	1.32177	0.660884	−	0.750488i	$-0.270182\pi$
$157$	2600.19	1.32177	0.660884	+	0.750488i	$0.270182\pi$
$158$	2730.91	1.37506
$159$	−4145.41	−2.06762
$160$	−1865.20	−0.921606
$161$	0	0
$162$	−2467.46	−1.19668
$163$	−1039.19	−0.499361	−0.249680	−	0.968328i	$-0.580326\pi$
$163$	−1039.19	−0.499361	−0.249680	+	0.968328i	$0.580326\pi$
$164$	−313.854	−0.149438
$165$	7448.86	3.51450
$166$	1637.77	0.765755
$167$	3556.42	1.64793	0.823965	−	0.566640i	$-0.191757\pi$
$167$	3556.42	1.64793	0.823965	+	0.566640i	$0.191757\pi$
$168$	0	0
$169$	−2130.57	−0.969761
$170$	−84.5403	−0.0381409
$171$	6864.26	3.06973
$172$	−1325.51	−0.587612
$173$	−3303.78	−1.45192	−0.725959	−	0.687738i	$-0.758604\pi$
$173$	−3303.78	−1.45192	−0.725959	+	0.687738i	$0.758604\pi$
$174$	−958.604	−0.417653
$175$	0	0
$176$	−1334.24	−0.571432
$177$	4115.34	1.74761
$178$	−505.863	−0.213011
$179$	3005.03	1.25478	0.627392	−	0.778704i	$-0.284122\pi$
$179$	3005.03	1.25478	0.627392	+	0.778704i	$0.284122\pi$
$180$	−2713.04	−1.12343
$181$	168.149	0.0690519	0.0345260	−	0.999404i	$-0.489008\pi$
$181$	168.149	0.0690519	0.0345260	+	0.999404i	$0.489008\pi$
$182$	0	0
$183$	−864.981	−0.349406
$184$	−1375.70	−0.551184
$185$	177.264	0.0704469
$186$	166.498	0.0656355
$187$	216.290	0.0845813
$188$	−174.606	−0.0677366
$189$	0	0
$190$	−2944.81	−1.12441
$191$	388.058	0.147010	0.0735049	−	0.997295i	$-0.476582\pi$
$191$	388.058	0.147010	0.0735049	+	0.997295i	$0.476582\pi$
$192$	4438.99	1.66852
$193$	2674.02	0.997307	0.498654	−	0.866801i	$-0.333828\pi$
$193$	2674.02	0.997307	0.498654	+	0.866801i	$0.333828\pi$
$194$	3656.64	1.35325
$195$	931.855	0.342213
$196$	0	0
$197$	−592.800	−0.214392	−0.107196	−	0.994238i	$-0.534187\pi$
$197$	−592.800	−0.214392	−0.107196	+	0.994238i	$0.534187\pi$
$198$	−8005.99	−2.87354
$199$	−2659.79	−0.947474	−0.473737	−	0.880666i	$-0.657095\pi$
$199$	−2659.79	−0.947474	−0.473737	+	0.880666i	$0.657095\pi$
$200$	639.006	0.225923
$201$	2730.68	0.958244
$202$	250.238	0.0871618
$203$	0	0
$204$	−114.609	−0.0393346
$205$	1039.34	0.354100
$206$	−646.789	−0.218757
$207$	−3367.51	−1.13072
$208$	−166.914	−0.0556413
$209$	7534.07	2.49350
$210$	0	0
$211$	−1363.76	−0.444952	−0.222476	−	0.974938i	$-0.571414\pi$
$211$	−1363.76	−0.444952	−0.222476	+	0.974938i	$0.571414\pi$
$212$	1657.18	0.536866
$213$	6484.25	2.08588
$214$	3427.12	1.09473
$215$	4389.48	1.39237
$216$	7292.92	2.29732
$217$	0	0
$218$	650.333	0.202046
$219$	−3736.28	−1.15285
$220$	−2977.78	−0.912553
$221$	27.0580	0.00823582
$222$	−277.179	−0.0837976
$223$	713.992	0.214406	0.107203	−	0.994237i	$-0.465811\pi$
$223$	713.992	0.214406	0.107203	+	0.994237i	$0.465811\pi$
$224$	0	0
$225$	1564.19	0.463464
$226$	803.139	0.236390
$227$	4382.50	1.28140	0.640698	−	0.767793i	$-0.278645\pi$
$227$	4382.50	1.28140	0.640698	+	0.767793i	$0.278645\pi$
$228$	−3992.20	−1.15961
$229$	−4923.75	−1.42083	−0.710417	−	0.703781i	$-0.751494\pi$
$229$	−4923.75	−1.42083	−0.710417	+	0.703781i	$0.751494\pi$
$230$	1444.68	0.414172
$231$	0	0
$232$	1208.43	0.341972
$233$	5083.41	1.42929	0.714646	−	0.699486i	$-0.246588\pi$
$233$	5083.41	1.42929	0.714646	+	0.699486i	$0.246588\pi$
$234$	−1001.55	−0.279802
$235$	578.215	0.160505
$236$	−1645.16	−0.453775
$237$	−12260.1	−3.36024
$238$	0	0
$239$	−1135.41	−0.307294	−0.153647	−	0.988126i	$-0.549102\pi$
$239$	−1135.41	−0.307294	−0.153647	+	0.988126i	$0.549102\pi$
$240$	−2341.24	−0.629694
$241$	−4502.81	−1.20353	−0.601766	−	0.798672i	$-0.705536\pi$
$241$	−4502.81	−1.20353	−0.601766	+	0.798672i	$0.705536\pi$
$242$	−6032.01	−1.60228
$243$	2957.49	0.780754
$244$	345.788	0.0907245
$245$	0	0
$246$	−1625.17	−0.421207
$247$	942.515	0.242797
$248$	−209.890	−0.0537421
$249$	−7352.54	−1.87128
$250$	2512.24	0.635552
$251$	3809.34	0.957943	0.478971	−	0.877830i	$-0.341010\pi$
$251$	3809.34	0.957943	0.478971	+	0.877830i	$0.341010\pi$
$252$	0	0
$253$	−3696.11	−0.918468
$254$	4408.84	1.08911
$255$	379.533	0.0932049
$256$	−4285.26	−1.04621
$257$	644.869	0.156521	0.0782603	−	0.996933i	$-0.475063\pi$
$257$	644.869	0.156521	0.0782603	+	0.996933i	$0.475063\pi$
$258$	−6863.65	−1.65625
$259$	0	0
$260$	−372.521	−0.0888569
$261$	2958.07	0.701532
$262$	−1044.06	−0.246191
$263$	7407.34	1.73672	0.868358	−	0.495938i	$-0.165176\pi$
$263$	7407.34	1.73672	0.868358	+	0.495938i	$0.165176\pi$
$264$	14683.0	3.42302
$265$	−5487.82	−1.27213
$266$	0	0
$267$	2271.00	0.520536
$268$	−1091.62	−0.248812
$269$	−8289.30	−1.87884	−0.939419	−	0.342771i	$-0.888634\pi$
$269$	−8289.30	−1.87884	−0.939419	+	0.342771i	$0.888634\pi$
$270$	−7658.61	−1.72625
$271$	−7593.80	−1.70218	−0.851089	−	0.525021i	$-0.824057\pi$
$271$	−7593.80	−1.70218	−0.851089	+	0.525021i	$0.824057\pi$
$272$	−67.9819	−0.0151544
$273$	0	0
$274$	3965.67	0.874360
$275$	1716.82	0.376467
$276$	1958.52	0.427134
$277$	−280.890	−0.0609280	−0.0304640	−	0.999536i	$-0.509698\pi$
$277$	−280.890	−0.0609280	−0.0304640	+	0.999536i	$0.509698\pi$
$278$	6033.58	1.30169
$279$	−513.781	−0.110248
$280$	0	0
$281$	6374.74	1.35333	0.676663	−	0.736293i	$-0.263425\pi$
$281$	6374.74	1.35333	0.676663	+	0.736293i	$0.263425\pi$
$282$	−904.131	−0.190923
$283$	1092.54	0.229487	0.114743	−	0.993395i	$-0.463395\pi$
$283$	1092.54	0.229487	0.114743	+	0.993395i	$0.463395\pi$
$284$	−2592.16	−0.541608
$285$	13220.3	2.74774
$286$	−1099.28	−0.227280
$287$	0	0
$288$	−8999.87	−1.84140
$289$	−4901.98	−0.997757
$290$	−1269.03	−0.256965
$291$	−16416.0	−3.30695
$292$	1493.63	0.299342
$293$	−2879.17	−0.574071	−0.287036	−	0.957920i	$-0.592670\pi$
$293$	−2879.17	−0.574071	−0.287036	+	0.957920i	$0.592670\pi$
$294$	0	0
$295$	5448.01	1.07524
$296$	349.418	0.0686132
$297$	19594.0	3.82814
$298$	2540.97	0.493940
$299$	−462.385	−0.0894328
$300$	−909.722	−0.175076
$301$	0	0
$302$	−6720.32	−1.28050
$303$	−1123.41	−0.212998
$304$	−2368.02	−0.446761
$305$	−1145.09	−0.214976
$306$	−407.920	−0.0762066
$307$	−3179.26	−0.591043	−0.295521	−	0.955336i	$-0.595493\pi$
$307$	−3179.26	−0.591043	−0.295521	+	0.955336i	$0.595493\pi$
$308$	0	0
$309$	2903.67	0.534577
$310$	220.415	0.0403830
$311$	5180.41	0.944548	0.472274	−	0.881452i	$-0.343433\pi$
$311$	5180.41	0.944548	0.472274	+	0.881452i	$0.343433\pi$
$312$	1836.85	0.333305
$313$	6111.40	1.10363	0.551816	−	0.833966i	$-0.313935\pi$
$313$	6111.40	1.10363	0.551816	+	0.833966i	$0.313935\pi$
$314$	−5382.43	−0.967351
$315$	0	0
$316$	4901.12	0.872498
$317$	4507.60	0.798650	0.399325	−	0.916809i	$-0.369244\pi$
$317$	4507.60	0.798650	0.399325	+	0.916809i	$0.369244\pi$
$318$	8581.07	1.51322
$319$	3246.72	0.569847
$320$	5876.47	1.02658
$321$	−15385.6	−2.67520
$322$	0	0
$323$	383.874	0.0661280
$324$	−4428.31	−0.759312
$325$	214.776	0.0366573
$326$	2151.15	0.365463
$327$	−2919.58	−0.493741
$328$	2048.72	0.344883
$329$	0	0
$330$	−15419.3	−2.57213
$331$	6433.69	1.06836	0.534180	−	0.845370i	$-0.320620\pi$
$331$	6433.69	1.06836	0.534180	+	0.845370i	$0.320620\pi$
$332$	2939.27	0.485884
$333$	855.323	0.140755
$334$	−7361.86	−1.20606
$335$	3614.95	0.589570
$336$	0	0
$337$	−7368.94	−1.19113	−0.595566	−	0.803306i	$-0.703072\pi$
$337$	−7368.94	−1.19113	−0.595566	+	0.803306i	$0.703072\pi$
$338$	4410.31	0.709731
$339$	−3605.59	−0.577666
$340$	−151.723	−0.0242010
$341$	−563.915	−0.0895534
$342$	−14209.1	−2.24661
$343$	0	0
$344$	8652.45	1.35613
$345$	−6485.71	−1.01211
$346$	6838.88	1.06260
$347$	7884.95	1.21985	0.609923	−	0.792461i	$-0.291200\pi$
$347$	7884.95	1.21985	0.609923	+	0.792461i	$0.291200\pi$
$348$	−1720.39	−0.265008
$349$	−9423.81	−1.44540	−0.722700	−	0.691162i	$-0.757099\pi$
$349$	−9423.81	−1.44540	−0.722700	+	0.691162i	$0.757099\pi$
$350$	0	0
$351$	2451.21	0.372753
$352$	−9878.06	−1.49575
$353$	211.472	0.0318853	0.0159426	−	0.999873i	$-0.494925\pi$
$353$	211.472	0.0318853	0.0159426	+	0.999873i	$0.494925\pi$
$354$	−8518.82	−1.27901
$355$	8584.05	1.28336
$356$	−907.864	−0.135159
$357$	0	0
$358$	−6220.46	−0.918328
$359$	8671.48	1.27483	0.637414	−	0.770522i	$-0.280004\pi$
$359$	8671.48	1.27483	0.637414	+	0.770522i	$0.280004\pi$
$360$	17709.7	2.59273
$361$	6512.56	0.949492
$362$	−348.071	−0.0505365
$363$	27079.9	3.91550
$364$	0	0
$365$	−4946.21	−0.709305
$366$	1790.53	0.255717
$367$	6403.31	0.910763	0.455382	−	0.890296i	$-0.349503\pi$
$367$	6403.31	0.910763	0.455382	+	0.890296i	$0.349503\pi$
$368$	1161.72	0.164562
$369$	5014.97	0.707503
$370$	−366.939	−0.0515574
$371$	0	0
$372$	298.811	0.0416468
$373$	−9741.01	−1.35220	−0.676099	−	0.736810i	$-0.736331\pi$
$373$	−9741.01	−1.35220	−0.676099	+	0.736810i	$0.736331\pi$
$374$	−447.724	−0.0619018
$375$	−11278.4	−1.55310
$376$	1139.76	0.156327
$377$	406.166	0.0554870
$378$	0	0
$379$	−3072.83	−0.416466	−0.208233	−	0.978079i	$-0.566771\pi$
$379$	−3072.83	−0.416466	−0.208233	+	0.978079i	$0.566771\pi$
$380$	−5285.00	−0.713460
$381$	−19792.9	−2.66147
$382$	−803.287	−0.107591
$383$	−9192.80	−1.22645	−0.613225	−	0.789909i	$-0.710128\pi$
$383$	−9192.80	−1.22645	−0.613225	+	0.789909i	$0.710128\pi$
$384$	2082.75	0.276783
$385$	0	0
$386$	−5535.27	−0.729891
$387$	21179.9	2.78200
$388$	6562.51	0.858662
$389$	−6021.04	−0.784779	−0.392389	−	0.919799i	$-0.628351\pi$
$389$	−6021.04	−0.784779	−0.392389	+	0.919799i	$0.628351\pi$
$390$	−1928.96	−0.250453
$391$	−188.323	−0.0243579
$392$	0	0
$393$	4687.16	0.601619
$394$	1227.11	0.156906
$395$	−16230.2	−2.06742
$396$	−14368.2	−1.82331
$397$	5245.01	0.663072	0.331536	−	0.943443i	$-0.392433\pi$
$397$	5245.01	0.663072	0.331536	+	0.943443i	$0.392433\pi$
$398$	5505.81	0.693420
$399$	0	0
$400$	−539.613	−0.0674516
$401$	−9387.42	−1.16904	−0.584520	−	0.811379i	$-0.698717\pi$
$401$	−9387.42	−1.16904	−0.584520	+	0.811379i	$0.698717\pi$
$402$	−5652.55	−0.701302
$403$	−70.5460	−0.00871997
$404$	449.098	0.0553056
$405$	14664.5	1.79922
$406$	0	0
$407$	938.785	0.114334
$408$	748.126	0.0907788
$409$	14375.4	1.73794	0.868972	−	0.494861i	$-0.164781\pi$
$409$	14375.4	1.73794	0.868972	+	0.494861i	$0.164781\pi$
$410$	−2151.45	−0.259153
$411$	−17803.3	−2.13668
$412$	−1160.78	−0.138805
$413$	0	0
$414$	6970.80	0.827527
$415$	−9733.51	−1.15132
$416$	−1235.75	−0.145643
$417$	−27087.0	−3.18095
$418$	−15595.7	−1.82490
$419$	−1545.97	−0.180252	−0.0901258	−	0.995930i	$-0.528727\pi$
$419$	−1545.97	−0.180252	−0.0901258	+	0.995930i	$0.528727\pi$
$420$	0	0
$421$	5914.86	0.684734	0.342367	−	0.939566i	$-0.388771\pi$
$421$	5914.86	0.684734	0.342367	+	0.939566i	$0.388771\pi$
$422$	2823.00	0.325644
$423$	2789.98	0.320693
$424$	−10817.5	−1.23901
$425$	87.4753	0.00998395
$426$	−13422.5	−1.52658
$427$	0	0
$428$	6150.59	0.694627
$429$	4935.09	0.555404
$430$	−9086.31	−1.01902
$431$	4068.63	0.454708	0.227354	−	0.973812i	$-0.426993\pi$
$431$	4068.63	0.454708	0.227354	+	0.973812i	$0.426993\pi$
$432$	−6158.56	−0.685888
$433$	10978.5	1.21846	0.609232	−	0.792992i	$-0.291478\pi$
$433$	10978.5	1.21846	0.609232	+	0.792992i	$0.291478\pi$
$434$	0	0
$435$	5697.14	0.627947
$436$	1167.14	0.128202
$437$	−6559.90	−0.718084
$438$	7734.17	0.843728
$439$	−13317.6	−1.44787	−0.723934	−	0.689869i	$-0.757668\pi$
$439$	−13317.6	−1.44787	−0.723934	+	0.689869i	$0.757668\pi$
$440$	19437.8	2.10605
$441$	0	0
$442$	−56.0105	−0.00602748
$443$	6118.61	0.656217	0.328109	−	0.944640i	$-0.393589\pi$
$443$	6118.61	0.656217	0.328109	+	0.944640i	$0.393589\pi$
$444$	−497.450	−0.0531710
$445$	3006.43	0.320266
$446$	−1477.98	−0.156915
$447$	−11407.3	−1.20704
$448$	0	0
$449$	−11826.2	−1.24301	−0.621506	−	0.783409i	$-0.713479\pi$
$449$	−11826.2	−1.24301	−0.621506	+	0.783409i	$0.713479\pi$
$450$	−3237.91	−0.339192
$451$	5504.32	0.574697
$452$	1441.38	0.149993
$453$	30170.0	3.12916
$454$	−9071.85	−0.937804
$455$	0	0
$456$	26059.6	2.67621
$457$	12934.4	1.32396	0.661978	−	0.749524i	$-0.269717\pi$
$457$	12934.4	1.32396	0.661978	+	0.749524i	$0.269717\pi$
$458$	10192.3	1.03985
$459$	998.348	0.101523
$460$	2592.75	0.262799
$461$	−10446.0	−1.05535	−0.527677	−	0.849445i	$-0.676937\pi$
$461$	−10446.0	−1.05535	−0.527677	+	0.849445i	$0.676937\pi$
$462$	0	0
$463$	10860.3	1.09011	0.545054	−	0.838401i	$-0.316509\pi$
$463$	10860.3	1.09011	0.545054	+	0.838401i	$0.316509\pi$
$464$	−1020.47	−0.102100
$465$	−989.524	−0.0986840
$466$	−10522.7	−1.04604
$467$	7431.42	0.736371	0.368185	−	0.929752i	$-0.379979\pi$
$467$	7431.42	0.736371	0.368185	+	0.929752i	$0.379979\pi$
$468$	−1797.47	−0.177539
$469$	0	0
$470$	−1196.92	−0.117467
$471$	24163.7	2.36392
$472$	10739.0	1.04725
$473$	23246.6	2.25979
$474$	25378.5	2.45923
$475$	3047.04	0.294333
$476$	0	0
$477$	−26479.6	−2.54175
$478$	2350.31	0.224897
$479$	−4952.39	−0.472402	−0.236201	−	0.971704i	$-0.575902\pi$
$479$	−4952.39	−0.472402	−0.236201	+	0.971704i	$0.575902\pi$
$480$	−17333.4	−1.64825
$481$	117.442	0.0111329
$482$	9320.89	0.880819
$483$	0	0
$484$	−10825.6	−1.01668
$485$	−21732.0	−2.03464
$486$	−6122.06	−0.571404
$487$	−9253.83	−0.861050	−0.430525	−	0.902579i	$-0.641672\pi$
$487$	−9253.83	−0.861050	−0.430525	+	0.902579i	$0.641672\pi$
$488$	−2257.17	−0.209380
$489$	−9657.29	−0.893083
$490$	0	0
$491$	−11828.7	−1.08722	−0.543608	−	0.839339i	$-0.682942\pi$
$491$	−11828.7	−1.08722	−0.543608	+	0.839339i	$0.682942\pi$
$492$	−2916.67	−0.267263
$493$	165.426	0.0151124
$494$	−1951.02	−0.177694
$495$	47580.9	4.32041
$496$	177.243	0.0160453
$497$	0	0
$498$	15219.9	1.36952
$499$	8187.23	0.734490	0.367245	−	0.930124i	$-0.380301\pi$
$499$	8187.23	0.734490	0.367245	+	0.930124i	$0.380301\pi$
$500$	4508.68	0.403268
$501$	33050.1	2.94725
$502$	−7885.41	−0.701082
$503$	16285.7	1.44362	0.721812	−	0.692089i	$-0.243310\pi$
$503$	16285.7	1.44362	0.721812	+	0.692089i	$0.243310\pi$
$504$	0	0
$505$	−1487.21	−0.131049
$506$	7651.01	0.672191
$507$	−19799.5	−1.73437
$508$	7912.47	0.691061
$509$	−10344.5	−0.900810	−0.450405	−	0.892824i	$-0.648720\pi$
$509$	−10344.5	−0.900810	−0.450405	+	0.892824i	$0.648720\pi$
$510$	−785.639	−0.0682131
$511$	0	0
$512$	7077.61	0.610917
$513$	34775.6	2.99295
$514$	−1334.89	−0.114551
$515$	3843.97	0.328904
$516$	−12318.1	−1.05092
$517$	3062.22	0.260496
$518$	0	0
$519$	−30702.3	−2.59669
$520$	2431.68	0.205070
$521$	8541.42	0.718246	0.359123	−	0.933290i	$-0.383076\pi$
$521$	8541.42	0.718246	0.359123	+	0.933290i	$0.383076\pi$
$522$	−6123.26	−0.513425
$523$	20023.3	1.67410	0.837052	−	0.547123i	$-0.184277\pi$
$523$	20023.3	1.67410	0.837052	+	0.547123i	$0.184277\pi$
$524$	−1873.75	−0.156213
$525$	0	0
$526$	−15333.3	−1.27104
$527$	−28.7325	−0.00237497
$528$	−12399.2	−1.02198
$529$	−8948.81	−0.735498
$530$	11359.9	0.931022
$531$	26287.5	2.14836
$532$	0	0
$533$	688.593	0.0559593
$534$	−4701.02	−0.380961
$535$	−20367.9	−1.64595
$536$	7125.71	0.574223
$537$	27925.9	2.24412
$538$	17159.0	1.37505
$539$	0	0
$540$	−13744.8	−1.09534
$541$	−22940.3	−1.82307	−0.911534	−	0.411225i	$-0.865101\pi$
$541$	−22940.3	−1.82307	−0.911534	+	0.411225i	$0.865101\pi$
$542$	15719.3	1.24576
$543$	1562.62	0.123496
$544$	−503.305	−0.0396674
$545$	−3865.04	−0.303780
$546$	0	0
$547$	6306.77	0.492976	0.246488	−	0.969146i	$-0.420723\pi$
$547$	6306.77	0.492976	0.246488	+	0.969146i	$0.420723\pi$
$548$	7117.12	0.554796
$549$	−5525.23	−0.429528
$550$	−3553.86	−0.275522
$551$	5762.31	0.445522
$552$	−12784.5	−0.985767
$553$	0	0
$554$	581.447	0.0445908
$555$	1647.32	0.125991
$556$	10828.4	0.825945
$557$	25573.9	1.94542	0.972711	−	0.232021i	$-0.0745338\pi$
$557$	25573.9	1.94542	0.972711	+	0.232021i	$0.0745338\pi$
$558$	1063.53	0.0806864
$559$	2908.16	0.220040
$560$	0	0
$561$	2010.00	0.151270
$562$	−13195.8	−0.990448
$563$	6919.91	0.518009	0.259005	−	0.965876i	$-0.416605\pi$
$563$	6919.91	0.518009	0.259005	+	0.965876i	$0.416605\pi$
$564$	−1622.63	−0.121144
$565$	−4773.19	−0.355415
$566$	−2261.57	−0.167952
$567$	0	0
$568$	16920.7	1.24996
$569$	16736.8	1.23312	0.616560	−	0.787308i	$-0.288526\pi$
$569$	16736.8	1.23312	0.616560	+	0.787308i	$0.288526\pi$
$570$	−27366.3	−2.01096
$571$	11310.5	0.828949	0.414474	−	0.910061i	$-0.363965\pi$
$571$	11310.5	0.828949	0.414474	+	0.910061i	$0.363965\pi$
$572$	−1972.87	−0.144213
$573$	3606.25	0.262920
$574$	0	0
$575$	−1494.84	−0.108416
$576$	28354.8	2.05113
$577$	24946.3	1.79988	0.899938	−	0.436018i	$-0.143612\pi$
$577$	24946.3	1.79988	0.899938	+	0.436018i	$0.143612\pi$
$578$	10147.2	0.730220
$579$	24849.9	1.78364
$580$	−2277.51	−0.163049
$581$	0	0
$582$	33981.4	2.42023
$583$	−29063.4	−2.06464
$584$	−9749.84	−0.690841
$585$	5952.40	0.420686
$586$	5959.93	0.420141
$587$	15559.0	1.09402	0.547008	−	0.837128i	$-0.315767\pi$
$587$	15559.0	1.09402	0.547008	+	0.837128i	$0.315767\pi$
$588$	0	0
$589$	−1000.84	−0.0700153
$590$	−11277.5	−0.786926
$591$	−5508.94	−0.383430
$592$	−295.068	−0.0204852
$593$	−5539.08	−0.383580	−0.191790	−	0.981436i	$-0.561429\pi$
$593$	−5539.08	−0.383580	−0.191790	+	0.981436i	$0.561429\pi$
$594$	−40559.8	−2.80167
$595$	0	0
$596$	4560.23	0.313413
$597$	−24717.6	−1.69451
$598$	957.145	0.0654524
$599$	15453.0	1.05408	0.527040	−	0.849840i	$-0.323302\pi$
$599$	15453.0	1.05408	0.527040	+	0.849840i	$0.323302\pi$
$600$	5938.33	0.404052
$601$	25436.5	1.72642	0.863208	−	0.504849i	$-0.168452\pi$
$601$	25436.5	1.72642	0.863208	+	0.504849i	$0.168452\pi$
$602$	0	0
$603$	17442.7	1.17798
$604$	−12060.8	−0.812498
$605$	35849.3	2.40906
$606$	2325.48	0.155885
$607$	26964.2	1.80304	0.901518	−	0.432742i	$-0.142454\pi$
$607$	26964.2	1.80304	0.901518	+	0.432742i	$0.142454\pi$
$608$	−17531.7	−1.16942
$609$	0	0
$610$	2370.35	0.157333
$611$	383.085	0.0253649
$612$	−732.087	−0.0483544
$613$	4223.68	0.278292	0.139146	−	0.990272i	$-0.455564\pi$
$613$	4223.68	0.278292	0.139146	+	0.990272i	$0.455564\pi$
$614$	6581.13	0.432562
$615$	9658.65	0.633292
$616$	0	0
$617$	2508.23	0.163659	0.0818294	−	0.996646i	$-0.473924\pi$
$617$	2508.23	0.163659	0.0818294	+	0.996646i	$0.473924\pi$
$618$	−6010.66	−0.391236
$619$	−29549.0	−1.91870	−0.959351	−	0.282216i	$-0.908930\pi$
$619$	−29549.0	−1.91870	−0.959351	+	0.282216i	$0.908930\pi$
$620$	395.575	0.0256237
$621$	−17060.4	−1.10243
$622$	−10723.5	−0.691278
$623$	0	0
$624$	−1551.14	−0.0995118
$625$	−18224.5	−1.16637
$626$	−12650.7	−0.807705
$627$	70014.6	4.45951
$628$	−9659.77	−0.613801
$629$	47.8328	0.00303214
$630$	0	0
$631$	16310.8	1.02904	0.514520	−	0.857478i	$-0.327970\pi$
$631$	16310.8	1.02904	0.514520	+	0.857478i	$0.327970\pi$
$632$	−31992.7	−2.01361
$633$	−12673.5	−0.795776
$634$	−9330.81	−0.584501
$635$	−26202.4	−1.63750
$636$	15400.3	0.960160
$637$	0	0
$638$	−6720.76	−0.417049
$639$	41419.3	2.56420
$640$	2757.20	0.170294
$641$	−12032.3	−0.741415	−0.370708	−	0.928750i	$-0.620885\pi$
$641$	−12032.3	−0.741415	−0.370708	+	0.928750i	$0.620885\pi$
$642$	31848.5	1.95788
$643$	−9156.48	−0.561581	−0.280790	−	0.959769i	$-0.590597\pi$
$643$	−9156.48	−0.561581	−0.280790	+	0.959769i	$0.590597\pi$
$644$	0	0
$645$	40791.8	2.49019
$646$	−794.627	−0.0483966
$647$	21753.8	1.32184	0.660920	−	0.750457i	$-0.270166\pi$
$647$	21753.8	1.32184	0.660920	+	0.750457i	$0.270166\pi$
$648$	28906.4	1.75239
$649$	28852.6	1.74509
$650$	−444.589	−0.0268280
$651$	0	0
$652$	3860.63	0.231892
$653$	1916.03	0.114824	0.0574120	−	0.998351i	$-0.481715\pi$
$653$	1916.03	0.114824	0.0574120	+	0.998351i	$0.481715\pi$
$654$	6043.59	0.361350
$655$	6205.01	0.370152
$656$	−1730.06	−0.102969
$657$	−23866.2	−1.41721
$658$	0	0
$659$	−7660.22	−0.452807	−0.226403	−	0.974034i	$-0.572697\pi$
$659$	−7660.22	−0.452807	−0.226403	+	0.974034i	$0.572697\pi$
$660$	−27672.7	−1.63206
$661$	25688.3	1.51158	0.755792	−	0.654811i	$-0.227252\pi$
$661$	25688.3	1.51158	0.755792	+	0.654811i	$0.227252\pi$
$662$	−13317.8	−0.781892
$663$	251.452	0.0147294
$664$	−19186.5	−1.12135
$665$	0	0
$666$	−1770.53	−0.103013
$667$	−2826.91	−0.164106
$668$	−13212.2	−0.765263
$669$	6635.18	0.383454
$670$	−7483.01	−0.431484
$671$	−6064.37	−0.348901
$672$	0	0
$673$	−12856.9	−0.736397	−0.368199	−	0.929747i	$-0.620025\pi$
$673$	−12856.9	−0.736397	−0.368199	+	0.929747i	$0.620025\pi$
$674$	15253.8	0.871745
$675$	7924.49	0.451872
$676$	7915.11	0.450336
$677$	−12106.5	−0.687281	−0.343640	−	0.939101i	$-0.611660\pi$
$677$	−12106.5	−0.687281	−0.343640	+	0.939101i	$0.611660\pi$
$678$	7463.63	0.422771
$679$	0	0
$680$	990.392	0.0558527
$681$	40726.9	2.29171
$682$	1167.31	0.0655407
$683$	−21777.7	−1.22006	−0.610029	−	0.792379i	$-0.708842\pi$
$683$	−21777.7	−1.22006	−0.610029	+	0.792379i	$0.708842\pi$
$684$	−25500.9	−1.42551
$685$	−23568.6	−1.31461
$686$	0	0
$687$	−45756.8	−2.54109
$688$	−7306.62	−0.404887
$689$	−3635.85	−0.201037
$690$	13425.5	0.740726
$691$	−23098.8	−1.27167	−0.635833	−	0.771827i	$-0.719343\pi$
$691$	−23098.8	−1.27167	−0.635833	+	0.771827i	$0.719343\pi$
$692$	12273.6	0.674239
$693$	0	0
$694$	−16322.0	−0.892758
$695$	−35858.6	−1.95711
$696$	11230.1	0.611602
$697$	280.455	0.0152410
$698$	19507.4	1.05783
$699$	47240.5	2.55622
$700$	0	0
$701$	5681.12	0.306095	0.153048	−	0.988219i	$-0.451091\pi$
$701$	5681.12	0.306095	0.153048	+	0.988219i	$0.451091\pi$
$702$	−5074.06	−0.272803
$703$	1666.17	0.0893894
$704$	31121.7	1.66611
$705$	5373.40	0.287055
$706$	−437.750	−0.0233356
$707$	0	0
$708$	−15288.6	−0.811555
$709$	−19449.1	−1.03022	−0.515110	−	0.857124i	$-0.672249\pi$
$709$	−19449.1	−1.03022	−0.515110	+	0.857124i	$0.672249\pi$
$710$	−17769.1	−0.939244
$711$	−78313.3	−4.13077
$712$	5926.19	0.311929
$713$	491.000	0.0257897
$714$	0	0
$715$	6533.22	0.341719
$716$	−11163.8	−0.582695
$717$	−10551.4	−0.549581
$718$	−17950.1	−0.932997
$719$	−12698.5	−0.658655	−0.329327	−	0.944216i	$-0.606822\pi$
$719$	−12698.5	−0.658655	−0.329327	+	0.944216i	$0.606822\pi$
$720$	−14955.1	−0.774089
$721$	0	0
$722$	−13481.1	−0.694897
$723$	−41844.9	−2.15246
$724$	−624.677	−0.0320662
$725$	1313.09	0.0672646
$726$	−56055.9	−2.86561
$727$	−21600.0	−1.10193	−0.550964	−	0.834529i	$-0.685740\pi$
$727$	−21600.0	−1.10193	−0.550964	+	0.834529i	$0.685740\pi$
$728$	0	0
$729$	−4699.79	−0.238774
$730$	10238.7	0.519113
$731$	1184.46	0.0599299
$732$	3213.43	0.162257
$733$	−29661.1	−1.49462	−0.747311	−	0.664474i	$-0.768656\pi$
$733$	−29661.1	−1.49462	−0.747311	+	0.664474i	$0.768656\pi$
$734$	−13255.0	−0.666553
$735$	0	0
$736$	8600.81	0.430748
$737$	19144.7	0.956859
$738$	−10381.1	−0.517795
$739$	10546.9	0.524996	0.262498	−	0.964933i	$-0.415454\pi$
$739$	10546.9	0.524996	0.262498	+	0.964933i	$0.415454\pi$
$740$	−658.539	−0.0327140
$741$	8758.86	0.434231
$742$	0	0
$743$	−3519.50	−0.173779	−0.0868896	−	0.996218i	$-0.527693\pi$
$743$	−3519.50	−0.173779	−0.0868896	+	0.996218i	$0.527693\pi$
$744$	−1950.53	−0.0961153
$745$	−15101.4	−0.742647
$746$	20164.1	0.989622
$747$	−46965.7	−2.30038
$748$	−803.523	−0.0392777
$749$	0	0
$750$	23346.4	1.13665
$751$	−2684.86	−0.130455	−0.0652277	−	0.997870i	$-0.520777\pi$
$751$	−2684.86	−0.130455	−0.0652277	+	0.997870i	$0.520777\pi$
$752$	−962.482	−0.0466730
$753$	35400.5	1.71324
$754$	−840.770	−0.0406088
$755$	39940.0	1.92525
$756$	0	0
$757$	−7569.96	−0.363454	−0.181727	−	0.983349i	$-0.558169\pi$
$757$	−7569.96	−0.363454	−0.181727	+	0.983349i	$0.558169\pi$
$758$	6360.80	0.304795
$759$	−34348.2	−1.64264
$760$	34498.5	1.64657
$761$	−34546.4	−1.64561	−0.822804	−	0.568326i	$-0.807591\pi$
$761$	−34546.4	−1.64561	−0.822804	+	0.568326i	$0.807591\pi$
$762$	40971.6	1.94783
$763$	0	0
$764$	−1441.65	−0.0682682
$765$	2424.33	0.114578
$766$	19029.3	0.897591
$767$	3609.47	0.169922
$768$	−39823.2	−1.87109
$769$	−6894.46	−0.323304	−0.161652	−	0.986848i	$-0.551682\pi$
$769$	−6894.46	−0.323304	−0.161652	+	0.986848i	$0.551682\pi$
$770$	0	0
$771$	5992.81	0.279930
$772$	−9934.07	−0.463128
$773$	12416.7	0.577744	0.288872	−	0.957368i	$-0.406720\pi$
$773$	12416.7	0.577744	0.288872	+	0.957368i	$0.406720\pi$
$774$	−43842.8	−2.03604
$775$	−228.067	−0.0105709
$776$	−42837.6	−1.98168
$777$	0	0
$778$	12463.7	0.574349
$779$	9769.14	0.449314
$780$	−3461.87	−0.158916
$781$	45461.0	2.08287
$782$	389.833	0.0178266
$783$	14986.1	0.683986
$784$	0	0
$785$	31988.7	1.45443
$786$	−9702.51	−0.440302
$787$	6049.63	0.274010	0.137005	−	0.990570i	$-0.456252\pi$
$787$	6049.63	0.274010	0.137005	+	0.990570i	$0.456252\pi$
$788$	2202.27	0.0995592
$789$	68837.0	3.10603
$790$	33596.9	1.51307
$791$	0	0
$792$	93790.4	4.20795
$793$	−758.656	−0.0339731
$794$	−10857.3	−0.485277
$795$	−50998.7	−2.27514
$796$	9881.19	0.439987
$797$	−4566.09	−0.202935	−0.101468	−	0.994839i	$-0.532354\pi$
$797$	−4566.09	−0.202935	−0.101468	+	0.994839i	$0.532354\pi$
$798$	0	0
$799$	156.026	0.00690837
$800$	−3995.04	−0.176557
$801$	14506.5	0.639901
$802$	19432.1	0.855576
$803$	−26195.0	−1.15119
$804$	−10144.5	−0.444988
$805$	0	0
$806$	146.031	0.00638181
$807$	−77033.0	−3.36021
$808$	−2931.54	−0.127638
$809$	21021.6	0.913572	0.456786	−	0.889577i	$-0.349000\pi$
$809$	21021.6	0.913572	0.456786	+	0.889577i	$0.349000\pi$
$810$	−30355.8	−1.31678
$811$	22039.2	0.954257	0.477128	−	0.878834i	$-0.341678\pi$
$811$	22039.2	0.954257	0.477128	+	0.878834i	$0.341678\pi$
$812$	0	0
$813$	−70569.7	−3.04427
$814$	−1943.30	−0.0836765
$815$	−12784.6	−0.549479
$816$	−631.760	−0.0271030
$817$	41258.4	1.76677
$818$	−29757.4	−1.27193
$819$	0	0
$820$	−3861.17	−0.164437
$821$	22384.2	0.951540	0.475770	−	0.879570i	$-0.342169\pi$
$821$	22384.2	0.951540	0.475770	+	0.879570i	$0.342169\pi$
$822$	36853.2	1.56375
$823$	−15330.9	−0.649332	−0.324666	−	0.945829i	$-0.605252\pi$
$823$	−15330.9	−0.649332	−0.324666	+	0.945829i	$0.605252\pi$
$824$	7577.15	0.320343
$825$	15954.6	0.673293
$826$	0	0
$827$	−10442.0	−0.439060	−0.219530	−	0.975606i	$-0.570452\pi$
$827$	−10442.0	−0.439060	−0.219530	+	0.975606i	$0.570452\pi$
$828$	12510.4	0.525080
$829$	15700.9	0.657797	0.328899	−	0.944365i	$-0.393323\pi$
$829$	15700.9	0.657797	0.328899	+	0.944365i	$0.393323\pi$
$830$	20148.5	0.842610
$831$	−2610.33	−0.108967
$832$	3893.34	0.162232
$833$	0	0
$834$	56070.5	2.32801
$835$	43752.8	1.81333
$836$	−27989.3	−1.15793
$837$	−2602.91	−0.107491
$838$	3200.18	0.131919
$839$	−8429.14	−0.346849	−0.173424	−	0.984847i	$-0.555483\pi$
$839$	−8429.14	−0.346849	−0.173424	+	0.984847i	$0.555483\pi$
$840$	0	0
$841$	−21905.8	−0.898184
$842$	−12243.9	−0.501130
$843$	59240.9	2.42036
$844$	5066.40	0.206626
$845$	−26211.2	−1.06709
$846$	−5775.30	−0.234703
$847$	0	0
$848$	9134.88	0.369921
$849$	10153.0	0.410426
$850$	−181.075	−0.00730687
$851$	−817.399	−0.0329260
$852$	−24089.2	−0.968640
$853$	−8967.06	−0.359937	−0.179969	−	0.983672i	$-0.557600\pi$
$853$	−8967.06	−0.359937	−0.179969	+	0.983672i	$0.557600\pi$
$854$	0	0
$855$	84447.3	3.37782
$856$	−40148.8	−1.60310
$857$	−30922.4	−1.23254	−0.616272	−	0.787534i	$-0.711358\pi$
$857$	−30922.4	−1.23254	−0.616272	+	0.787534i	$0.711358\pi$
$858$	−10215.7	−0.406479
$859$	−26645.2	−1.05835	−0.529176	−	0.848512i	$-0.677499\pi$
$859$	−26645.2	−1.05835	−0.529176	+	0.848512i	$0.677499\pi$
$860$	−16307.0	−0.646588
$861$	0	0
$862$	−8422.14	−0.332783
$863$	−4823.34	−0.190253	−0.0951266	−	0.995465i	$-0.530326\pi$
$863$	−4823.34	−0.190253	−0.0951266	+	0.995465i	$0.530326\pi$
$864$	−45595.0	−1.79534
$865$	−40644.6	−1.59764
$866$	−22725.8	−0.891747
$867$	−45554.5	−1.78444
$868$	0	0
$869$	−85955.0	−3.35538
$870$	−11793.2	−0.459570
$871$	2395.01	0.0931710
$872$	−7618.67	−0.295872
$873$	−104860.	−4.06527
$874$	13579.1	0.525538
$875$	0	0
$876$	13880.4	0.535360
$877$	−6370.57	−0.245289	−0.122645	−	0.992451i	$-0.539138\pi$
$877$	−6370.57	−0.245289	−0.122645	+	0.992451i	$0.539138\pi$
$878$	27567.7	1.05964
$879$	−26756.3	−1.02670
$880$	−16414.4	−0.628784
$881$	41202.5	1.57565	0.787825	−	0.615899i	$-0.211207\pi$
$881$	41202.5	1.57565	0.787825	+	0.615899i	$0.211207\pi$
$882$	0	0
$883$	28478.2	1.08535	0.542677	−	0.839941i	$-0.317411\pi$
$883$	28478.2	1.08535	0.542677	+	0.839941i	$0.317411\pi$
$884$	−100.521	−0.00382454
$885$	50628.8	1.92301
$886$	−12665.6	−0.480260
$887$	10178.2	0.385288	0.192644	−	0.981269i	$-0.438294\pi$
$887$	10178.2	0.385288	0.192644	+	0.981269i	$0.438294\pi$
$888$	3247.17	0.122711
$889$	0	0
$890$	−6223.35	−0.234390
$891$	77663.0	2.92010
$892$	−2652.50	−0.0995653
$893$	5434.87	0.203663
$894$	23613.4	0.883389
$895$	36969.2	1.38072
$896$	0	0
$897$	−4296.98	−0.159946
$898$	24480.4	0.909713
$899$	−431.301	−0.0160008
$900$	−5811.02	−0.215223
$901$	−1480.83	−0.0547544
$902$	−11394.0	−0.420599
$903$	0	0
$904$	−9408.80	−0.346164
$905$	2068.64	0.0759823
$906$	−62452.4	−2.29011
$907$	−31024.1	−1.13577	−0.567883	−	0.823109i	$-0.692237\pi$
$907$	−31024.1	−1.13577	−0.567883	+	0.823109i	$0.692237\pi$
$908$	−16281.1	−0.595052
$909$	−7175.99	−0.261840
$910$	0	0
$911$	−48847.5	−1.77650	−0.888248	−	0.459363i	$-0.848078\pi$
$911$	−48847.5	−1.77650	−0.888248	+	0.459363i	$0.848078\pi$
$912$	−22006.2	−0.799012
$913$	−51548.5	−1.86857
$914$	−26774.5	−0.968952
$915$	−10641.4	−0.384474
$916$	18291.9	0.659804
$917$	0	0
$918$	−2066.60	−0.0743005
$919$	−32216.4	−1.15639	−0.578194	−	0.815899i	$-0.696242\pi$
$919$	−32216.4	−1.15639	−0.578194	+	0.815899i	$0.696242\pi$
$920$	−16924.5	−0.606504
$921$	−29545.1	−1.05705
$922$	21623.4	0.772374
$923$	5687.19	0.202813
$924$	0	0
$925$	379.678	0.0134959
$926$	−22481.0	−0.797808
$927$	18547.7	0.657161
$928$	−7555.08	−0.267250
$929$	24018.9	0.848261	0.424130	−	0.905601i	$-0.360580\pi$
$929$	24018.9	0.848261	0.424130	+	0.905601i	$0.360580\pi$
$930$	2048.33	0.0722230
$931$	0	0
$932$	−18885.0	−0.663733
$933$	48142.0	1.68928
$934$	−15383.2	−0.538921
$935$	2660.90	0.0930703
$936$	11733.2	0.409735
$937$	−23021.8	−0.802658	−0.401329	−	0.915934i	$-0.631452\pi$
$937$	−23021.8	−0.802658	−0.401329	+	0.915934i	$0.631452\pi$
$938$	0	0
$939$	56793.7	1.97379
$940$	−2148.09	−0.0745349
$941$	−6101.21	−0.211364	−0.105682	−	0.994400i	$-0.533703\pi$
$941$	−6101.21	−0.211364	−0.105682	+	0.994400i	$0.533703\pi$
$942$	−50019.3	−1.73006
$943$	−4792.60	−0.165502
$944$	−9068.62	−0.312668
$945$	0	0
$946$	−48120.9	−1.65385
$947$	−47231.0	−1.62070	−0.810349	−	0.585947i	$-0.800723\pi$
$947$	−47231.0	−1.62070	−0.810349	+	0.585947i	$0.800723\pi$
$948$	45546.4	1.56042
$949$	−3277.01	−0.112093
$950$	−6307.43	−0.215411
$951$	41889.5	1.42835
$952$	0	0
$953$	16046.3	0.545425	0.272713	−	0.962096i	$-0.412079\pi$
$953$	16046.3	0.545425	0.272713	+	0.962096i	$0.412079\pi$
$954$	54813.1	1.86021
$955$	4774.07	0.161765
$956$	4218.07	0.142701
$957$	30172.0	1.01914
$958$	10251.5	0.345733
$959$	0	0
$960$	54610.4	1.83598
$961$	−29716.1	−0.997485
$962$	−243.108	−0.00814773
$963$	−98278.3	−3.28865
$964$	16728.0	0.558894
$965$	32897.0	1.09740
$966$	0	0
$967$	14313.0	0.475983	0.237991	−	0.971267i	$-0.423511\pi$
$967$	14313.0	0.475983	0.237991	+	0.971267i	$0.423511\pi$
$968$	70665.2	2.34635
$969$	3567.37	0.118267
$970$	44985.6	1.48907
$971$	−3470.09	−0.114686	−0.0573431	−	0.998355i	$-0.518263\pi$
$971$	−3470.09	−0.114686	−0.0573431	+	0.998355i	$0.518263\pi$
$972$	−10987.2	−0.362565
$973$	0	0
$974$	19155.6	0.630169
$975$	1995.93	0.0655598
$976$	1906.09	0.0625126
$977$	28421.2	0.930681	0.465340	−	0.885132i	$-0.345932\pi$
$977$	28421.2	0.930681	0.465340	+	0.885132i	$0.345932\pi$
$978$	19990.8	0.653613
$979$	15922.0	0.519784
$980$	0	0
$981$	−18649.4	−0.606961
$982$	24485.7	0.795692
$983$	17642.8	0.572449	0.286224	−	0.958163i	$-0.407600\pi$
$983$	17642.8	0.572449	0.286224	+	0.958163i	$0.407600\pi$
$984$	19038.9	0.616807
$985$	−7292.90	−0.235910
$986$	−342.435	−0.0110602
$987$	0	0
$988$	−3501.47	−0.112750
$989$	−20240.8	−0.650779
$990$	−98493.3	−3.16194
$991$	34935.1	1.11983	0.559914	−	0.828551i	$-0.310834\pi$
$991$	34935.1	1.11983	0.559914	+	0.828551i	$0.310834\pi$
$992$	1312.23	0.0419992
$993$	59788.7	1.91071
$994$	0	0
$995$	−32721.9	−1.04257
$996$	27314.9	0.868981
$997$	61063.2	1.93971	0.969855	−	0.243683i	$-0.0783557\pi$
$997$	61063.2	1.93971	0.969855	+	0.243683i	$0.0783557\pi$
$998$	−16947.7	−0.537545
$999$	4333.23	0.137235

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2303.4.a.h.1.12	yes	35
7.6	odd	2		2303.4.a.g.1.12	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2303.4.a.g.1.12	✓	35	7.6	odd	2
2303.4.a.h.1.12	yes	35	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 2303 = 7^{2} \cdot 47 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	2303.a (trivial)

\(f(q)\)	\(=\)	\(q-2.07002 q^{2} +9.29307 q^{3} -3.71503 q^{4} +12.3025 q^{5} -19.2368 q^{6} +24.2503 q^{8} +59.3612 q^{9} +O(q^{10})\)	\(q-2.07002 q^{2} +9.29307 q^{3} -3.71503 q^{4} +12.3025 q^{5} -19.2368 q^{6} +24.2503 q^{8} +59.3612 q^{9} -25.4663 q^{10} +65.1536 q^{11} -34.5240 q^{12} +8.15075 q^{13} +114.328 q^{15} -20.4784 q^{16} +3.31969 q^{17} -122.879 q^{18} +115.635 q^{19} -45.7040 q^{20} -134.869 q^{22} -56.7291 q^{23} +225.360 q^{24} +26.3504 q^{25} -16.8722 q^{26} +300.735 q^{27} +49.8317 q^{29} -236.660 q^{30} -8.65516 q^{31} -151.612 q^{32} +605.477 q^{33} -6.87183 q^{34} -220.528 q^{36} +14.4088 q^{37} -239.367 q^{38} +75.7455 q^{39} +298.338 q^{40} +84.4822 q^{41} +356.797 q^{43} -242.047 q^{44} +730.288 q^{45} +117.430 q^{46} +47.0000 q^{47} -190.307 q^{48} -54.5458 q^{50} +30.8502 q^{51} -30.2802 q^{52} -446.075 q^{53} -622.527 q^{54} +801.549 q^{55} +1074.61 q^{57} -103.153 q^{58} +442.839 q^{59} -424.730 q^{60} -93.0781 q^{61} +17.9163 q^{62} +477.666 q^{64} +100.274 q^{65} -1253.35 q^{66} +293.840 q^{67} -12.3328 q^{68} -527.188 q^{69} +697.751 q^{71} +1439.53 q^{72} -402.050 q^{73} -29.8265 q^{74} +244.876 q^{75} -429.589 q^{76} -156.794 q^{78} -1319.27 q^{79} -251.934 q^{80} +1192.00 q^{81} -174.880 q^{82} -791.185 q^{83} +40.8404 q^{85} -738.577 q^{86} +463.090 q^{87} +1580.00 q^{88} +244.376 q^{89} -1511.71 q^{90} +210.750 q^{92} -80.4330 q^{93} -97.2908 q^{94} +1422.60 q^{95} -1408.94 q^{96} -1766.48 q^{97} +3867.60 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9}+O(q^{10}) \) 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9	\( 35 q + 5 q^{2} + 12 q^{3} + 139 q^{4} + 20 q^{5} + 24 q^{6} + 39 q^{8} + 303 q^{9} + 100 q^{10} + 40 q^{11} + 144 q^{12} + 328 q^{13} + 20 q^{15} + 643 q^{16} + 152 q^{17} + 51 q^{18} + 266 q^{19} + 1064 q^{20} - 168 q^{22} - 134 q^{23} + 288 q^{24} + 1137 q^{25} + 156 q^{26} + 672 q^{27} + 248 q^{29} - 216 q^{30} + 276 q^{31} + 347 q^{32} + 1056 q^{33} + 908 q^{34} + 909 q^{36} - 418 q^{37} + 164 q^{38} - 548 q^{39} + 1200 q^{40} + 918 q^{41} + 608 q^{43} + 1288 q^{44} + 876 q^{45} - 972 q^{46} + 1645 q^{47} + 1252 q^{48} - 367 q^{50} - 464 q^{51} + 3798 q^{52} - 218 q^{53} - 744 q^{54} + 1004 q^{55} - 436 q^{57} - 1270 q^{58} + 3760 q^{59} - 424 q^{60} + 956 q^{61} + 84 q^{62} + 2189 q^{64} - 596 q^{65} + 5500 q^{66} - 476 q^{67} + 256 q^{68} + 444 q^{69} + 852 q^{71} - 883 q^{72} + 6250 q^{73} + 1366 q^{74} - 2568 q^{75} + 1742 q^{76} - 1460 q^{78} + 632 q^{79} + 10124 q^{80} + 1267 q^{81} + 792 q^{82} + 796 q^{83} - 1228 q^{85} - 2864 q^{86} + 8360 q^{87} - 50 q^{88} + 908 q^{89} - 1858 q^{90} + 1696 q^{92} + 644 q^{93} + 235 q^{94} + 1320 q^{95} + 2688 q^{96} + 6184 q^{97} - 1812 q^{99}+O(q^{100}) \) 35 * q + 5 * q^2 + 12 * q^3 + 139 * q^4 + 20 * q^5 + 24 * q^6 + 39 * q^8 + 303 * q^9 + 100 * q^10 + 40 * q^11 + 144 * q^12 + 328 * q^13 + 20 * q^15 + 643 * q^16 + 152 * q^17 + 51 * q^18 + 266 * q^19 + 1064 * q^20 - 168 * q^22 - 134 * q^23 + 288 * q^24 + 1137 * q^25 + 156 * q^26 + 672 * q^27 + 248 * q^29 - 216 * q^30 + 276 * q^31 + 347 * q^32 + 1056 * q^33 + 908 * q^34 + 909 * q^36 - 418 * q^37 + 164 * q^38 - 548 * q^39 + 1200 * q^40 + 918 * q^41 + 608 * q^43 + 1288 * q^44 + 876 * q^45 - 972 * q^46 + 1645 * q^47 + 1252 * q^48 - 367 * q^50 - 464 * q^51 + 3798 * q^52 - 218 * q^53 - 744 * q^54 + 1004 * q^55 - 436 * q^57 - 1270 * q^58 + 3760 * q^59 - 424 * q^60 + 956 * q^61 + 84 * q^62 + 2189 * q^64 - 596 * q^65 + 5500 * q^66 - 476 * q^67 + 256 * q^68 + 444 * q^69 + 852 * q^71 - 883 * q^72 + 6250 * q^73 + 1366 * q^74 - 2568 * q^75 + 1742 * q^76 - 1460 * q^78 + 632 * q^79 + 10124 * q^80 + 1267 * q^81 + 792 * q^82 + 796 * q^83 - 1228 * q^85 - 2864 * q^86 + 8360 * q^87 - 50 * q^88 + 908 * q^89 - 1858 * q^90 + 1696 * q^92 + 644 * q^93 + 235 * q^94 + 1320 * q^95 + 2688 * q^96 + 6184 * q^97 - 1812 * q^99

Introduction

L-functions

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Database

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